User:Nick Vuci/TonalityDiamond: Difference between revisions

Line 1:

WORK-IN-PROGRESS AS OF 07MAY2025

The tonality diamond is a symmetric organization of otonal and utonal chords based around a central note and bounded by an odd-limit. First formalized in the 7-odd-limit by 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 intervals~~ of temperaments) and practically (such as for instrument layouts) in xenharmonics ever since.

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.

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

Line 18:

== 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. 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.

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

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

[[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|George Secor's]] later-named "[[Miracle]]" temperament — was made to approximate Partch's 11-limit diamond.

== Uses ==

=== Instrument layout ===

The most famous example of the tonality diamond as a practical layout for an instrument is Harry Partch's "Diamond Marimba," which uses the 11-odd-limit tonality diamond exactly. This idea was explored further with Partch's "Quadrangularis Reversum," and by Cris Forster with his 13-odd-limit "Diamond Marimba."

The most famous example of the tonality diamond as a practical layout for an instrument is Harry Partch's "Diamond Marimba," which uses the 11-odd-limit tonality diamond exactly. This idea was explored further with Partch's "Quadrangularis Reversum," and by Cris Forster with his [[13-odd-limit]] "Diamond Marimba."

[https://sintel.website/posts/diamond_marimba.html '''Play with Partch’s Diamond Marimba here.''']

== See also ==

* [[Cross-set scale]]

* [[Diamond function|Diamond Function]]

* [[Lattice]]

== References ==

@@ Line 1: / Line 1: @@
   WORK-IN-PROGRESS AS OF 07MAY2025
-The tonality diamond is a symmetric organization of otonal and utonal chords based around a central note and bounded by an odd-limit. First formalized in the 7-odd-limit by 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 intervals of temperaments) and practically (such as for instrument layouts) in xenharmonics ever since.
+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.
 [https://nickvuci.github.io/wiki-applets/tonalityDiamond.html '''Play some tonality diamonds to hear how they sound.''']
@@ Line 18: / Line 18: @@
 == 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. 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.
-Erv Wilson in particular was inspired by the tonality diamond and developed a number of "diamonds" himself.<ref>https://anaphoria.com/diamond.pdf</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.
-The first novel xenharmonic temperament — George Secor's later-named "Miracle" temperament — was made to approximate Partch's 11-limit diamond.
+[[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|George Secor's]] later-named "[[Miracle]]" temperament — was made to approximate Partch's 11-limit diamond.
 == Uses ==
 === Instrument layout ===
-The most famous example of the tonality diamond as a practical layout for an instrument is Harry Partch's "Diamond Marimba," which uses the 11-odd-limit tonality diamond exactly. This idea was explored further with Partch's "Quadrangularis Reversum," and by Cris Forster with his 13-odd-limit "Diamond Marimba."
+The most famous example of the tonality diamond as a practical layout for an instrument is Harry Partch's "Diamond Marimba," which uses the 11-odd-limit tonality diamond exactly. This idea was explored further with Partch's "Quadrangularis Reversum," and by Cris Forster with his [[13-odd-limit]] "Diamond Marimba."
 [https://sintel.website/posts/diamond_marimba.html '''Play with Partch’s Diamond Marimba here.''']
+== See also ==
+* [[Cross-set scale]]
+* [[Diamond function|Diamond Function]]
+* [[Lattice]]
 == References ==