User:Nick Vuci/TonalityDiamond: Difference between revisions

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Some finer points:

- the numbers of the odd-limit are generally arranged in one of ~~two~~ ways: a) ascending numerically (ie, 2 3 5 7 etc) or, b) ascending by tonal order (ie 2 5 3 7)

- the numbers of the odd-limit are generally arranged in one of three ways: a) ascending numerically (ie, 2 3 5 7 9 11 etc) or, b) ascending by tonal order (ie 2 9 5 11 3 7), or c) ascending chordally (ie, 2 5 3 7 9 11).

- in order to make the rows play rooted chords, one half of the diamond (not including the middle unison row) must be lowered by an octave.

== History ==

The tonality diamond was first formally explained by [https://archive.org/details/max-f-meyer-the-musicians-arithmetic ~~Max F Meyer in his 1929 publication ''The Musician's Arithmetic'']~~ using the 7-odd-limit. 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.

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. 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.

Erv Wilson in particular was inspired by the tonality diamond and developed a number of "diamonds" himself.<ref>https://anaphoria.com/diamond.pdf</ref>

The first novel xenharmonic temperament — George Secor's later-named "Miracle" temperament — was made to approximate Partch's 11-limit diamond.

@@ Line 15: / Line 15: @@
 Some finer points:
-- the numbers of the odd-limit are generally arranged in one of two ways: a) ascending numerically (ie, 2 3 5 7 etc) or, b) ascending by tonal order (ie 2 5 3 7)
+- the numbers of the odd-limit are generally arranged in one of three ways: a) ascending numerically (ie, 2 3 5 7 9 11 etc) or, b) ascending by tonal order (ie 2 9 5 11 3 7), or c) ascending chordally (ie, 2 5 3 7 9 11).
 - in order to make the rows play rooted chords, one half of the diamond (not including the middle unison row) must be lowered by an octave.
 == History ==
-The tonality diamond was first formally explained by [https://archive.org/details/max-f-meyer-the-musicians-arithmetic Max F Meyer in his 1929 publication ''The Musician's Arithmetic''] using the 7-odd-limit. 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.
+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. 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.
+Erv Wilson in particular was inspired by the tonality diamond and developed a number of "diamonds" himself.<ref>https://anaphoria.com/diamond.pdf</ref>
 The first novel xenharmonic temperament — George Secor's later-named "Miracle" temperament — was made to approximate Partch's 11-limit diamond.