Tonality diamond - Revision history

Nick Vuci: Updated applet to v2

2025-08-17T05:17:36Z

Updated applet to v2

← Older revision		Revision as of 05:17, 17 August 2025
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	A '''tonality diamond''' is a symmetric organization of [[otonality and utonality\|otonal and utonal]] [[chord]]s based around a central note and bounded by an [[odd limit]]. First formalized in the [[7-odd-limit]] by {{w\|Max Friedrich Meyer\|Max F. Meyer}} in 1929,<ref name="meyer1929">Meyer, Max F. (1929) [https://archive.org/details/max-f-meyer-the-musicians-arithmetic/page/22/mode/2up ''The Musician’s Arithmetic: Drill Problems for an Introduction to the Scientific Study of Musical Composition'']. The University of Missouri Studies. Vol. 4, no. 1. University of Missouri. January 1, 1929. p. 22.</ref> the idea became central to the music and theories of [[Harry Partch]],<ref>Harry Partch (1949), ''Genesis of a Music'', University of Wisconsin Press</ref> 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]] [[chord]]s based around a central note and bounded by an [[odd limit]]. First formalized in the [[7-odd-limit]] by {{w\|Max Friedrich Meyer\|Max F. Meyer}} in 1929,<ref name="meyer1929">Meyer, Max F. (1929) [https://archive.org/details/max-f-meyer-the-musicians-arithmetic/page/22/mode/2up ''The Musician’s Arithmetic: Drill Problems for an Introduction to the Scientific Study of Musical Composition'']. The University of Missouri Studies. Vol. 4, no. 1. University of Missouri. January 1, 1929. p. 22.</ref> the idea became central to the music and theories of [[Harry Partch]],<ref>Harry Partch (1949), ''Genesis of a Music'', University of Wisconsin Press</ref> 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.

	[https://nickvuci.~~github.io~~/~~wiki-applets/TonalityDiamond/tonalityDiamond.html~~ Play some tonality diamonds on your browser here.]		[https://tonalitydiamondapplet.nickvuci.com/ Play some tonality diamonds on your browser here.]

	== Construction ==		== Construction ==

FloraC: Cleanup

2025-07-30T11:01:26Z

Cleanup

Show changes

Nick Vuci: added video and changed size of player

2025-05-28T20:54:44Z

added video and changed size of player

← Older revision		Revision as of 20:54, 28 May 2025
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	Here's a short video illustrating the interlocking nature of the otonal and utonal chords and constant presence of the 1/1 interval in the 5-limit tonality diamond:		Here's a short video illustrating the interlocking nature of the otonal and utonal chords and constant presence of the 1/1 interval in the 5-limit tonality diamond:

	[[File:5-Limit Tonality Diamond original format.mp4]]		[[File:5-Limit Tonality Diamond original format.mp4\|1000x400px]]

	== History ==		== History ==

Nick Vuci: added video

2025-05-28T20:46:12Z

added video

← Older revision		Revision as of 20:46, 28 May 2025
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	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.		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.

	[https://nickvuci.github.io/wiki-applets/TonalityDiamond/tonalityDiamond.html Play some tonality diamonds ~~to hear how they sound~~.]		[https://nickvuci.github.io/wiki-applets/TonalityDiamond/tonalityDiamond.html Play some tonality diamonds on your browser here.]

	== Construction ==		== Construction ==
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	* Tonally: (1, 9, 5, 11, 3, 7) as in Partch's 11-limit diamond.		* Tonally: (1, 9, 5, 11, 3, 7) as in Partch's 11-limit diamond.
	* Chordally: (1, 5, 3, 7, 9, 11) as in the layout for the Diamond Marimba. This creates a 4:5:6:7:9:11 extended 11th chord on the diagonal, arranged in thirds.		* Chordally: (1, 5, 3, 7, 9, 11) as in the layout for the Diamond Marimba. This creates a 4:5:6:7:9:11 extended 11th chord on the diagonal, arranged in thirds.
			Here's a short video illustrating the interlocking nature of the otonal and utonal chords and constant presence of the 1/1 interval in the 5-limit tonality diamond:

			[[File:5-Limit Tonality Diamond original format.mp4]]

	== History ==		== History ==

Nick Vuci at 20:22, 28 May 2025

2025-05-28T20:22:13Z

← Older revision		Revision as of 20:22, 28 May 2025
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	}}		}}
	{{Wikipedia\|Tonality diamond}}		{{Wikipedia\|Tonality diamond}}
	~~[[File:5-Limit_Tonality_Diamond_Manim.mp4\|frameless]]~~

	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,<ref name="meyer1929">Meyer, Max F. (1929) [https://archive.org/details/max-f-meyer-the-musicians-arithmetic/page/22/mode/2up ''The Musician’s Arithmetic: Drill Problems for an Introduction to the Scientific Study of Musical Composition'']. The University of Missouri Studies. Vol. 4, no. 1. University of Missouri. January 1, 1929. p. 22.</ref> the idea became central to the music and theories of [[Harry Partch]],<ref>Harry Partch (1949), ''Genesis of a Music'', University of Wisconsin Press</ref> who built his tonal system around the [[11-odd-limit]] 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,<ref name="meyer1929">Meyer, Max F. (1929) [https://archive.org/details/max-f-meyer-the-musicians-arithmetic/page/22/mode/2up ''The Musician’s Arithmetic: Drill Problems for an Introduction to the Scientific Study of Musical Composition'']. The University of Missouri Studies. Vol. 4, no. 1. University of Missouri. January 1, 1929. p. 22.</ref> the idea became central to the music and theories of [[Harry Partch]],<ref>Harry Partch (1949), ''Genesis of a Music'', University of Wisconsin Press</ref> who built his tonal system around the [[11-odd-limit]] tonality diamond.

Nick Vuci at 20:21, 28 May 2025

2025-05-28T20:21:50Z

← Older revision		Revision as of 20:21, 28 May 2025
Line 4:		Line 4:
	}}		}}
	{{Wikipedia\|Tonality diamond}}		{{Wikipedia\|Tonality diamond}}
	[[File:5-~~Limit Tonality Diamond Manim~~.mp4\|~~thumb~~]]		[[File:5-Limit_Tonality_Diamond_Manim.mp4\|frameless]]

	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,<ref name="meyer1929">Meyer, Max F. (1929) [https://archive.org/details/max-f-meyer-the-musicians-arithmetic/page/22/mode/2up ''The Musician’s Arithmetic: Drill Problems for an Introduction to the Scientific Study of Musical Composition'']. The University of Missouri Studies. Vol. 4, no. 1. University of Missouri. January 1, 1929. p. 22.</ref> the idea became central to the music and theories of [[Harry Partch]],<ref>Harry Partch (1949), ''Genesis of a Music'', University of Wisconsin Press</ref> who built his tonal system around the [[11-odd-limit]] 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,<ref name="meyer1929">Meyer, Max F. (1929) [https://archive.org/details/max-f-meyer-the-musicians-arithmetic/page/22/mode/2up ''The Musician’s Arithmetic: Drill Problems for an Introduction to the Scientific Study of Musical Composition'']. The University of Missouri Studies. Vol. 4, no. 1. University of Missouri. January 1, 1929. p. 22.</ref> the idea became central to the music and theories of [[Harry Partch]],<ref>Harry Partch (1949), ''Genesis of a Music'', University of Wisconsin Press</ref> 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.		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.

Nick Vuci: testing video

2025-05-28T20:20:02Z

testing video

← Older revision		Revision as of 20:20, 28 May 2025
Line 4:		Line 4:
	}}		}}
	{{Wikipedia\|Tonality diamond}}		{{Wikipedia\|Tonality diamond}}
			[[File:5-Limit Tonality Diamond Manim.mp4\|thumb]]
	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,<ref name="meyer1929">Meyer, Max F. (1929) [https://archive.org/details/max-f-meyer-the-musicians-arithmetic/page/22/mode/2up ''The Musician’s Arithmetic: Drill Problems for an Introduction to the Scientific Study of Musical Composition'']. The University of Missouri Studies. Vol. 4, no. 1. University of Missouri. January 1, 1929. p. 22.</ref> the idea became central to the music and theories of [[Harry Partch]],<ref>Harry Partch (1949), ''Genesis of a Music'', University of Wisconsin Press</ref> who built his tonal system around the [[11-odd-limit]] 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,<ref name="meyer1929">Meyer, Max F. (1929) [https://archive.org/details/max-f-meyer-the-musicians-arithmetic/page/22/mode/2up ''The Musician’s Arithmetic: Drill Problems for an Introduction to the Scientific Study of Musical Composition'']. The University of Missouri Studies. Vol. 4, no. 1. University of Missouri. January 1, 1929. p. 22.</ref> the idea became central to the music and theories of [[Harry Partch]],<ref>Harry Partch (1949), ''Genesis of a Music'', University of Wisconsin Press</ref> 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.		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.

Nick Vuci at 17:43, 28 May 2025

2025-05-28T17:43:40Z

← Older revision		Revision as of 17:43, 28 May 2025
Line 22:		Line 22:

	== History ==		== History ==
	[[File:Diamond_marimba_layout.png\|thumb\|Layout of the Diamond Marimba. Ratios are shown unreduced to highlight the structure. [https://sintel.website/posts/diamond_marimba.html Click here to play the Diamond Marimba on your browser.]\|332x332px]]
	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 name="meyer1929"/>		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 name="meyer1929"/>

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	The first novel xenharmonic temperament—[[George Secor\|George Secor's]] later-named [[Miracle]] temperament—was made to approximate Partch's 11-limit diamond.<ref>Secor, George (1975). [https://www.anaphoria.com/SecorMiracle.pdf ''A New Look at the Partch Monophonic Fabric.''] Xenharmonicon. Vol. 3</ref><ref>Secor, George. (2006) [https://www.anaphoria.com/SecorMiracle.pdf ''The Miracle Temperament and Decimal Keyboard'']. Xenharmonikon. Vol. 18. 2006. pp. 5–15</ref>		The first novel xenharmonic temperament—[[George Secor\|George Secor's]] later-named [[Miracle]] temperament—was made to approximate Partch's 11-limit diamond.<ref>Secor, George (1975). [https://www.anaphoria.com/SecorMiracle.pdf ''A New Look at the Partch Monophonic Fabric.''] Xenharmonicon. Vol. 3</ref><ref>Secor, George. (2006) [https://www.anaphoria.com/SecorMiracle.pdf ''The Miracle Temperament and Decimal Keyboard'']. Xenharmonikon. Vol. 18. 2006. pp. 5–15</ref>
	=== Instrument layout ===		=== 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.<ref>https://web.archive.org/web/20220901100217/https://www.chrysalis-foundation.org/instruments-and-music/diamond-marimba-i/</ref>		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.<ref>https://web.archive.org/web/20220901100217/https://www.chrysalis-foundation.org/instruments-and-music/diamond-marimba-i/</ref>[[File:Diamond_marimba_layout.png\|thumb\|Layout of the Diamond Marimba. Ratios are shown unreduced to highlight the structure. [https://sintel.website/posts/diamond_marimba.html Click here to play the Diamond Marimba on your browser.]\|488x488px\|none]]

	== Music ==		== Music ==
	; Banjo Boogie		; Banjo Boogie

Nick Vuci: /* Instrument layout */

2025-05-28T17:41:03Z

Instrument layout

← Older revision		Revision as of 17:41, 28 May 2025
Line 22:		Line 22:

	== History ==		== History ==
			[[File:Diamond_marimba_layout.png\|thumb\|Layout of the Diamond Marimba. Ratios are shown unreduced to highlight the structure. [https://sintel.website/posts/diamond_marimba.html Click here to play the Diamond Marimba on your browser.]\|332x332px]]
	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 name="meyer1929"/>		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 name="meyer1929"/>

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	[[Erv Wilson]] in particular was inspired by Partch's use of the tonality diamond and it's extended form. He developed a number of "diamonds" himself,<ref>Wilson, Erv. (1965-1970) [https://anaphoria.com/diamond.pdf ''Letters on Diamond Lattices''] (PDF) Self-published.</ref> as well as other concepts inspired by Partch's use of the extended tonality diamond such as [[constant structure]].<ref>Wilson, Erv. (1964-2002) [https://www.anaphoria.com/Partchpapers.pdf ''The Partch Papers''] (collection of documents on Harry Partch's 11-limit diamond and its extensions, PDF). Self-published.</ref> A related idea of Wilson's is the [[Cross-set scale\|cross-set]], of which the tonality diamond is a special case.		[[Erv Wilson]] in particular was inspired by Partch's use of the tonality diamond and it's extended form. He developed a number of "diamonds" himself,<ref>Wilson, Erv. (1965-1970) [https://anaphoria.com/diamond.pdf ''Letters on Diamond Lattices''] (PDF) Self-published.</ref> as well as other concepts inspired by Partch's use of the extended tonality diamond such as [[constant structure]].<ref>Wilson, Erv. (1964-2002) [https://www.anaphoria.com/Partchpapers.pdf ''The Partch Papers''] (collection of documents on Harry Partch's 11-limit diamond and its extensions, PDF). Self-published.</ref> A related idea of Wilson's is the [[Cross-set scale\|cross-set]], of which the tonality diamond is a special case.

	The first novel xenharmonic temperament—[[George Secor\|George Secor's]] later-named [[Miracle]] temperament—was made to approximate Partch's 11-limit diamond.<ref>Secor, George (1975). [https://www.anaphoria.com/SecorMiracle.pdf ''A New Look at the Partch Monophonic Fabric.''] Xenharmonicon. Vol. 3</ref><ref>Secor, George. (2006) [https://www.anaphoria.com/SecorMiracle.pdf ''The Miracle Temperament and Decimal Keyboard'']. Xenharmonikon. Vol. 18. 2006. pp. 5–15</ref>[[File:Diamond_marimba_layout.png\|thumb\|Layout of the Diamond Marimba. Ratios are shown unreduced to highlight the structure. [https://sintel.website/posts/diamond_marimba.html Click here to play the Diamond Marimba on your browser.]]]		The first novel xenharmonic temperament—[[George Secor\|George Secor's]] later-named [[Miracle]] temperament—was made to approximate Partch's 11-limit diamond.<ref>Secor, George (1975). [https://www.anaphoria.com/SecorMiracle.pdf ''A New Look at the Partch Monophonic Fabric.''] Xenharmonicon. Vol. 3</ref><ref>Secor, George. (2006) [https://www.anaphoria.com/SecorMiracle.pdf ''The Miracle Temperament and Decimal Keyboard'']. Xenharmonikon. Vol. 18. 2006. pp. 5–15</ref>
	=== Instrument layout ===		=== 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.<ref>https://web.archive.org/web/20220901100217/https://www.chrysalis-foundation.org/instruments-and-music/diamond-marimba-i/</ref>

	== Music ==		== Music ==

Nick Vuci at 13:46, 28 May 2025

2025-05-28T13:46:36Z

← Older revision		Revision as of 13:46, 28 May 2025
Line 7:		Line 7:
	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.		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.

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

	== Construction ==		== Construction ==

← Older revision		Revision as of 20:21, 28 May 2025
Line 4:		Line 4:
	}}		}}
	{{Wikipedia\|Tonality diamond}}		{{Wikipedia\|Tonality diamond}}
	[[File:5-~~Limit Tonality Diamond Manim~~.mp4\|~~thumb~~]]		[[File:5-Limit_Tonality_Diamond_Manim.mp4\|frameless]]

	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,<ref name="meyer1929">Meyer, Max F. (1929) [https://archive.org/details/max-f-meyer-the-musicians-arithmetic/page/22/mode/2up ''The Musician’s Arithmetic: Drill Problems for an Introduction to the Scientific Study of Musical Composition'']. The University of Missouri Studies. Vol. 4, no. 1. University of Missouri. January 1, 1929. p. 22.</ref> the idea became central to the music and theories of [[Harry Partch]],<ref>Harry Partch (1949), ''Genesis of a Music'', University of Wisconsin Press</ref> who built his tonal system around the [[11-odd-limit]] 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,<ref name="meyer1929">Meyer, Max F. (1929) [https://archive.org/details/max-f-meyer-the-musicians-arithmetic/page/22/mode/2up ''The Musician’s Arithmetic: Drill Problems for an Introduction to the Scientific Study of Musical Composition'']. The University of Missouri Studies. Vol. 4, no. 1. University of Missouri. January 1, 1929. p. 22.</ref> the idea became central to the music and theories of [[Harry Partch]],<ref>Harry Partch (1949), ''Genesis of a Music'', University of Wisconsin Press</ref> 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.		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.

← Older revision		Revision as of 20:20, 28 May 2025
Line 4:		Line 4:
	}}		}}
	{{Wikipedia\|Tonality diamond}}		{{Wikipedia\|Tonality diamond}}
			[[File:5-Limit Tonality Diamond Manim.mp4\|thumb]]
	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,<ref name="meyer1929">Meyer, Max F. (1929) [https://archive.org/details/max-f-meyer-the-musicians-arithmetic/page/22/mode/2up ''The Musician’s Arithmetic: Drill Problems for an Introduction to the Scientific Study of Musical Composition'']. The University of Missouri Studies. Vol. 4, no. 1. University of Missouri. January 1, 1929. p. 22.</ref> the idea became central to the music and theories of [[Harry Partch]],<ref>Harry Partch (1949), ''Genesis of a Music'', University of Wisconsin Press</ref> who built his tonal system around the [[11-odd-limit]] 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,<ref name="meyer1929">Meyer, Max F. (1929) [https://archive.org/details/max-f-meyer-the-musicians-arithmetic/page/22/mode/2up ''The Musician’s Arithmetic: Drill Problems for an Introduction to the Scientific Study of Musical Composition'']. The University of Missouri Studies. Vol. 4, no. 1. University of Missouri. January 1, 1929. p. 22.</ref> the idea became central to the music and theories of [[Harry Partch]],<ref>Harry Partch (1949), ''Genesis of a Music'', University of Wisconsin Press</ref> 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.		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.