# Stearnsmic clan

(Redirected from Stearnscape)

The stearnsmic clan tempers out the stearnsma, the no-fives comma [1 10 0 -6 = 118098/117649.

## No-five stearnsmic

Subgroup: 2.3.7

Comma list: 118098/117649

Sval mapping[2 1 2], 0 3 5]]

mapping generators: ~343/243, ~9/7

Gencom mapping[2 1 0 2], 0 3 0 5]]

Optimal tuning (POTE): ~343/243 = 1\2, ~9/7 = 433.888

### Overview to extensions

The second comma in the comma list determines how we extend it to include the harmonic 5. Pogo adds 32805/32768, supers 5120/5103, echidna 1728/1715, and hedgehog 50/49. Those are strong extensions. The others are weak. Wizard adds 225/224. Harry adds 2401/2400. Those split the generator in two. Septisuperfourth adds 6144/6125 and splits the generator in three. Stearnscape adds 250047/250000 and splits the period in three. Octoid adds 4375/4374 and splits the period in four. Decistearn adds 3136/3125 splits the period in five. They all have neat extensions to the 11-limit via tempering out both 540/539 and 4000/3993.

Stearnsmic temperaments not listed include:

Considered below are pogo, supers, stearnscape, garistearn and decistearn.

## Pogo

The pogo temperament (94 & 130) tempers out the schisma, whose amount of tempering of the fifth is just about right for the stearnsma.

Subgroup: 2.3.5.7

Comma list: 32805/32768, 118098/117649

Mapping[2 1 22 2], 0 3 -24 5]]

Wedgie⟨⟨6 -48 10 -90 -1 158]]

Optimal tuning (POTE): ~343/243 = 1\2, ~9/7 = 433.901

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 32805/32768

Mapping: [2 1 22 2 25], 0 3 -24 5 -25]]

Optimal tuning (POTE): ~99/70 = 1\2, ~9/7 = 433.911

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 1575/1573, 4096/4095

Mapping: [2 1 22 2 25 -2], 0 3 -24 5 -25 13]]

Optimal tuning (POTE): ~99/70 = 1\2, ~9/7 = 433.911

## Supers

Subgroup: 2.3.5.7

Comma list: 5120/5103, 118098/117649

Mapping[2 1 -12 2], 0 3 23 5]]

Wedgie⟨⟨6 46 10 59 -1 -106]]

Optimal tuning (POTE): ~343/243 = 1\2, ~9/7 = 434.218

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 5120/5103

Mapping: [2 1 -12 2 -9], 0 3 23 5 22]]

Optimal tuning (POTE): ~99/70 = 1\2, ~9/7 = 434.217

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 540/539, 729/728, 1575/1573

Mapping: [2 1 -12 2 -9 -2], 0 3 23 5 22 13]]

Optimal tuning (POTE): ~99/70 = 1\2, ~9/7 = 434.221

### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 170/169, 289/288, 352/351, 442/441, 561/560

Mapping: [2 1 -12 2 -9 -2 6], 0 3 23 5 22 13 3]]

Optimal tuning (POTE): ~17/12 = 1\2, ~9/7 = 434.181

## Stearnscape

Subgroup: 2.3.5.7

Comma list: 118098/117649, 250047/250000

Mapping[6 3 2 6], 0 6 11 10]]

mapping generators: ~2450/2187, ~567/500

Wedgie⟨⟨36 66 60 21 -6 -46]]

Optimal tuning (CTE): ~2450/2187 = 1\6, ~567/500 = 216.9394 (~245/243 = 16.9394)

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 137781/137500

Mapping: [6 3 2 6 11], 0 6 11 10 9]]

Optimal tuning (CTE): ~55/49 = 1\6, ~567/500 = 216.9242 (~100/99 = 16.9242)

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 1575/1573, 34398/34375

Mapping: [6 3 2 6 11 -6], 0 6 11 10 9 26]]

Optimal tuning (CTE): ~55/49 = 1\6, ~312/275 = 216.9332 (~105/104 = 16.9332)

### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 540/539, 729/728, 936/935, 1156/1155, 1575/1573

Mapping: [6 3 2 6 11 -6 5], 0 6 11 10 9 26 18]]

Optimal tuning (CTE): ~55/49 = 1\6, ~17/15 = 216.9345 (~105/104 = 16.9345)

## Garistearn

The garistearn temperament (94 & 282) has a period of 1/94-octave and tempers out 118098/117649 and the garischisma, 33554432/33480783.

Subgroup: 2.3.5.7

Comma list: 118098/117649, 33554432/33480783

Mapping[94 149 0 264], 0 0 1 0]]

Wedgie⟨⟨0 94 0 149 0 -264]]

Optimal tuning (POTE): ~1029/1024 = 1\94, ~5/4 = 386.7805

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 33554432/33480783

Mapping: [94 149 0 264 107], 0 0 1 0 1]]

Optimal tuning (POTE): ~1029/1024 = 1\94, ~5/4 = 386.5968

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 1575/1573, 28672/28561

Mapping: [94 149 0 264 107 348], 0 0 1 0 1 0]]

Optimal tuning (POTE): ~169/168 = 1\94, ~5/4 = 386.8141

### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 540/539, 729/728, 1156/1155, 1575/1573, 2880/2873

Mapping: [94 149 0 264 107 348 166], 0 0 1 0 1 0 1]]

Optimal tuning (POTE): ~169/168 = 1\94, ~5/4 = 386.8420

## Decistearn

The decistearn temperament (80 & 130) has a period of 1/10-octave and tempers out the hemimean comma, 3136/3125 as well as the linus comma.

Subgroup: 2.3.5.7

Comma list: 3136/3125, 118098/117649

Mapping[10 2 14 5], 0 3 2 5]]

mapping generators: ~15/14, ~135/98

Wedgie⟨⟨30 20 50 -38 -5 60]]

Optimal tuning (CTE): ~15/14 = 1\10, ~135/98 = 553.810 (~36/35 = 46.190)

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 3136/3125, 4000/3993

Mapping: [10 2 14 5 30], 0 3 2 5 1]]

Optimal tuning (CTE): ~15/14 = 1\10, ~11/8 = 553.783 (~36/35 = 46.217)

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 364/363, 540/539, 3136/3125

Mapping: [10 2 14 5 30 37], 0 3 2 5 1 0]]

Optimal tuning (CTE): ~15/14 = 1\10, ~11/8 = 553.783 (~36/35 = 46.217)

### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 221/220, 289/288, 351/350, 540/539, 1632/1625

Mapping: [10 2 14 5 30 37 27], 0 3 2 5 1 0 3]]

Optimal tuning (CTE): ~15/14 = 1\10, ~11/8 = 553.862 (~36/35 = 46.138)

### 19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 221/220, 289/288, 351/350, 361/360, 456/455, 476/475

Mapping: [10 2 14 5 30 37 27 24], 0 3 2 5 1 0 3 4]]

Optimal tuning (CTE): ~15/14 = 1\10, ~11/8 = 553.913 (~36/35 = 46.087)

### 23-limit

By equating 16/13 with 69/56 and 85/69 (enabling 56:69:85 chords), we find 23/16 at 2 generators underneath 6 periods (which is the 5edo fifth, 6\10).

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 221/220, 289/288, 351/350, 361/360, 456/455, 476/475, 897/896

Mapping: [10 2 14 5 30 37 27 24 36], 0 3 2 5 1 0 3 4 2]]

Optimal tuning (CTE): ~161/150 = 1\10, ~11/8 = 553.918 (~36/35 = 46.082)