Shibboleth family: Difference between revisions

Revision as of 17:17, 6 May 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The shibboleth family tempers out the shibboleth comma, 1953125/1889568.

Temperaments discussed elsewhere include:

superthird, {245/243, 78125/76832} → Sensamagic clan #Superthird

Shibboleth

Subgroup: 2.3.5

Comma list: 1953125/1889568

Mapping: [⟨1 4 5], ⟨0 -9 -10]]

Optimal tunings:

CTE: ~2 = 1\1, ~6/5 = 321.773
POTE: ~2 = 1\1, ~6/5 = 321.852

Optimal ET sequence: 15, 26, 41, 179c, 220c, 261cc, 302cc

Badness: 0.227553

Gilead

Subgroup: 2.3.5.7

Comma list: 126/125, 343/324

Mapping: [⟨1 4 5 6], ⟨0 -9 -10 -12]]

Wedgie: ⟨⟨ 9 10 12 -5 -6 0 ]]

Optimal tunings:

CTE: ~2 = 1\1, ~6/5 = 321.109
POTE: ~2 = 1\1, ~6/5 = 321.423

Optimal ET sequence: 11cd, 15, 41dd, 56dd

Badness: 0.115292

@@ Line 19: / Line 19: @@
 [[Badness]]: 0.227553
-== Superkleismic ==
-{{Main| Superkleismic }}
-The [[S-expression]]-based comma list of superkleismic is {[[875/864|S5/S6]], [[1029/1024|S7/S8]], [[100/99|S10]], [[144/143|S12]](, [[441/440|S21]])}. Through careful observation of the equivalences therein one can derive that a sharpened ~6/5 is the generator as well as the mapping of the full 13-limit.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 875/864, 1029/1024
-{{Mapping|legend=1| 1 4 5 2 | 0 -9 -10 3 }}
-{{Multival|legend=1| 9 10 -3 -5 -30 -35 }}
-[[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1\1, ~6/5 = 321.798
-* [[POTE]]: ~2 = 1\1, ~6/5 = 321.930
-{{Optimal ET sequence|legend=1| 11c, 15, 26, 41 }}
-[[Badness]]: 0.047932
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 100/99, 245/242, 385/384
-Mapping: {{mapping| 1 4 5 2 4 | 0 -9 -10 3 -2 }}
-Optimal tunings:
-* CTE: ~2 = 1\1, ~6/5 = 321.815
-* POTE: ~2 = 1\1, ~6/5 = 321.847
-Optimal ET sequence: {{Optimal ET sequence| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}
-Badness: 0.025659
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 100/99, 105/104, 144/143, 245/242
-Mapping: {{mapping| 1 4 5 2 4 8 | 0 -9 -10 3 -2 -16 }}
-Optimal tunings:
-* CTE: ~2 = 1\1, ~6/5 = 321.986
-* POTE: ~2 = 1\1, ~6/5 = 321.994
-Optimal ET sequence: {{Optimal ET sequence| 11cf, 15, 26, 41 }}
-Badness: 0.021478
 == Gilead ==

Shibboleth family: Difference between revisions

Revision as of 17:17, 6 May 2025

Shibboleth

Gilead

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