User:Eliora/Proposed concept names: Difference between revisions
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== Leaves == | == Leaves == | ||
Defined as the 323 & 2023 temperament | Defined as the 323 & 2023 temperament in the 17-limit. Originally intended to be no-11, Eliora later included the 11th harmonic. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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Vals: 323, 1700, 2023 | Vals: 323, 1700, 2023 | ||
=== | === 13-limit === | ||
10 generators map to 13/11. | |||
Subgroup: 2.3.5.7.13 | Subgroup: 2.3.5.7.13 | ||
Comma list: 1990656/1990625, 3502727631/3500000000, 134521003125/134296804096 | Comma list: 1990656/1990625, 3502727631/3500000000, 134521003125/134296804096 | ||
Sval mapping: | Sval mapping: 17 10 31 9 106 98, 0 14 7 32 -39 -29 | ||
Sval maping generators: ~25/24, ~1024/975 | Sval maping generators: ~25/24, ~1024/975 | ||
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Optimal tuning (CTE): ~1024/975 = ... | Optimal tuning (CTE): ~1024/975 = ... | ||
=== | === 17-limit === | ||
2 generators correspond to 17/13. | |||
Subgroup: | Subgroup: | ||
Comma list: | Comma list: | ||
Sval mapping: 17 10 31 9 98 107, 0 14 7 32 -29 -31 | Sval mapping: 17 10 31 9 106 98 107, 0 14 7 32 -39 -29 -31 | ||
Sval mapping generators: ~25/24, ~765/728 | Sval mapping generators: ~25/24, ~765/728 | ||
Optimal tuning (CTE): ~765/728 = 85.424 | Optimal tuning (CTE): ~765/728 = 85.424 | ||
== Lamina == | |||
Leaves temperament in the 51L 1s 1|1 scale has a meantone fifth which is flat of 17edo fifth by a leaves' reduced generator. Lamina takes the said fifth and uses it as a generator. Name comes from the flat surface that makes up the texture of a leaf. Defined as 33 & 323 in the 17-limit, and with step size difference of around JND it can be treated as a barely noticeable well temperament for [[33edo]]. | |||
The fifth reaches 13/11 in 10 steps, just as generator of lamina does. In addition, 21/16 is reached in 8 steps, 7/5 is reached in 13 steps, 16/15 is reached in 21 steps. | |||
=== Grand lamina === | |||
Grand lamina is defined as 257 & 2023, and it is a metatemperament for lamina, with both having the same relationships in the 33-note MOS. | |||
== Tritonopod == | == Tritonopod == | ||
Revision as of 17:51, 3 January 2023
Pseudovishnuzma
Comma: 6106906624/6103515625
Name reasoning: The denominator is the same as for vishnuzma, numerator is close, yet it's different.
Temperaments:
Rank 2: 1261 & 1789 (2.5.7.11.13), 1236 & 764, 1236 & 1084, 1236 & 441, 764 & 1084, 1236 & 87
Major Arcana JI scale (detempering of 22edo)
A Factor 9-Grid style detempering, where in the first octave which goes from A = 432 Hz to A = 864 Hz all frequency values are integers.
| Step | Card | Frequency | JI ratio |
|---|---|---|---|
| 0 | The Fool | 432 | 1/1 |
| 1 | 448 | ||
| 2 | 464 | ||
| 3 | 486 | ||
| 4 | 495 | ||
| 5 | 504 | 7/6 | |
| 6 | 513 | 19/16 | |
| 7 | 540 | ||
| 8 | 558 | ||
| 9 | 576 | ||
| 10 | 594 | ||
| 11 | 612 | ||
| 12 | 630 | ||
| 13 | 648 | ||
| 14 | 672 | ||
| 15 | 696 | ||
| 16 | 720 | ||
| 17 | 744 | ||
| 18 | 768 | ||
| 19 | 792 | ||
| 20 | 816 | ||
| 21 | 840 | ||
| 22 | 864 | 2/1 |
Thulium
Period-69 temperament conceptualized as having a period of 100/99 and a generator of 3/2. Conceptualized as the 759(some kind of val) & 7797 temperament.
Nuclear matter
Defined as the 22 & 69 temperament, and the comma in the 5-limit is [-41, 1, 17⟩. The name comes from the fact that nuclear matter density is 4.1 * 10^17 kg/m^3.
Subgroup: 2.3.5
Comma list: [-41, 1, 17⟩
Optimal tuning (CTE): ~5/4
Vals: 22, 69
Berkelium (two varieties)
A remarkable high-limit temperament, extended as high as the 29-limit owing to the fact that both 388edo and 2619edo are consistent that high. Named after the 97th element.
Variety 1: 388 & 2619
Subgroup: 2.3.5.7.11.13
Comma list: 4375/4374, 405769/405504, 1063348/1063125, ...
Mapping generators: ~144/143, ~3/2
Optimal tuning (CTE): ~3/2 = 701.945
EDOs: 388, 2619, ...
Variety 2: 388 & 3395
...
Point Zero Seven
A meantone version of sextilififths that's quite bad at JI. Named because the generator is 7\100, and since the name sounds like an alcohol percentage, it corresponds to the "drunken and imprecise feel" of the badness of JI of the scale.
Subgroup: 2.3.5.7
Comma list: 81/80, 121500/117649
Mapping: [1 2 4 4], [0 -6 -24 -17]
Optimal tuning (CTE): ~21/20 = 83.888
Vals: 14, 43, 100
Leaves
Defined as the 323 & 2023 temperament in the 17-limit. Originally intended to be no-11, Eliora later included the 11th harmonic.
Subgroup: 2.3.5.7
Comma list: -21 11 10 -7, 31 28 -24 -7
Mapping: 17 10 31 9, 0 14 7 32
Mapping generators: ~25/24, ~6125/5832
Optimal tuning (CTE): ~6125/5832 = 85.427
Vals: 323, 1700, 2023
13-limit
10 generators map to 13/11.
Subgroup: 2.3.5.7.13
Comma list: 1990656/1990625, 3502727631/3500000000, 134521003125/134296804096
Sval mapping: 17 10 31 9 106 98, 0 14 7 32 -39 -29
Sval maping generators: ~25/24, ~1024/975
Optimal tuning (CTE): ~1024/975 = ...
17-limit
2 generators correspond to 17/13.
Subgroup:
Comma list:
Sval mapping: 17 10 31 9 106 98 107, 0 14 7 32 -39 -29 -31
Sval mapping generators: ~25/24, ~765/728
Optimal tuning (CTE): ~765/728 = 85.424
Lamina
Leaves temperament in the 51L 1s 1|1 scale has a meantone fifth which is flat of 17edo fifth by a leaves' reduced generator. Lamina takes the said fifth and uses it as a generator. Name comes from the flat surface that makes up the texture of a leaf. Defined as 33 & 323 in the 17-limit, and with step size difference of around JND it can be treated as a barely noticeable well temperament for 33edo.
The fifth reaches 13/11 in 10 steps, just as generator of lamina does. In addition, 21/16 is reached in 8 steps, 7/5 is reached in 13 steps, 16/15 is reached in 21 steps.
Grand lamina
Grand lamina is defined as 257 & 2023, and it is a metatemperament for lamina, with both having the same relationships in the 33-note MOS.
Tritonopod
Period-35, 17 generators are equal to 7/5, 18 generators are equal to 10/7.
Possibly rank-3?
Playing cards
Work in progress