# Metric microtemperaments

(Redirected from Geb)

These are rank-2 temperaments that temper out the meter, 703125/702464 = [-11 2 7 -3.

Temperaments discussed elsewhere include:

## Luminal

Luminal is the intersection of metric and lux, tempering out 3025/3024 in the 11-limit, 2080/2079, 4096/4095 in the 13-limit, and 1156/1155 and 2601/2600 in the 17-limit.

Subgroup: 2.3.5.7

Comma list: 703125/702464, 26843545600/26795786661

Mapping[1 0 5 8], 0 29 -49 -95]]

Wedgie⟨⟨29 -49 -95 -145 -232 -82]]

Optimal tuning (POTE): ~2 = 1\1, ~8505/8192 = 65.5883

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 131072/130977, 703125/702464

Mapping: [1 0 5 8 1], 0 29 -49 -95 45]]

Optimal tuning (POTE): ~2 = 1\1, ~80/77 = 65.5881

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 3025/3024, 4096/4095, 31250/31213

Mapping: [1 0 5 8 1 -1], 0 29 -49 -95 45 86]]

Optimal tuning (POTE): ~2 = 1\1, ~27/26 = 65.5883

### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 1156/1155, 1275/1274, 2080/2079, 2431/2430, 4096/4095

Mapping: [1 0 5 8 1 -1 6], 0 29 -49 -95 45 86 -35]]

Optimal tuning (POTE): ~2 = 1\1, ~27/26 = 65.5878

## Decimetra

The decimetra temperament (50 & 140) tempers out the procyon comma, 823543/820125 = [0 -8 -3 7 as well as linus comma.

Subgroup: 2.3.5.7

Comma list: 703125/702464, 823543/820125

Mapping[10 3 20 12], 0 4 1 5]]

Wedgie⟨⟨40 10 50 -77 -33 88]]

Optimal tuning (POTE): ~15/14 = 1\10, ~5/4 = 385.495

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 9801/9800, 391314/390625

Mapping: [10 3 20 12 41], 0 4 1 5 -2]]

Optimal tuning (POTE): ~15/14 = 1\10, ~5/4 = 385.396

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 385/384, 625/624, 847/845, 4459/4455

Mapping: [10 3 20 12 41 37], 0 4 1 5 -2 0]]

Optimal tuning (POTE): ~15/14 = 1\10, ~5/4 = 385.419

### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 289/288, 385/384, 561/560, 625/624, 847/845

Mapping: [10 3 20 12 41 37 28], 0 4 1 5 -2 0 4]]

Optimal tuning (POTE): ~15/14 = 1\10, ~5/4 = 385.435

## Stockhausenic

The stockhausenic temperament (140 & 183, named after Karlheinz Stockhausen) is related to 25ed5 tuning, and tempers out the hemfiness comma (saquadru-atriyo), 4096000/4084101 = [15 -5 3 -5.

Subgroup: 2.3.5.7

Comma list: 703125/702464, 4096000/4084101

Mapping[1 4 0 -1], 0 -26 25 41]]

Wedgie⟨⟨26 -25 -41 -100 -138 -25]]

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.453

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 1375/1372, 5632/5625, 35937/35840

Mapping: [1 4 0 -1 -1], 0 -26 25 41 48]]

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.460

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 1375/1372, 4096/4095

Mapping: [1 4 0 -1 -1 5], 0 -26 25 41 48 -14]]

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.458

### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 442/441, 561/560, 676/675, 715/714, 4096/4095

Mapping: [1 4 0 -1 -1 5 0], 0 -26 25 41 48 -14 44]]

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 111.459

## Geb

The geb temperament (171 & 506, named after the earth god of ancient Egyptian religion) tempers out [-31 43 -16 (quadla-quadquadgu) in the 5-limit; the meter and the euzenius comma, 78125000/78121827 as well as skeetsma (14348907/14336000, lalarutrigu) in the 7-limit. Osiris temperament (171&670, named after the eldest son of Geb) tempers out the same 5-limit comma as the geb, but with the breedsma rather than the meter tempered out.

Subgroup: 2.3.5

Comma list: [-31 43 -16

Mapping[1 -3 -10], 0 16 43]]

Optimal tuning (POTE): ~2 = 1\1, ~8000/6561 = 343.868

### 7-limit

Subgroup: 2.3.5.7

Comma list: 703125/702464, 14348907/14336000

Mapping[1 -3 -10 -29], 0 16 43 111]]

Wedgie⟨⟨16 43 111 31 131 137]]

Optimal tuning (POTE): ~2 = 1\1, ~8000/6561 = 343.863