Subgroup temperaments - Revision history

Overthink: /* Sburb */ cent value

2026-06-02T17:45:59Z

Sburb: cent value

← Older revision		Revision as of 17:45, 2 June 2026
Line 165:		Line 165:

	===== Sburb =====		===== Sburb =====
	This temperament sets the 413th harmonic (~~octave-reduced~~) to the diminished seventh.		This temperament sets the [[octave reduction\|octave-reduced]] 413th harmonic (413/256, 827.998{{c}}) to the diminished seventh.

	Subgroup: 2.3.7.23.25.41.59		Subgroup: 2.3.7.23.25.41.59

2026-06-02T04:45:12Z

Novisept

← Older revision		Revision as of 04:45, 2 June 2026
Line 317:		Line 317:

	=== Novisept ===		=== Novisept ===
	Novisept is generated by a one-cent-flat 9/7, such that stacking 5 of them gives you 7/4.		Novisept is generated by a one-cent-flat 9/7, such that stacking 5 of them gives you 7/4. It can be formed by doubling both generator and period of [[gizzard]].

	[[Subgroup]]: 2.9.7.13.17		[[Subgroup]]: 2.9.7.13.17

2026-06-02T03:42:54Z

Baldi: revert change for now (see talk)

← Older revision		Revision as of 03:42, 2 June 2026
Line 71:		Line 71:
	[[Support]]ing [[ET]]s: {{Optimal ET sequence\|47, 65f, 112, 159, 206, 253}}		[[Support]]ing [[ET]]s: {{Optimal ET sequence\|47, 65f, 112, 159, 206, 253}}

	=== ~~Baldi~~ ===		=== Baldy ===
	{{See also\|Schismatic family #Garibaldi}}		{{See also\|Schismatic family #Garibaldi}}
	{{See also\|No-threes subgroup temperaments #Frostburn}}		{{See also\|No-threes subgroup temperaments #Frostburn}}

	~~Baldi~~ results from taking every other generator of the [[garibaldi]] temperament. One of the best extension is 2.9.5.7.13 subgroup with mapping 13/8 to +10 whole tones, as well as the cassandra temperament.		Baldy results from taking every other generator of the [[garibaldi]] temperament. One of the best extension is 2.9.5.7.13 subgroup with mapping 13/8 to +10 whole tones, as well as the cassandra temperament.

	[[Subgroup]]: 2.9.5.7		[[Subgroup]]: 2.9.5.7

2026-06-02T02:04:40Z

2.9.7.13.17 subgroup

← Older revision		Revision as of 02:04, 2 June 2026
Line 71:		Line 71:
	[[Support]]ing [[ET]]s: {{Optimal ET sequence\|47, 65f, 112, 159, 206, 253}}		[[Support]]ing [[ET]]s: {{Optimal ET sequence\|47, 65f, 112, 159, 206, 253}}

	=== ~~Baldy~~ ===		=== Baldi ===
	{{See also\|Schismatic family #Garibaldi}}		{{See also\|Schismatic family #Garibaldi}}
	{{See also\|No-threes subgroup temperaments #Frostburn}}		{{See also\|No-threes subgroup temperaments #Frostburn}}

	~~Baldy~~ results from taking every other generator of the [[garibaldi]] temperament. One of the best extension is 2.9.5.7.13 subgroup with mapping 13/8 to +10 whole tones, as well as the cassandra temperament.		Baldi results from taking every other generator of the [[garibaldi]] temperament. One of the best extension is 2.9.5.7.13 subgroup with mapping 13/8 to +10 whole tones, as well as the cassandra temperament.

	[[Subgroup]]: 2.9.5.7		[[Subgroup]]: 2.9.5.7
Line 317:		Line 317:

	=== Novisept ===		=== Novisept ===
	Novisept is generated by a one-cent-flat 9/7.		Novisept is generated by a one-cent-flat 9/7, such that stacking 5 of them gives you 7/4.

	[[Subgroup]]: 2.9.7.13.17		[[Subgroup]]: 2.9.7.13.17

2026-06-02T01:32:22Z

Sister

← Older revision		Revision as of 01:32, 2 June 2026
Line 316:		Line 316:
	== 2.9.7.13.17 subgroup ==		== 2.9.7.13.17 subgroup ==

	=== ~~Sister~~ ===		=== Novisept ===
	~~Sister (named due to being "double, double" [[wizard]] after the three sisters in Macbeth), doubles the period and generator of [[gizzard]] and~~ is generated by a one-cent-flat 9/7.		Novisept is generated by a one-cent-flat 9/7.

	[[Subgroup]]: 2.9.7.13.17		[[Subgroup]]: 2.9.7.13.17

2026-06-02T01:29:00Z

Composite subgroup temperaments

← Older revision		Revision as of 01:29, 2 June 2026
Line 313:		Line 313:

	Scales: [[penta5]], [[penta8]], [[penta11]], [[penta19]]		Scales: [[penta5]], [[penta8]], [[penta11]], [[penta19]]

			== 2.9.7.13.17 subgroup ==

			=== Sister ===
			Sister (named due to being "double, double" [[wizard]] after the three sisters in Macbeth), doubles the period and generator of [[gizzard]] and is generated by a one-cent-flat 9/7.

			[[Subgroup]]: 2.9.7.13.17

			[[Comma list]]: 729/728, 442/441, 833/832

			{{Mapping\|legend=2\| 1 1 1 -1 3\| 0 6 5 13 3 }}

			[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~9/7 = 433.836

	== 2.9.11 subgroup ==		== 2.9.11 subgroup ==

2026-05-30T19:51:28Z

2.….19/7.… subgroups: add a temperament

@@ Line 1,669: / Line 1,669: @@
 [[Subgroup]]: 2.3.19/7
-[[Comma list]]: [[57/56]] ({{monzo| -3 1 1 }})
+[[Comma list]]: [[57/56]] ({{Monzo| -3 1 1 }})
 {{Mapping|legend=2| 1 0 3 | 0 1 -1 }}
@@ Line 1,683: / Line 1,683: @@
 [[Badness]] (Sintel): 0.082
 == 3/2.5/2.… subgroups ==

2026-05-29T20:30:15Z

← Older revision		Revision as of 20:30, 29 May 2026
Line 137:		Line 137:

	{{Optimal ET sequence\|legend=1\| 6, 23def, 29f, 35, 41, 47 }}		{{Optimal ET sequence\|legend=1\| 6, 23def, 29f, 35, 41, 47 }}

			== 2.3.25 subgroup ==

			=== Shrub ===
			This is a restriction of diaschismic which omits the tritone to produce a diatonic scale. True to its name, it generates a [[shrubmajor]] third (~425c) in quarter-comma tuning.

			Subgroup: 2.3.25

			Edo join: 17 & 12

			Comma list: [[2048/2025]]

			{{Mapping\|legend=2\| 1 1 7\| 0 1 -4}}

			Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.136

			==== 2.3.23.25.41 subgroup ====
			''See also: [[Reversed meantone]]''

			Edo join: 17 & 12

			Comma list: 2048/2025, 576/575, 82/81

			{{Mapping\|legend=2\| 1 1 1 7 3\| 0 1 6 -4 4}}

			Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.264

			===== Sburb =====
			This temperament sets the 413th harmonic (octave-reduced) to the diminished seventh.

			Subgroup: 2.3.7.23.25.41.59

			Edo join: 17 & 12

			Comma list: 64/63, 225/224, 162/161, 82/81, 177/175

			{{Mapping\|legend=2\| 1 1 4 1 7 3 10\| 0 1 -2 6 -4 4 -7}}

			Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 706.387

	== 2.9.5.11 subgroup ==		== 2.9.5.11 subgroup ==

2026-05-18T23:48:02Z

Tridecimal guanyintet: note

← Older revision		Revision as of 23:48, 18 May 2026
Line 1,052:		Line 1,052:

	==== Tridecimal guanyintet ====		==== Tridecimal guanyintet ====
	Guanyintet can extend to the 13th harmonic by the equivalences ([[12/11]])<sup>3</sup> = [[13/10]] and ([[15/14]])<sup>3</sup> = [[16/13]], therefore tempering out {S11/S12/S14/S15}. [[40edo]] remains an excellent tuning.		Guanyintet can extend to the 13th harmonic by the equivalences ([[12/11]])<sup>3</sup> = [[13/10]] and ([[15/14]])<sup>3</sup> = [[16/13]], therefore tempering out {S11/S12/S14/S15}. However, note that it is not supported by the 31 & 53 orwell extension dubbed "tridecimal orwell", but instead the less accurate [[winston]] (22f & 31), as orwell prefers slightly sharper tunings than guanyintet. [[40edo]] remains an excellent tuning.

	[[Subgroup]]: 2.5.7/3.11/3.13		[[Subgroup]]: 2.5.7/3.11/3.13

2026-05-18T16:06:11Z

Tridecimal guanyintet

← Older revision		Revision as of 16:06, 18 May 2026
Line 1,052:		Line 1,052:

	==== Tridecimal guanyintet ====		==== Tridecimal guanyintet ====
	Guanyintet can extend to the 13th harmonic by the equivalences ([[12/11]])<sup>3</sup> = [[13/10]] and ([[15/14]])<sup>3</sup> = [[16/13]]. [[40edo]] remains an excellent tuning.		Guanyintet can extend to the 13th harmonic by the equivalences ([[12/11]])<sup>3</sup> = [[13/10]] and ([[15/14]])<sup>3</sup> = [[16/13]], therefore tempering out {S11/S12/S14/S15}. [[40edo]] remains an excellent tuning.

	[[Subgroup]]: 2.5.7/3.11/3.13		[[Subgroup]]: 2.5.7/3.11/3.13