Sensamagic family

(Redirected from Sensigh)

The sensamagic family of rank-3 temperaments tempers out 245/243. For a list of rank-2 temperaments, see Sensamagic clan.

Sensamagic

Subgroup: 2.3.5.7

Comma list: 245/243

Mapping[1 0 0 0], 0 1 1 2], 0 0 2 -1]]

mapping generators: ~2, ~3, ~9/7

Mapping to lattice: [0 1 1 2], 0 0 2 -1]]

Lattice basis:

3/2 length = 0.9644, 9/7 length = 1.0807
Angle (3/2, 9/7) = 86.5288°

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.7424, ~9/7 = 440.9020

[[1 0 0 0, [0 0 1/5 2/5, [0 0 1 0, [0 0 0 1]
eigenmonzo (unchanged-interval) basis: 2.5.7
[[1 0 0 0, [0 1 0 0, [0 5/3 2/3 -2/3, [0 5/3 -1/3 1/3]
eigenmonzo (unchanged-interval) basis: 2.3.7/5

Optimal ET sequence5, 8d, 14c, 17, 19, 27, 41, 68, 87, 128, 196, 283

Projection pair: 5 243/49 to 2.3.7

Minkowski blocks

2.3.7 subgroup

• 12: 729/686, 64/63
• 17: 64/63, 19683/19208
• 19: 49/48, 177147/175616
• 22: 64/63, 537824/531441
• 24: 64/63, 15059072/14348907

Overview to extensions

Temperaments discussed elsewhere include supernatural (→ Keemic family). Considered below are undecimal sensamagic, sensawer, octarod, shrusus, bisector and sensigh.

Undecimal sensamagic

Subgroup: 2.3.5.7.11

Comma list: 245/243, 385/384

Mapping[1 0 0 0 7], 0 1 1 2 -2], 0 0 2 -1 -1]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.8004, ~9/7 = 440.9178

[[1 0 0 0 0, [21/13 6/13 -1/13 1/13 -3/13, [35/13 10/13 7/13 -7/13 -5/13, [35/13 10/13 -6/13 6/13 -5/13, [42/13 -14/13 -2/13 2/13 7/13]
eigenmonzo (unchanged-interval) basis: 2.7/5.11/9

Projection pairs: 5 243/49 11 896/81 to 2.3.7

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 245/243, 352/351, 364/363

Mapping: [1 0 0 0 7 12], 0 1 1 2 -2 -5], 0 0 2 -1 -1 -1]]

Sensawer

Subgroup: 2.3.5.7.11

Comma list: 245/243, 441/440

Mapping[1 0 0 0 -3], 0 1 1 2 5], 0 0 2 -1 -4]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.1900, ~9/7 = 441.1359

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 245/243, 352/351

Mapping: [1 0 0 0 -3 2], 0 1 1 2 5 2], 0 0 2 -1 -4 -4]]

Octarod

Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/243

Mapping[1 0 0 0 2], 0 1 1 2 0], 0 0 2 -1 4]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 705.0464, ~9/7 = 439.5050

Scales: octarod1, octarod2, octarod3, octarod4, octarod5

Shrusus

Subgroup: 2.3.5.7.11

Comma list: 176/175, 245/243

Mapping[1 0 0 0 -4], 0 1 1 2 4], 0 0 2 -1 3]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 706.3702, ~9/7 = 442.1147

Shrusic

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 176/175, 245/243

Mapping: [1 0 0 0 -4 1], 0 1 1 2 4 1], 0 0 2 -1 3 3]]

Bisector

Subgroup: 2.3.5.7.11

Comma list: 121/120, 245/243

Mapping[2 0 0 0 3], 0 1 1 2 1], 0 0 2 -1 1]]

mapping generators: ~77/54, ~3, ~9/7

Optimal tuning (POTE): ~77/54 = 1\2, ~3/2 = 703.0884, ~9/7 = 441.1060

Sensigh

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 126/125, 169/168

Mapping: [1 6 8 11 0 10], 0 -7 -9 -13 0 -10], 0 0 0 0 1 0]]

mapping generators: ~2, ~9/7, ~11