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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)
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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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