Omnidiatonic - Revision history

Sintel: /* Tunings */ fix broken latex

2025-04-23T00:21:54Z

Tunings: fix broken latex

← Older revision		Revision as of 00:21, 23 April 2025
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	\|-		\|-
	! Outer generator <br>(''G''<sub>1</sub> = L + 2M + s)		! Outer generator <br>(''G''<sub>1</sub> = L + 2M + s)
	\| <math>\displaystyle \frac{1}{2} < G_\text{1} < \frac{3}{5}</math>		\| <math>\displaystyle \frac{1}{2} \lt G_\text{1} \lt \frac{3}{5}</math>
	\|-		\|-
	! RH inner generator <br>(''G''<sub>2R</sub> = M + s)		! RH inner generator <br>(''G''<sub>2R</sub> = M + s)
	\| <math>\displaystyle 2 G_\text{1} - 1 < G_\text{2R} < 4 G_\text{1} - 2 \text{ for }\frac{1}{2} < G_\text{1} ≤ \frac{4}{7}</math> <br><math>\displaystyle 2 G_\text{1} - 1 < G_\text{2R} < 2 - 3 G_\text{1} \text{ for }\frac{4}{7} ≤ G_\text{1} < \frac{3}{5}</math>		\| <math>\displaystyle 2 G_\text{1} - 1 \lt G_\text{2R} \lt 4 G_\text{1} - 2 \text{ for }\frac{1}{2} \lt G_\text{1} \le \frac{4}{7}</math> <br><math>\displaystyle 2 G_\text{1} - 1 \lt G_\text{2R} \lt 2 - 3 G_\text{1} \text{ for }\frac{4}{7} \le G_\text{1} \lt \frac{3}{5}</math>
	\|-		\|-
	! LH inner generator <br>(''G''<sub>2L</sub> = L + M)		! LH inner generator <br>(''G''<sub>2L</sub> = L + M)
	\| <math>\displaystyle 2 - 3 G_\text{1} < G_\text{2L} < 1 - G_\text{1} \text{ for } \frac{1}{2} < G_\text{1} ≤ \frac{4}{7}</math> <br><math>\displaystyle 4 G_\text{1} - 2 < G_\text{2L} < 1 - G_\text{1} \text{ for }\frac{4}{7} ≤ G_\text{1} < \frac{3}{5}</math>		\| <math>\displaystyle 2 - 3 G_\text{1} \lt G_\text{2L} \lt 1 - G_\text{1} \text{ for } \frac{1}{2} \lt G_\text{1} \le \frac{4}{7}</math> <br><math>\displaystyle 4 G_\text{1} - 2 \lt G_\text{2L} \lt 1 - G_\text{1} \text{ for }\frac{4}{7} \le G_\text{1} \lt \frac{3}{5}</math>
	\|-		\|-
	! Large step <br>(L = 1 - ''G''<sub>1</sub> - ''G''<sub>2R</sub>)		! Large step <br>(L = 1 - ''G''<sub>1</sub> - ''G''<sub>2R</sub>)
	\| <math>\displaystyle \frac{1}{7} < L < \frac{1}{2}</math>		\| <math>\displaystyle \frac{1}{7} \lt L \lt \frac{1}{2}</math>
	\|-		\|-
	! Middle step <br>(M = 2''G''<sub>1</sub> - 1)		! Middle step <br>(M = 2''G''<sub>1</sub> - 1)
	\| <math>\displaystyle \frac{1}{5} (1 - 2 L) < M < L \text{ for } \frac{1}{7} < L ≤ \frac{1}{5}</math> <br><math>\displaystyle \frac{1}{5} (1 - 2 L) < M < \frac{1}{3} (1 - 2 L) \text{ for } \frac{1}{5} ≤ L < \frac{1}{2}</math>		\| <math>\displaystyle \frac{1}{5} (1 - 2 L) \lt M \lt L \text{ for } \frac{1}{7} \lt L \le \frac{1}{5}</math> <br><math>\displaystyle \frac{1}{5} (1 - 2 L) \lt M \lt \frac{1}{3} (1 - 2 L) \text{ for } \frac{1}{5} \le L \lt \frac{1}{2}</math>
	\|-		\|-
	! Small step <br>(s = 1 - ''G''<sub>1</sub> - ''G''<sub>2L</sub>)		! Small step <br>(s = 1 - ''G''<sub>1</sub> - ''G''<sub>2L</sub>)
	\| <math>\displaystyle \frac{1}{2} (1 - 5 L) < s < \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{7} < L ≤ \frac{1}{5}</math> <br><math>\displaystyle 0 < s < \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{5} ≤ L < \frac{1}{2}</math>		\| <math>\displaystyle \frac{1}{2} (1 - 5 L) \lt s \lt \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{7} \lt L \le \frac{1}{5}</math> <br><math>\displaystyle 0 \lt s \lt \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{5} \le L \lt \frac{1}{2}</math>
	\|}		\|}

VectorGraphics at 09:27, 28 March 2025

2025-03-28T09:27:04Z

← Older revision		Revision as of 09:27, 28 March 2025
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	'''Omnidiatonic''' (also known as '''interdia''' and '''archylino''') is a 7-note [[Maximum variety\|maximum-variety-3]] scale with the [[step signature]] 2L 3M 2s. Omnidiatonic is a [[chiral]] scale with LMsMLsM and LMsLMsM variants. [[14edo]] is the first equal division that supports omnidiatonic. The name "omnidiatonic" was given by [[User:CompactStar\|CompactStar]] and the name "interdia" was given by [[User:Xenllium\|Xenllium]], both of which refer to this scale being intermediate between the [[5L 2s]] diatonic scale and the [[2L 5s]] antidiatonic scale. The name "archylino" was given by [[User:AthiTrydhen\|Praveen Venkataramana]], which refers to intervals separated by 64/63, the Archytas comma, being mapped to the same number of scale steps of 2.3.7 JI archylino 1/1 9/8 7/6 4/3 3/2 14/9 7/4 2/1 (MsLMsML).		'''Omnidiatonic''' (also known as '''interdia''' and '''archylino''') is a 7-note [[Maximum variety\|maximum-variety-3]] scale with the [[step signature]] 2L 3M 2s. Omnidiatonic is a [[chiral]] scale with LMsMLsM and LMsLMsM variants. [[14edo]] is the first equal division that supports omnidiatonic. The name "omnidiatonic" was given by [[User:CompactStar\|CompactStar]] and the name "interdia" was given by [[User:Xenllium\|Xenllium]], both of which refer to this scale being intermediate between the [[5L 2s]] diatonic scale and the [[2L 5s]] antidiatonic scale. The name "archylino" was given by [[User:AthiTrydhen\|Praveen Venkataramana]], which refers to intervals separated by 64/63, the Archytas comma, being mapped to the same number of scale steps of 2.3.7 JI archylino 1/1 9/8 7/6 4/3 3/2 14/9 7/4 2/1 (MsLMsML). In terms of Greek scales, this can be seen as Archytas' diatonic.

	Omnidiatonic can be tuned as a 7-limit JI scale or a tempered version thereof, where L represents 8/7, M represents 9/8, and s represents 28/27.		Omnidiatonic can be tuned as a 7-limit JI scale or a tempered version thereof, where L represents 8/7, M represents 9/8, and s represents 28/27.

Fredg999: Terms, step label casing, misc. edits

2024-08-12T18:25:33Z

Terms, step label casing, misc. edits

← Older revision		Revision as of 18:25, 12 August 2024
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	'''Omnidiatonic''' (also known as '''interdia''' and '''archylino''') is a 7-note [[Maximum variety\|~~max~~-variety-3]] scale with the step ~~pattern~~ 2L 3m 2s. Omnidiatonic is a chiral scale with ~~LmsmLsm~~ and ~~LmsLmsm~~ variants. [[14edo]] is the first equal division that supports omnidiatonic. The name "omnidiatonic" was given by [[User:CompactStar\|CompactStar]] and the name "interdia" was given by [[User:Xenllium\|Xenllium]], both of which refer to this scale being intermediate between the [[5L 2s]] diatonic scale and the [[2L 5s]] antidiatonic scale. The name "archylino" was given by [[User:AthiTrydhen\|Praveen Venkataramana]], which refers to intervals separated by 64/63, the Archytas comma, being mapped to the same number of scale steps of 2.3.7 JI archylino 1/1 9/8 7/6 4/3 3/2 14/9 7/4 2/1 (~~msLmsmL~~).		'''Omnidiatonic''' (also known as '''interdia''' and '''archylino''') is a 7-note [[Maximum variety\|maximum-variety-3]] scale with the [[step signature]] 2L 3M 2s. Omnidiatonic is a [[chiral]] scale with LMsMLsM and LMsLMsM variants. [[14edo]] is the first equal division that supports omnidiatonic. The name "omnidiatonic" was given by [[User:CompactStar\|CompactStar]] and the name "interdia" was given by [[User:Xenllium\|Xenllium]], both of which refer to this scale being intermediate between the [[5L 2s]] diatonic scale and the [[2L 5s]] antidiatonic scale. The name "archylino" was given by [[User:AthiTrydhen\|Praveen Venkataramana]], which refers to intervals separated by 64/63, the Archytas comma, being mapped to the same number of scale steps of 2.3.7 JI archylino 1/1 9/8 7/6 4/3 3/2 14/9 7/4 2/1 (MsLMsML).

	Omnidiatonic can be tuned as a 7-limit JI scale or a tempered version thereof, where L represents 8/7, m represents 9/8, and s represents 28/27.		Omnidiatonic can be tuned as a 7-limit JI scale or a tempered version thereof, where L represents 8/7, M represents 9/8, and s represents 28/27.

	== Modes ==		== Modes ==
Line 11:		Line 11:
	!Right handed		!Right handed
	\|-		\|-
	\|~~LmsmLsm~~		\|LMsMLsM
	\|~~LmsLmsm~~		\|LMsLMsM
	\|-		\|-
	\|~~LsmLmsm~~		\|LsMLMsM
	\|~~LmsmLms~~		\|LMsMLMs
	\|-		\|-
	\|~~mLmsmLs~~		\|MLMsMLs
	\|~~mLmsLms~~		\|MLMsLMs
	\|-		\|-
	\|~~mLsmLms~~		\|MLsMLMs
	\|~~msLmsmL~~		\|MsLMsML
	\|-		\|-
	\|~~msmLsmL~~		\|MsMLsML
	\|~~msmLmsL~~		\|MsMLMsL
	\|-		\|-
	\|~~smLmsmL~~		\|sMLMsML
	\|~~sLmsmLm~~		\|sLMsMLM
	\|-		\|-
	\|~~smLsmLm~~		\|sMLsMLM
	\|~~smLmsLm~~		\|sMLMsLM
	\|}		\|}

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	! Tuning range (in [[octave]]s)		! Tuning range (in [[octave]]s)
	\|-		\|-
	! Outer generator <br>(''G''<sub>1</sub> = L + 2m + s)		! Outer generator <br>(''G''<sub>1</sub> = L + 2M + s)
	\| <math>\displaystyle \frac{1}{2} < G_\text{1} < \frac{3}{5}</math>		\| <math>\displaystyle \frac{1}{2} < G_\text{1} < \frac{3}{5}</math>
	\|-		\|-
	! RH inner generator <br>(''G''<sub>2R</sub> = m + s)		! RH inner generator <br>(''G''<sub>2R</sub> = M + s)
	\| <math>\displaystyle 2 G_\text{1} - 1 < G_\text{2R} < 4 G_\text{1} - 2 \text{ for }\frac{1}{2} < G_\text{1} ≤ \frac{4}{7}</math> <br><math>\displaystyle 2 G_\text{1} - 1 < G_\text{2R} < 2 - 3 G_\text{1} \text{ for }\frac{4}{7} ≤ G_\text{1} < \frac{3}{5}</math>		\| <math>\displaystyle 2 G_\text{1} - 1 < G_\text{2R} < 4 G_\text{1} - 2 \text{ for }\frac{1}{2} < G_\text{1} ≤ \frac{4}{7}</math> <br><math>\displaystyle 2 G_\text{1} - 1 < G_\text{2R} < 2 - 3 G_\text{1} \text{ for }\frac{4}{7} ≤ G_\text{1} < \frac{3}{5}</math>
	\|-		\|-
	! LH inner generator <br>(''G''<sub>2L</sub> = L + m)		! LH inner generator <br>(''G''<sub>2L</sub> = L + M)
	\| <math>\displaystyle 2 - 3 G_\text{1} < G_\text{2L} < 1 - G_\text{1} \text{ for } \frac{1}{2} < G_\text{1} ≤ \frac{4}{7}</math> <br><math>\displaystyle 4 G_\text{1} - 2 < G_\text{2L} < 1 - G_\text{1} \text{ for }\frac{4}{7} ≤ G_\text{1} < \frac{3}{5}</math>		\| <math>\displaystyle 2 - 3 G_\text{1} < G_\text{2L} < 1 - G_\text{1} \text{ for } \frac{1}{2} < G_\text{1} ≤ \frac{4}{7}</math> <br><math>\displaystyle 4 G_\text{1} - 2 < G_\text{2L} < 1 - G_\text{1} \text{ for }\frac{4}{7} ≤ G_\text{1} < \frac{3}{5}</math>
	\|-		\|-
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	\| <math>\displaystyle \frac{1}{7} < L < \frac{1}{2}</math>		\| <math>\displaystyle \frac{1}{7} < L < \frac{1}{2}</math>
	\|-		\|-
	! Middle step <br>(m = 2''G''<sub>1</sub> - 1)		! Middle step <br>(M = 2''G''<sub>1</sub> - 1)
	\| <math>\displaystyle \frac{1}{5} (1 - 2 L) < M < L \text{ for } \frac{1}{7} < L ≤ \frac{1}{5}</math> <br><math>\displaystyle \frac{1}{5} (1 - 2 L) < M < \frac{1}{3} (1 - 2 L) \text{ for } \frac{1}{5} ≤ L < \frac{1}{2}</math>		\| <math>\displaystyle \frac{1}{5} (1 - 2 L) < M < L \text{ for } \frac{1}{7} < L ≤ \frac{1}{5}</math> <br><math>\displaystyle \frac{1}{5} (1 - 2 L) < M < \frac{1}{3} (1 - 2 L) \text{ for } \frac{1}{5} ≤ L < \frac{1}{2}</math>
	\|-		\|-
	! Small step <br>(s = 1 - ''G''<sub>1</sub> - ''G''<sub>2L</sub>)		! Small step <br>(s = 1 - ''G''<sub>1</sub> - ''G''<sub>2L</sub>)
	\| <math>\displaystyle \frac{1}{2} (1 - 5 L) < S < \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{7} < L ≤ \frac{1}{5}</math> <br><math>\displaystyle 0 < S < \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{5} ≤ L < \frac{1}{2}</math>		\| <math>\displaystyle \frac{1}{2} (1 - 5 L) < s < \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{7} < L ≤ \frac{1}{5}</math> <br><math>\displaystyle 0 < s < \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{5} ≤ L < \frac{1}{2}</math>
	\|}		\|}

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	!Tuning		!Tuning
	!L		!L
	!m		!M
	!s		!s
	!Comments		!Comments
Line 121:		Line 121:

	== See also ==		== See also ==
	* [[Nicetone]] – sister 3L 2m 2s scale		* [[Nicetone]] – sister 3L 2M 2s scale
	* [[Antinicetone]] – sister 2L 2m 3s scale		* [[Antinicetone]] – sister 2L 2M 3s scale
	* [[5L 2s]] – LM-equalized version of omnidiatonic		* [[5L 2s]] – LM-equalized version of omnidiatonic
	** [[5L 2s Muddles]] – other diatonic muddles		** [[5L 2s Muddles]] – other diatonic muddles

Xenllium at 04:13, 15 October 2023

2023-10-15T04:13:04Z

@@ Line 3: / Line 3: @@
 Omnidiatonic can be tuned as a 7-limit JI scale or a tempered version thereof, where L represents 8/7, m represents 9/8, and s represents 28/27.
 == Tunings ==
 {|class="wikitable"
 |-
@@ Line 66: / Line 119: @@
+|
 |}
 [[Category:Rank-3 scales]]

Inthar at 01:42, 21 May 2023

2023-05-21T01:42:15Z

← Older revision		Revision as of 01:42, 21 May 2023
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	'''Omnidiatonic''' (also known as '''interdia''' and '''archylino''') is a 7-note [[Maximum variety\|max-variety-3]] scale with the step pattern 2L 3m 2s. Omnidiatonic is a chiral scale with LmsmLsm and LmsLmsm variants. [[14edo]] is the first equal division that supports omnidiatonic. The name "omnidiatonic" was given by [[User:CompactStar\|CompactStar]] and the name "interdia" was given by [[User:Xenllium\|Xenllium]], both of which refer to this scale being intermediate between the [[5L 2s]] diatonic scale and the [[2L 5s]] ~~andiatonic~~ scale. As The name "archylino" was given by [[User:AthiTrydhen\|Praveen Venkataramana]], which refers to intervals separated by 64/63, the Archytas comma, being mapped to the same number of scale steps of 2.3.7 JI archylino 1/1 9/8 7/6 4/3 3/2 14/9 7/4 2/1 (msLmsmL).		'''Omnidiatonic''' (also known as '''interdia''' and '''archylino''') is a 7-note [[Maximum variety\|max-variety-3]] scale with the step pattern 2L 3m 2s. Omnidiatonic is a chiral scale with LmsmLsm and LmsLmsm variants. [[14edo]] is the first equal division that supports omnidiatonic. The name "omnidiatonic" was given by [[User:CompactStar\|CompactStar]] and the name "interdia" was given by [[User:Xenllium\|Xenllium]], both of which refer to this scale being intermediate between the [[5L 2s]] diatonic scale and the [[2L 5s]] antidiatonic scale. The name "archylino" was given by [[User:AthiTrydhen\|Praveen Venkataramana]], which refers to intervals separated by 64/63, the Archytas comma, being mapped to the same number of scale steps of 2.3.7 JI archylino 1/1 9/8 7/6 4/3 3/2 14/9 7/4 2/1 (msLmsmL).

	Omnidiatonic can be tuned as a 7-limit JI scale or a tempered version thereof, where L represents 8/7, m represents 9/8, and s represents 28/27.		Omnidiatonic can be tuned as a 7-limit JI scale or a tempered version thereof, where L represents 8/7, m represents 9/8, and s represents 28/27.

CompactStar at 00:44, 21 May 2023

2023-05-21T00:44:43Z

← Older revision		Revision as of 00:44, 21 May 2023
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	\|2		\|2
	\|1		\|1
	\|~~Also has antidiatonic (but non-Mavila) MOS~~		\|
	\|-		\|-
	\|rowspan="2"\|[[21edo]]		\|rowspan="2"\|[[21edo]]
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	\|1		\|1
	\|		\|
			\|-
			\|[[22edo]]
			\|7
			\|2
			\|1
			\|Also has diatonic MOS
	\|-		\|-
	\|[[23edo]]		\|[[23edo]]

CompactStar at 00:43, 21 May 2023

2023-05-21T00:43:42Z

← Older revision		Revision as of 00:43, 21 May 2023
Line 52:		Line 52:
	\|3		\|3
	\|1		\|1
			\|
			\|-
			\|[[23edo]]
			\|5
			\|3
			\|2
	\|		\|
	\|}		\|}

	[[Category:Rank-3 scales]]		[[Category:Rank-3 scales]]

CompactStar at 00:42, 21 May 2023

2023-05-21T00:42:46Z

← Older revision		Revision as of 00:42, 21 May 2023
Line 36:		Line 36:
	\|1		\|1
	\|Also has diatonic MOS		\|Also has diatonic MOS
			\|-
			\|[[20edo]]
			\|6
			\|2
			\|1
			\|Also has antidiatonic (but non-Mavila) MOS
	\|-		\|-
	\|rowspan="2"\|[[21edo]]		\|rowspan="2"\|[[21edo]]
Line 46:		Line 52:
	\|3		\|3
	\|1		\|1
	\|
	\|-
	\|		\|
	\|}		\|}

	[[Category:Rank-3 scales]]		[[Category:Rank-3 scales]]

CompactStar at 00:40, 21 May 2023

2023-05-21T00:40:40Z

← Older revision		Revision as of 00:40, 21 May 2023
Line 1:		Line 1:
	'''Omnidiatonic''' (also known as '''interdia''' and '''archylino''') is a 7-note [[Maximum variety\|max-variety-3]] scale with the step pattern 2L 3m 2s. Omnidiatonic is a chiral scale with LmsmLsm and LmsLmsm variants. [[14edo]] is the first equal division that supports omnidiatonic. The name "omnidiatonic" was given by [[User:CompactStar\|CompactStar]] and the name "interdia" was given by [[User:Xenllium\|Xenllium]], both of which refer to this scale being intermediate between the [[5L 2s]] diatonic scale and the [[2L 5s]] andiatonic scale. As The name "archylino" was given by [[User:AthiTrydhen\|Praveen Venkataramana]], which refers to intervals separated by 64/63, the Archytas comma, being mapped to the same number of scale steps of 2.3.7 JI archylino 1/1 9/8 7/6 4/3 3/2 14/9 7/4 2/1 (msLmsmL).		'''Omnidiatonic''' (also known as '''interdia''' and '''archylino''') is a 7-note [[Maximum variety\|max-variety-3]] scale with the step pattern 2L 3m 2s. Omnidiatonic is a chiral scale with LmsmLsm and LmsLmsm variants. [[14edo]] is the first equal division that supports omnidiatonic. The name "omnidiatonic" was given by [[User:CompactStar\|CompactStar]] and the name "interdia" was given by [[User:Xenllium\|Xenllium]], both of which refer to this scale being intermediate between the [[5L 2s]] diatonic scale and the [[2L 5s]] andiatonic scale. As The name "archylino" was given by [[User:AthiTrydhen\|Praveen Venkataramana]], which refers to intervals separated by 64/63, the Archytas comma, being mapped to the same number of scale steps of 2.3.7 JI archylino 1/1 9/8 7/6 4/3 3/2 14/9 7/4 2/1 (msLmsmL).

			Omnidiatonic can be tuned as a 7-limit JI scale or a tempered version thereof, where L represents 8/7, m represents 9/8, and s represents 28/27.


	== Tunings ==		== Tunings ==
	{\|class="wikitable"		{\|class="wikitable"
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	\|Also has diatonic MOS		\|Also has diatonic MOS
	\|-		\|-
	\|[[21edo]]		\|rowspan="2"\|[[21edo]]
	\|4		\|4
	\|3		\|3
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	\|		\|
	\|-		\|-
	~~\|[[21edo]]~~
	\|5		\|5
	\|3		\|3
	\|1		\|1
			\|
			\|-
	\|		\|
	\|}		\|}

	[[Category:Rank-3 scales]]		[[Category:Rank-3 scales]]

CompactStar at 00:38, 21 May 2023

2023-05-21T00:38:07Z

← Older revision		Revision as of 00:38, 21 May 2023
Line 33:		Line 33:
	\|Also has diatonic MOS		\|Also has diatonic MOS
	\|-		\|-
			\|[[21edo]]
			\|4
			\|3
			\|2
			\|
			\|-
			\|[[21edo]]
			\|5
			\|3
			\|1
	\|		\|
	\|}		\|}

	[[Category:Rank-3 scales]]		[[Category:Rank-3 scales]]