9edo - Revision history

Overthink: /* Rank-2 temperaments */ use backslashes for edo steps

2026-02-13T02:18:24Z

Rank-2 temperaments: use backslashes for edo steps

← Older revision		Revision as of 02:18, 13 February 2026
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	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	9edo contains a pentatonic [[mos scale]] produced by stacking 4/9 of [[2L 3s]] (1 3 1 3 1), which has a heptatonic extension, [[2L 5s]] (1 1 2 1 1 2 1, sometimes called "mavila" or "antidiatonic").		9edo contains a pentatonic [[mos scale]] produced by stacking 4\9 of [[2L 3s]] (1 3 1 3 1), which has a heptatonic extension, [[2L 5s]] (1 1 2 1 1 2 1, sometimes called "mavila" or "antidiatonic").

	You can also use ~~the~~ 2/9, which generates mos scales of [[1L 3s]] (3 2 2 2) and [[4L 1s]] (2 2 2 2 1) and can be interpreted as either an extremely sharp [[bug]] scale or an extremely flat [[orwell]] one.		You can also use 2\9, which generates mos scales of [[1L 3s]] (3 2 2 2) and [[4L 1s]] (2 2 2 2 1) and can be interpreted as either an extremely sharp [[bug]] scale or an extremely flat [[orwell]] one.

	== Historical (and other) relevance ==		== Historical (and other) relevance ==

BudjarnLambeth: /* Octave stretch or compression */

2025-09-23T02:21:50Z

Octave stretch or compression

← Older revision		Revision as of 02:21, 23 September 2025
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	9edo's [[prime]]s 3, 7, 11 and 13 are all tuned flat, so it can benefit from [[octave stretching]].		9edo's [[prime]]s 3, 7, 11 and 13 are all tuned flat, so it can benefit from [[octave stretching]].

	~~; 9edo~~
	* Step size: 133.333{{c}}, octave size: 1200.0{{c}}
	Pure-octaves 9edo makes a decent 2.5.11 tuning, approximating all those three primes within 18{{c}}.		Pure-octaves 9edo makes a decent 2.5.11 tuning, approximating all those three primes within 18{{c}}.
	~~{{Harmonics in equal\|9\|2\|1\|intervals=integer\|columns=11\|collapsed=true\|title=Approximation of harmonics in 9edo}}~~
	~~{{Harmonics in equal\|9\|2\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 9edo (continued)}}~~

	~~; [[zpi\|22zpi]]~~
	* Step size: 134.078{{c}}, octave size: 1206.7{{c}}
	9edo with octaves stretched about 5{{c}}, as in [[zpi\|22zpi]], makes a decent 2.7.11.13 tuning, approximating all those four primes within 17{{c}}.		9edo with octaves stretched about 5{{c}}, as in [[zpi\|22zpi]], makes a decent 2.7.11.13 tuning, approximating all those four primes within 17{{c}}.
	~~{{Harmonics in cet\|134.078\|intervals=integer\|columns=11\|collapsed=true\|title=Approximation of harmonics in 22zpi}}~~
	~~{{Harmonics in cet\|134.078\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 22zpi (continued)}}~~

	~~; [[32ed12]]~~
	* Step size: 134.436{{c}}, octave size: 1209.9{{c}}
	9edo with octaves stretched about 10{{c}}, as in [[ed12\|32ed12]], makes a decent 2.3.7.11.13 tuning, approximating all those five primes within 20{{c}}.		9edo with octaves stretched about 10{{c}}, as in [[ed12\|32ed12]], makes a decent 2.3.7.11.13 tuning, approximating all those five primes within 20{{c}}.
	~~{{Harmonics in equal\|32\|12\|1\|intervals=integer\|columns=11\|collapsed=true\|title=Approximation of harmonics in 32ed12}}~~
	~~{{Harmonics in equal\|32\|12\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 32ed12 (continued)}}~~

	== Diagrams ==		== Diagrams ==

BudjarnLambeth: /* See also */ I've to own page (deserves its own full page)

2025-09-21T07:55:28Z

See also: I've to own page (deserves its own full page)

← Older revision		Revision as of 07:55, 21 September 2025
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	* [https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&usp=sharing#list 9edo ear-training exercises] by [[Alex Ness]].		* [https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&usp=sharing#list 9edo ear-training exercises] by [[Alex Ness]].

	=== Werntz ~~Nocture Scale~~ ===		=== Werntz Nocturne scale ===
	~~The~~ Werntz Nocture Scale, created by [[Julia Werntz]], consists of 9edo with three notes inserted from 12edo to use as "embellishing notes", thereby making use of all twelve keys in each octave of a piano-style keyboard. In terms of temperament, this scale ~~can be viewed as the union of 9edo with [[6edo]], with three notes shared; or as a threefold-symmetrical 12 note non-MOS scale of [[36edo]], with intervals 4 2 2 4 4 2 2 4 4 2 2 4.~~		{{main\|Werntz Nocturne scale}}

	~~This scale is explained in the following video:~~
	* [https://www.youtube.com/watch?v=8Ckz2sljh98 ''Werntz Nocturne Scale--a Special Microtonal Scale''] ([[Julia Werntz]], 2025)

	== Notes ==		== Notes ==

BudjarnLambeth: /* Werntz Nocture Scale */

2025-09-21T07:43:31Z

Werntz Nocture Scale

← Older revision		Revision as of 07:43, 21 September 2025
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	This scale is explained in the following video:		This scale is explained in the following video:
	* [https://www.youtube.com/watch?v=8Ckz2sljh98 ''Werntz Nocturne Scale--a Special Microtonal Scale''] (Julia Werntz, 2025)		* [https://www.youtube.com/watch?v=8Ckz2sljh98 ''Werntz Nocturne Scale--a Special Microtonal Scale''] ([[Julia Werntz]], 2025)

	== Notes ==		== Notes ==

BudjarnLambeth: /* Werntz Nocture Scale */

2025-09-21T07:43:16Z

Werntz Nocture Scale

← Older revision		Revision as of 07:43, 21 September 2025
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	This scale is explained in the following video:		This scale is explained in the following video:
	* [https://www.youtube.com/watch?v=8Ckz2sljh98 ''Werntz Nocturne Scale--a Special Microtonal Scale''] (2025)		* [https://www.youtube.com/watch?v=8Ckz2sljh98 ''Werntz Nocturne Scale--a Special Microtonal Scale''] (Julia Werntz, 2025)

	== Notes ==		== Notes ==

BudjarnLambeth: /* Werntz Nocture Scale */

2025-09-21T07:42:55Z

Werntz Nocture Scale

← Older revision		Revision as of 07:42, 21 September 2025
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	=== Werntz Nocture Scale ===		=== Werntz Nocture Scale ===
	The Werntz Nocture Scale, created by [[Julia Werntz]], consists of 9edo with three notes inserted from 12edo to use as "embellishing notes", thereby making use of all twelve keys in each octave of a piano-style keyboard. In terms of temperament, this scale can be viewed as the union of 9edo with [[6edo]], with three notes shared; or as a threefold-symmetrical 12 note non-MOS scale of [[36edo]], with intervals 4 2 2 4 4 2 2 4 4 2 2 4. This scale is explained in the following video:		The Werntz Nocture Scale, created by [[Julia Werntz]], consists of 9edo with three notes inserted from 12edo to use as "embellishing notes", thereby making use of all twelve keys in each octave of a piano-style keyboard. In terms of temperament, this scale can be viewed as the union of 9edo with [[6edo]], with three notes shared; or as a threefold-symmetrical 12 note non-MOS scale of [[36edo]], with intervals 4 2 2 4 4 2 2 4 4 2 2 4.
	~~; [[Julia Werntz]]~~
			This scale is explained in the following video:
	* [https://www.youtube.com/watch?v=8Ckz2sljh98 ''Werntz Nocturne Scale--a Special Microtonal Scale''] (2025)		* [https://www.youtube.com/watch?v=8Ckz2sljh98 ''Werntz Nocturne Scale--a Special Microtonal Scale''] (2025)

BudjarnLambeth: /* Werntz Nocture Scale */ Add link to Julia Werntz

2025-09-21T07:19:29Z

Werntz Nocture Scale: Add link to Julia Werntz

← Older revision		Revision as of 07:19, 21 September 2025
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	=== Werntz Nocture Scale ===		=== Werntz Nocture Scale ===
	The Werntz Nocture Scale, created by Julia Werntz, consists of 9edo with three notes inserted from 12edo to use as "embellishing notes", thereby making use of all twelve keys in each octave of a piano-style keyboard. In terms of temperament, this scale can be viewed as the union of 9edo with [[6edo]], with three notes shared; or as a threefold-symmetrical 12 note non-MOS scale of [[36edo]], with intervals 4 2 2 4 4 2 2 4 4 2 2 4. This scale is explained in the following video:		The Werntz Nocture Scale, created by [[Julia Werntz]], consists of 9edo with three notes inserted from 12edo to use as "embellishing notes", thereby making use of all twelve keys in each octave of a piano-style keyboard. In terms of temperament, this scale can be viewed as the union of 9edo with [[6edo]], with three notes shared; or as a threefold-symmetrical 12 note non-MOS scale of [[36edo]], with intervals 4 2 2 4 4 2 2 4 4 2 2 4. This scale is explained in the following video:
	; [[Julia Werntz]]		; [[Julia Werntz]]
	* [https://www.youtube.com/watch?v=8Ckz2sljh98 ''Werntz Nocturne Scale--a Special Microtonal Scale''] (2025)		* [https://www.youtube.com/watch?v=8Ckz2sljh98 ''Werntz Nocturne Scale--a Special Microtonal Scale''] (2025)

Lucius Chiaraviglio: /* Werntz Nocture Scale */ Add a bit to the explanation

2025-09-20T22:50:39Z

Werntz Nocture Scale: Add a bit to the explanation

← Older revision		Revision as of 22:50, 20 September 2025
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	=== Werntz Nocture Scale ===		=== Werntz Nocture Scale ===
	The Werntz Nocture Scale, created by Julia Werntz, consists of 9edo with three notes inserted from 12edo to use as "embellishing notes", thereby making use of all twelve keys in each octave of a piano-style keyboard. This is explained in the following video:		The Werntz Nocture Scale, created by Julia Werntz, consists of 9edo with three notes inserted from 12edo to use as "embellishing notes", thereby making use of all twelve keys in each octave of a piano-style keyboard. In terms of temperament, this scale can be viewed as the union of 9edo with [[6edo]], with three notes shared; or as a threefold-symmetrical 12 note non-MOS scale of [[36edo]], with intervals 4 2 2 4 4 2 2 4 4 2 2 4. This scale is explained in the following video:
	; [[Julia Werntz]]		; [[Julia Werntz]]
	* [https://www.youtube.com/watch?v=8Ckz2sljh98 ''Werntz Nocturne Scale--a Special Microtonal Scale''] (2025)		* [https://www.youtube.com/watch?v=8Ckz2sljh98 ''Werntz Nocturne Scale--a Special Microtonal Scale''] (2025)

Lucius Chiaraviglio: /* Ear training */ Reorganize to Ear training (existing subsection) + (new subsection) Werntz Nocturne Scale

2025-09-20T21:17:34Z

Ear training: Reorganize to Ear training (existing subsection) + (new subsection) Werntz Nocturne Scale

← Older revision		Revision as of 21:17, 20 September 2025
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	{{Main\|Music in 9edo}}		{{Main\|Music in 9edo}}

	== Ear training ==		== See also ==

			=== Ear training ===
	* [https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&usp=sharing#list 9edo ear-training exercises] by [[Alex Ness]].		* [https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&usp=sharing#list 9edo ear-training exercises] by [[Alex Ness]].

			=== Werntz Nocture Scale ===
			The Werntz Nocture Scale, created by Julia Werntz, consists of 9edo with three notes inserted from 12edo to use as "embellishing notes", thereby making use of all twelve keys in each octave of a piano-style keyboard. This is explained in the following video:
			; [[Julia Werntz]]
			* [https://www.youtube.com/watch?v=8Ckz2sljh98 ''Werntz Nocturne Scale--a Special Microtonal Scale''] (2025)

	== Notes ==		== Notes ==

BudjarnLambeth: /* Octave stretch and compression */

2025-09-16T07:35:26Z

Octave stretch and compression

← Older revision		Revision as of 07:35, 16 September 2025
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	[http://%5B%5Bhttps://www.youtube.com/watch?v=1LjcBv-OWtQ%5D%5D Levi McClain, Klingon music theory is weird]		[http://%5B%5Bhttps://www.youtube.com/watch?v=1LjcBv-OWtQ%5D%5D Levi McClain, Klingon music theory is weird]

	== Octave stretch ~~and~~ compression ==		== Octave stretch or compression ==
	9edo's [[prime]]s 3, 7, 11 and 13 are all tuned flat, so it can benefit from [[octave stretching]].		9edo's [[prime]]s 3, 7, 11 and 13 are all tuned flat, so it can benefit from [[octave stretching]].