User:Eliora/Proposed concept names

Surmarvelpyth

Named because the generator fifth is 225/224 sharp of 3/2. Defined as the 311 & 742 temperament to the 19-limit.

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 2926/2925, 4096/4095, 3136/3135, 12376/12375, 5985/5984, 11016/11011

Mapping:

Optimal tuning (CTE): ~675/448 = 709.972

Barium

Named after the 56th element, and tempers out the [-225 224 -56] comma, which sets 56 syntonic commas equal to the octave.

Subgroup: 2.3.5

Comma list: [-225 24 -56]

Mapping: 56 89 131, 0 -1 -4

Mapping generators: ~81/80, ~3/2

Optimal tuning (CTE): ~3/2 = 701.938

Vals: 56, 224, 2072, 1848, 2296, 1624, 448, 3920, 4144, 3696, 2520

7-limit

Subgroup: 2.3.5.7

Comma list: [ -12 29 -11 -3], [  47 -7  -7 -7]

Mapping: 56 56 -1 321, 0 1 4 5

Mapping generators: ~81/80, ~3/2

Optimal tuning (CTE): ~3/2 = 701.943

Vals: 224, 1848, 2072

Syntose

As opposed to barium, this one does not have a stack of syntonic commas close at the octave. Defined as 56 & 279 using maximal evenness method and continued fraction search.

Protactinium

Defined as a 364 & 1547 temperament, has a period of 91, hence named after the 91st element.

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 4096/4095, 91125/91091, 2912000/2910897, 369754/369603

Mapping: 91 91 371 149 581 390, 0 1 -3 -2 -5 -1

Mapping generators: ~1728/1715, ~3/2

Optimal tuning (CTE): ~3/2 = 702.020c

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 4096/4095, 14400/14399, 42500/42471, 75735/75712, 2100875/2100384

Mapping: 91 91 371 149 581 390 159, 0 1 -3 -2 -5 -1 4

Mapping generators: ~3773/3744, ~3/2

Optimal tuning (CTE): ~3/2 = 702.027c

Oganesson

Reserved for a temp with period 118 and a 13/8 as the generator