User:Eliora/Proposed concept names: Difference between revisions

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== Prequartismic ==
== Prequartismic ==
Named because 3125edo was the only one confirmed for tempering out the quartisma before it's discovery as significance of the difference between 5 33/32s and 7/6. Defined as the 1259 & 3125 temperament.
Named because 3125edo was the only one confirmed for tempering out the quartisma before it's discovery as significance of the difference between 5 33/32s and 7/6. Defined as the 1259e & 3125 temperament, but in terms of patent vals it can also be described as 3125 & 4991 or 3125 & 1866.


== Mercury ==
Defined as 720 & 1600, and named after the 80th element.
Subgroup: 2.3.5
Comma list: {{monzo|-1377 400 320}}
Mapping: [{{val|80 1 343}}, {{val|0 4 -5}}]
Mapping generators: {{monzo|-568 165 132}}, {{monzo|142 -41 -33}}
Optimal tuning (CTE): ~{{monzo|142 -41 -33}} = 471.738
=== 7-limit ===
Subgroup: 2.3.5.7
Comma list: 31528360107421875/31525197391593472, 3671492030322070514237964288/3666984506893654025644140625
Mapping:[{{val| 80 1 343 -27}}, {{val|0 4 -5 8}}]
Mapping generators: ~31637227888/31381059609, ~7381125/5619712
Optimal tuning (CTE): ~7381125/5619712 = 471.734
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 9801/9800, 928760463360/928426965851, 68116944363978752/68116827392578125
Comma list: [24, -6, 0, 1, -5⟩, [-1, 4, 11, -11, 0⟩, [-19 -25 14  13 -3⟩
 
Mapping:[{{val|80 1 343 -27 434}}, {{val|0 4 -5 8 5}}]
 
Mapping generators: ~262144/259875, ~2278125/1734656
 
Optimal tuning (CTE): ~2278125/1734656 = 471.734
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 9801/9800, 4100625/4100096, 14236560/14235529, 143327232/143286143


Mapping: [{{val|80 1 343 -27 434 13}}, {{val|0 4 -5 8 5 9}}]
Mapping: 1 -63 -39 -62 68, 0 1452 929 1457 -1451


Mapping generators: ~77760/77077, ~130/99
Optimal tuning (CTE): ~64/33 = 1146.624


Optimal tuning (CTE): ~130/99 = 471.734
Vals: 1259e, 1866, 3125, 4384e, 4991, 6250e, 8116d, 7509ee, 9375e, 11241de

Revision as of 19:55, 22 September 2022

Prequartismic

Named because 3125edo was the only one confirmed for tempering out the quartisma before it's discovery as significance of the difference between 5 33/32s and 7/6. Defined as the 1259e & 3125 temperament, but in terms of patent vals it can also be described as 3125 & 4991 or 3125 & 1866.

Subgroup: 2.3.5.7.11

Comma list: [24, -6, 0, 1, -5⟩, [-1, 4, 11, -11, 0⟩, [-19 -25 14  13 -3⟩

Mapping: 1 -63 -39 -62 68, 0 1452 929 1457 -1451

Optimal tuning (CTE): ~64/33 = 1146.624

Vals: 1259e, 1866, 3125, 4384e, 4991, 6250e, 8116d, 7509ee, 9375e, 11241de

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