Diasem - Revision history

Fredg999: A "Tas" page was created

2025-08-18T20:31:22Z

A "Tas" page was created

← Older revision		Revision as of 20:31, 18 August 2025
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	'''Diasem''' (also denoted 2s in [[groundfault]]'s [[aberrismic theory]]) is a 9-note [[Maximum variety\|max-variety-3]], [[generator-offset]] scale with [[step signature]] 5L 2m 2s, equivalent to the [[semiquartal]] ([[5L 4s]]) mos with two of the small steps made larger and the other two made smaller. Diasem is [[chiral]], with two rotationally non-equivalent variants: ''right-handed (RH) diasem'' LmLsLmLsL and ''left-handed (LH) diasem'' LsLmLsLmL; these [[step pattern]]s are mirror images. The fact that the small step of diatonic is made smaller results in [[26edo]] and [[31edo]] diasem having better melodic properties than the respective diatonic scales. [[21edo]] is the smallest edo to support a non-degenerate diasem.		'''Diasem''' (also denoted 2s in [[groundfault]]'s [[aberrismic theory]]) is a 9-note [[Maximum variety\|max-variety-3]], [[generator-offset]] scale with [[step signature]] 5L 2m 2s, equivalent to the [[semiquartal]] ([[5L 4s]]) mos with two of the small steps made larger and the other two made smaller. Diasem is [[chiral]], with two rotationally non-equivalent variants: ''right-handed (RH) diasem'' LmLsLmLsL and ''left-handed (LH) diasem'' LsLmLsLmL; these [[step pattern]]s are mirror images. The fact that the small step of diatonic is made smaller results in [[26edo]] and [[31edo]] diasem having better melodic properties than the respective diatonic scales. [[21edo]] is the smallest edo to support a non-degenerate diasem.

	Diasem can be tuned as a [[Just intonation subgroup\|2.3.7 subgroup]] JI scale or a tempered version thereof, where L represents [[9/8]], m represents [[28/27]], and s represents [[64/63]]. This interpretation, or more generally the series of [[generator sequence]] scales generated by GS(7/6, 8/7) or GS(8/7, 7/6), has been named ~~'''Tas''' (from Archytas) by~~ [[~~Scott Dakota~~]].		Diasem can be tuned as a [[Just intonation subgroup\|2.3.7 subgroup]] JI scale or a tempered version thereof, where L represents [[9/8]], m represents [[28/27]], and s represents [[64/63]]. This interpretation, or more generally the series of [[generator sequence]] scales generated by GS(7/6, 8/7) or GS(8/7, 7/6), has been named [[Tas]].

	"Diasem" is a name given by [[groundfault]] (though others have discussed the scale before her). The name is a portmanteau of "diatonic" and "semiquartal" (or "[[Semaphore]]") since its step sizes are intermediate between that of [[diatonic]] (5L 2s) and [[semiquartal]] (5L 4s); it is also a pun based on the [[diesis]], which appears as the small step in the scale in the [[31edo]] and [[36edo]] tunings.		"Diasem" is a name given by [[groundfault]] (though others have discussed the scale before her). The name is a portmanteau of "diatonic" and "semiquartal" (or "[[Semaphore]]") since its step sizes are intermediate between that of [[diatonic]] (5L 2s) and [[semiquartal]] (5L 4s); it is also a pun based on the [[diesis]], which appears as the small step in the scale in the [[31edo]] and [[36edo]] tunings.

VectorGraphics at 00:26, 28 June 2025

2025-06-28T00:26:20Z

← Older revision		Revision as of 00:26, 28 June 2025
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	The notes of diasem form the {49/48, 567/512} Fokker block, which is a fundamental domain of the 2.3.7 pitch class lattice; it is possible to tile the entire infinite lattice with copies of right-hand diasem transLated by (49/48)<sup>''m''</sup>(567/512)<sup>''n''</sup> for integer ''m'' and ''n''. Including any one of the other three points on the boundary (28/27, 147/128, or 64/63) instead of 9/8 aLso yields Fokker blocks, more specifically, modes of three of the other [[dome]]s of diasem, and transLates of the parallelogram that do not have lattice points on the boundary lead to other domes of this Fokker block. However, only one other choice, 28/27, yields a diasem scale, and it yields the left-handed diasem mode mLLsLmLsL.		The notes of diasem form the {49/48, 567/512} Fokker block, which is a fundamental domain of the 2.3.7 pitch class lattice; it is possible to tile the entire infinite lattice with copies of right-hand diasem transLated by (49/48)<sup>''m''</sup>(567/512)<sup>''n''</sup> for integer ''m'' and ''n''. Including any one of the other three points on the boundary (28/27, 147/128, or 64/63) instead of 9/8 aLso yields Fokker blocks, more specifically, modes of three of the other [[dome]]s of diasem, and transLates of the parallelogram that do not have lattice points on the boundary lead to other domes of this Fokker block. However, only one other choice, 28/27, yields a diasem scale, and it yields the left-handed diasem mode mLLsLmLsL.

	As a Fokker block, 2.3.7 JI diasem is aLso a product ~~scale pattern~~ of the tempered 2.3.7 mosses Semaphore[9] (LsLsLsLsL) and septimal Mavila[9] (LLLsLLLsL).		As a Fokker block, 2.3.7 JI diasem is aLso a product of the tempered 2.3.7 mosses Semaphore[9] (LsLsLsLsL) and septimal Mavila[9] (LLLsLLLsL).

	== Tunings ==		== Tunings ==

VectorGraphics at 00:15, 28 June 2025

2025-06-28T00:15:11Z

← Older revision		Revision as of 00:15, 28 June 2025
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	The notes of diasem form the {49/48, 567/512} Fokker block, which is a fundamental domain of the 2.3.7 pitch class lattice; it is possible to tile the entire infinite lattice with copies of right-hand diasem transLated by (49/48)<sup>''m''</sup>(567/512)<sup>''n''</sup> for integer ''m'' and ''n''. Including any one of the other three points on the boundary (28/27, 147/128, or 64/63) instead of 9/8 aLso yields Fokker blocks, more specifically, modes of three of the other [[dome]]s of diasem, and transLates of the parallelogram that do not have lattice points on the boundary lead to other domes of this Fokker block. However, only one other choice, 28/27, yields a diasem scale, and it yields the left-handed diasem mode mLLsLmLsL.		The notes of diasem form the {49/48, 567/512} Fokker block, which is a fundamental domain of the 2.3.7 pitch class lattice; it is possible to tile the entire infinite lattice with copies of right-hand diasem transLated by (49/48)<sup>''m''</sup>(567/512)<sup>''n''</sup> for integer ''m'' and ''n''. Including any one of the other three points on the boundary (28/27, 147/128, or 64/63) instead of 9/8 aLso yields Fokker blocks, more specifically, modes of three of the other [[dome]]s of diasem, and transLates of the parallelogram that do not have lattice points on the boundary lead to other domes of this Fokker block. However, only one other choice, 28/27, yields a diasem scale, and it yields the left-handed diasem mode mLLsLmLsL.

	As a Fokker block, 2.3.7 JI diasem is aLso a product ~~word~~ scale~~, a product~~ of the tempered 2.3.7 mosses Semaphore[9] (LsLsLsLsL) and septimal Mavila[9] (LLLsLLLsL).		As a Fokker block, 2.3.7 JI diasem is aLso a product scale pattern of the tempered 2.3.7 mosses Semaphore[9] (LsLsLsLsL) and septimal Mavila[9] (LLLsLLLsL).

	== Tunings ==		== Tunings ==

Hkm at 18:00, 24 June 2025

2025-06-24T18:00:46Z

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	[[Category:36edo]]		[[Category:36edo]]
	[[Category:Just intonation scales]]		[[Category:Just intonation scales]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:7-limit]]		[[Category:7-limit]]
	[[Category:Trivalent scales]]		[[Category:Trivalent scales]]

Lériendil: Text replacement - "Category:Just intonation scales" to "Category:Just intonation scales Category:Pages with mostly numerical content"

2025-06-24T00:40:14Z

Text replacement - "Category:Just intonation scales" to "Category:Just intonation scales Category:Pages with mostly numerical content"

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	[[Category:36edo]]		[[Category:36edo]]
	[[Category:Just intonation scales]]		[[Category:Just intonation scales]]
			[[Category:Pages with mostly numerical content]]
	[[Category:7-limit]]		[[Category:7-limit]]
	[[Category:Trivalent scales]]		[[Category:Trivalent scales]]

Lériendil at 18:12, 9 January 2025

2025-01-09T18:12:16Z

← Older revision		Revision as of 18:12, 9 January 2025
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	2.3.7 JI diasem also has the following generator-offset, SV3 supersets:		2.3.7 JI diasem also has the following generator-offset, SV3 supersets:
	* a 19-note superset: mLsmsLmsmLsmsLmsmLs (5L 7m 7s), with L = 2187/2048, m = 28/27, and s = 64/63,		* a 19-note superset: mLsmsLmsmLsmsLmsmLs (5L 7m 7s), with L = 2187/2048, m = 28/27, and s = 64/63,
	* a 29-note superset: mLsmLmLsmLmLmsLmLmLsmLmLmsLmL (12L 12m 5s), with L = 28/27, m = 64/63, and s = 531441/~~524188~~.		* a 29-note superset: mLsmLmLsmLmLmsLmLmLsmLmLmsLmL (12L 12m 5s), with L = 28/27, m = 64/63, and s = 531441/524288.

	== See also ==		== See also ==

Inthar: /* Properties */

2024-12-08T05:02:21Z

Properties

← Older revision		Revision as of 05:02, 8 December 2024
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	The scale has two chains of fifth generators (with 5 notes and 4 notes, respectively) with offset L + m or L + s (respectively a flat minor third or a sharp major second in tunings of diasem with "reasonable" fifths and small s steps).		The scale has two chains of fifth generators (with 5 notes and 4 notes, respectively) with offset L + m or L + s (respectively a flat minor third or a sharp major second in tunings of diasem with "reasonable" fifths and small s steps).

	~~<!--~~== Modes ==		== Modes ==
	Diasem has 18 modes, 9 modes of LH diasem and 9 modes of RH diasem. We have provided names based on the modes of the [[5L 4s]], [[5L 2s]] and [[7L 2s]] temperings of each mode.		Diasem has 18 modes, 9 modes of LH diasem and 9 modes of RH diasem. We have provided names based on the modes of the [[5L 4s]], [[5L 2s]] and [[7L 2s]] temperings of each mode.

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	Notice that we have two generator chains of equal length. To give this scale a generator-offset structure we can treat the large 7-step as the offset of the 10-note scale. We treat L+S as one scale step and consider the scale an interleaving of two pentatonic scales, using the notes of C-D-F-G-Bb for the even numbered notes and Cv-Ebv-Fv-Abv-Bbv for the odd ones. This gives the following ordering: C Cv D Ebv F Fv G Abv Bb Bbv C, or in step sizes, -s L+s M L+s -s L+s M L+s -s L+s. This is formally a [[blackdye]] (sL'mL's'L'mL's'L') pattern, albeit with a negative step size s' = -s! This scale has been called '''negative blackdye''' or '''negative-s blackdye'''.		Notice that we have two generator chains of equal length. To give this scale a generator-offset structure we can treat the large 7-step as the offset of the 10-note scale. We treat L+S as one scale step and consider the scale an interleaving of two pentatonic scales, using the notes of C-D-F-G-Bb for the even numbered notes and Cv-Ebv-Fv-Abv-Bbv for the odd ones. This gives the following ordering: C Cv D Ebv F Fv G Abv Bb Bbv C, or in step sizes, -s L+s M L+s -s L+s M L+s -s L+s. This is formally a [[blackdye]] (sL'mL's'L'mL's'L') pattern, albeit with a negative step size s' = -s! This scale has been called '''negative blackdye''' or '''negative-s blackdye'''.
	~~-->~~

	== Alterations ==		== Alterations ==

Fredg999: Uniformize "denoted" with similar pages

2024-08-12T18:27:11Z

Uniformize "denoted" with similar pages

← Older revision		Revision as of 18:27, 12 August 2024
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	\|ja =		\|ja =
	}}		}}
	'''Diasem''' (also ~~known as~~ 2s in [[groundfault]]'s [[aberrismic theory]]) is a 9-note [[Maximum variety\|max-variety-3]], [[generator-offset]] scale with [[step signature]] 5L 2m 2s, equivalent to the [[semiquartal]] ([[5L 4s]]) mos with two of the small steps made larger and the other two made smaller. Diasem is [[chiral]], with two rotationally non-equivalent variants: ''right-handed (RH) diasem'' LmLsLmLsL and ''left-handed (LH) diasem'' LsLmLsLmL; these [[step pattern]]s are mirror images. The fact that the small step of diatonic is made smaller results in [[26edo]] and [[31edo]] diasem having better melodic properties than the respective diatonic scales. [[21edo]] is the smallest edo to support a non-degenerate diasem.		'''Diasem''' (also denoted 2s in [[groundfault]]'s [[aberrismic theory]]) is a 9-note [[Maximum variety\|max-variety-3]], [[generator-offset]] scale with [[step signature]] 5L 2m 2s, equivalent to the [[semiquartal]] ([[5L 4s]]) mos with two of the small steps made larger and the other two made smaller. Diasem is [[chiral]], with two rotationally non-equivalent variants: ''right-handed (RH) diasem'' LmLsLmLsL and ''left-handed (LH) diasem'' LsLmLsLmL; these [[step pattern]]s are mirror images. The fact that the small step of diatonic is made smaller results in [[26edo]] and [[31edo]] diasem having better melodic properties than the respective diatonic scales. [[21edo]] is the smallest edo to support a non-degenerate diasem.

	Diasem can be tuned as a [[Just intonation subgroup\|2.3.7 subgroup]] JI scale or a tempered version thereof, where L represents [[9/8]], m represents [[28/27]], and s represents [[64/63]]. This interpretation, or more generally the series of [[generator sequence]] scales generated by GS(7/6, 8/7) or GS(8/7, 7/6), has been named '''Tas''' (from Archytas) by [[Scott Dakota]].		Diasem can be tuned as a [[Just intonation subgroup\|2.3.7 subgroup]] JI scale or a tempered version thereof, where L represents [[9/8]], m represents [[28/27]], and s represents [[64/63]]. This interpretation, or more generally the series of [[generator sequence]] scales generated by GS(7/6, 8/7) or GS(8/7, 7/6), has been named '''Tas''' (from Archytas) by [[Scott Dakota]].

Inthar: /* Tunings */

2024-08-12T16:41:38Z

Tunings

← Older revision		Revision as of 16:41, 12 August 2024
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	! rowspan="2" class="unsortable" \|Good JI approximations		! rowspan="2" class="unsortable" \|Good JI approximations
	! rowspan="2" class="unsortable" \|other comments		! rowspan="2" class="unsortable" \|other comments
	! colspan="8" \|Degrees of the mode ~~LMLSLMLSL~~		! colspan="8" \|Degrees of the mode LmLsLmLsL
	\|-		\|-
	!1!!2!!3!!4!!5 !!6 !! 7!!8		!1!!2!!3!!4!!5 !!6 !! 7!!8

Fredg999: Terms, step label casing, misc. edits

2024-08-12T16:33:16Z

Terms, step label casing, misc. edits

Show changes