Pianotech

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

Yes, this is very interesting. 

Chris Chernobieff has demonstrated to me that the base frequency of a soundboard (new or old) is around 49hz (Chris, correct me if I'm wrong here).

Is it possible that the string is in fact generating the fundamental but the soundboard simply is not amplifying it? And as noted, the smaller the piano the worse the situation?

It would make sense that the pianosens pickup could detect it whereas the mic would not.

Peter Grey Piano Doctor 

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

Yes, this is very interesting. 

Chris Chernobieff has demonstrated to me that the base frequency of a soundboard (new or old) is around 49hz (Chris, correct me if I'm wrong here).

Is it possible that the string is in fact generating the fundamental but the soundboard simply is not amplifying it? And as noted, the smaller the piano the worse the situation?

It would make sense that the pianosens pickup could detect it whereas the mic would not.

Peter Grey Piano Doctor 

------------------------------
Peter Grey
Stratham NH
(603) 686-2395
pianodoctor57@gmail.com

Original Message:
Sent: 01-22-2024 06:24
From: Arnold Duin
Subject: Dispelling the 'Myth' of the Missing Fundamental

Interesting discussion. What I have always understood is that "missing fundamental" refers to the challenge that the soundboard faces in radiating these low frequencies, not the strings. When you realize that the wavelength at frequencies below 30 Hz is more than 10 meters, you can imagine that.


Original Message:
Sent: 1/22/2024 3:17:00 AM
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

Yes, this is very interesting. 

Chris Chernobieff has demonstrated to me that the base frequency of a soundboard (new or old) is around 49hz (Chris, correct me if I'm wrong here).

Is it possible that the string is in fact generating the fundamental but the soundboard simply is not amplifying it? And as noted, the smaller the piano the worse the situation?

It would make sense that the pianosens pickup could detect it whereas the mic would not.

Peter Grey Piano Doctor 

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

> 

• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 

Really? Missing? Where did you learn about this? I always thought it was well a known fact that while the fundamental in the lower bass register is of such a low level as to be unusable, (in tuning), and usually inaudible in performance, it has, nevertheless, always been there. 

------------------------------
Geoff Sykes, RPT
Los Angeles CA
------------------------------

Original Message:
Sent: 01-22-2024 03:16
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

> 

• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 

Really? Missing? Where did you learn about this? I always thought it was well a known fact that while the fundamental in the lower bass register is of such a low level as to be unusable, (in tuning), and usually inaudible in performance, it has, nevertheless, always been there. 

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

> 

• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 

Really? Missing? Where did you learn about this? I always thought it was well a known fact that while the fundamental in the lower bass register is of such a low level as to be unusable, (in tuning), and usually inaudible in performance, it has, nevertheless, always been there. 

------------------------------
Geoff Sykes, RPT
Los Angeles CA

Original Message:
Sent: 01-22-2024 03:16
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

You are correct, Geoff, that it was not universally assumed to be entirely absent.  For example, in Physics of the Piano, Nicholas Giordano does indeed refer to it as "the missing fundamental", but in the text itself he makes it clear that the fundamental need not be gone entirely, just weak enough to be "essentially inaudible".  Rather, he uses the term in reference to the phenomenon that human hearing will perceive a note at the fundamental frequency even when that frequency is missing or very weak:

This is on pages 130-131 if you want to read the rest. So I think what we have here is just a misunderstanding (perhaps widespread among piano techs) of what was really meant in the first place by "missing fundamental". The point, at least the way Giordano tells it, is that we have the ability to perceive missing or weak fundamentals based on higher partials -- not that the fundamental is truly missing in the low registers of the piano.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-22-2024 13:40
From: Geoff Sykes
Subject: Dispelling the 'Myth' of the Missing Fundamental

> 

• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 

Really? Missing? Where did you learn about this? I always thought it was well a known fact that while the fundamental in the lower bass register is of such a low level as to be unusable, (in tuning), and usually inaudible in performance, it has, nevertheless, always been there. 

------------------------------
Geoff Sykes, RPT
Los Angeles CA

Original Message:
Sent: 01-22-2024 03:16
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

That is why I often use the fifth as a reference whentuning the low bass.

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

That is why I often use the fifth as a reference whentuning the low bass.

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

For tuning the lowest notes on a nice piano, since I am tuning 12 TET based on the octave (i.e., ET), I will often start with a double octave for initial placement. Then testing with a progression of seventeenths (5:1), and on a good day I can also bring in minor sevenths (7:4) or minor sixths (8:5) as additional testing and with their slightly improved accuracy over the seventeenth..

Mark, resonance works well going from a string that is partial #2 or #3 (as well as higher partials) down to the fundamental string. But for me the strongest resonance created is always equal to the partial in frequency. Maybe with non-linearities the fundamental might also be there, but much reduced in amplitude. Regards, Norman.

That is why I often use the fifth as a reference whentuning the low bass.

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

Peter has 'challenged me' indirectly (ha ha) to do the A0 with my Neumann KM183 mics. Then I use the same parameters of Matlab as I did before when I captured the A0 with the PianoSens sensor.

The pic is below. Double click it to see it better. The top view is amplitude vs time. The startup is messy compared with my prior presentation using the sensor, but there are still very clearly defined periods of A0 that I have marked.

Now look at the spectral view on the bottom. Look at the 3rd and 6th levels as the highest of the first 10 harmonics, but look at the fundamental which is only 5 dB below the 2nd harmonic. Amazing. So, it all boils down to how to set up the experiment and how to perform the frequency analysis.

Best,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 21:06
From: Norman Brickman
Subject: Dispelling the 'Myth' of the Missing Fundamental

For tuning the lowest notes on a nice piano, since I am tuning 12 TET based on the octave (i.e., ET), I will often start with a double octave for initial placement. Then testing with a progression of seventeenths (5:1), and on a good day I can also bring in minor sevenths (7:4) or minor sixths (8:5) as additional testing and with their slightly improved accuracy over the seventeenth..

Mark, resonance works well going from a string that is partial #2 or #3 (as well as higher partials) down to the fundamental string. But for me the strongest resonance created is always equal to the partial in frequency. Maybe with non-linearities the fundamental might also be there, but much reduced in amplitude. Regards, Norman.

------------------------------
Norman Brickman
Potomac Piano Service
Potomac, Maryland
potomacpiano@verizon.net
https://potomacpiano.com
(301) 983.9321

Original Message:
Sent: 01-23-2024 20:05
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Parker, better yet, use the 12th, not the 5th. -Steve


Original Message:
Sent: 1/23/2024 7:12:00 PM
From: Parker Leigh
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

That is why I often use the fifth as a reference whentuning the low bass.

------------------------------
Parker Leigh RPT
Winchester VA
(540) 722-3865

Original Message:
Sent: 01-23-2024 13:48
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 11:00
From: Mark Schecter
Subject: Dispelling the 'Myth' of the Missing Fundamental

Original Message:
Sent: 1/23/2024 9:02:00 AM
From: Robert Anderson
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I have always assumed that A0 has a fundamental and the myth hasn't penetrated to me, anyway. My understanding is that the fundamental of A0 is so weak compared to its higher partials that it is pretty inaudible. In organ building a 32' pipe is needed for the fundamental of A0 but the combination of a 16' and and 8' pipe can give the illusion of hearing A0. I expect I'll hear about it if my understanding is wrong.

Bob Anderson, RPT
Tucson, AZ


Original Message:
Sent: 1/22/2024 3:17:00 AM
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

Colleagues, 

There is big difference between 'acoustics' and 'psycho-acoustics'. There is a big difference between what we 'think' is so, and what we can 'measure' as so!

Some things are hard to find evidence of, but we know to be true, but the best is when there is some evidence so that it is not 'blind faith' but 'evidence-based' faith. It is my job to base every statement on actual evidence that is non-contradictory to all other evidence. 

For example, I posted above the evidence of measured data of the harmonic levels of both the sensor data (the original post and video that started this) and microphone data (last night and above post) of the first 10+ harmonics of A0, showing both the time and frequency domain. The measured harmonic magnitude levels were different due to the EQ of the two pickup devices, but both showed the full evidence of the presence of a significant level of A0 fundamental. If you google 'missing fundamental' there are lots of hits and this is what started me on the venture for the post. I am glad I took the time to actually make the measurements and post the data.

I explained in an earlier post that there is no such thing as a subharmonic in reality unless there is an actual spectral component, which cannot come from a linear system but it can come from a strong non-linearity that creates a spectral component that is the result of the subtraction and addition of two frequencies.

Hope that helps!

Respectfully submitted,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-24-2024 00:29
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Peter has 'challenged me' indirectly (ha ha) to do the A0 with my Neumann KM183 mics. Then I use the same parameters of Matlab as I did before when I captured the A0 with the PianoSens sensor.

The pic is below. Double click it to see it better. The top view is amplitude vs time. The startup is messy compared with my prior presentation using the sensor, but there are still very clearly defined periods of A0 that I have marked.

Now look at the spectral view on the bottom. Look at the 3rd and 6th levels as the highest of the first 10 harmonics, but look at the fundamental which is only 5 dB below the 2nd harmonic. Amazing. So, it all boils down to how to set up the experiment and how to perform the frequency analysis.

Best,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 21:06
From: Norman Brickman
Subject: Dispelling the 'Myth' of the Missing Fundamental

For tuning the lowest notes on a nice piano, since I am tuning 12 TET based on the octave (i.e., ET), I will often start with a double octave for initial placement. Then testing with a progression of seventeenths (5:1), and on a good day I can also bring in minor sevenths (7:4) or minor sixths (8:5) as additional testing and with their slightly improved accuracy over the seventeenth..

Mark, resonance works well going from a string that is partial #2 or #3 (as well as higher partials) down to the fundamental string. But for me the strongest resonance created is always equal to the partial in frequency. Maybe with non-linearities the fundamental might also be there, but much reduced in amplitude. Regards, Norman.

------------------------------
Norman Brickman
Potomac Piano Service
Potomac, Maryland
potomacpiano@verizon.net
https://potomacpiano.com
(301) 983.9321

Original Message:
Sent: 01-23-2024 20:05
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Parker, better yet, use the 12th, not the 5th. -Steve


Original Message:
Sent: 1/23/2024 7:12:00 PM
From: Parker Leigh
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

That is why I often use the fifth as a reference whentuning the low bass.

------------------------------
Parker Leigh RPT
Winchester VA
(540) 722-3865

Original Message:
Sent: 01-23-2024 13:48
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 11:00
From: Mark Schecter
Subject: Dispelling the 'Myth' of the Missing Fundamental

Original Message:
Sent: 1/23/2024 9:02:00 AM
From: Robert Anderson
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I have always assumed that A0 has a fundamental and the myth hasn't penetrated to me, anyway. My understanding is that the fundamental of A0 is so weak compared to its higher partials that it is pretty inaudible. In organ building a 32' pipe is needed for the fundamental of A0 but the combination of a 16' and and 8' pipe can give the illusion of hearing A0. I expect I'll hear about it if my understanding is wrong.

Bob Anderson, RPT
Tucson, AZ


Original Message:
Sent: 1/22/2024 3:17:00 AM
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

I was arguing that the term "Missing Fundamental", used correctly, referred to a psychoacoustic phenomenon in the first place -- not an acoustic one.  Wikipedia seems to agree with me as well, for what it's worth: https://en.wikipedia.org/wiki/Missing_fundamental.

I don't doubt that some piano technicians have gotten this mixed up, even prominent ones.

Colleagues, 

There is big difference between 'acoustics' and 'psycho-acoustics'. There is a big difference between what we 'think' is so, and what we can 'measure' as so!

Some things are hard to find evidence of, but we know to be true, but the best is when there is some evidence so that it is not 'blind faith' but 'evidence-based' faith. It is my job to base every statement on actual evidence that is non-contradictory to all other evidence. 

For example, I posted above the evidence of measured data of the harmonic levels of both the sensor data (the original post and video that started this) and microphone data (last night and above post) of the first 10+ harmonics of A0, showing both the time and frequency domain. The measured harmonic magnitude levels were different due to the EQ of the two pickup devices, but both showed the full evidence of the presence of a significant level of A0 fundamental. If you google 'missing fundamental' there are lots of hits and this is what started me on the venture for the post. I am glad I took the time to actually make the measurements and post the data.

I explained in an earlier post that there is no such thing as a subharmonic in reality unless there is an actual spectral component, which cannot come from a linear system but it can come from a strong non-linearity that creates a spectral component that is the result of the subtraction and addition of two frequencies.

Hope that helps!

Respectfully submitted,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-24-2024 00:29
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Peter has 'challenged me' indirectly (ha ha) to do the A0 with my Neumann KM183 mics. Then I use the same parameters of Matlab as I did before when I captured the A0 with the PianoSens sensor.

The pic is below. Double click it to see it better. The top view is amplitude vs time. The startup is messy compared with my prior presentation using the sensor, but there are still very clearly defined periods of A0 that I have marked.

Now look at the spectral view on the bottom. Look at the 3rd and 6th levels as the highest of the first 10 harmonics, but look at the fundamental which is only 5 dB below the 2nd harmonic. Amazing. So, it all boils down to how to set up the experiment and how to perform the frequency analysis.

Best,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 21:06
From: Norman Brickman
Subject: Dispelling the 'Myth' of the Missing Fundamental

For tuning the lowest notes on a nice piano, since I am tuning 12 TET based on the octave (i.e., ET), I will often start with a double octave for initial placement. Then testing with a progression of seventeenths (5:1), and on a good day I can also bring in minor sevenths (7:4) or minor sixths (8:5) as additional testing and with their slightly improved accuracy over the seventeenth..

Mark, resonance works well going from a string that is partial #2 or #3 (as well as higher partials) down to the fundamental string. But for me the strongest resonance created is always equal to the partial in frequency. Maybe with non-linearities the fundamental might also be there, but much reduced in amplitude. Regards, Norman.

------------------------------
Norman Brickman
Potomac Piano Service
Potomac, Maryland
potomacpiano@verizon.net
https://potomacpiano.com
(301) 983.9321

Original Message:
Sent: 01-23-2024 20:05
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Parker, better yet, use the 12th, not the 5th. -Steve


Original Message:
Sent: 1/23/2024 7:12:00 PM
From: Parker Leigh
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

That is why I often use the fifth as a reference whentuning the low bass.

------------------------------
Parker Leigh RPT
Winchester VA
(540) 722-3865

Original Message:
Sent: 01-23-2024 13:48
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 11:00
From: Mark Schecter
Subject: Dispelling the 'Myth' of the Missing Fundamental

Original Message:
Sent: 1/23/2024 9:02:00 AM
From: Robert Anderson
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I have always assumed that A0 has a fundamental and the myth hasn't penetrated to me, anyway. My understanding is that the fundamental of A0 is so weak compared to its higher partials that it is pretty inaudible. In organ building a 32' pipe is needed for the fundamental of A0 but the combination of a 16' and and 8' pipe can give the illusion of hearing A0. I expect I'll hear about it if my understanding is wrong.

Bob Anderson, RPT
Tucson, AZ


Original Message:
Sent: 1/22/2024 3:17:00 AM
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

I was arguing that the term "Missing Fundamental", used correctly, referred to a psychoacoustic phenomenon in the first place -- not an acoustic one.  Wikipedia seems to agree with me as well, for what it's worth: https://en.wikipedia.org/wiki/Missing_fundamental.

I don't doubt that some piano technicians have gotten this mixed up, even prominent ones.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 14:41
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Colleagues, 

There is big difference between 'acoustics' and 'psycho-acoustics'. There is a big difference between what we 'think' is so, and what we can 'measure' as so!

Some things are hard to find evidence of, but we know to be true, but the best is when there is some evidence so that it is not 'blind faith' but 'evidence-based' faith. It is my job to base every statement on actual evidence that is non-contradictory to all other evidence. 

For example, I posted above the evidence of measured data of the harmonic levels of both the sensor data (the original post and video that started this) and microphone data (last night and above post) of the first 10+ harmonics of A0, showing both the time and frequency domain. The measured harmonic magnitude levels were different due to the EQ of the two pickup devices, but both showed the full evidence of the presence of a significant level of A0 fundamental. If you google 'missing fundamental' there are lots of hits and this is what started me on the venture for the post. I am glad I took the time to actually make the measurements and post the data.

I explained in an earlier post that there is no such thing as a subharmonic in reality unless there is an actual spectral component, which cannot come from a linear system but it can come from a strong non-linearity that creates a spectral component that is the result of the subtraction and addition of two frequencies.

Hope that helps!

Respectfully submitted,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-24-2024 00:29
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Peter has 'challenged me' indirectly (ha ha) to do the A0 with my Neumann KM183 mics. Then I use the same parameters of Matlab as I did before when I captured the A0 with the PianoSens sensor.

The pic is below. Double click it to see it better. The top view is amplitude vs time. The startup is messy compared with my prior presentation using the sensor, but there are still very clearly defined periods of A0 that I have marked.

Now look at the spectral view on the bottom. Look at the 3rd and 6th levels as the highest of the first 10 harmonics, but look at the fundamental which is only 5 dB below the 2nd harmonic. Amazing. So, it all boils down to how to set up the experiment and how to perform the frequency analysis.

Best,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 21:06
From: Norman Brickman
Subject: Dispelling the 'Myth' of the Missing Fundamental

For tuning the lowest notes on a nice piano, since I am tuning 12 TET based on the octave (i.e., ET), I will often start with a double octave for initial placement. Then testing with a progression of seventeenths (5:1), and on a good day I can also bring in minor sevenths (7:4) or minor sixths (8:5) as additional testing and with their slightly improved accuracy over the seventeenth..

Mark, resonance works well going from a string that is partial #2 or #3 (as well as higher partials) down to the fundamental string. But for me the strongest resonance created is always equal to the partial in frequency. Maybe with non-linearities the fundamental might also be there, but much reduced in amplitude. Regards, Norman.

------------------------------
Norman Brickman
Potomac Piano Service
Potomac, Maryland
potomacpiano@verizon.net
https://potomacpiano.com
(301) 983.9321

Original Message:
Sent: 01-23-2024 20:05
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Parker, better yet, use the 12th, not the 5th. -Steve


Original Message:
Sent: 1/23/2024 7:12:00 PM
From: Parker Leigh
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

That is why I often use the fifth as a reference whentuning the low bass.

------------------------------
Parker Leigh RPT
Winchester VA
(540) 722-3865

Original Message:
Sent: 01-23-2024 13:48
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 11:00
From: Mark Schecter
Subject: Dispelling the 'Myth' of the Missing Fundamental

Original Message:
Sent: 1/23/2024 9:02:00 AM
From: Robert Anderson
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I have always assumed that A0 has a fundamental and the myth hasn't penetrated to me, anyway. My understanding is that the fundamental of A0 is so weak compared to its higher partials that it is pretty inaudible. In organ building a 32' pipe is needed for the fundamental of A0 but the combination of a 16' and and 8' pipe can give the illusion of hearing A0. I expect I'll hear about it if my understanding is wrong.

Bob Anderson, RPT
Tucson, AZ


Original Message:
Sent: 1/22/2024 3:17:00 AM
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

I don't follow. Do you feel like I'm not providing enough evidence as to what the correct interpretation of the term is?  Do you mean that you want to see evidence of the legitimate psychoacoustic phenomenon?

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com
------------------------------

Original Message:
Sent: 01-24-2024 15:15
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Nathan, I cannot emphasize enough the importance of evidence-based data in these discussions. Without evidence-based real data and precise measurements, all things devolve into endless debate. -- Respectfully, Steve


Original Message:
Sent: 1/24/2024 3:10:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I was arguing that the term "Missing Fundamental", used correctly, referred to a psychoacoustic phenomenon in the first place -- not an acoustic one.  Wikipedia seems to agree with me as well, for what it's worth: https://en.wikipedia.org/wiki/Missing_fundamental.

I don't doubt that some piano technicians have gotten this mixed up, even prominent ones.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 14:41
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Colleagues, 

There is big difference between 'acoustics' and 'psycho-acoustics'. There is a big difference between what we 'think' is so, and what we can 'measure' as so!

Some things are hard to find evidence of, but we know to be true, but the best is when there is some evidence so that it is not 'blind faith' but 'evidence-based' faith. It is my job to base every statement on actual evidence that is non-contradictory to all other evidence. 

For example, I posted above the evidence of measured data of the harmonic levels of both the sensor data (the original post and video that started this) and microphone data (last night and above post) of the first 10+ harmonics of A0, showing both the time and frequency domain. The measured harmonic magnitude levels were different due to the EQ of the two pickup devices, but both showed the full evidence of the presence of a significant level of A0 fundamental. If you google 'missing fundamental' there are lots of hits and this is what started me on the venture for the post. I am glad I took the time to actually make the measurements and post the data.

I explained in an earlier post that there is no such thing as a subharmonic in reality unless there is an actual spectral component, which cannot come from a linear system but it can come from a strong non-linearity that creates a spectral component that is the result of the subtraction and addition of two frequencies.

Hope that helps!

Respectfully submitted,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-24-2024 00:29
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Peter has 'challenged me' indirectly (ha ha) to do the A0 with my Neumann KM183 mics. Then I use the same parameters of Matlab as I did before when I captured the A0 with the PianoSens sensor.

The pic is below. Double click it to see it better. The top view is amplitude vs time. The startup is messy compared with my prior presentation using the sensor, but there are still very clearly defined periods of A0 that I have marked.

Now look at the spectral view on the bottom. Look at the 3rd and 6th levels as the highest of the first 10 harmonics, but look at the fundamental which is only 5 dB below the 2nd harmonic. Amazing. So, it all boils down to how to set up the experiment and how to perform the frequency analysis.

Best,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 21:06
From: Norman Brickman
Subject: Dispelling the 'Myth' of the Missing Fundamental

For tuning the lowest notes on a nice piano, since I am tuning 12 TET based on the octave (i.e., ET), I will often start with a double octave for initial placement. Then testing with a progression of seventeenths (5:1), and on a good day I can also bring in minor sevenths (7:4) or minor sixths (8:5) as additional testing and with their slightly improved accuracy over the seventeenth..

Mark, resonance works well going from a string that is partial #2 or #3 (as well as higher partials) down to the fundamental string. But for me the strongest resonance created is always equal to the partial in frequency. Maybe with non-linearities the fundamental might also be there, but much reduced in amplitude. Regards, Norman.

------------------------------
Norman Brickman
Potomac Piano Service
Potomac, Maryland
potomacpiano@verizon.net
https://potomacpiano.com
(301) 983.9321

Original Message:
Sent: 01-23-2024 20:05
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Parker, better yet, use the 12th, not the 5th. -Steve


Original Message:
Sent: 1/23/2024 7:12:00 PM
From: Parker Leigh
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

That is why I often use the fifth as a reference whentuning the low bass.

------------------------------
Parker Leigh RPT
Winchester VA
(540) 722-3865

Original Message:
Sent: 01-23-2024 13:48
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 11:00
From: Mark Schecter
Subject: Dispelling the 'Myth' of the Missing Fundamental

Original Message:
Sent: 1/23/2024 9:02:00 AM
From: Robert Anderson
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I have always assumed that A0 has a fundamental and the myth hasn't penetrated to me, anyway. My understanding is that the fundamental of A0 is so weak compared to its higher partials that it is pretty inaudible. In organ building a 32' pipe is needed for the fundamental of A0 but the combination of a 16' and and 8' pipe can give the illusion of hearing A0. I expect I'll hear about it if my understanding is wrong.

Bob Anderson, RPT
Tucson, AZ


Original Message:
Sent: 1/22/2024 3:17:00 AM
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

Not anyone specifically. Take no offense, please. I don't think many understand just how much work it is to make engineering tests / measurements and explain the results in precise language. Engineers usually get paid handsomely to do this kind of work in commercial and military fields with a paying customer. The quality of my work I post is at that level because I have been doing it for major customers for 40 years. I am doing this signal processing research on piano, only because I want to educate serious PTG members who want to learn about the subject. I post things that we normally cannot find in the prior piano research journals. I am just giving away the time and effort. I do hope one day people appreciate it. It distracts me from my current paid customer tasks and sometimes I just think it is falling on deaf ears and I should just stop and go back to my professional signal processing work.


Original Message:
Sent: 1/24/2024 3:18:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I don't follow. Do you feel like I'm not providing enough evidence as to what the correct interpretation of the term is?  Do you mean that you want to see evidence of the legitimate psychoacoustic phenomenon?

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 15:15
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Nathan, I cannot emphasize enough the importance of evidence-based data in these discussions. Without evidence-based real data and precise measurements, all things devolve into endless debate. -- Respectfully, Steve


Original Message:
Sent: 1/24/2024 3:10:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I was arguing that the term "Missing Fundamental", used correctly, referred to a psychoacoustic phenomenon in the first place -- not an acoustic one.  Wikipedia seems to agree with me as well, for what it's worth: https://en.wikipedia.org/wiki/Missing_fundamental.

I don't doubt that some piano technicians have gotten this mixed up, even prominent ones.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 14:41
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Colleagues, 

There is big difference between 'acoustics' and 'psycho-acoustics'. There is a big difference between what we 'think' is so, and what we can 'measure' as so!

Some things are hard to find evidence of, but we know to be true, but the best is when there is some evidence so that it is not 'blind faith' but 'evidence-based' faith. It is my job to base every statement on actual evidence that is non-contradictory to all other evidence. 

For example, I posted above the evidence of measured data of the harmonic levels of both the sensor data (the original post and video that started this) and microphone data (last night and above post) of the first 10+ harmonics of A0, showing both the time and frequency domain. The measured harmonic magnitude levels were different due to the EQ of the two pickup devices, but both showed the full evidence of the presence of a significant level of A0 fundamental. If you google 'missing fundamental' there are lots of hits and this is what started me on the venture for the post. I am glad I took the time to actually make the measurements and post the data.

I explained in an earlier post that there is no such thing as a subharmonic in reality unless there is an actual spectral component, which cannot come from a linear system but it can come from a strong non-linearity that creates a spectral component that is the result of the subtraction and addition of two frequencies.

Hope that helps!

Respectfully submitted,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-24-2024 00:29
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Peter has 'challenged me' indirectly (ha ha) to do the A0 with my Neumann KM183 mics. Then I use the same parameters of Matlab as I did before when I captured the A0 with the PianoSens sensor.

The pic is below. Double click it to see it better. The top view is amplitude vs time. The startup is messy compared with my prior presentation using the sensor, but there are still very clearly defined periods of A0 that I have marked.

Now look at the spectral view on the bottom. Look at the 3rd and 6th levels as the highest of the first 10 harmonics, but look at the fundamental which is only 5 dB below the 2nd harmonic. Amazing. So, it all boils down to how to set up the experiment and how to perform the frequency analysis.

Best,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 21:06
From: Norman Brickman
Subject: Dispelling the 'Myth' of the Missing Fundamental

For tuning the lowest notes on a nice piano, since I am tuning 12 TET based on the octave (i.e., ET), I will often start with a double octave for initial placement. Then testing with a progression of seventeenths (5:1), and on a good day I can also bring in minor sevenths (7:4) or minor sixths (8:5) as additional testing and with their slightly improved accuracy over the seventeenth..

Mark, resonance works well going from a string that is partial #2 or #3 (as well as higher partials) down to the fundamental string. But for me the strongest resonance created is always equal to the partial in frequency. Maybe with non-linearities the fundamental might also be there, but much reduced in amplitude. Regards, Norman.

------------------------------
Norman Brickman
Potomac Piano Service
Potomac, Maryland
potomacpiano@verizon.net
https://potomacpiano.com
(301) 983.9321

Original Message:
Sent: 01-23-2024 20:05
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Parker, better yet, use the 12th, not the 5th. -Steve


Original Message:
Sent: 1/23/2024 7:12:00 PM
From: Parker Leigh
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

That is why I often use the fifth as a reference whentuning the low bass.

------------------------------
Parker Leigh RPT
Winchester VA
(540) 722-3865

Original Message:
Sent: 01-23-2024 13:48
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 11:00
From: Mark Schecter
Subject: Dispelling the 'Myth' of the Missing Fundamental

Original Message:
Sent: 1/23/2024 9:02:00 AM
From: Robert Anderson
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I have always assumed that A0 has a fundamental and the myth hasn't penetrated to me, anyway. My understanding is that the fundamental of A0 is so weak compared to its higher partials that it is pretty inaudible. In organ building a 32' pipe is needed for the fundamental of A0 but the combination of a 16' and and 8' pipe can give the illusion of hearing A0. I expect I'll hear about it if my understanding is wrong.

Bob Anderson, RPT
Tucson, AZ


Original Message:
Sent: 1/22/2024 3:17:00 AM
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

Not anyone specifically. Take no offense, please. I don't think many understand just how much work it is to make engineering tests / measurements and explain the results in precise language. Engineers usually get paid handsomely to do this kind of work in commercial and military fields with a paying customer. The quality of my work I post is at that level because I have been doing it for major customers for 40 years. I am doing this signal processing research on piano, only because I want to educate serious PTG members who want to learn about the subject. I post things that we normally cannot find in the prior piano research journals. I am just giving away the time and effort. I do hope one day people appreciate it. It distracts me from my current paid customer tasks and sometimes I just think it is falling on deaf ears and I should just stop and go back to my professional signal processing work.


Original Message:
Sent: 1/24/2024 3:18:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I don't follow. Do you feel like I'm not providing enough evidence as to what the correct interpretation of the term is?  Do you mean that you want to see evidence of the legitimate psychoacoustic phenomenon?

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 15:15
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Nathan, I cannot emphasize enough the importance of evidence-based data in these discussions. Without evidence-based real data and precise measurements, all things devolve into endless debate. -- Respectfully, Steve


Original Message:
Sent: 1/24/2024 3:10:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I was arguing that the term "Missing Fundamental", used correctly, referred to a psychoacoustic phenomenon in the first place -- not an acoustic one.  Wikipedia seems to agree with me as well, for what it's worth: https://en.wikipedia.org/wiki/Missing_fundamental.

I don't doubt that some piano technicians have gotten this mixed up, even prominent ones.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 14:41
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Colleagues, 

There is big difference between 'acoustics' and 'psycho-acoustics'. There is a big difference between what we 'think' is so, and what we can 'measure' as so!

Some things are hard to find evidence of, but we know to be true, but the best is when there is some evidence so that it is not 'blind faith' but 'evidence-based' faith. It is my job to base every statement on actual evidence that is non-contradictory to all other evidence. 

For example, I posted above the evidence of measured data of the harmonic levels of both the sensor data (the original post and video that started this) and microphone data (last night and above post) of the first 10+ harmonics of A0, showing both the time and frequency domain. The measured harmonic magnitude levels were different due to the EQ of the two pickup devices, but both showed the full evidence of the presence of a significant level of A0 fundamental. If you google 'missing fundamental' there are lots of hits and this is what started me on the venture for the post. I am glad I took the time to actually make the measurements and post the data.

I explained in an earlier post that there is no such thing as a subharmonic in reality unless there is an actual spectral component, which cannot come from a linear system but it can come from a strong non-linearity that creates a spectral component that is the result of the subtraction and addition of two frequencies.

Hope that helps!

Respectfully submitted,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-24-2024 00:29
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Peter has 'challenged me' indirectly (ha ha) to do the A0 with my Neumann KM183 mics. Then I use the same parameters of Matlab as I did before when I captured the A0 with the PianoSens sensor.

The pic is below. Double click it to see it better. The top view is amplitude vs time. The startup is messy compared with my prior presentation using the sensor, but there are still very clearly defined periods of A0 that I have marked.

Now look at the spectral view on the bottom. Look at the 3rd and 6th levels as the highest of the first 10 harmonics, but look at the fundamental which is only 5 dB below the 2nd harmonic. Amazing. So, it all boils down to how to set up the experiment and how to perform the frequency analysis.

Best,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 21:06
From: Norman Brickman
Subject: Dispelling the 'Myth' of the Missing Fundamental

For tuning the lowest notes on a nice piano, since I am tuning 12 TET based on the octave (i.e., ET), I will often start with a double octave for initial placement. Then testing with a progression of seventeenths (5:1), and on a good day I can also bring in minor sevenths (7:4) or minor sixths (8:5) as additional testing and with their slightly improved accuracy over the seventeenth..

Mark, resonance works well going from a string that is partial #2 or #3 (as well as higher partials) down to the fundamental string. But for me the strongest resonance created is always equal to the partial in frequency. Maybe with non-linearities the fundamental might also be there, but much reduced in amplitude. Regards, Norman.

------------------------------
Norman Brickman
Potomac Piano Service
Potomac, Maryland
potomacpiano@verizon.net
https://potomacpiano.com
(301) 983.9321

Original Message:
Sent: 01-23-2024 20:05
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Parker, better yet, use the 12th, not the 5th. -Steve


Original Message:
Sent: 1/23/2024 7:12:00 PM
From: Parker Leigh
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

That is why I often use the fifth as a reference whentuning the low bass.

------------------------------
Parker Leigh RPT
Winchester VA
(540) 722-3865

Original Message:
Sent: 01-23-2024 13:48
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 11:00
From: Mark Schecter
Subject: Dispelling the 'Myth' of the Missing Fundamental

Original Message:
Sent: 1/23/2024 9:02:00 AM
From: Robert Anderson
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I have always assumed that A0 has a fundamental and the myth hasn't penetrated to me, anyway. My understanding is that the fundamental of A0 is so weak compared to its higher partials that it is pretty inaudible. In organ building a 32' pipe is needed for the fundamental of A0 but the combination of a 16' and and 8' pipe can give the illusion of hearing A0. I expect I'll hear about it if my understanding is wrong.

Bob Anderson, RPT
Tucson, AZ


Original Message:
Sent: 1/22/2024 3:17:00 AM
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

So, I think there's a couple things that really might ease your path if you acknowledged them.  First, you're not the only person in here with an engineering background, who could be making more money doing something else.  Second, if you really stuck to posting hard data as you advocate, I think you'd see a lot fewer protests.  The problem, for me, comes in with claims like
 * "There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano." (I've tried to explain that "the missing fundamental" refers to something different than assumed here.)
 * "So let's say your standard deviation error is 0.5 cents from acoustic interference. The square root of 88 is 9.38, so if you have increased the probability of the spread of out-of-tune-ness by at least 5 cents or more." (This is simply incorrect, that's not how standard deviation works. I tried to gently explain that but you then claimed you were uninterested in talking about statistical models.  Why did you present one in the first place then?)

Again, I think your device is interesting, and I think several of your findings are interesting.  But I don't think it's in anyone's best interest for me to ignore it when I spot something in a claim that looks incomplete or incorrect.  I think we can learn a lot from you here, but I think you can learn from us too if you're willing to listen.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com
------------------------------

Original Message:
Sent: 01-24-2024 15:26
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Not anyone specifically. Take no offense, please. I don't think many understand just how much work it is to make engineering tests / measurements and explain the results in precise language. Engineers usually get paid handsomely to do this kind of work in commercial and military fields with a paying customer. The quality of my work I post is at that level because I have been doing it for major customers for 40 years. I am doing this signal processing research on piano, only because I want to educate serious PTG members who want to learn about the subject. I post things that we normally cannot find in the prior piano research journals. I am just giving away the time and effort. I do hope one day people appreciate it. It distracts me from my current paid customer tasks and sometimes I just think it is falling on deaf ears and I should just stop and go back to my professional signal processing work.


Original Message:
Sent: 1/24/2024 3:18:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I don't follow. Do you feel like I'm not providing enough evidence as to what the correct interpretation of the term is?  Do you mean that you want to see evidence of the legitimate psychoacoustic phenomenon?

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 15:15
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Nathan, I cannot emphasize enough the importance of evidence-based data in these discussions. Without evidence-based real data and precise measurements, all things devolve into endless debate. -- Respectfully, Steve


Original Message:
Sent: 1/24/2024 3:10:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I was arguing that the term "Missing Fundamental", used correctly, referred to a psychoacoustic phenomenon in the first place -- not an acoustic one.  Wikipedia seems to agree with me as well, for what it's worth: https://en.wikipedia.org/wiki/Missing_fundamental.

I don't doubt that some piano technicians have gotten this mixed up, even prominent ones.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 14:41
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Colleagues, 

There is big difference between 'acoustics' and 'psycho-acoustics'. There is a big difference between what we 'think' is so, and what we can 'measure' as so!

Some things are hard to find evidence of, but we know to be true, but the best is when there is some evidence so that it is not 'blind faith' but 'evidence-based' faith. It is my job to base every statement on actual evidence that is non-contradictory to all other evidence. 

For example, I posted above the evidence of measured data of the harmonic levels of both the sensor data (the original post and video that started this) and microphone data (last night and above post) of the first 10+ harmonics of A0, showing both the time and frequency domain. The measured harmonic magnitude levels were different due to the EQ of the two pickup devices, but both showed the full evidence of the presence of a significant level of A0 fundamental. If you google 'missing fundamental' there are lots of hits and this is what started me on the venture for the post. I am glad I took the time to actually make the measurements and post the data.

I explained in an earlier post that there is no such thing as a subharmonic in reality unless there is an actual spectral component, which cannot come from a linear system but it can come from a strong non-linearity that creates a spectral component that is the result of the subtraction and addition of two frequencies.

Hope that helps!

Respectfully submitted,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-24-2024 00:29
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Peter has 'challenged me' indirectly (ha ha) to do the A0 with my Neumann KM183 mics. Then I use the same parameters of Matlab as I did before when I captured the A0 with the PianoSens sensor.

The pic is below. Double click it to see it better. The top view is amplitude vs time. The startup is messy compared with my prior presentation using the sensor, but there are still very clearly defined periods of A0 that I have marked.

Now look at the spectral view on the bottom. Look at the 3rd and 6th levels as the highest of the first 10 harmonics, but look at the fundamental which is only 5 dB below the 2nd harmonic. Amazing. So, it all boils down to how to set up the experiment and how to perform the frequency analysis.

Best,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 21:06
From: Norman Brickman
Subject: Dispelling the 'Myth' of the Missing Fundamental

For tuning the lowest notes on a nice piano, since I am tuning 12 TET based on the octave (i.e., ET), I will often start with a double octave for initial placement. Then testing with a progression of seventeenths (5:1), and on a good day I can also bring in minor sevenths (7:4) or minor sixths (8:5) as additional testing and with their slightly improved accuracy over the seventeenth..

Mark, resonance works well going from a string that is partial #2 or #3 (as well as higher partials) down to the fundamental string. But for me the strongest resonance created is always equal to the partial in frequency. Maybe with non-linearities the fundamental might also be there, but much reduced in amplitude. Regards, Norman.

------------------------------
Norman Brickman
Potomac Piano Service
Potomac, Maryland
potomacpiano@verizon.net
https://potomacpiano.com
(301) 983.9321

Original Message:
Sent: 01-23-2024 20:05
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Parker, better yet, use the 12th, not the 5th. -Steve


Original Message:
Sent: 1/23/2024 7:12:00 PM
From: Parker Leigh
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

That is why I often use the fifth as a reference whentuning the low bass.

------------------------------
Parker Leigh RPT
Winchester VA
(540) 722-3865

Original Message:
Sent: 01-23-2024 13:48
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 11:00
From: Mark Schecter
Subject: Dispelling the 'Myth' of the Missing Fundamental

Original Message:
Sent: 1/23/2024 9:02:00 AM
From: Robert Anderson
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I have always assumed that A0 has a fundamental and the myth hasn't penetrated to me, anyway. My understanding is that the fundamental of A0 is so weak compared to its higher partials that it is pretty inaudible. In organ building a 32' pipe is needed for the fundamental of A0 but the combination of a 16' and and 8' pipe can give the illusion of hearing A0. I expect I'll hear about it if my understanding is wrong.

Bob Anderson, RPT
Tucson, AZ


Original Message:
Sent: 1/22/2024 3:17:00 AM
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

Nathan,

Please send us your resume bio. I have attached mine. Obviously you want to keep hammering me on the square root of 88. I more than clarified the variances by another means. You are ignoring my clarifications. So I guess I have no choice but to refer you to my bio. I have attached it. We can compare.

I am being hammered. Take my responses that followed as the right answer. I welcome your data you will be collecting, your signal processing insights and analyses, and your conclusions from your actual data. I welcome your statistics you will be gathering, the actual variance measurements, the spectral analysis on the interferences and the window of the FFT and your FFT intra-bin algorithms you will describe that show the PPM of the intra-bin accuracy, and many other things that you have great expertise in. We need more people like you doing this work. We need highly credentialed signal processing engineers with books, papers, patents, so that we can trust their work output. If you have these skills, I welcome that. I have an MIT professor friend who is probably the top person in the DSP field, a pioneer, checking my work. So far he approves 100%. Nice to know. We were colleagues back in the 80's when DSP and high quality spectral analysis was being invented at Bell Labs and MIT. I was in the DSP department at Bell Labs and he was at MIT.

Best,

Steve

Original Message:
Sent: 1/24/2024 4:38:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

So, I think there's a couple things that really might ease your path if you acknowledged them.  First, you're not the only person in here with an engineering background, who could be making more money doing something else.  Second, if you really stuck to posting hard data as you advocate, I think you'd see a lot fewer protests.  The problem, for me, comes in with claims like
 * "There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano." (I've tried to explain that "the missing fundamental" refers to something different than assumed here.)
 * "So let's say your standard deviation error is 0.5 cents from acoustic interference. The square root of 88 is 9.38, so if you have increased the probability of the spread of out-of-tune-ness by at least 5 cents or more." (This is simply incorrect, that's not how standard deviation works. I tried to gently explain that but you then claimed you were uninterested in talking about statistical models.  Why did you present one in the first place then?)

Again, I think your device is interesting, and I think several of your findings are interesting.  But I don't think it's in anyone's best interest for me to ignore it when I spot something in a claim that looks incomplete or incorrect.  I think we can learn a lot from you here, but I think you can learn from us too if you're willing to listen.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 15:26
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Not anyone specifically. Take no offense, please. I don't think many understand just how much work it is to make engineering tests / measurements and explain the results in precise language. Engineers usually get paid handsomely to do this kind of work in commercial and military fields with a paying customer. The quality of my work I post is at that level because I have been doing it for major customers for 40 years. I am doing this signal processing research on piano, only because I want to educate serious PTG members who want to learn about the subject. I post things that we normally cannot find in the prior piano research journals. I am just giving away the time and effort. I do hope one day people appreciate it. It distracts me from my current paid customer tasks and sometimes I just think it is falling on deaf ears and I should just stop and go back to my professional signal processing work.


Original Message:
Sent: 1/24/2024 3:18:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I don't follow. Do you feel like I'm not providing enough evidence as to what the correct interpretation of the term is?  Do you mean that you want to see evidence of the legitimate psychoacoustic phenomenon?

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 15:15
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Nathan, I cannot emphasize enough the importance of evidence-based data in these discussions. Without evidence-based real data and precise measurements, all things devolve into endless debate. -- Respectfully, Steve


Original Message:
Sent: 1/24/2024 3:10:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I was arguing that the term "Missing Fundamental", used correctly, referred to a psychoacoustic phenomenon in the first place -- not an acoustic one.  Wikipedia seems to agree with me as well, for what it's worth: https://en.wikipedia.org/wiki/Missing_fundamental.

I don't doubt that some piano technicians have gotten this mixed up, even prominent ones.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 14:41
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Colleagues, 

There is big difference between 'acoustics' and 'psycho-acoustics'. There is a big difference between what we 'think' is so, and what we can 'measure' as so!

Some things are hard to find evidence of, but we know to be true, but the best is when there is some evidence so that it is not 'blind faith' but 'evidence-based' faith. It is my job to base every statement on actual evidence that is non-contradictory to all other evidence. 

For example, I posted above the evidence of measured data of the harmonic levels of both the sensor data (the original post and video that started this) and microphone data (last night and above post) of the first 10+ harmonics of A0, showing both the time and frequency domain. The measured harmonic magnitude levels were different due to the EQ of the two pickup devices, but both showed the full evidence of the presence of a significant level of A0 fundamental. If you google 'missing fundamental' there are lots of hits and this is what started me on the venture for the post. I am glad I took the time to actually make the measurements and post the data.

I explained in an earlier post that there is no such thing as a subharmonic in reality unless there is an actual spectral component, which cannot come from a linear system but it can come from a strong non-linearity that creates a spectral component that is the result of the subtraction and addition of two frequencies.

Hope that helps!

Respectfully submitted,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-24-2024 00:29
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Peter has 'challenged me' indirectly (ha ha) to do the A0 with my Neumann KM183 mics. Then I use the same parameters of Matlab as I did before when I captured the A0 with the PianoSens sensor.

The pic is below. Double click it to see it better. The top view is amplitude vs time. The startup is messy compared with my prior presentation using the sensor, but there are still very clearly defined periods of A0 that I have marked.

Now look at the spectral view on the bottom. Look at the 3rd and 6th levels as the highest of the first 10 harmonics, but look at the fundamental which is only 5 dB below the 2nd harmonic. Amazing. So, it all boils down to how to set up the experiment and how to perform the frequency analysis.

Best,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 21:06
From: Norman Brickman
Subject: Dispelling the 'Myth' of the Missing Fundamental

For tuning the lowest notes on a nice piano, since I am tuning 12 TET based on the octave (i.e., ET), I will often start with a double octave for initial placement. Then testing with a progression of seventeenths (5:1), and on a good day I can also bring in minor sevenths (7:4) or minor sixths (8:5) as additional testing and with their slightly improved accuracy over the seventeenth..

Mark, resonance works well going from a string that is partial #2 or #3 (as well as higher partials) down to the fundamental string. But for me the strongest resonance created is always equal to the partial in frequency. Maybe with non-linearities the fundamental might also be there, but much reduced in amplitude. Regards, Norman.

------------------------------
Norman Brickman
Potomac Piano Service
Potomac, Maryland
potomacpiano@verizon.net
https://potomacpiano.com
(301) 983.9321

Original Message:
Sent: 01-23-2024 20:05
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Parker, better yet, use the 12th, not the 5th. -Steve


Original Message:
Sent: 1/23/2024 7:12:00 PM
From: Parker Leigh
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

That is why I often use the fifth as a reference whentuning the low bass.

------------------------------
Parker Leigh RPT
Winchester VA
(540) 722-3865

Original Message:
Sent: 01-23-2024 13:48
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 11:00
From: Mark Schecter
Subject: Dispelling the 'Myth' of the Missing Fundamental

Original Message:
Sent: 1/23/2024 9:02:00 AM
From: Robert Anderson
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I have always assumed that A0 has a fundamental and the myth hasn't penetrated to me, anyway. My understanding is that the fundamental of A0 is so weak compared to its higher partials that it is pretty inaudible. In organ building a 32' pipe is needed for the fundamental of A0 but the combination of a 16' and and 8' pipe can give the illusion of hearing A0. I expect I'll hear about it if my understanding is wrong.

Bob Anderson, RPT
Tucson, AZ


Original Message:
Sent: 1/22/2024 3:17:00 AM
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

Nice try, but I fear my background is far humbler than yours.  And yet I was still able to find and demonstrate an error in your math, and point out something you missed w/rt the correct meaning of missing fundamentals.  If you require extensive credentials before you're willing to listen to such simple corrections, I simply cannot provide them.  Have a nice day.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com
------------------------------

Original Message:
Sent: 01-24-2024 17:17
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Nathan,

Please send us your resume bio. I have attached mine. Obviously you want to keep hammering me on the square root of 88. I more than clarified the variances by another means. You are ignoring my clarifications. So I guess I have no choice but to refer you to my bio. I have attached it. We can compare.

I am being hammered. Take my responses that followed as the right answer. I welcome your data you will be collecting, your signal processing insights and analyses, and your conclusions from your actual data. I welcome your statistics you will be gathering, the actual variance measurements, the spectral analysis on the interferences and the window of the FFT and your FFT intra-bin algorithms you will describe that show the PPM of the intra-bin accuracy, and many other things that you have great expertise in. We need more people like you doing this work. We need highly credentialed signal processing engineers with books, papers, patents, so that we can trust their work output. If you have these skills, I welcome that. I have an MIT professor friend who is probably the top person in the DSP field, a pioneer, checking my work. So far he approves 100%. Nice to know. We were colleagues back in the 80's when DSP and high quality spectral analysis was being invented at Bell Labs and MIT. I was in the DSP department at Bell Labs and he was at MIT.

Best,

Steve

Original Message:
Sent: 1/24/2024 4:38:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

So, I think there's a couple things that really might ease your path if you acknowledged them.  First, you're not the only person in here with an engineering background, who could be making more money doing something else.  Second, if you really stuck to posting hard data as you advocate, I think you'd see a lot fewer protests.  The problem, for me, comes in with claims like
 * "There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano." (I've tried to explain that "the missing fundamental" refers to something different than assumed here.)
 * "So let's say your standard deviation error is 0.5 cents from acoustic interference. The square root of 88 is 9.38, so if you have increased the probability of the spread of out-of-tune-ness by at least 5 cents or more." (This is simply incorrect, that's not how standard deviation works. I tried to gently explain that but you then claimed you were uninterested in talking about statistical models.  Why did you present one in the first place then?)

Again, I think your device is interesting, and I think several of your findings are interesting.  But I don't think it's in anyone's best interest for me to ignore it when I spot something in a claim that looks incomplete or incorrect.  I think we can learn a lot from you here, but I think you can learn from us too if you're willing to listen.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 15:26
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Not anyone specifically. Take no offense, please. I don't think many understand just how much work it is to make engineering tests / measurements and explain the results in precise language. Engineers usually get paid handsomely to do this kind of work in commercial and military fields with a paying customer. The quality of my work I post is at that level because I have been doing it for major customers for 40 years. I am doing this signal processing research on piano, only because I want to educate serious PTG members who want to learn about the subject. I post things that we normally cannot find in the prior piano research journals. I am just giving away the time and effort. I do hope one day people appreciate it. It distracts me from my current paid customer tasks and sometimes I just think it is falling on deaf ears and I should just stop and go back to my professional signal processing work.


Original Message:
Sent: 1/24/2024 3:18:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I don't follow. Do you feel like I'm not providing enough evidence as to what the correct interpretation of the term is?  Do you mean that you want to see evidence of the legitimate psychoacoustic phenomenon?

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 15:15
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Nathan, I cannot emphasize enough the importance of evidence-based data in these discussions. Without evidence-based real data and precise measurements, all things devolve into endless debate. -- Respectfully, Steve


Original Message:
Sent: 1/24/2024 3:10:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I was arguing that the term "Missing Fundamental", used correctly, referred to a psychoacoustic phenomenon in the first place -- not an acoustic one.  Wikipedia seems to agree with me as well, for what it's worth: https://en.wikipedia.org/wiki/Missing_fundamental.

I don't doubt that some piano technicians have gotten this mixed up, even prominent ones.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 14:41
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Colleagues, 

There is big difference between 'acoustics' and 'psycho-acoustics'. There is a big difference between what we 'think' is so, and what we can 'measure' as so!

Some things are hard to find evidence of, but we know to be true, but the best is when there is some evidence so that it is not 'blind faith' but 'evidence-based' faith. It is my job to base every statement on actual evidence that is non-contradictory to all other evidence. 

For example, I posted above the evidence of measured data of the harmonic levels of both the sensor data (the original post and video that started this) and microphone data (last night and above post) of the first 10+ harmonics of A0, showing both the time and frequency domain. The measured harmonic magnitude levels were different due to the EQ of the two pickup devices, but both showed the full evidence of the presence of a significant level of A0 fundamental. If you google 'missing fundamental' there are lots of hits and this is what started me on the venture for the post. I am glad I took the time to actually make the measurements and post the data.

I explained in an earlier post that there is no such thing as a subharmonic in reality unless there is an actual spectral component, which cannot come from a linear system but it can come from a strong non-linearity that creates a spectral component that is the result of the subtraction and addition of two frequencies.

Hope that helps!

Respectfully submitted,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-24-2024 00:29
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Peter has 'challenged me' indirectly (ha ha) to do the A0 with my Neumann KM183 mics. Then I use the same parameters of Matlab as I did before when I captured the A0 with the PianoSens sensor.

The pic is below. Double click it to see it better. The top view is amplitude vs time. The startup is messy compared with my prior presentation using the sensor, but there are still very clearly defined periods of A0 that I have marked.

Now look at the spectral view on the bottom. Look at the 3rd and 6th levels as the highest of the first 10 harmonics, but look at the fundamental which is only 5 dB below the 2nd harmonic. Amazing. So, it all boils down to how to set up the experiment and how to perform the frequency analysis.

Best,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 21:06
From: Norman Brickman
Subject: Dispelling the 'Myth' of the Missing Fundamental

For tuning the lowest notes on a nice piano, since I am tuning 12 TET based on the octave (i.e., ET), I will often start with a double octave for initial placement. Then testing with a progression of seventeenths (5:1), and on a good day I can also bring in minor sevenths (7:4) or minor sixths (8:5) as additional testing and with their slightly improved accuracy over the seventeenth..

Mark, resonance works well going from a string that is partial #2 or #3 (as well as higher partials) down to the fundamental string. But for me the strongest resonance created is always equal to the partial in frequency. Maybe with non-linearities the fundamental might also be there, but much reduced in amplitude. Regards, Norman.

------------------------------
Norman Brickman
Potomac Piano Service
Potomac, Maryland
potomacpiano@verizon.net
https://potomacpiano.com
(301) 983.9321

Original Message:
Sent: 01-23-2024 20:05
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Parker, better yet, use the 12th, not the 5th. -Steve


Original Message:
Sent: 1/23/2024 7:12:00 PM
From: Parker Leigh
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

That is why I often use the fifth as a reference whentuning the low bass.

------------------------------
Parker Leigh RPT
Winchester VA
(540) 722-3865

Original Message:
Sent: 01-23-2024 13:48
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 11:00
From: Mark Schecter
Subject: Dispelling the 'Myth' of the Missing Fundamental

Original Message:
Sent: 1/23/2024 9:02:00 AM
From: Robert Anderson
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I have always assumed that A0 has a fundamental and the myth hasn't penetrated to me, anyway. My understanding is that the fundamental of A0 is so weak compared to its higher partials that it is pretty inaudible. In organ building a 32' pipe is needed for the fundamental of A0 but the combination of a 16' and and 8' pipe can give the illusion of hearing A0. I expect I'll hear about it if my understanding is wrong.

Bob Anderson, RPT
Tucson, AZ


Original Message:
Sent: 1/22/2024 3:17:00 AM
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

Hammer me forever without reading my clarifications. Get your own MIT DSP professor to review my work and my replies, I will then listen. What if I simply declare to the world out loud that I was only trying to show how the Gaussian Curve would give us more and more outliers with larger numbers of notes? Yes, the square root of the variance is the standard deviation. The standard deviation is also the RMS value. The RMS value comes from a significant number of measurements. There is an old expression "Torture people until they cry 'uncle'. What are you trying to prove? That on a small technicality that was more than clarified, that you sill relentlessly not let to until the 'big boy' cries 'uncle' and then you can strut around saying you took down the big boy? Is this all about some ego thing? 

HERE is what I propose you do. Start taking your own measurements and set up a great methodology of experiments. Take the data into Matlab. Show us your algorithms and describe your experiments. Then I will more than gladly welcome your engineering expertise and painstaking work. 

Respectfully 

Steve

Original Message:
Sent: 1/24/2024 5:33:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

Nice try, but I fear my background is far humbler than yours.  And yet I was still able to find and demonstrate an error in your math, and point out something you missed w/rt the correct meaning of missing fundamentals.  If you require extensive credentials before you're willing to listen to such simple corrections, I simply cannot provide them.  Have a nice day.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 17:17
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Nathan,

Please send us your resume bio. I have attached mine. Obviously you want to keep hammering me on the square root of 88. I more than clarified the variances by another means. You are ignoring my clarifications. So I guess I have no choice but to refer you to my bio. I have attached it. We can compare.

I am being hammered. Take my responses that followed as the right answer. I welcome your data you will be collecting, your signal processing insights and analyses, and your conclusions from your actual data. I welcome your statistics you will be gathering, the actual variance measurements, the spectral analysis on the interferences and the window of the FFT and your FFT intra-bin algorithms you will describe that show the PPM of the intra-bin accuracy, and many other things that you have great expertise in. We need more people like you doing this work. We need highly credentialed signal processing engineers with books, papers, patents, so that we can trust their work output. If you have these skills, I welcome that. I have an MIT professor friend who is probably the top person in the DSP field, a pioneer, checking my work. So far he approves 100%. Nice to know. We were colleagues back in the 80's when DSP and high quality spectral analysis was being invented at Bell Labs and MIT. I was in the DSP department at Bell Labs and he was at MIT.

Best,

Steve

Original Message:
Sent: 1/24/2024 4:38:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

So, I think there's a couple things that really might ease your path if you acknowledged them.  First, you're not the only person in here with an engineering background, who could be making more money doing something else.  Second, if you really stuck to posting hard data as you advocate, I think you'd see a lot fewer protests.  The problem, for me, comes in with claims like
 * "There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano." (I've tried to explain that "the missing fundamental" refers to something different than assumed here.)
 * "So let's say your standard deviation error is 0.5 cents from acoustic interference. The square root of 88 is 9.38, so if you have increased the probability of the spread of out-of-tune-ness by at least 5 cents or more." (This is simply incorrect, that's not how standard deviation works. I tried to gently explain that but you then claimed you were uninterested in talking about statistical models.  Why did you present one in the first place then?)

Again, I think your device is interesting, and I think several of your findings are interesting.  But I don't think it's in anyone's best interest for me to ignore it when I spot something in a claim that looks incomplete or incorrect.  I think we can learn a lot from you here, but I think you can learn from us too if you're willing to listen.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 15:26
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Not anyone specifically. Take no offense, please. I don't think many understand just how much work it is to make engineering tests / measurements and explain the results in precise language. Engineers usually get paid handsomely to do this kind of work in commercial and military fields with a paying customer. The quality of my work I post is at that level because I have been doing it for major customers for 40 years. I am doing this signal processing research on piano, only because I want to educate serious PTG members who want to learn about the subject. I post things that we normally cannot find in the prior piano research journals. I am just giving away the time and effort. I do hope one day people appreciate it. It distracts me from my current paid customer tasks and sometimes I just think it is falling on deaf ears and I should just stop and go back to my professional signal processing work.


Original Message:
Sent: 1/24/2024 3:18:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I don't follow. Do you feel like I'm not providing enough evidence as to what the correct interpretation of the term is?  Do you mean that you want to see evidence of the legitimate psychoacoustic phenomenon?

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 15:15
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Nathan, I cannot emphasize enough the importance of evidence-based data in these discussions. Without evidence-based real data and precise measurements, all things devolve into endless debate. -- Respectfully, Steve


Original Message:
Sent: 1/24/2024 3:10:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I was arguing that the term "Missing Fundamental", used correctly, referred to a psychoacoustic phenomenon in the first place -- not an acoustic one.  Wikipedia seems to agree with me as well, for what it's worth: https://en.wikipedia.org/wiki/Missing_fundamental.

I don't doubt that some piano technicians have gotten this mixed up, even prominent ones.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 14:41
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Colleagues, 

There is big difference between 'acoustics' and 'psycho-acoustics'. There is a big difference between what we 'think' is so, and what we can 'measure' as so!

Some things are hard to find evidence of, but we know to be true, but the best is when there is some evidence so that it is not 'blind faith' but 'evidence-based' faith. It is my job to base every statement on actual evidence that is non-contradictory to all other evidence. 

For example, I posted above the evidence of measured data of the harmonic levels of both the sensor data (the original post and video that started this) and microphone data (last night and above post) of the first 10+ harmonics of A0, showing both the time and frequency domain. The measured harmonic magnitude levels were different due to the EQ of the two pickup devices, but both showed the full evidence of the presence of a significant level of A0 fundamental. If you google 'missing fundamental' there are lots of hits and this is what started me on the venture for the post. I am glad I took the time to actually make the measurements and post the data.

I explained in an earlier post that there is no such thing as a subharmonic in reality unless there is an actual spectral component, which cannot come from a linear system but it can come from a strong non-linearity that creates a spectral component that is the result of the subtraction and addition of two frequencies.

Hope that helps!

Respectfully submitted,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-24-2024 00:29
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Peter has 'challenged me' indirectly (ha ha) to do the A0 with my Neumann KM183 mics. Then I use the same parameters of Matlab as I did before when I captured the A0 with the PianoSens sensor.

The pic is below. Double click it to see it better. The top view is amplitude vs time. The startup is messy compared with my prior presentation using the sensor, but there are still very clearly defined periods of A0 that I have marked.

Now look at the spectral view on the bottom. Look at the 3rd and 6th levels as the highest of the first 10 harmonics, but look at the fundamental which is only 5 dB below the 2nd harmonic. Amazing. So, it all boils down to how to set up the experiment and how to perform the frequency analysis.

Best,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 21:06
From: Norman Brickman
Subject: Dispelling the 'Myth' of the Missing Fundamental

For tuning the lowest notes on a nice piano, since I am tuning 12 TET based on the octave (i.e., ET), I will often start with a double octave for initial placement. Then testing with a progression of seventeenths (5:1), and on a good day I can also bring in minor sevenths (7:4) or minor sixths (8:5) as additional testing and with their slightly improved accuracy over the seventeenth..

Mark, resonance works well going from a string that is partial #2 or #3 (as well as higher partials) down to the fundamental string. But for me the strongest resonance created is always equal to the partial in frequency. Maybe with non-linearities the fundamental might also be there, but much reduced in amplitude. Regards, Norman.

------------------------------
Norman Brickman
Potomac Piano Service
Potomac, Maryland
potomacpiano@verizon.net
https://potomacpiano.com
(301) 983.9321

Original Message:
Sent: 01-23-2024 20:05
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Parker, better yet, use the 12th, not the 5th. -Steve


Original Message:
Sent: 1/23/2024 7:12:00 PM
From: Parker Leigh
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

That is why I often use the fifth as a reference whentuning the low bass.

------------------------------
Parker Leigh RPT
Winchester VA
(540) 722-3865

Original Message:
Sent: 01-23-2024 13:48
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 11:00
From: Mark Schecter
Subject: Dispelling the 'Myth' of the Missing Fundamental

Original Message:
Sent: 1/23/2024 9:02:00 AM
From: Robert Anderson
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I have always assumed that A0 has a fundamental and the myth hasn't penetrated to me, anyway. My understanding is that the fundamental of A0 is so weak compared to its higher partials that it is pretty inaudible. In organ building a 32' pipe is needed for the fundamental of A0 but the combination of a 16' and and 8' pipe can give the illusion of hearing A0. I expect I'll hear about it if my understanding is wrong.

Bob Anderson, RPT
Tucson, AZ


Original Message:
Sent: 1/22/2024 3:17:00 AM
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

Steve-

Piano technicians are simple folk trying to support themselves practicing a rather antiquated trade in a shrinking corner of a musical world that is rapidly changing. Most of us do not understand at your level of detail what you are writing about. We see the streaming arguments and think "Enough."

If you have invented something that can help  our work, demonstrate and communicate clearly how to use it within the constraints of our daily work and you will soon have a group of eager followers, happily promoting your product. Learn from your friend Frank I. how he developed PianoScope through extended communication with piano technicians.

This would be very helpful to your potentially much larger audience.

Hammer me forever without reading my clarifications. Get your own MIT DSP professor to review my work and my replies, I will then listen. What if I simply declare to the world out loud that I was only trying to show how the Gaussian Curve would give us more and more outliers with larger numbers of notes? Yes, the square root of the variance is the standard deviation. The standard deviation is also the RMS value. The RMS value comes from a significant number of measurements. There is an old expression "Torture people until they cry 'uncle'. What are you trying to prove? That on a small technicality that was more than clarified, that you sill relentlessly not let to until the 'big boy' cries 'uncle' and then you can strut around saying you took down the big boy? Is this all about some ego thing? 

HERE is what I propose you do. Start taking your own measurements and set up a great methodology of experiments. Take the data into Matlab. Show us your algorithms and describe your experiments. Then I will more than gladly welcome your engineering expertise and painstaking work. 

Respectfully 

Steve

Original Message:
Sent: 1/24/2024 5:33:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

Nice try, but I fear my background is far humbler than yours.  And yet I was still able to find and demonstrate an error in your math, and point out something you missed w/rt the correct meaning of missing fundamentals.  If you require extensive credentials before you're willing to listen to such simple corrections, I simply cannot provide them.  Have a nice day.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 17:17
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Nathan,

Please send us your resume bio. I have attached mine. Obviously you want to keep hammering me on the square root of 88. I more than clarified the variances by another means. You are ignoring my clarifications. So I guess I have no choice but to refer you to my bio. I have attached it. We can compare.

I am being hammered. Take my responses that followed as the right answer. I welcome your data you will be collecting, your signal processing insights and analyses, and your conclusions from your actual data. I welcome your statistics you will be gathering, the actual variance measurements, the spectral analysis on the interferences and the window of the FFT and your FFT intra-bin algorithms you will describe that show the PPM of the intra-bin accuracy, and many other things that you have great expertise in. We need more people like you doing this work. We need highly credentialed signal processing engineers with books, papers, patents, so that we can trust their work output. If you have these skills, I welcome that. I have an MIT professor friend who is probably the top person in the DSP field, a pioneer, checking my work. So far he approves 100%. Nice to know. We were colleagues back in the 80's when DSP and high quality spectral analysis was being invented at Bell Labs and MIT. I was in the DSP department at Bell Labs and he was at MIT.

Best,

Steve

Original Message:
Sent: 1/24/2024 4:38:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

So, I think there's a couple things that really might ease your path if you acknowledged them.  First, you're not the only person in here with an engineering background, who could be making more money doing something else.  Second, if you really stuck to posting hard data as you advocate, I think you'd see a lot fewer protests.  The problem, for me, comes in with claims like
 * "There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano." (I've tried to explain that "the missing fundamental" refers to something different than assumed here.)
 * "So let's say your standard deviation error is 0.5 cents from acoustic interference. The square root of 88 is 9.38, so if you have increased the probability of the spread of out-of-tune-ness by at least 5 cents or more." (This is simply incorrect, that's not how standard deviation works. I tried to gently explain that but you then claimed you were uninterested in talking about statistical models.  Why did you present one in the first place then?)

Again, I think your device is interesting, and I think several of your findings are interesting.  But I don't think it's in anyone's best interest for me to ignore it when I spot something in a claim that looks incomplete or incorrect.  I think we can learn a lot from you here, but I think you can learn from us too if you're willing to listen.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 15:26
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Not anyone specifically. Take no offense, please. I don't think many understand just how much work it is to make engineering tests / measurements and explain the results in precise language. Engineers usually get paid handsomely to do this kind of work in commercial and military fields with a paying customer. The quality of my work I post is at that level because I have been doing it for major customers for 40 years. I am doing this signal processing research on piano, only because I want to educate serious PTG members who want to learn about the subject. I post things that we normally cannot find in the prior piano research journals. I am just giving away the time and effort. I do hope one day people appreciate it. It distracts me from my current paid customer tasks and sometimes I just think it is falling on deaf ears and I should just stop and go back to my professional signal processing work.


Original Message:
Sent: 1/24/2024 3:18:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I don't follow. Do you feel like I'm not providing enough evidence as to what the correct interpretation of the term is?  Do you mean that you want to see evidence of the legitimate psychoacoustic phenomenon?

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 15:15
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Nathan, I cannot emphasize enough the importance of evidence-based data in these discussions. Without evidence-based real data and precise measurements, all things devolve into endless debate. -- Respectfully, Steve


Original Message:
Sent: 1/24/2024 3:10:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I was arguing that the term "Missing Fundamental", used correctly, referred to a psychoacoustic phenomenon in the first place -- not an acoustic one.  Wikipedia seems to agree with me as well, for what it's worth: https://en.wikipedia.org/wiki/Missing_fundamental.

I don't doubt that some piano technicians have gotten this mixed up, even prominent ones.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 14:41
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Colleagues, 

There is big difference between 'acoustics' and 'psycho-acoustics'. There is a big difference between what we 'think' is so, and what we can 'measure' as so!

Some things are hard to find evidence of, but we know to be true, but the best is when there is some evidence so that it is not 'blind faith' but 'evidence-based' faith. It is my job to base every statement on actual evidence that is non-contradictory to all other evidence. 

For example, I posted above the evidence of measured data of the harmonic levels of both the sensor data (the original post and video that started this) and microphone data (last night and above post) of the first 10+ harmonics of A0, showing both the time and frequency domain. The measured harmonic magnitude levels were different due to the EQ of the two pickup devices, but both showed the full evidence of the presence of a significant level of A0 fundamental. If you google 'missing fundamental' there are lots of hits and this is what started me on the venture for the post. I am glad I took the time to actually make the measurements and post the data.

I explained in an earlier post that there is no such thing as a subharmonic in reality unless there is an actual spectral component, which cannot come from a linear system but it can come from a strong non-linearity that creates a spectral component that is the result of the subtraction and addition of two frequencies.

Hope that helps!

Respectfully submitted,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-24-2024 00:29
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Peter has 'challenged me' indirectly (ha ha) to do the A0 with my Neumann KM183 mics. Then I use the same parameters of Matlab as I did before when I captured the A0 with the PianoSens sensor.

The pic is below. Double click it to see it better. The top view is amplitude vs time. The startup is messy compared with my prior presentation using the sensor, but there are still very clearly defined periods of A0 that I have marked.

Now look at the spectral view on the bottom. Look at the 3rd and 6th levels as the highest of the first 10 harmonics, but look at the fundamental which is only 5 dB below the 2nd harmonic. Amazing. So, it all boils down to how to set up the experiment and how to perform the frequency analysis.

Best,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 21:06
From: Norman Brickman
Subject: Dispelling the 'Myth' of the Missing Fundamental

For tuning the lowest notes on a nice piano, since I am tuning 12 TET based on the octave (i.e., ET), I will often start with a double octave for initial placement. Then testing with a progression of seventeenths (5:1), and on a good day I can also bring in minor sevenths (7:4) or minor sixths (8:5) as additional testing and with their slightly improved accuracy over the seventeenth..

Mark, resonance works well going from a string that is partial #2 or #3 (as well as higher partials) down to the fundamental string. But for me the strongest resonance created is always equal to the partial in frequency. Maybe with non-linearities the fundamental might also be there, but much reduced in amplitude. Regards, Norman.

------------------------------
Norman Brickman
Potomac Piano Service
Potomac, Maryland
potomacpiano@verizon.net
https://potomacpiano.com
(301) 983.9321

Original Message:
Sent: 01-23-2024 20:05
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Parker, better yet, use the 12th, not the 5th. -Steve


Original Message:
Sent: 1/23/2024 7:12:00 PM
From: Parker Leigh
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

That is why I often use the fifth as a reference whentuning the low bass.

------------------------------
Parker Leigh RPT
Winchester VA
(540) 722-3865

Original Message:
Sent: 01-23-2024 13:48
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 11:00
From: Mark Schecter
Subject: Dispelling the 'Myth' of the Missing Fundamental

Original Message:
Sent: 1/23/2024 9:02:00 AM
From: Robert Anderson
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I have always assumed that A0 has a fundamental and the myth hasn't penetrated to me, anyway. My understanding is that the fundamental of A0 is so weak compared to its higher partials that it is pretty inaudible. In organ building a 32' pipe is needed for the fundamental of A0 but the combination of a 16' and and 8' pipe can give the illusion of hearing A0. I expect I'll hear about it if my understanding is wrong.

Bob Anderson, RPT
Tucson, AZ


Original Message:
Sent: 1/22/2024 3:17:00 AM
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

Hammer me forever without reading my clarifications. Get your own MIT DSP professor to review my work and my replies, I will then listen. What if I simply declare to the world out loud that I was only trying to show how the Gaussian Curve would give us more and more outliers with larger numbers of notes? Yes, the square root of the variance is the standard deviation. The standard deviation is also the RMS value. The RMS value comes from a significant number of measurements. There is an old expression "Torture people until they cry 'uncle'. What are you trying to prove? That on a small technicality that was more than clarified, that you sill relentlessly not let to until the 'big boy' cries 'uncle' and then you can strut around saying you took down the big boy? Is this all about some ego thing? 

HERE is what I propose you do. Start taking your own measurements and set up a great methodology of experiments. Take the data into Matlab. Show us your algorithms and describe your experiments. Then I will more than gladly welcome your engineering expertise and painstaking work. 

Respectfully 

Steve

Original Message:
Sent: 1/24/2024 5:33:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

Nice try, but I fear my background is far humbler than yours.  And yet I was still able to find and demonstrate an error in your math, and point out something you missed w/rt the correct meaning of missing fundamentals.  If you require extensive credentials before you're willing to listen to such simple corrections, I simply cannot provide them.  Have a nice day.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 17:17
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Nathan,

Please send us your resume bio. I have attached mine. Obviously you want to keep hammering me on the square root of 88. I more than clarified the variances by another means. You are ignoring my clarifications. So I guess I have no choice but to refer you to my bio. I have attached it. We can compare.

I am being hammered. Take my responses that followed as the right answer. I welcome your data you will be collecting, your signal processing insights and analyses, and your conclusions from your actual data. I welcome your statistics you will be gathering, the actual variance measurements, the spectral analysis on the interferences and the window of the FFT and your FFT intra-bin algorithms you will describe that show the PPM of the intra-bin accuracy, and many other things that you have great expertise in. We need more people like you doing this work. We need highly credentialed signal processing engineers with books, papers, patents, so that we can trust their work output. If you have these skills, I welcome that. I have an MIT professor friend who is probably the top person in the DSP field, a pioneer, checking my work. So far he approves 100%. Nice to know. We were colleagues back in the 80's when DSP and high quality spectral analysis was being invented at Bell Labs and MIT. I was in the DSP department at Bell Labs and he was at MIT.

Best,

Steve

Original Message:
Sent: 1/24/2024 4:38:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

So, I think there's a couple things that really might ease your path if you acknowledged them.  First, you're not the only person in here with an engineering background, who could be making more money doing something else.  Second, if you really stuck to posting hard data as you advocate, I think you'd see a lot fewer protests.  The problem, for me, comes in with claims like
 * "There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano." (I've tried to explain that "the missing fundamental" refers to something different than assumed here.)
 * "So let's say your standard deviation error is 0.5 cents from acoustic interference. The square root of 88 is 9.38, so if you have increased the probability of the spread of out-of-tune-ness by at least 5 cents or more." (This is simply incorrect, that's not how standard deviation works. I tried to gently explain that but you then claimed you were uninterested in talking about statistical models.  Why did you present one in the first place then?)

Again, I think your device is interesting, and I think several of your findings are interesting.  But I don't think it's in anyone's best interest for me to ignore it when I spot something in a claim that looks incomplete or incorrect.  I think we can learn a lot from you here, but I think you can learn from us too if you're willing to listen.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 15:26
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Not anyone specifically. Take no offense, please. I don't think many understand just how much work it is to make engineering tests / measurements and explain the results in precise language. Engineers usually get paid handsomely to do this kind of work in commercial and military fields with a paying customer. The quality of my work I post is at that level because I have been doing it for major customers for 40 years. I am doing this signal processing research on piano, only because I want to educate serious PTG members who want to learn about the subject. I post things that we normally cannot find in the prior piano research journals. I am just giving away the time and effort. I do hope one day people appreciate it. It distracts me from my current paid customer tasks and sometimes I just think it is falling on deaf ears and I should just stop and go back to my professional signal processing work.


Original Message:
Sent: 1/24/2024 3:18:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I don't follow. Do you feel like I'm not providing enough evidence as to what the correct interpretation of the term is?  Do you mean that you want to see evidence of the legitimate psychoacoustic phenomenon?

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 15:15
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Nathan, I cannot emphasize enough the importance of evidence-based data in these discussions. Without evidence-based real data and precise measurements, all things devolve into endless debate. -- Respectfully, Steve


Original Message:
Sent: 1/24/2024 3:10:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I was arguing that the term "Missing Fundamental", used correctly, referred to a psychoacoustic phenomenon in the first place -- not an acoustic one.  Wikipedia seems to agree with me as well, for what it's worth: https://en.wikipedia.org/wiki/Missing_fundamental.

I don't doubt that some piano technicians have gotten this mixed up, even prominent ones.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 14:41
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Colleagues, 

There is big difference between 'acoustics' and 'psycho-acoustics'. There is a big difference between what we 'think' is so, and what we can 'measure' as so!

Some things are hard to find evidence of, but we know to be true, but the best is when there is some evidence so that it is not 'blind faith' but 'evidence-based' faith. It is my job to base every statement on actual evidence that is non-contradictory to all other evidence. 

For example, I posted above the evidence of measured data of the harmonic levels of both the sensor data (the original post and video that started this) and microphone data (last night and above post) of the first 10+ harmonics of A0, showing both the time and frequency domain. The measured harmonic magnitude levels were different due to the EQ of the two pickup devices, but both showed the full evidence of the presence of a significant level of A0 fundamental. If you google 'missing fundamental' there are lots of hits and this is what started me on the venture for the post. I am glad I took the time to actually make the measurements and post the data.

I explained in an earlier post that there is no such thing as a subharmonic in reality unless there is an actual spectral component, which cannot come from a linear system but it can come from a strong non-linearity that creates a spectral component that is the result of the subtraction and addition of two frequencies.

Hope that helps!

Respectfully submitted,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-24-2024 00:29
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Peter has 'challenged me' indirectly (ha ha) to do the A0 with my Neumann KM183 mics. Then I use the same parameters of Matlab as I did before when I captured the A0 with the PianoSens sensor.

The pic is below. Double click it to see it better. The top view is amplitude vs time. The startup is messy compared with my prior presentation using the sensor, but there are still very clearly defined periods of A0 that I have marked.

Now look at the spectral view on the bottom. Look at the 3rd and 6th levels as the highest of the first 10 harmonics, but look at the fundamental which is only 5 dB below the 2nd harmonic. Amazing. So, it all boils down to how to set up the experiment and how to perform the frequency analysis.

Best,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 21:06
From: Norman Brickman
Subject: Dispelling the 'Myth' of the Missing Fundamental

For tuning the lowest notes on a nice piano, since I am tuning 12 TET based on the octave (i.e., ET), I will often start with a double octave for initial placement. Then testing with a progression of seventeenths (5:1), and on a good day I can also bring in minor sevenths (7:4) or minor sixths (8:5) as additional testing and with their slightly improved accuracy over the seventeenth..

Mark, resonance works well going from a string that is partial #2 or #3 (as well as higher partials) down to the fundamental string. But for me the strongest resonance created is always equal to the partial in frequency. Maybe with non-linearities the fundamental might also be there, but much reduced in amplitude. Regards, Norman.

------------------------------
Norman Brickman
Potomac Piano Service
Potomac, Maryland
potomacpiano@verizon.net
https://potomacpiano.com
(301) 983.9321

Original Message:
Sent: 01-23-2024 20:05
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Parker, better yet, use the 12th, not the 5th. -Steve


Original Message:
Sent: 1/23/2024 7:12:00 PM
From: Parker Leigh
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

That is why I often use the fifth as a reference whentuning the low bass.

------------------------------
Parker Leigh RPT
Winchester VA
(540) 722-3865

Original Message:
Sent: 01-23-2024 13:48
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 11:00
From: Mark Schecter
Subject: Dispelling the 'Myth' of the Missing Fundamental

Original Message:
Sent: 1/23/2024 9:02:00 AM
From: Robert Anderson
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I have always assumed that A0 has a fundamental and the myth hasn't penetrated to me, anyway. My understanding is that the fundamental of A0 is so weak compared to its higher partials that it is pretty inaudible. In organ building a 32' pipe is needed for the fundamental of A0 but the combination of a 16' and and 8' pipe can give the illusion of hearing A0. I expect I'll hear about it if my understanding is wrong.

Bob Anderson, RPT
Tucson, AZ


Original Message:
Sent: 1/22/2024 3:17:00 AM
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

Steve --

I know I said I'd keep quiet and just watch for a while but...

> "Is this all about some ego thing? "

You a funny guy!

Hammer me forever without reading my clarifications. Get your own MIT DSP professor to review my work and my replies, I will then listen. What if I simply declare to the world out loud that I was only trying to show how the Gaussian Curve would give us more and more outliers with larger numbers of notes? Yes, the square root of the variance is the standard deviation. The standard deviation is also the RMS value. The RMS value comes from a significant number of measurements. There is an old expression "Torture people until they cry 'uncle'. What are you trying to prove? That on a small technicality that was more than clarified, that you sill relentlessly not let to until the 'big boy' cries 'uncle' and then you can strut around saying you took down the big boy? Is this all about some ego thing? 

HERE is what I propose you do. Start taking your own measurements and set up a great methodology of experiments. Take the data into Matlab. Show us your algorithms and describe your experiments. Then I will more than gladly welcome your engineering expertise and painstaking work. 

Respectfully 

Steve

Original Message:
Sent: 1/24/2024 5:33:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

Nice try, but I fear my background is far humbler than yours.  And yet I was still able to find and demonstrate an error in your math, and point out something you missed w/rt the correct meaning of missing fundamentals.  If you require extensive credentials before you're willing to listen to such simple corrections, I simply cannot provide them.  Have a nice day.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 17:17
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Nathan,

Please send us your resume bio. I have attached mine. Obviously you want to keep hammering me on the square root of 88. I more than clarified the variances by another means. You are ignoring my clarifications. So I guess I have no choice but to refer you to my bio. I have attached it. We can compare.

I am being hammered. Take my responses that followed as the right answer. I welcome your data you will be collecting, your signal processing insights and analyses, and your conclusions from your actual data. I welcome your statistics you will be gathering, the actual variance measurements, the spectral analysis on the interferences and the window of the FFT and your FFT intra-bin algorithms you will describe that show the PPM of the intra-bin accuracy, and many other things that you have great expertise in. We need more people like you doing this work. We need highly credentialed signal processing engineers with books, papers, patents, so that we can trust their work output. If you have these skills, I welcome that. I have an MIT professor friend who is probably the top person in the DSP field, a pioneer, checking my work. So far he approves 100%. Nice to know. We were colleagues back in the 80's when DSP and high quality spectral analysis was being invented at Bell Labs and MIT. I was in the DSP department at Bell Labs and he was at MIT.

Best,

Steve

Original Message:
Sent: 1/24/2024 4:38:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

So, I think there's a couple things that really might ease your path if you acknowledged them.  First, you're not the only person in here with an engineering background, who could be making more money doing something else.  Second, if you really stuck to posting hard data as you advocate, I think you'd see a lot fewer protests.  The problem, for me, comes in with claims like
 * "There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano." (I've tried to explain that "the missing fundamental" refers to something different than assumed here.)
 * "So let's say your standard deviation error is 0.5 cents from acoustic interference. The square root of 88 is 9.38, so if you have increased the probability of the spread of out-of-tune-ness by at least 5 cents or more." (This is simply incorrect, that's not how standard deviation works. I tried to gently explain that but you then claimed you were uninterested in talking about statistical models.  Why did you present one in the first place then?)

Again, I think your device is interesting, and I think several of your findings are interesting.  But I don't think it's in anyone's best interest for me to ignore it when I spot something in a claim that looks incomplete or incorrect.  I think we can learn a lot from you here, but I think you can learn from us too if you're willing to listen.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 15:26
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Not anyone specifically. Take no offense, please. I don't think many understand just how much work it is to make engineering tests / measurements and explain the results in precise language. Engineers usually get paid handsomely to do this kind of work in commercial and military fields with a paying customer. The quality of my work I post is at that level because I have been doing it for major customers for 40 years. I am doing this signal processing research on piano, only because I want to educate serious PTG members who want to learn about the subject. I post things that we normally cannot find in the prior piano research journals. I am just giving away the time and effort. I do hope one day people appreciate it. It distracts me from my current paid customer tasks and sometimes I just think it is falling on deaf ears and I should just stop and go back to my professional signal processing work.


Original Message:
Sent: 1/24/2024 3:18:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I don't follow. Do you feel like I'm not providing enough evidence as to what the correct interpretation of the term is?  Do you mean that you want to see evidence of the legitimate psychoacoustic phenomenon?

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 15:15
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Nathan, I cannot emphasize enough the importance of evidence-based data in these discussions. Without evidence-based real data and precise measurements, all things devolve into endless debate. -- Respectfully, Steve


Original Message:
Sent: 1/24/2024 3:10:00 PM
From: Nathan Monteleone
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I was arguing that the term "Missing Fundamental", used correctly, referred to a psychoacoustic phenomenon in the first place -- not an acoustic one.  Wikipedia seems to agree with me as well, for what it's worth: https://en.wikipedia.org/wiki/Missing_fundamental.

I don't doubt that some piano technicians have gotten this mixed up, even prominent ones.

------------------------------
Nathan Monteleone RPT
Fort Worth TX
(817) 675-9494
nbmont@gmail.com

Original Message:
Sent: 01-24-2024 14:41
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Colleagues, 

There is big difference between 'acoustics' and 'psycho-acoustics'. There is a big difference between what we 'think' is so, and what we can 'measure' as so!

Some things are hard to find evidence of, but we know to be true, but the best is when there is some evidence so that it is not 'blind faith' but 'evidence-based' faith. It is my job to base every statement on actual evidence that is non-contradictory to all other evidence. 

For example, I posted above the evidence of measured data of the harmonic levels of both the sensor data (the original post and video that started this) and microphone data (last night and above post) of the first 10+ harmonics of A0, showing both the time and frequency domain. The measured harmonic magnitude levels were different due to the EQ of the two pickup devices, but both showed the full evidence of the presence of a significant level of A0 fundamental. If you google 'missing fundamental' there are lots of hits and this is what started me on the venture for the post. I am glad I took the time to actually make the measurements and post the data.

I explained in an earlier post that there is no such thing as a subharmonic in reality unless there is an actual spectral component, which cannot come from a linear system but it can come from a strong non-linearity that creates a spectral component that is the result of the subtraction and addition of two frequencies.

Hope that helps!

Respectfully submitted,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-24-2024 00:29
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Peter has 'challenged me' indirectly (ha ha) to do the A0 with my Neumann KM183 mics. Then I use the same parameters of Matlab as I did before when I captured the A0 with the PianoSens sensor.

The pic is below. Double click it to see it better. The top view is amplitude vs time. The startup is messy compared with my prior presentation using the sensor, but there are still very clearly defined periods of A0 that I have marked.

Now look at the spectral view on the bottom. Look at the 3rd and 6th levels as the highest of the first 10 harmonics, but look at the fundamental which is only 5 dB below the 2nd harmonic. Amazing. So, it all boils down to how to set up the experiment and how to perform the frequency analysis.

Best,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 21:06
From: Norman Brickman
Subject: Dispelling the 'Myth' of the Missing Fundamental

For tuning the lowest notes on a nice piano, since I am tuning 12 TET based on the octave (i.e., ET), I will often start with a double octave for initial placement. Then testing with a progression of seventeenths (5:1), and on a good day I can also bring in minor sevenths (7:4) or minor sixths (8:5) as additional testing and with their slightly improved accuracy over the seventeenth..

Mark, resonance works well going from a string that is partial #2 or #3 (as well as higher partials) down to the fundamental string. But for me the strongest resonance created is always equal to the partial in frequency. Maybe with non-linearities the fundamental might also be there, but much reduced in amplitude. Regards, Norman.

------------------------------
Norman Brickman
Potomac Piano Service
Potomac, Maryland
potomacpiano@verizon.net
https://potomacpiano.com
(301) 983.9321

Original Message:
Sent: 01-23-2024 20:05
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Parker, better yet, use the 12th, not the 5th. -Steve


Original Message:
Sent: 1/23/2024 7:12:00 PM
From: Parker Leigh
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

That is why I often use the fifth as a reference whentuning the low bass.

------------------------------
Parker Leigh RPT
Winchester VA
(540) 722-3865

Original Message:
Sent: 01-23-2024 13:48
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Mark,

A 'subharmonic' does not exist in a linear process because what you describe is not an actual spectral component if you do a Fourier Transform of the waveform. The only way it can be a spectral component is a nonlinear system, wherein two harmonics are 'mixed' or effectively multiplied together as in modulation, creating actual sum and difference frequencies from the modulation.

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 11:00
From: Mark Schecter
Subject: Dispelling the 'Myth' of the Missing Fundamental

Original Message:
Sent: 1/23/2024 9:02:00 AM
From: Robert Anderson
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental

I have always assumed that A0 has a fundamental and the myth hasn't penetrated to me, anyway. My understanding is that the fundamental of A0 is so weak compared to its higher partials that it is pretty inaudible. In organ building a 32' pipe is needed for the fundamental of A0 but the combination of a 16' and and 8' pipe can give the illusion of hearing A0. I expect I'll hear about it if my understanding is wrong.

Bob Anderson, RPT
Tucson, AZ


Original Message:
Sent: 1/22/2024 3:17:00 AM
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

• Dispelling the 'Myth' of the Missing Fundamental
• Video Presentation YouTube Link: 
• https://youtu.be/Gj0xobcBpdM
• There is a widely held 'myth' called 'the missing fundamental' in the bass register of a piano. 
• 
  * This myth is very unfortunate and very untrue.
  * I am here today to dispel that myth once and for all with irrefutable evidence. 
  * Is the fundamental present all the way down to A0. Of course!
  * This evidence was collected from a PianoSens sensor on a large concert grand, a Fazioli F308. However, I did a similar experiment over 15 years ago using an instrumentation quality microphone on a Steinway D and got a similar result.
  * As you watch the video and hear the explanation, you will clearly and unequivocally see that there are clean, pristine periods of repetition at the fundamental frequency all the way down to A0. 
  * You will see the spectral view of the time domain showing that the fundamental A0 is down only 9 dB from the 2nd harmonic A1. A factor of 9 dB is still very easily heard by human perception even at that frequency.
  * I also show just how 'messy' the transient response is from the hammer strike moment, compared with the PianoSens sensor.

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101
------------------------------

Colleagues, 

There is big difference between 'acoustics' and 'psycho-acoustics'. There is a big difference between what we 'think' is so, and what we can 'measure' as so!

Some things are hard to find evidence of, but we know to be true, but the best is when there is some evidence so that it is not 'blind faith' but 'evidence-based' faith. It is my job to base every statement on actual evidence that is non-contradictory to all other evidence. 

For example, I posted above the evidence of measured data of the harmonic levels of both the sensor data (the original post and video that started this) and microphone data (last night and above post) of the first 10+ harmonics of A0, showing both the time and frequency domain. The measured harmonic magnitude levels were different due to the EQ of the two pickup devices, but both showed the full evidence of the presence of a significant level of A0 fundamental. If you google 'missing fundamental' there are lots of hits and this is what started me on the venture for the post. I am glad I took the time to actually make the measurements and post the data.

I explained in an earlier post that there is no such thing as a subharmonic in reality unless there is an actual spectral component, which cannot come from a linear system but it can come from a strong non-linearity that creates a spectral component that is the result of the subtraction and addition of two frequencies.

Hope that helps!

Respectfully submitted,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-24-2024 00:29
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Peter has 'challenged me' indirectly (ha ha) to do the A0 with my Neumann KM183 mics. Then I use the same parameters of Matlab as I did before when I captured the A0 with the PianoSens sensor.

The pic is below. Double click it to see it better. The top view is amplitude vs time. The startup is messy compared with my prior presentation using the sensor, but there are still very clearly defined periods of A0 that I have marked.

Now look at the spectral view on the bottom. Look at the 3rd and 6th levels as the highest of the first 10 harmonics, but look at the fundamental which is only 5 dB below the 2nd harmonic. Amazing. So, it all boils down to how to set up the experiment and how to perform the frequency analysis.

Best,

Steve

------------------------------
Steven Norsworthy
Cardiff By The Sea CA
(619) 964-0101

Original Message:
Sent: 01-23-2024 21:06
From: Norman Brickman
Subject: Dispelling the 'Myth' of the Missing Fundamental

For tuning the lowest notes on a nice piano, since I am tuning 12 TET based on the octave (i.e., ET), I will often start with a double octave for initial placement. Then testing with a progression of seventeenths (5:1), and on a good day I can also bring in minor sevenths (7:4) or minor sixths (8:5) as additional testing and with their slightly improved accuracy over the seventeenth..

Mark, resonance works well going from a string that is partial #2 or #3 (as well as higher partials) down to the fundamental string. But for me the strongest resonance created is always equal to the partial in frequency. Maybe with non-linearities the fundamental might also be there, but much reduced in amplitude. Regards, Norman.

------------------------------
Norman Brickman
Potomac Piano Service
Potomac, Maryland
potomacpiano@verizon.net
https://potomacpiano.com
(301) 983.9321

Original Message:
Sent: 01-23-2024 20:05
From: Steven Norsworthy
Subject: Dispelling the 'Myth' of the Missing Fundamental

Parker, better yet, use the 12th, not the 5th. -Steve


Original Message:
Sent: 1/23/2024 7:12:00 PM
From: Parker Leigh
Subject: RE: Dispelling the 'Myth' of the Missing Fundamental