Diaslen - Revision history

Inthar: /* Huntmic (2.3.7.13/5[640/637, 676/675]) */

2025-03-06T23:05:35Z

Huntmic (2.3.7.13/5[640/637, 676/675])

← Older revision		Revision as of 23:05, 6 March 2025
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	The standard untempered 2.3.7 interpretation for diaslen has L = [[9/8]], m = [[49/48]], s = [[64/63]].		The standard untempered 2.3.7 interpretation for diaslen has L = [[9/8]], m = [[49/48]], s = [[64/63]].

	=== ~~Huntmic~~ (2.3.7.13/5[640/637, 676/675]) ===		=== Buzzard (2.3.7.13/5[640/637, 676/675]) ===
	[[~~Huntmic~~]] is an important temperament for diaslen offering an elegant combination of interordinals and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]] and [[676/675]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.		[[Buzzard]] is an important temperament for diaslen offering an elegant combination of interordinals and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]] and [[676/675]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.

	== External links ==		== External links ==

Inthar at 23:04, 6 March 2025

2025-03-06T23:04:40Z

← Older revision		Revision as of 23:04, 6 March 2025
Line 35:		Line 35:
	The standard untempered 2.3.7 interpretation for diaslen has L = [[9/8]], m = [[49/48]], s = [[64/63]].		The standard untempered 2.3.7 interpretation for diaslen has L = [[9/8]], m = [[49/48]], s = [[64/63]].

	=== Huntmic (2.3.7.13/5[640/637]) ===		=== Huntmic (2.3.7.13/5[640/637, 676/675]) ===
	[[Huntmic]] is an important temperament for diaslen offering an elegant combination of interordinals and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.		[[Huntmic]] is an important temperament for diaslen offering an elegant combination of interordinals and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]] and [[676/675]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.

			== External links ==
			* [https://sw3.lumipakkanen.com/scale/LboZJ9YLp 4sC in 53edo tuning]
			* [https://sw3.lumipakkanen.com/scale/Lbo60GpgU 4sR in 53edo tuning]
			* [https://sw3.lumipakkanen.com/scale/LboMdyjGJ 4sL in 53edo tuning]
	[[Category:Rank-3 scales]]		[[Category:Rank-3 scales]]
	[[Category:Aberrismic theory]]		[[Category:Aberrismic theory]]

Inthar at 01:26, 2 December 2024

2024-12-02T01:26:27Z

← Older revision		Revision as of 01:26, 2 December 2024
Line 2:		Line 2:

	== Structure ==		== Structure ==
	The three standard ~~diamech~~ scale patterns, denoted 4sL (LsLsLmLsLsm), 4sC (LmLsLsLmLss), and 4sR (LsLmLsLsLms), may be constructed via [[MOS substitution]], giving [[generator sequence]]s for the three scales:		The three standard diaslen scale patterns, denoted 4sL (LsLsLmLsLsm), 4sC (LmLsLsLmLss), and 4sR (LsLmLsLsLms), may be constructed via [[MOS substitution]], giving [[generator sequence]]s for the three scales:

	{\| class="wikitable"		{\| class="wikitable"
	\|+ ~~Diamech~~ scales as MOS substitution scales		\|+ diaslen scales as MOS substitution scales
	\|-		\|-
	!rowspan=2\| chirality		!rowspan=2\| chirality
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	== Tunings and interpretations ==		== Tunings and interpretations ==
	=== Untempered 2.3.7 ===		=== Untempered 2.3.7 ===
	The standard untempered 2.3.7 interpretation for ~~diamech~~ has L = [[9/8]], m = [[49/48]], s = [[64/63]].		The standard untempered 2.3.7 interpretation for diaslen has L = [[9/8]], m = [[49/48]], s = [[64/63]].

	=== Huntmic (2.3.7.13/5[640/637]) ===		=== Huntmic (2.3.7.13/5[640/637]) ===
	[[Huntmic]] is an important temperament for ~~diamech~~ offering an elegant combination of interordinals and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.		[[Huntmic]] is an important temperament for diaslen offering an elegant combination of interordinals and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.

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

Inthar at 01:10, 2 December 2024

2024-12-02T01:10:05Z

← Older revision		Revision as of 01:10, 2 December 2024
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	'''{{PAGENAME}}''' (also denoted 4s in [[groundfault]]'s [[aberrismic theory]]) is a family of quasi-[[diatonic]] [[scale pattern]]s with [[step signature]] 5L 2m 4s, so named by groundfault who considers [[33edo]]'s L:m:s = 5:2:1 a good tuning for it. The name ''~~diamech~~'' is a blend of ''dia-'' and ~~the~~ [[~~TAMNAMS]] prefix ''mech-'' for [[machinoid~~]]. [[23edo]] is the only [[edo]] without a diatonic fifth that has a 5L 2m ks [[ternary]] scale pattern, namely 5L 2m 4s with L:m:s = 3:2:1.		'''{{PAGENAME}}''' (also denoted 4s in [[groundfault]]'s [[aberrismic theory]]) is a family of quasi-[[diatonic]] [[scale pattern]]s with [[step signature]] 5L 2m 4s, so named by groundfault who considers [[33edo]]'s L:m:s = 5:2:1 a good tuning for it. The name ''diaslen'' is a blend of ''dia-'' and [[slendric]]. [[23edo]] is the only [[edo]] without a diatonic fifth that has a 5L 2m ks [[ternary]] scale pattern, namely 5L 2m 4s with L:m:s = 3:2:1.

	== Structure ==		== Structure ==

Inthar: Inthar moved page Diamech to Diaslen

2024-12-02T01:09:49Z

Inthar moved page Diamech to Diaslen

← Older revision	Revision as of 01:09, 2 December 2024
(No difference)

Fredg999: Internal link

2024-08-12T18:33:14Z

Internal link

← Older revision		Revision as of 18:33, 12 August 2024
Line 1:		Line 1:
	'''{{PAGENAME}}''' (also denoted 4s in [[groundfault]]'s [[aberrismic theory]]) is a family of quasi-[[diatonic]] [[scale pattern]]s with [[step signature]] 5L 2m 4s, so named by groundfault who considers [[33edo]]'s L:m:s = 5:2:1 a good tuning for it. The name ''diamech'' is a blend of ''dia-'' and the [[TAMNAMS]] prefix ''mech-'' for [[machinoid]]. [[23edo]] is the only edo without a diatonic fifth that has a 5L 2m ks [[ternary]] scale pattern, namely 5L 2m 4s with L:m:s = 3:2:1.		'''{{PAGENAME}}''' (also denoted 4s in [[groundfault]]'s [[aberrismic theory]]) is a family of quasi-[[diatonic]] [[scale pattern]]s with [[step signature]] 5L 2m 4s, so named by groundfault who considers [[33edo]]'s L:m:s = 5:2:1 a good tuning for it. The name ''diamech'' is a blend of ''dia-'' and the [[TAMNAMS]] prefix ''mech-'' for [[machinoid]]. [[23edo]] is the only [[edo]] without a diatonic fifth that has a 5L 2m ks [[ternary]] scale pattern, namely 5L 2m 4s with L:m:s = 3:2:1.

	== Structure ==		== Structure ==

Fredg999: Terms, misc. edits

2024-08-12T16:21:21Z

Terms, misc. edits

← Older revision		Revision as of 16:21, 12 August 2024
Line 1:		Line 1:
	'''{{PAGENAME}}''' (also denoted 4s in [[groundfault]]'s [[aberrismic theory]]) is a family of quasi-diatonic ~~ternary~~ scale ~~patterns~~ with [[~~scale~~ signature]] ~~5L2m4s~~, so named by groundfault who considers [[33edo]]'s L:m:s = 5:2:1 a good tuning for it. The name ''diamech'' is a blend of ''dia-'' and the [[TAMNAMS]] prefix ''mech-'' for [[machinoid]]. [[23edo]] is the only edo without a diatonic fifth that has a ~~5L2mks~~ ternary scale pattern, namely ~~5L2m4s~~ with L:m:s = 3:2:1.		'''{{PAGENAME}}''' (also denoted 4s in [[groundfault]]'s [[aberrismic theory]]) is a family of quasi-[[diatonic]] [[scale pattern]]s with [[step signature]] 5L 2m 4s, so named by groundfault who considers [[33edo]]'s L:m:s = 5:2:1 a good tuning for it. The name ''diamech'' is a blend of ''dia-'' and the [[TAMNAMS]] prefix ''mech-'' for [[machinoid]]. [[23edo]] is the only edo without a diatonic fifth that has a 5L 2m ks [[ternary]] scale pattern, namely 5L 2m 4s with L:m:s = 3:2:1.

	== Structure ==		== Structure ==
	The three standard diamech scale patterns, denoted 4sL (LsLsLmLsLsm), 4sC (LmLsLsLmLss), and 4sR (LsLmLsLsLms), may be constructed via [[MOS substitution]], giving [[generator sequence]]s for the three scales:		The three standard diamech scale patterns, denoted 4sL (LsLsLmLsLsm), 4sC (LmLsLsLmLss), and 4sR (LsLmLsLsLms), may be constructed via [[MOS substitution]], giving [[generator sequence]]s for the three scales:
Line 29:		Line 30:
	\|colspan=2\| GS('''L'''+'''s''', '''L'''+'''s''', '''L'''+'''m''')		\|colspan=2\| GS('''L'''+'''s''', '''L'''+'''s''', '''L'''+'''m''')
	\|}		\|}

	== Tunings and interpretations ==		== Tunings and interpretations ==
	=== Untempered 2.3.7 ===		=== Untempered 2.3.7 ===
	The standard untempered 2.3.7 interpretation for diamech has L = [[9/8]], m = [[49/48]], s = [[64/63]].		The standard untempered 2.3.7 interpretation for diamech has L = [[9/8]], m = [[49/48]], s = [[64/63]].

	=== Huntmic (2.3.7.13/5[640/637]) ===		=== Huntmic (2.3.7.13/5[640/637]) ===
	[[Huntmic]] is an important temperament for diamech offering an elegant combination of interordinals and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.		[[Huntmic]] is an important temperament for diamech offering an elegant combination of interordinals and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.

Inthar: /* Huntmic (2.3.7.13/5[640/637]) */

2024-07-18T01:07:13Z

Huntmic (2.3.7.13/5[640/637])

← Older revision		Revision as of 01:07, 18 July 2024
Line 33:		Line 33:
	The standard untempered 2.3.7 interpretation for diamech has L = [[9/8]], m = [[49/48]], s = [[64/63]].		The standard untempered 2.3.7 interpretation for diamech has L = [[9/8]], m = [[49/48]], s = [[64/63]].
	=== Huntmic (2.3.7.13/5[640/637]) ===		=== Huntmic (2.3.7.13/5[640/637]) ===
	[[Huntmic]] is an important temperament for diamech~~, since it elegantly combines semiquartal~~ and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.		[[Huntmic]] is an important temperament for diamech offering an elegant combination of interordinals and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.

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

Inthar: /* Huntmic (2.3.7.13/5[640/637]) */

2024-07-18T00:53:51Z

Huntmic (2.3.7.13/5[640/637])

← Older revision		Revision as of 00:53, 18 July 2024
Line 33:		Line 33:
	The standard untempered 2.3.7 interpretation for diamech has L = [[9/8]], m = [[49/48]], s = [[64/63]].		The standard untempered 2.3.7 interpretation for diamech has L = [[9/8]], m = [[49/48]], s = [[64/63]].
	=== Huntmic (2.3.7.13/5[640/637]) ===		=== Huntmic (2.3.7.13/5[640/637]) ===
	[[Huntmic]] is ~~a particularly elegant~~ temperament for diamech. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.		[[Huntmic]] is an important temperament for diamech, since it elegantly combines semiquartal and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.

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

Inthar: /* Huntmic (2.3.7.13/5[640/637]) */

2024-07-18T00:52:22Z

Huntmic (2.3.7.13/5[640/637])

← Older revision		Revision as of 00:52, 18 July 2024
Line 33:		Line 33:
	The standard untempered 2.3.7 interpretation for diamech has L = [[9/8]], m = [[49/48]], s = [[64/63]].		The standard untempered 2.3.7 interpretation for diamech has L = [[9/8]], m = [[49/48]], s = [[64/63]].
	=== Huntmic (2.3.7.13/5[640/637]) ===		=== Huntmic (2.3.7.13/5[640/637]) ===
	[[Huntmic]] is a particularly elegant temperament for diamech. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, ~~the former tuning~~ has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.		[[Huntmic]] is a particularly elegant temperament for diamech. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.

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