# Olympic clan

The olympic clan of rank-3 temperaments tempers out the olympia, 131072/130977 = [17 -5 0 -2 -1. This has the effect of equating the undecimal quartertone (33/32) with a stack of two septimal commas (64/63).

For the rank-4 olympic temperament, see Rank-4 temperament #Olympic (131072/130977).

## Olympian

Subgroup: 2.3.7.11

Comma list: 131072/130977

Sval mapping[1 0 0 17], 0 1 0 -5], 0 0 1 -2]]

sval mapping generators: ~2, ~3, ~7

Optimal tuning (POTE): ~3/2 = 702.0805, ~7/4 = 969.0275

### Overview to extensions

The second comma in the comma list determines how we extend olympian to include the harmonic 5. Akea adds 385/384, and finds the harmonic 5 by equating the syntonic comma (81/80) with the septimal comma. Orthoschismic adds 32805/32768, and finds the harmonic 5 on the chain of fifths. Cassaschismic adds 19712/19683 with an independent generator for harmonic 5. Pessoal adds 9801/9800, splitting the octave into two. Lif adds 2401/2400, splitting the perfect fifth into two. Baffin adds 5632/5625, splitting the perfect twelfth into two. Lux adds 3025/3024, splitting the ~21/16 into two. Hera adds 6144/6125 or 8019/8000, splitting the ~21/16 into three. Finally, sophia adds 42875/42768, splitting the ~8/7 into three. These all have neat extensions to the 13-limit via tempering out both 2080/2079 and 4096/4095.

Temperaments discussed elsewhere are:

Considered below are orthoschismic, cassaschismic, baffin and sophia.

## Orthoschismic

Subgroup: 2.3.5.7.11

Comma list: 540/539, 32805/32768

Mapping[1 0 15 0 17], 0 1 -8 0 -5], 0 0 0 1 2]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.7405, ~7/4 = 969.6950

### 13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [1 0 15 0 17 -3], 0 1 -8 0 -5 6], 0 0 0 1 2 -1]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.7333, ~7/4 = 969.7085

## Cassaschismic

### 7-limit (garischismic)

Subgroup: 2.3.5.7

Comma list: 33554432/33480783

Mapping[1 0 0 25], 0 1 0 -14], 0 0 1 0]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2224, ~5/4 = 386.3137

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 19712/19683, 41503/41472

Mapping[1 0 0 25 -33], 0 1 0 -14 23], 0 0 1 0 0]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2280, ~5/4 = 386.3137

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 4096/4095, 19712/19683

Mapping: [1 0 0 25 -33 -13], 0 1 0 -14 23 12], 0 0 1 0 0 -1]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2289, ~5/4 = 386.2869

### 2.3.5.7.11.13.19 subgroup

Subgroup: 2.3.5.7.11.13.19

Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079

Sval mapping: [1 0 0 25 -33 -13 -6], 0 1 0 -14 23 12 5], 0 0 1 0 0 -1 1]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2293, ~5/4 = 386.3021

## Baffin

### 7-limit (decovulture)

Subgroup: 2.3.5.7

Comma list: 67108864/66976875

Mapping[1 0 0 13], 0 2 0 -7], 0 0 1 -2]]

mapping generators: ~2, ~8192/4725, ~5

Optimal tuning (POTE): ~2 = 1\1, ~8192/4725 = 951.0868, ~5/4 = 386.6183

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 5632/5625, 131072/130977

Mapping[1 0 0 13 -9], 0 2 0 -7 4], 0 0 1 -2 4]]

Optimal tuning (POTE): ~2 = 1\1, ~400/231 = 951.0585, ~5/4 = 386.7912

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 4096/4095

Mapping: [1 0 0 13 -9 1], 0 2 0 -7 4 3], 0 0 1 -2 4 1]]

Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 951.0882, ~5/4 = 386.7507

Complexity spectrum: 15/13, 16/15, 13/12, 4/3, 16/13, 5/4, 18/13, 13/10, 6/5, 9/8, 11/10, 8/7, 7/5, 15/11, 10/9, 13/11, 15/14, 11/8, 7/6, 14/13, 12/11, 9/7, 11/9, 14/11

## Sophia

Subgroup: 2.3.5.7.11

Comma list: 42875/42768, 131072/130977

Mapping[1 0 2 3 11], 0 1 0 0 -5], 0 0 5 -3 6]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.3024, ~256/245 = 77.1952

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 4096/4095, 13720/13689

Mapping: [1 0 2 3 11 7], 0 1 0 0 -5 -2], 0 0 5 -3 6 -2]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.3319, ~117/112 = 77.2152