User:VIxen/Temperament proposals - Revision history

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T18:37:21Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 18:37, 7 May 2023
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	Mapping generators: ~2, ~3, ~266/165		Mapping generators: ~2, ~3, ~266/165

	{{~~Val list~~\|legend=1\| 29g, 74g, 103h, 132degh, 222cdeefgh, 251eh, 354, 486g, 737, 840 }}		{{Optimal ET sequence\|legend=1\| 29g, 74g, 103h, 132degh, 222cdeefgh, 251eh, 354, 486g, 737, 840 }}

	[[Badness]]: 1.78 × 10<sup>-3</sup>		[[Badness]]: 1.78 × 10<sup>-3</sup>

VIxen: /* Kibi */ fixed the TE error mention in the preamble

2022-06-26T14:08:05Z

Kibi: fixed the TE error mention in the preamble

← Older revision		Revision as of 14:08, 26 June 2022
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	Extensions to higher limits, perhaps 31-limit at least, seem possible but will require using blocks of 82 notes corresponding to the 103h val.		Extensions to higher limits, perhaps 31-limit at least, seem possible but will require using blocks of 82 notes corresponding to the 103h val.

	Data for equave 2/1 is provided below for compatibility. The TE error is small enough - 0.~~012~~ cents/octave - but the complexity of most intervals involving powers of 2 is high like in ennealimmal, which makes the badness high.		Data for equave 2/1 is provided below for compatibility. The TE error is small enough - 0.011 cents/octave - but the complexity of most intervals involving powers of 2 is high like in ennealimmal, which makes the badness high.

	Subgroup: 2.3.5.7.11.13.17.19		Subgroup: 2.3.5.7.11.13.17.19

VIxen: /* Kibi */ forgot to change to 103h at one place

2022-06-26T14:01:09Z

Kibi: forgot to change to 103h at one place

← Older revision		Revision as of 14:01, 26 June 2022
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	In the 33/19.2.3.5.7.11.13.17 basis of the full 19-limit subgroup, it is q23 & q82 & q282 (with equave 2/1, it is 29g & 103h & 354), and a Fokker block of 23 notes per equave is available, corresponding to the [[29edo\|29g]] val, although it is complex - perhaps the simplest of the highly available intervals is 7/5 - with a preference for open harmonies, and just about enough to contain the chord of prime harmonics (1:2:3:5:7:11:13:17:19) on one root per equave.		In the 33/19.2.3.5.7.11.13.17 basis of the full 19-limit subgroup, it is q23 & q82 & q282 (with equave 2/1, it is 29g & 103h & 354), and a Fokker block of 23 notes per equave is available, corresponding to the [[29edo\|29g]] val, although it is complex - perhaps the simplest of the highly available intervals is 7/5 - with a preference for open harmonies, and just about enough to contain the chord of prime harmonics (1:2:3:5:7:11:13:17:19) on one root per equave.

	Extensions to higher limits, perhaps 31-limit at least, seem possible but will require using blocks of 82 notes corresponding to the ~~103p~~ val.		Extensions to higher limits, perhaps 31-limit at least, seem possible but will require using blocks of 82 notes corresponding to the 103h val.

	Data for equave 2/1 is provided below for compatibility. The TE error is small enough - 0.012 cents/octave - but the complexity of most intervals involving powers of 2 is high like in ennealimmal, which makes the badness high.		Data for equave 2/1 is provided below for compatibility. The TE error is small enough - 0.012 cents/octave - but the complexity of most intervals involving powers of 2 is high like in ennealimmal, which makes the badness high.

VIxen: kibi data fixed

2022-06-26T13:58:20Z

kibi data fixed

← Older revision		Revision as of 13:58, 26 June 2022
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	= Not logged in the main namespace =		= Not logged in the main namespace =

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	Subgroup: 2.3.5.7.11.13.17.19		Subgroup: 2.3.5.7.11.13.17.19

	[[Comma list]]: 969/968, 1275/1274, 1521/1520, ~~4120~~/4199, 6175/6171		[[Comma list]]: 969/968, 1275/1274, 1521/1520, 4200/4199, 6175/6171

	[[Mapping]]: [{{val\| 1 0 23 29 26 23 36 15 }}, {{val\| 0 1 0 0 1 0 -1 -2 }}, {{val\| 0 0 -30 -38 -35 -28 -44 -11 }}]		[[Mapping]]: [{{val\| 1 0 23 29 26 23 36 19 }}, {{val\| 0 1 0 0 1 0 -1 2 }}, {{val\| 0 0 -30 -38 -35 -28 -44 -26 }}]

	Mapping generators: ~2, ~3, ~~~931~~/~~578~~		Mapping generators: ~2, ~3, ~266/165

	{{Val list\|legend=1\| 29g, ~~74gh~~, ~~103~~, ~~132deg~~, ~~251e~~, ~~325deg~~, 354, 737 }}		{{Val list\|legend=1\| 29g, 74g, 103h, 132degh, 222cdeefgh, 251eh, 354, 486g, 737, 840 }}

	[[Badness]]: 3.19 × 10<sup>-3</sup>		[[Badness]]: 1.78 × 10<sup>-3</sup>

	= Logged in the main namespace =		= Logged in the main namespace =

VIxen: fix comma basis; other data corrections are coming

2022-06-26T13:48:55Z

fix comma basis; other data corrections are coming

← Older revision		Revision as of 13:48, 26 June 2022
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	This temperament is heavily tailored towards 19-limit use with the 33/19 equave, inspired by that the smallest 19-limit superparticular is (91/10) × (33/19)<sup>-4</sup>. It was named after minor planet 3319.		This temperament is heavily tailored towards 19-limit use with the 33/19 equave, inspired by that the smallest 19-limit superparticular is (91/10) × (33/19)<sup>-4</sup>. It was named after minor planet 3319.

	In the 33/19.2.3.5.7.11.13.17 basis of the full 19-limit subgroup, it is q23 & q82 & q282 (with equave 2/1, it is 29g & ~~103p~~ & 354), and a Fokker block of 23 notes per equave is available, corresponding to the [[29edo\|29g]] val, although it is complex - perhaps the simplest of the highly available intervals is 7/5 - with a preference for open harmonies, and just about enough to contain the chord of prime harmonics (1:2:3:5:7:11:13:17:19) on one root per equave.		In the 33/19.2.3.5.7.11.13.17 basis of the full 19-limit subgroup, it is q23 & q82 & q282 (with equave 2/1, it is 29g & 103h & 354), and a Fokker block of 23 notes per equave is available, corresponding to the [[29edo\|29g]] val, although it is complex - perhaps the simplest of the highly available intervals is 7/5 - with a preference for open harmonies, and just about enough to contain the chord of prime harmonics (1:2:3:5:7:11:13:17:19) on one root per equave.

	Extensions to higher limits, perhaps 31-limit at least, seem possible but will require using blocks of 82 notes corresponding to the 103p val.		Extensions to higher limits, perhaps 31-limit at least, seem possible but will require using blocks of 82 notes corresponding to the 103p val.
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	Subgroup: 2.3.5.7.11.13.17.19		Subgroup: 2.3.5.7.11.13.17.19

	[[Comma list]]: 1275/1274, ~~1575/1573, 2601~~/~~2600~~, ~~2720~~/~~2717~~, ~~4394~~/~~4389~~		[[Comma list]]: 969/968, 1275/1274, 1521/1520, 4120/4199, 6175/6171

	[[Mapping]]: [{{val\| 1 0 23 29 26 23 36 15 }}, {{val\| 0 1 0 0 1 0 -1 -2 }}, {{val\| 0 0 -30 -38 -35 -28 -44 -11 }}]		[[Mapping]]: [{{val\| 1 0 23 29 26 23 36 15 }}, {{val\| 0 1 0 0 1 0 -1 -2 }}, {{val\| 0 0 -30 -38 -35 -28 -44 -11 }}]

VIxen: force TOC

2022-06-26T13:21:08Z

force TOC

← Older revision		Revision as of 13:21, 26 June 2022
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	=== Kibi ===		== Kibi ==

	This temperament is heavily tailored towards 19-limit use with the 33/19 equave, inspired by that the smallest 19-limit superparticular is (91/10) × (33/19)<sup>-4</sup>. It was named after minor planet 3319.		This temperament is heavily tailored towards 19-limit use with the 33/19 equave, inspired by that the smallest 19-limit superparticular is (91/10) × (33/19)<sup>-4</sup>. It was named after minor planet 3319.

VIxen: force TOC

2022-06-26T13:18:35Z

force TOC

← Older revision		Revision as of 13:18, 26 June 2022
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VIxen at 13:08, 26 June 2022

2022-06-26T13:08:07Z

← Older revision		Revision as of 13:08, 26 June 2022
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	~~=== [[User:VIxen/Sandbox#Rishi\|Rishi]] =~~==

	~~When this temperament was proposed, [[Diaschismic_family#Sruti\|sruti]] was its only known rank-2 subtemperament, and rishis (sages) are believed to have created shruti texts.~~		=== Kibi ===

	~~Preferred~~ equave ~~and subgroup: 3~~/~~2.2.5.7~~.11.13		This temperament is heavily tailored towards 19-limit use with the 33/19 equave, inspired by that the smallest 19-limit superparticular is (91/10) × (33/19)<sup>-4</sup>. It was named after minor planet 3319.

	~~Vals:~~ [[~~20edf~~\|~~q20f~~]], ~~[[34edf\|q34]]~~, ~~q269~~		In the 33/19.2.3.5.7.11.13.17 basis of the full 19-limit subgroup, it is q23 & q82 & q282 (with equave 2/1, it is 29g & 103p & 354), and a Fokker block of 23 notes per equave is available, corresponding to the [[29edo\|29g]] val, although it is complex - perhaps the simplest of the highly available intervals is 7/5 - with a preference for open harmonies, and just about enough to contain the chord of prime harmonics (1:2:3:5:7:11:13:17:19) on one root per equave.

	~~=== [[User:VIxen/Sandbox#Skald\|Skald]] ===~~		Extensions to higher limits, perhaps 31-limit at least, seem possible but will require using blocks of 82 notes corresponding to the 103p val.

	The ~~name~~ is ~~a portmanteau~~ of ~~[[skeetsma]] and [[kalisma]]~~, ~~with the Old Norse theme that's common in~~ the ~~naming of kalismic temperaments~~.		Data for equave 2/1 is provided below for compatibility. The TE error is small enough - 0.012 cents/octave - but the complexity of most intervals involving powers of 2 is high like in ennealimmal, which makes the badness high.

	~~Preferred equave and subgroup~~: 3/2.2.5.7.11.13		Subgroup: 2.3.5.7.11.13.17.19

	~~Vals:~~ [[~~34edf\|q34~~]], ~~q131~~, ~~q138~~		[[Comma list]]: 1275/1274, 1575/1573, 2601/2600, 2720/2717, 4394/4389

	~~===~~ [[~~User~~:~~VIxen/Sandbox#Gersemi~~\|~~Gersemi]~~] ~~===~~		[[Mapping]]: [{{val\| 1 0 23 29 26 23 36 15 }}, {{val\| 0 1 0 0 1 0 -1 -2 }}, {{val\| 0 0 -30 -38 -35 -28 -44 -11 }}]

	~~Named after one of Odr's and Freya's daughters. In 11-limit~~, ~~it tempers out one comma of [[Kalismic temperaments#Odin\|odin]] (9801/9800) and one of [[Breed family#Freya\|freya]] (41503~~/~~41472). There's also a word play on the semi- prefix that hints at the split of the octave in halves.~~		Mapping generators: ~2, ~3, ~931/578

	~~Other name ideas are possible. Rank-2 subtemperaments include hemiennealimmal~~, ~~wizard~~, ~~and octowerck.~~		{{Val list\|legend=1\| 29g, 74gh, 103, 132deg, 251e, 325deg, 354, 737 }}

	~~Preferred equave~~: 18/7		[[Badness]]: 3.19 × 10<sup>-3</sup>

	~~Vals: q128, q98(i), q368(i)~~		= Logged in the main namespace =

	Potentially extensible to 23-limit, still looking for the best warts there; q30 and q68 are supported too, but I'm more interested in 23-limit extensions, where 30 notes aren't enough; q226, q338, q466, q564 are supported alternative vals to try in 23-limit, may make a good extension.		[[Kalismic_temperaments #Gersemi\|Gersemi]] ([[Temperament_names #Gersemi\|etymology]])

			[[Kalismic_temperaments #Hnoss\|Hnoss]] ([[Temperament_names #Hnoss\|etymology]])

			[[Kalismic_temperaments #Rishi\|Rishi]] ([[Temperament_names #Rishi\|etymology]])

VIxen: /* Rishi */ q20f is a val of interest

2022-06-21T16:15:47Z

Rishi: q20f is a val of interest

← Older revision		Revision as of 16:15, 21 June 2022
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	Preferred equave and subgroup: 3/2.2.5.7.11.13		Preferred equave and subgroup: 3/2.2.5.7.11.13

	Vals: [[34edf\|q34]], q269~~, q289~~		Vals: [[20edf\|q20f]], [[34edf\|q34]], q269

	=== [[User:VIxen/Sandbox#Skald\|Skald]] ===		=== [[User:VIxen/Sandbox#Skald\|Skald]] ===

VIxen: +links to 34edf

2022-06-21T15:01:45Z

+links to 34edf

← Older revision		Revision as of 15:01, 21 June 2022
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	Preferred equave and subgroup: 3/2.2.5.7.11.13		Preferred equave and subgroup: 3/2.2.5.7.11.13

	Vals: q34, q269, q289		Vals: [[34edf\|q34]], q269, q289

	=== [[User:VIxen/Sandbox#Skald\|Skald]] ===		=== [[User:VIxen/Sandbox#Skald\|Skald]] ===
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	Preferred equave and subgroup: 3/2.2.5.7.11.13		Preferred equave and subgroup: 3/2.2.5.7.11.13

	Vals: q34, q131, q138		Vals: [[34edf\|q34]], q131, q138

	=== [[User:VIxen/Sandbox#Gersemi\|Gersemi]] ===		=== [[User:VIxen/Sandbox#Gersemi\|Gersemi]] ===