Pianotech

Pure 5th Equal Temperament. Pure Octave Equal Temperament. Pure 12th Equal Temperament.

Each of these equal temperaments contains one pure interval. It is the interval upon which each of these equal temperaments is based. Pure 5th Equal Temperament only has Pure Fifths. Pure Octave Equal Temperament only has Pure Octaves. Pure 12th Equal Temperament only has Pure Twelfths.


Does every equal temperament need to contain at least one pure interval?

The answer is no. There are a plethora of equal temperaments that do not contain any pure intervals that should also be explored.


An example of a temperament that contains no pure intervals is Roshan Kakiya's 12-Tone Equal Temperament (RK 12-TET):

RK 12-TET lies exactly in the middle between Pure 5th Equal Temperament and Pure Octave Equal Temperament.

RK 12-TET accounts for inharmonicity by having intervals that are sharper than the harmonics to which they correspond:

1st harmonic (Ratio: 1/1) = 0.00 cents.
RK 12-TET = 0.00 cents.

2nd harmonic (Ratio: 2/1) = 1200.00 cents.
RK 12-TET = 1201.68 cents.

3rd harmonic (Ratio: 3/1) = 1901.96 cents.
RK 12-TET = 1902.65 cents.

4th harmonic (Ratio: 4/1) = 2400.00 cents.
RK 12-TET = 2403.35 cents.


The full potential of the equal temperament tuning system can only be unlocked by exploring the equal temperaments that do not contain any pure intervals as well as the equal temperaments that contain at least one pure interval.

------------------------------
Roshan Kakiya
------------------------------

Original Message------

Pure 5th Equal Temperament. Pure Octave Equal Temperament. Pure 12th Equal Temperament.

Each of these equal temperaments contains one pure interval. It is the interval upon which each of these equal temperaments is based. Pure 5th Equal Temperament only has Pure Fifths. Pure Octave Equal Temperament only has Pure Octaves. Pure 12th Equal Temperament only has Pure Twelfths.


Does every equal temperament need to contain at least one pure interval?

The answer is no. There are a plethora of equal temperaments that do not contain any pure intervals that should also be explored.


An example of a temperament that contains no pure intervals is Roshan Kakiya's 12-Tone Equal Temperament (RK 12-TET):

RK 12-TET lies exactly in the middle between Pure 5th Equal Temperament and Pure Octave Equal Temperament.

RK 12-TET accounts for inharmonicity by having intervals that are sharper than the harmonics to which they correspond:

1st harmonic (Ratio: 1/1) = 0.00 cents.
RK 12-TET = 0.00 cents.

2nd harmonic (Ratio: 2/1) = 1200.00 cents.
RK 12-TET = 1201.68 cents.

3rd harmonic (Ratio: 3/1) = 1901.96 cents.
RK 12-TET = 1902.65 cents.

4th harmonic (Ratio: 4/1) = 2400.00 cents.
RK 12-TET = 2403.35 cents.


The full potential of the equal temperament tuning system can only be unlocked by exploring the equal temperaments that do not contain any pure intervals as well as the equal temperaments that contain at least one pure interval.

------------------------------
Roshan Kakiya
------------------------------

Roshan, please forgive my lack of erudition, but I do have some questions.
>If by "pure" intervals you mean beatless, aren't the pure intervals mentioned above not found as simple integers but in combination with the inharmonicity of a given string? (i.e. 2/1 +/- inharmonicity)
>Aren't there 100 cents between each half step regardless of the distance between the intervals? How do you get more than 1200 cents in your octave?
>The final question with regard to the utility of a temperament is, is it musical? Is it beautiful? Have you applied your temperament to an acoustic piano? How did you like it? What is it like?


------------------------------
Steven Rosenthal
Honolulu HI
808-521-7129
------------------------------

Original Message:
Sent: 08-10-2019 08:43
From: David Pinnegar
Subject: Unlocking the Full Potential of the Equal Temperament Tuning System

And then the result is what I call hotel foyer tuning for hotel foyer pianos for hotel foyer music and the very reason why the modern tuning makes the music uninteresting for the performer, removing dimensions of nuances beyond loud soft, fast slow, and preferably in concert as fast as possible as loud as possible, an entertainment or  merely the comfort noise of muzak in the background.

In the UK for the revival of meaning of music we need instruments more rewarding to play musically so that others shine beyond merely Lang Lang, who as far as ClassicFM radio station in the UK is the pinnacle of musicianship.

Music isn't about robotic adherence to equalness but to the conveyance of feelings. Is a state of happiness permanent? You can only know happiness if you have experienced pain. Happiness without knowledge of the other is meaningless. Wouldn't your outlook in life be ever so dull were you to know only unending flat land? No sea, no mountains? 

In the nature of the piano as the Queen if not the King of instruments it has to be capable of expression as a reduction of the orchestra. That means the ability of intervals to be pure. Raw. A whole host of things that dissappear if the tuning tunes them out to grey or bristling silver.

Best wishes

David P

--

- - - - - - - - - - - - - - - - - - - - - - - -
David Pinnegar, B.Sc., A.R.C.S.
- - - - - - - - - - - - - - - - - - - - - - - -
+44 1342 850594

Original Message------

Pure 5th Equal Temperament. Pure Octave Equal Temperament. Pure 12th Equal Temperament.

Each of these equal temperaments contains one pure interval. It is the interval upon which each of these equal temperaments is based. Pure 5th Equal Temperament only has Pure Fifths. Pure Octave Equal Temperament only has Pure Octaves. Pure 12th Equal Temperament only has Pure Twelfths.


Does every equal temperament need to contain at least one pure interval?

The answer is no. There are a plethora of equal temperaments that do not contain any pure intervals that should also be explored.


An example of a temperament that contains no pure intervals is Roshan Kakiya's 12-Tone Equal Temperament (RK 12-TET):

RK 12-TET lies exactly in the middle between Pure 5th Equal Temperament and Pure Octave Equal Temperament.

RK 12-TET accounts for inharmonicity by having intervals that are sharper than the harmonics to which they correspond:

1st harmonic (Ratio: 1/1) = 0.00 cents.
RK 12-TET = 0.00 cents.

2nd harmonic (Ratio: 2/1) = 1200.00 cents.
RK 12-TET = 1201.68 cents.

3rd harmonic (Ratio: 3/1) = 1901.96 cents.
RK 12-TET = 1902.65 cents.

4th harmonic (Ratio: 4/1) = 2400.00 cents.
RK 12-TET = 2403.35 cents.


The full potential of the equal temperament tuning system can only be unlocked by exploring the equal temperaments that do not contain any pure intervals as well as the equal temperaments that contain at least one pure interval.

------------------------------
Roshan Kakiya
------------------------------

>Inharmonicity will affect the purity of the theoretically pure intervals.

>A pure octave has a theoretical value of 1200 cents and a theoretical frequency ratio of 2/1.

Inharmonicity will cause partials to sharpen so the octaves will need to be stretched.

If an octave is stretched, its value will be higher than 1200 cents and its frequency ratio will be higher than 2/1.

If the value of an octave is higher than 1200 cents, the value of each of the 12 semitones will be higher than 100 cents.

>The purpose of the example that I have provided in my original post is to show that the equal temperament tuning system is very flexible.

The other tuning systems such as just/rational intonation, meantone temperament and unequal temperament have been extensively explored.

Unfortunately, the equal temperament tuning system does not seem to have been explored as much as these other tuning systems.

I want to demonstrate that the current method of constructing equal temperaments via equal division of a particular theoretically pure interval is only one method among many.

For example, equal temperaments can also be constructed by using a constant semitone ratio that only contains rational numbers such as 89/84.

------------------------------
Roshan Kakiya
------------------------------

Original Message:
Sent: 08-11-2019 00:32
From: Steven Rosenthal
Subject: Unlocking the Full Potential of the Equal Temperament Tuning System

Roshan, please forgive my lack of erudition, but I do have some questions.
>If by "pure" intervals you mean beatless, aren't the pure intervals mentioned above not found as simple integers but in combination with the inharmonicity of a given string? (i.e. 2/1 +/- inharmonicity)
>Aren't there 100 cents between each half step regardless of the distance between the intervals? How do you get more than 1200 cents in your octave?
>The final question with regard to the utility of a temperament is, is it musical? Is it beautiful? Have you applied your temperament to an acoustic piano? How did you like it? What is it like?


------------------------------
Steven Rosenthal
Honolulu HI
808-521-7129

Original Message:
Sent: 08-10-2019 08:43
From: David Pinnegar
Subject: Unlocking the Full Potential of the Equal Temperament Tuning System

And then the result is what I call hotel foyer tuning for hotel foyer pianos for hotel foyer music and the very reason why the modern tuning makes the music uninteresting for the performer, removing dimensions of nuances beyond loud soft, fast slow, and preferably in concert as fast as possible as loud as possible, an entertainment or  merely the comfort noise of muzak in the background.

In the UK for the revival of meaning of music we need instruments more rewarding to play musically so that others shine beyond merely Lang Lang, who as far as ClassicFM radio station in the UK is the pinnacle of musicianship.

Music isn't about robotic adherence to equalness but to the conveyance of feelings. Is a state of happiness permanent? You can only know happiness if you have experienced pain. Happiness without knowledge of the other is meaningless. Wouldn't your outlook in life be ever so dull were you to know only unending flat land? No sea, no mountains? 

In the nature of the piano as the Queen if not the King of instruments it has to be capable of expression as a reduction of the orchestra. That means the ability of intervals to be pure. Raw. A whole host of things that dissappear if the tuning tunes them out to grey or bristling silver.

Best wishes

David P

--

- - - - - - - - - - - - - - - - - - - - - - - -
David Pinnegar, B.Sc., A.R.C.S.
- - - - - - - - - - - - - - - - - - - - - - - -
+44 1342 850594

Original Message------

Pure 5th Equal Temperament. Pure Octave Equal Temperament. Pure 12th Equal Temperament.

Each of these equal temperaments contains one pure interval. It is the interval upon which each of these equal temperaments is based. Pure 5th Equal Temperament only has Pure Fifths. Pure Octave Equal Temperament only has Pure Octaves. Pure 12th Equal Temperament only has Pure Twelfths.


Does every equal temperament need to contain at least one pure interval?

The answer is no. There are a plethora of equal temperaments that do not contain any pure intervals that should also be explored.


An example of a temperament that contains no pure intervals is Roshan Kakiya's 12-Tone Equal Temperament (RK 12-TET):

RK 12-TET lies exactly in the middle between Pure 5th Equal Temperament and Pure Octave Equal Temperament.

RK 12-TET accounts for inharmonicity by having intervals that are sharper than the harmonics to which they correspond:

1st harmonic (Ratio: 1/1) = 0.00 cents.
RK 12-TET = 0.00 cents.

2nd harmonic (Ratio: 2/1) = 1200.00 cents.
RK 12-TET = 1201.68 cents.

3rd harmonic (Ratio: 3/1) = 1901.96 cents.
RK 12-TET = 1902.65 cents.

4th harmonic (Ratio: 4/1) = 2400.00 cents.
RK 12-TET = 2403.35 cents.


The full potential of the equal temperament tuning system can only be unlocked by exploring the equal temperaments that do not contain any pure intervals as well as the equal temperaments that contain at least one pure interval.

------------------------------
Roshan Kakiya
------------------------------

Original Message------

>Inharmonicity will affect the purity of the theoretically pure intervals.

>A pure octave has a theoretical value of 1200 cents and a theoretical frequency ratio of 2/1.

Inharmonicity will cause partials to sharpen so the octaves will need to be stretched.

If an octave is stretched, its value will be higher than 1200 cents and its frequency ratio will be higher than 2/1.

If the value of an octave is higher than 1200 cents, the value of each of the 12 semitones will be higher than 100 cents.

>The purpose of the example that I have provided in my original post is to show that the equal temperament tuning system is very flexible.

The other tuning systems such as just/rational intonation, meantone temperament and unequal temperament have been extensively explored.

Unfortunately, the equal temperament tuning system does not seem to have been explored as much as these other tuning systems.

I want to demonstrate that the current method of constructing equal temperaments via equal division of a particular theoretically pure interval is only one method among many.

For example, equal temperaments can also be constructed by using a constant semitone ratio that only contains rational numbers such as 89/84.

------------------------------
Roshan Kakiya
------------------------------

Original Message:
Sent: 08-11-2019 00:32
From: Steven Rosenthal
Subject: Unlocking the Full Potential of the Equal Temperament Tuning System

Roshan, please forgive my lack of erudition, but I do have some questions.
>If by "pure" intervals you mean beatless, aren't the pure intervals mentioned above not found as simple integers but in combination with the inharmonicity of a given string? (i.e. 2/1 +/- inharmonicity)
>Aren't there 100 cents between each half step regardless of the distance between the intervals? How do you get more than 1200 cents in your octave?
>The final question with regard to the utility of a temperament is, is it musical? Is it beautiful? Have you applied your temperament to an acoustic piano? How did you like it? What is it like?


------------------------------
Steven Rosenthal
Honolulu HI
808-521-7129

Original Message:
Sent: 08-10-2019 08:43
From: David Pinnegar
Subject: Unlocking the Full Potential of the Equal Temperament Tuning System

And then the result is what I call hotel foyer tuning for hotel foyer pianos for hotel foyer music and the very reason why the modern tuning makes the music uninteresting for the performer, removing dimensions of nuances beyond loud soft, fast slow, and preferably in concert as fast as possible as loud as possible, an entertainment or  merely the comfort noise of muzak in the background.

In the UK for the revival of meaning of music we need instruments more rewarding to play musically so that others shine beyond merely Lang Lang, who as far as ClassicFM radio station in the UK is the pinnacle of musicianship.

Music isn't about robotic adherence to equalness but to the conveyance of feelings. Is a state of happiness permanent? You can only know happiness if you have experienced pain. Happiness without knowledge of the other is meaningless. Wouldn't your outlook in life be ever so dull were you to know only unending flat land? No sea, no mountains? 

In the nature of the piano as the Queen if not the King of instruments it has to be capable of expression as a reduction of the orchestra. That means the ability of intervals to be pure. Raw. A whole host of things that dissappear if the tuning tunes them out to grey or bristling silver.

Best wishes

David P

--

- - - - - - - - - - - - - - - - - - - - - - - -
David Pinnegar, B.Sc., A.R.C.S.
- - - - - - - - - - - - - - - - - - - - - - - -
+44 1342 850594

Original Message------

Pure 5th Equal Temperament. Pure Octave Equal Temperament. Pure 12th Equal Temperament.

Each of these equal temperaments contains one pure interval. It is the interval upon which each of these equal temperaments is based. Pure 5th Equal Temperament only has Pure Fifths. Pure Octave Equal Temperament only has Pure Octaves. Pure 12th Equal Temperament only has Pure Twelfths.


Does every equal temperament need to contain at least one pure interval?

The answer is no. There are a plethora of equal temperaments that do not contain any pure intervals that should also be explored.


An example of a temperament that contains no pure intervals is Roshan Kakiya's 12-Tone Equal Temperament (RK 12-TET):

RK 12-TET lies exactly in the middle between Pure 5th Equal Temperament and Pure Octave Equal Temperament.

RK 12-TET accounts for inharmonicity by having intervals that are sharper than the harmonics to which they correspond:

1st harmonic (Ratio: 1/1) = 0.00 cents.
RK 12-TET = 0.00 cents.

2nd harmonic (Ratio: 2/1) = 1200.00 cents.
RK 12-TET = 1201.68 cents.

3rd harmonic (Ratio: 3/1) = 1901.96 cents.
RK 12-TET = 1902.65 cents.

4th harmonic (Ratio: 4/1) = 2400.00 cents.
RK 12-TET = 2403.35 cents.


The full potential of the equal temperament tuning system can only be unlocked by exploring the equal temperaments that do not contain any pure intervals as well as the equal temperaments that contain at least one pure interval.

------------------------------
Roshan Kakiya
------------------------------