Orgonia: Difference between revisions
Cmloegcmluin (talk | contribs) add unchanged-intervals along with eigenmonzo, per prior agreement on Xenwiki Work Group |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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* [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)<sup>1/5</sup>, which is 1.679 cents, and the [[5-limit]] just. | * [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)<sup>1/5</sup>, which is 1.679 cents, and the [[5-limit]] just. | ||
{{ | {{Optimal ET sequence|legend=1| 15, 19, 22, 37, 41, 89, 111, 130, 152, 282 }} | ||
[[Complexity spectrum]]: 4/3, 11/8, 12/11, 5/4, 8/7, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/11 | [[Complexity spectrum]]: 4/3, 11/8, 12/11, 5/4, 8/7, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/11 | ||
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[[POTE generator]]: ~77/64 = 323.372 | [[POTE generator]]: ~77/64 = 323.372 | ||
{{ | {{Optimal ET sequence|legend=1| 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc }} | ||
==== Oregon ==== | ==== Oregon ==== | ||
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POTE generator: ~6/5 = 326.139 | POTE generator: ~6/5 = 326.139 | ||
Optimal | {{Optimal ET sequence|legend=1| 7, 11, 59b, 70bc, 81bcd, 92bcd }} | ||
===== Orca ===== | ===== Orca ===== | ||
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POTE generator: ~6/5 = 326.644 | POTE generator: ~6/5 = 326.644 | ||
Optimal | {{Optimal ET sequence|legend=1| 7, 11, 92bcd, 103bcd }} | ||
===== Ork ===== | ===== Ork ===== | ||
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POTE generator: ~17/14 = 325.714 | POTE generator: ~17/14 = 325.714 | ||
Optimal | {{Optimal ET sequence|legend=1| 11, 37, 48, 59, 70c }} | ||
[[Category:Orgonia]] | [[Category:Orgonia]] | ||
[[Category:Commatic realms]] | [[Category:Commatic realms]] | ||
Revision as of 16:22, 7 May 2023
Welcome to Orgonia, the commatic realm of the orgonisma, the 11-limit comma 65536/65219!
Orgonismic
Subgroup: 2.3.5.7.11
Comma list: 65536/65219
Mapping:
[⟨1 0 0 2 4]
⟨0 1 0 0 0]
⟨0 0 1 0 0]
⟨0 0 0 3 -2]]
- Eigenmonzo basis (unchanged-interval basis): 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)1/5, which is 1.679 cents, and the 5-limit just.
Optimal ET sequence: 15, 19, 22, 37, 41, 89, 111, 130, 152, 282
Complexity spectrum: 4/3, 11/8, 12/11, 5/4, 8/7, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/11
Subgroup temperaments
Orgone
Subgroup: 2.7.11
Comma list: 65536/65219
Sval mapping: [⟨1 2 4], ⟨0 3 -2]]
POTE generator: ~77/64 = 323.372
Optimal ET sequence: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc
Oregon
The subgroup 2.9.15.7.11 is the 11-limit 2*11 subgroup, the largest subgroup of the 11-limit on which 11edo acts like 22edo, in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit porcupine restricted to this subgroup.
Subgroup: 2.9.15.7.11
Comma list: 55/54, 64/63, 100/99
Sval mapping: [⟨1 1 1 5 2], ⟨0 3 4 -3 2]]
POTE generator: ~6/5 = 326.139
Optimal ET sequence: 7, 11, 59b, 70bc, 81bcd, 92bcd
Orca
Subgroup: 2.9.15.7.11.17
Comma list: 55/54, 64/63, 100/99, 85/84
Sval mapping: [⟨1 1 1 5 2 7], ⟨0 3 4 -3 2 -4]]
POTE generator: ~6/5 = 326.644
Optimal ET sequence: 7, 11, 92bcd, 103bcd
Ork
Subgroup: 2.9.15.7.11.17
Comma list: 99/98, 121/120, 136/135, 256/255
Sval mapping: [⟨1 1 5 2 4 3], ⟨0 8 -4 3 -2 4]]
POTE generator: ~17/14 = 325.714