User:Nick Vuci/TonalityDiamond: Difference between revisions
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WORK-IN-PROGRESS AS OF 10MAY2025 | WORK-IN-PROGRESS AS OF 10MAY2025 | ||
{{Wikipedia|https://en.wikipedia.org/wiki/Tonality_diamond=Tonality diamond}} | |||
A '''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, the idea became central to the music and theories of [[Harry Partch]], who built his tonal system around the [[11-odd-limit]] tonality diamond. Tonality diamonds have been used both conceptually (such as for [[Target tuning|targets]] of [[temperaments]]) and practically (such as for instrument layouts) in xenharmonics ever since. | A '''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, the idea became central to the music and theories of [[Harry Partch]], who built his tonal system around the [[11-odd-limit]] tonality diamond. Tonality diamonds have been used both conceptually (such as for [[Target tuning|targets]] of [[temperaments]]) and practically (such as for instrument layouts) in xenharmonics ever since. | ||
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<gallery mode="nolines" widths="200" heights="200"> | <gallery mode="nolines" widths="200" heights="200"> | ||
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 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 | File:How to tonality diamond 2.png|'''Step 2: Using one axis 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: Octave-reduce the ratios (ie, make sure the decimal form of each ratio 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 (ie, make sure the decimal form of each ratio 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).''' | 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).''' | ||
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* numerically (ie, 1 3 5 7 9 11) as in Meyer's 7-limit diamond | * numerically (ie, 1 3 5 7 9 11) as in Meyer's 7-limit diamond | ||
* | * tonally (ie, 1 9 5 11 3 7) as in Partch's 11-limit diamond | ||
* chordally (ie, 1 5 3 7 9 11) as in the layout for the Diamond Marimba | * chordally (ie, 1 5 3 7 9 11) as in the layout for the Diamond Marimba | ||