# Wizmic microtemperaments

(Redirected from Tertiathirds)

This is a collection of microtemperaments which tempers out the wizma, [-6 -8 2 5 = 420175/419904.

Discussed elsewhere are:

Considered below are qak, tokko, tertiathirds, and witch.

## Qak

Subgroup: 2.3.5.7

Comma list: 420175/419904, 703125/702464

Mapping: [1 27 11 40], 0 -41 -14 -60]]

Mapping generators: ~2, ~192/125

Wedgie⟨⟨41 14 60 -73 -20 100]]

POTE generator: ~125/96 = 456.144

## Tokko

Subgroup: 2.3.5.7

Comma list: 420175/419904, 5250987/5242880

Mapping: [1 12 56 -2], 0 -13 -67 6]]

Mapping generators: ~2, ~256/147

Wedgie⟨⟨13 67 -6 76 -46 -202]]

POTE generator: ~147/128 = 238.599

## Tertiathirds

The tertiathirds temperament (121&270) tempers out the quasiorwellisma, 29360128/29296875 in the 7-limit, as well as the wizma. This temperament splits the interval of 5/4 into three 14/13 generators.

Subgroup: 2.3.5.7

Comma list: 420175/419904, 29360128/29296875

Mapping: [1 48 5 76], 0 -52 -3 -82]]

Mapping generators: ~2, ~6272/3375

Wedgie⟨⟨52 3 82 -116 -16 182]]

POTE generator: ~3375/3136 = 128.888

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 5632/5625, 117649/117612

Mapping: [1 48 5 76 107], 0 -52 -3 -82 -116]]

POTE generator: ~264/245 = 128.890

Optimal GPV sequence: 121, 149, 270, 2551bc, 2821bc, 3091bc, 3361bc, 3631bbcc, 3901bbccd, 4171bbccd, 4441bbccd, 4711bbccd

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224

Mapping: [1 48 5 76 107 76], 0 -52 -3 -82 -116 -81]]

POTE generator: ~14/13 = 128.890

Optimal GPV sequence: 121, 149, 270, 1741bc, 2011bcf, 2281bcf, 2551bcf, 2821bcf, 3091bcff, 3361bcff

### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 676/675, 715/714, 936/935, 1225/1224, 4225/4224

Mapping: [1 48 5 76 107 76 63], 0 -52 -3 -82 -116 -81 -66]]

POTE generator: ~14/13 = 128.891

Optimal GPV sequence: 121, 149, 270

### 19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 676/675, 715/714, 936/935, 1225/1224, 1540/1539, 2128/2125

Mapping: [1 48 5 76 107 76 63 -2], 0 -52 -3 -82 -116 -81 -66 7]]

POTE generator: ~14/13 = 128.890

Optimal GPV sequence: 121, 149, 270

## Witch

The witch temperament (99&166) tempers out wizma (420175/419904) and the amity comma (1600000/1594323) as well as the hemfiness comma (4096000/4084101, saquinru-atriyo).

Subgroup: 2.3.5.7

Comma list: 420175/419904, 1600000/1594323

Mapping: [1 18 45 12], 0 -25 -65 -14]]

Mapping generators: ~2, ~63/40

Wedgie⟨⟨25 65 14 45 -48 -150]]

POTE generator: ~80/63 = 412.098

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4375/4356, 1240029/1239040

Mapping: [1 18 45 12 77], 0 -25 -65 -14 -112]]

POTE generator: ~80/63 = 412.079

Optimal GPV sequence: 99e, 166, 265

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 4375/4356, 10648/10647

Mapping: [1 18 45 12 77 93], 0 -25 -65 -14 -112 -136]]

POTE generator: ~33/26 = 412.070

Optimal GPV sequence: 99ef, 166, 265, 431c, 696cc

### Semiwitch

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 41503/41472, 585640/583443

Mapping: [2 11 25 10 16], 0 -25 -65 -14 -29]]

Mapping generators: ~99/70, ~49/44

POTE generator: ~49/44 = 187.904

Optimal GPV sequence: 166, 198, 364, 562, 926, 1488bd, 2414bdd

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1716/1715, 2080/2079, 2200/2197, 17303/17280

Mapping: [2 11 25 10 16 24], 0 -25 -65 -14 -29 -53]]

POTE generator: ~39/35 = 187.904

Optimal GPV sequence: 166, 198, 364, 562, 926

### Hitch

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 117649/117612, 1600000/1594323

Mapping: [1 18 45 12 -10], 0 -50 -130 -28 41]]

Mapping generators: ~2, ~1120/891

POTE generator: ~1120/891 = 393.950

Optimal GPV sequence: 198, 463, 661, 1124bde

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1716/1715, 3025/3024, 1600000/1594323

Mapping: [1 18 45 12 -10 71], 0 -50 -130 -28 41 -205]]

POTE generator: ~1120/891 = 393.948

Optimal GPV sequence: 198, 463, 661

#### Hitcher

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 3025/3024, 13720/13689, 28672/28561

Mapping: [1 18 45 12 -10 6], 0 -50 -130 -28 41 -7]]

POTE generator: ~49/39 = 393.949

Optimal GPV sequence: 198, 463f, 661ff