Back when I was into ham radio I learned about the "superheterodyne receiver," which relied on difference frequencies. The frequency of the signal received over the air (the "
radio frequency" or "
RF") was too high to amplify and process efficiently, so the electronics would convert the frequency down to an
intermediate frequency (the "
IF"). This is done by generating tunable
local oscillator signal that is offset from the desired frequency by exactly the
IF frequency. The generated signal and the
RF signal are combined in a non-linear fashion so that a real (not just a psychological) difference frequency is generated. The sum frequency is also generated, but that is filtered out by a narrow band-pass filter in the
IF section of the receiver. The advantage of this method is that the
IF section (usually 455 kHz for AM radios) can be fixed-tuned, to process only that one frequency. The circuit that did the non-linear mixing of the
RF and the
local oscillator was called (unsurprisingly) a mixer circuit. It usually involved diodes to chop the
RF using the
local oscillator as the knife to do the chopping. The point is, these two signals did not just peacefully coexist together. In this way a mixer in a superheterodyne receiver is very different from the kind of mixer used in high-end recording studios. In those kinds of mixers, the various audio inputs are combined in a (hopefully) very linear way. The result is that signals combined in an ideal audio mixer board do not generate any (real) difference tones.
So, what happens when tones from various piano strings are combined in the soundboard? Well, if things are working properly, that mixing is linear. That is, the signals add together without affecting each other in any way. But things are not always ideal. Sometimes there is a loose connection somewhere in the piano. In the extreme case it might even produce an audible buzz. But in the less extreme case it might just produce some non-linear interaction between signals, causing difference frequencies (and sum frequencies). This is real, not psychological. The sum and difference frequencies produced this way would even show up on a spectrum analyzer. The non-linear interaction might be amplitude dependent. That is, below a certain sound level, everything is linear. That loose screw does not rub at all. But above a certain threshold, non-linearity kicks in and real difference tones are generated. There can even be non-linear interaction within the structures of the human ear, although they would probably be noticeable only near the levels where actual hearing damage could occur. People who use hearing aids may also hear real difference tones when the sound levels exceed the linear range of the hearing aid circuitry.
Here's an experiment. Try to engineer something that will buzz on the soundboard - maybe a paper clip or something made out of paper. Then play various pairs of notes. You will probably hear difference tones that you did not hear without that device touching the soundboard.
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Robert Scott
Real-Time Specialties (TuneLab)
fixthatpiano@yahoo.comHopkins MN
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Original Message:
Sent: 10-27-2021 20:29
From: Bill Ballard
Subject: Using difference tones to tune?
https://en.wikipedia.org/wiki/Combination_tone
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William Ballard RPT
WBPS
Saxtons River VT
802-869-9107
"Our lives contain a thousand springs
and dies if one be gone
Strange that a harp of a thousand strings
should keep in tune so long."
...........Dr. Watts, "The Continental Harmony,1774
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Original Message:
Sent: 10-25-2021 21:48
From: Daniel Achten
Subject: Using difference tones to tune?
Hi Cobrun,
Here is the way I am using them. It's a little different than the scenario you suggested.
The intervals I am using are a 5th and a 4th.
So if I was playing D5/A5 5th I would hear a difference tone that corresponded to D4. D4 and A5 will have already been tuned and I would be working on D5 as I tune up through the treble. While tuning the D5 I listen to the 5th, 4th, octave and 12th below it. If I have to I also listen to M10 chromatically. I use the M6/M17 beat speed test for the D5 to try for a P12. Always making sure the octave is not over stretched.
What i I have noticed is that the difference tone beat speed from the D5/A5 which matches the D4 is very clean (no perceivable beat) while the 12th checks out as perfect.
More importantly, the increase in resonance/presence happens when this difference tone is clean with no perceivable beat speed. All other checks check out.
The sustain of this difference tone also seems to be related to how clean it is.
I hear it all over the piano now. I thought it was just in then 5th octave but the resonance that I have used to tune the bass is exactly this.
Your example of using difference tones to tune A0-A1 is very interesting. I'll have to try that. I have simple
Been switching to octaves and 12ths down there while listening and feeing for resonance. Also, checking where the 6/3 octave check is. (Except for 9').
Its also interesting that you mentioned "feeling". I feel the beat speeds in my key hand (left hand) and in the tuning hammer (right hand) while tuning through the the base too. I also feel the different pressures on the ear drum as they move around depending on beat speed and resonance all throughout the piano. Sometimes I am sitting just right to sort of jig the piano with my waist as I sit and can feel the whole piano come alive right when I find the resonance.
All this "come alive" seems to correspond with the clean difference tones I am mentioning.
Daniel
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Daniel Achten
Chattanooga TN
423-760-2458
Original Message:
Sent: 10-25-2021 00:59
From: Cobrun Sells
Subject: Using difference tones to tune?
Let's supppse D4 and A5 is the P12 we are using: A5 is 880Hz and D4 is somewhere around 293.3Hz. This difference tone you speak of would be 880-293.3=586.7Hz. 586.7Hz would be D5. So by what I understand you are saying is that you are using a P12 (D4A5) to tune the note in the middle of the outer two notes (D5)??? If that's the case I'm certain it'd be incredibly hard to hear or feel over all the partials in that same area.
I typically use difference tones between A0-A1. Say B0 is 30Hz and B1 is 60Hz. 60-30=30...so in this scenario our difference tone is at the same frequency as B0...30Hz. Thus B0 and the difference tone between B0 and B1 octave (played together) is in-tune.
But if we lower B0 to 28Hz then when you play B0 and B1 together you get 60-28=32Hz. In this case the difference tone is 32Hz which you will hear OR feel as fighting/beating against B0 at 4 beats per second. Thus B0 and the difference tone between B0 and B1 octave (played together) is out-of-tune.
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Cobrun Sells
cobrun94@yahoo.com
Original Message:
Sent: 10-24-2021 20:18
From: Daniel Achten
Subject: Using difference tones to tune?
Hi Everyone,
Does anyone use "difference tones" to help tune octave 5? Maybe perhaps other ranges in the piano too?
Interested in other's experience with them. One major writer said they were not helpful and I wrote them off a while ago but as I continue to listen/search for resonance and try to tune a P12 tuning the difference tones seem to line up very cleanly (oct 5ish). And better than that they seem to add a ton of resonance.
Daniel
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Daniel Achten
Chattanooga TN
423-760-2458
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