User:VIxen/Temperament proposals: Difference between revisions

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=~~== [[User:VIxen/Sandbox#Rishi|Rishi]] ==~~=

= Not logged in the main namespace =

~~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 & 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.

~~=== [[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 103h 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 - 0.011 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]]: 969/968, 1275/1274, 1521/1520, 4200/4199, 6175/6171

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

[[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 }}]

~~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, ~266/165

~~Other name ideas are possible. Rank-2 subtemperaments include hemiennealimmal~~, ~~wizard~~, ~~and octowerck.~~

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

~~Preferred equave~~: 18/7

[[Badness]]: 1.78 × 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]])

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-=== [[User:VIxen/Sandbox#Rishi|Rishi]] ===
+= Not logged in the main namespace =
-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 & 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.
-=== [[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 103h 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 - 0.011 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]]: 969/968, 1275/1274, 1521/1520, 4200/4199, 6175/6171
-=== [[User:VIxen/Sandbox#Gersemi|Gersemi]] ===
+[[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 }}]
-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, ~266/165
-Other name ideas are possible. Rank-2 subtemperaments include hemiennealimmal, wizard, and octowerck.
+{{Optimal ET sequence|legend=1| 29g, 74g, 103h, 132degh, 222cdeefgh, 251eh, 354, 486g, 737, 840 }}
-Preferred equave: 18/7
+[[Badness]]: 1.78 × 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]])