User:Nick Vuci/TonalityDiamond: Difference between revisions

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WORK-IN-PROGRESS AS OF 07MAY2025

~~The tonality diamond is~~ a symmetric organization of [[Otonality and utonality|otonal and utonal]] chords based around a central note and bounded by an [[Odd limit|odd-limit]]. First formalized in the [[7-odd-limit]] by [[wikipedia:Max_Friedrich_Meyer|Max F. Meyer]] in 1929, they became central to the music and theories of [[Harry Partch]], who built his tonal system around the [[11-odd-limit]] tonality diamond. ~~The principle has~~ been used both conceptually (such as for [[Target tuning|targets]] of [[temperaments]]) and practically (such as for instrument layouts) in xenharmonics ever since.

Tonality diamonds are a symmetric organization of [[Otonality and utonality|otonal and utonal]] chords based around a central note and bounded by an [[Odd limit|odd-limit]]. First formalized in the [[7-odd-limit]] by [[wikipedia:Max_Friedrich_Meyer|Max F. Meyer]] in 1929, they became central to the music and theories of [[Harry Partch]], who built his tonal system around the [[11-odd-limit]] tonality diamond. They have been used both conceptually (such as for [[Target tuning|targets]] of [[temperaments]]) and practically (such as for instrument layouts) in xenharmonics ever since.

[https://nickvuci.github.io/wiki-applets/tonalityDiamond.html '''Play some tonality diamonds to hear how they sound.''']

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File:How to tonality diamond 1.png|'''Step 1: Take the numbers of an odd-limit and arrange them along two axes.'''

File:How to tonality diamond 2.png|'''Step 2: Using one row as the numerator and the other as the denominator, fill in the cells with the ratios they form.'''

File:How to tonality diamond 3.png|'''Step 3: ~~Make~~ sure the decimal form of the ratios is between 1 and 2. If it is not, double one of the numbers until it is.'''

File:How to tonality diamond 3.png|'''Step 3: Octave-reduce the ratios, or make sure the decimal form of the ratios is between 1 and 2. If it is not, double one of the numbers until it is.'''

File:How to tonality diamond 4.png|'''Optional step: to make the rows play rooted chords, one half of the diamond (not including the middle unison row) must be lowered by an octave (represented by grey cells in image).'''

</gallery>Note: the numbers of the odd-limit are generally arranged in one of three ways:

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== History ==

The tonality diamond was first formally explained by Max F. Meyer in his 1929 publication ''The Musician's Arithmetic''<ref>https://archive.org/details/max-f-meyer-the-musicians-arithmetic/page/22/mode/2up</ref> ~~using the 7-odd-limit.~~

The tonality diamond was first formally explained by Max F. Meyer in his 1929 publication ''The Musician's Arithmetic'' using the 7-odd-limit.<ref>https://archive.org/details/max-f-meyer-the-musicians-arithmetic/page/22/mode/2up</ref>

Even though Harry Partch gives a different story for how he discovered the concept, it is likely this source that gave him the idea, which he then extended to the 11-odd-limit and made the basis of his tonal system.

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   WORK-IN-PROGRESS AS OF 07MAY2025
-The tonality diamond is a symmetric organization of [[Otonality and utonality|otonal and utonal]] chords based around a central note and bounded by an [[Odd limit|odd-limit]]. First formalized in the [[7-odd-limit]] by [[wikipedia:Max_Friedrich_Meyer|Max F. Meyer]] in 1929, they became central to the music and theories of [[Harry Partch]], who built his tonal system around the [[11-odd-limit]] tonality diamond. The principle has been used both conceptually (such as for [[Target tuning|targets]] of [[temperaments]]) and practically (such as for instrument layouts) in xenharmonics ever since.
+Tonality diamonds are a symmetric organization of [[Otonality and utonality|otonal and utonal]] chords based around a central note and bounded by an [[Odd limit|odd-limit]]. First formalized in the [[7-odd-limit]] by [[wikipedia:Max_Friedrich_Meyer|Max F. Meyer]] in 1929, they became central to the music and theories of [[Harry Partch]], who built his tonal system around the [[11-odd-limit]] tonality diamond. They have been used both conceptually (such as for [[Target tuning|targets]] of [[temperaments]]) and practically (such as for instrument layouts) in xenharmonics ever since.
 [https://nickvuci.github.io/wiki-applets/tonalityDiamond.html '''Play some tonality diamonds to hear how they sound.''']
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 File:How to tonality diamond 1.png|'''Step 1: Take the numbers of an odd-limit and arrange them along two axes.'''
 File:How to tonality diamond 2.png|'''Step 2: Using one row as the numerator and the other as the denominator, fill in the cells with the ratios they form.'''
-File:How to tonality diamond 3.png|'''Step 3: Make sure the decimal form of the ratios is between 1 and 2. If it is not, double one of the numbers until it is.'''
+File:How to tonality diamond 3.png|'''Step 3: Octave-reduce the ratios, or make sure the decimal form of the ratios is between 1 and 2. If it is not, double one of the numbers until it is.'''
 File:How to tonality diamond 4.png|'''Optional step: to make the rows play rooted chords, one half of the diamond (not including the middle unison row) must be lowered by an octave (represented by grey cells in image).'''
 </gallery>Note: the numbers of the odd-limit are generally arranged in one of three ways:
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 == History ==
-The tonality diamond was first formally explained by Max F. Meyer in his 1929 publication ''The Musician's Arithmetic''<ref>https://archive.org/details/max-f-meyer-the-musicians-arithmetic/page/22/mode/2up</ref> using the 7-odd-limit.
+The tonality diamond was first formally explained by Max F. Meyer in his 1929 publication ''The Musician's Arithmetic'' using the 7-odd-limit.<ref>https://archive.org/details/max-f-meyer-the-musicians-arithmetic/page/22/mode/2up</ref>
 Even though Harry Partch gives a different story for how he discovered the concept, it is likely this source that gave him the idea, which he then extended to the 11-odd-limit and made the basis of his tonal system.