# Very low accuracy temperaments

Below are listed some **very low accuracy temperaments**. Temperaments with exceedingly low accuracy such as these tend to temper out very large “commas” such as 9/8, 32/27, or 15/14, equating wildly different interval sizes. All temperaments listed temper out an interval of at least size 15/14.

## Antitonic

This temperament is characterized by 9/8 being tempering out, and has been termed a "troll temperament". It is named on account of 4/3 and 3/2 both being represented by the 600 cent half octave, which, in terms of diatonic function, serves as an antitonic. Surprisingly, it has extensions all the way up to the 11-limit, as confirmed by the data from x31eq. The original 5-limit is basically the 3-limit music of 2edo with the addition of harmonic 5 represented by an independent generator.

Subgroup: 2.3.5

Mapping: [⟨2 3 0], ⟨0 0 1]]

Mapping generators: ~3/2, ~5

POTE generator: ~5/4 = 313.690 or ~6/5 = 286.310

Badness: 0.021647

### 7-limit

Subgroup: 2.3.5.7

Comma list: 9/8, 15/14

Mapping: [⟨2 3 0 1], ⟨0 0 1 1]]

POTE generator: ~5/4 = 301.997 or ~6/5 = 298.003

Badness: 0.019373

#### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 9/8, 12/11, 15/14

Mapping: [⟨2 3 0 1 7], ⟨0 0 1 1 0]]

POTE generator: ~5/4 = 340.293 or ~6/5 = 259.707

Badness: 0.021810

#### Antietam

Subgroup: 2.3.5.7.11

Comma list: 9/8, 11/10, 15/14

Mapping: [⟨2 3 0 1 2], ⟨0 0 1 1 1]]

POTE generator: ~5/4 = 322.080 or ~6/5 = 277.920

Badness: 0.018993

### Antaeus

Subgroup: 2.3.5.7

Comma list: 9/8, 35/32

Mapping: [⟨2 3 0 10], ⟨0 0 1 -1]]

POTE generator: ~5/4 = 315.962 or ~6/5 = 284.038

Badness: 0.037537

#### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 9/8, 12/11, 35/32

Mapping: [⟨2 3 0 10 7], ⟨0 0 1 -1 0]]

POTE generator: ~5/4 = 318.173 or ~6/5 = 281.827

Badness: 0.033786

## Alteraugment

Like augmented, but the generator provides 5/4 instead of 3/2.

Subgroup: 2.3.5

Mapping: [⟨3 5 7], ⟨0 0 1]]

POTE generator: ~10/9 = 59.935

Optimal ET sequence: 3, 12bcc, 15bbcc, 18bbcc

Badness: 0.078042

## Yellow (2c&3)

This temperament family is characterized by 10/9 being tempering out.

Subgroup: 2.3.5

Mapping: [⟨1 0 -1], ⟨0 1 2]]

POTE generator: ~3/2 = 775.970

Optimal ET sequence: 3, 11bc, 14bc, 17bb

Badness: 0.016712

### Brutus

Subgroup: 2.3.5.7

Comma list: 10/9, 28/25

Mapping: [⟨1 0 -1 -4], ⟨0 1 2 4]]

POTE generator: ~3/2 = 848.221

Optimal ET sequence: 3, 7bc, 10bc

Badness: 0.053389

### Phlegyas

Subgroup: 2.3.5.7

Comma list: 10/9, 35/32

Mapping: [⟨1 0 -1 6], ⟨0 1 2 -2]]

POTE generator: ~3/2 = 743.135

Optimal ET sequence: 3, 5c, 8c, 13bcc

Badness: 0.051293

### Charon

Subgroup: 2.3.5.7

Comma list: 10/9, 49/45

Mapping: [⟨2 0 -2 -1], ⟨0 1 2 2]]

POTE generator: ~3/2 = 782.604 (or ~10/9 = 182.604)

Optimal ET sequence: 6, 14bc, 20bb

Badness: 0.056404

### Nessus

Subgroup: 2.3.5.7

Comma list: 10/9, 49/48

Mapping: [⟨1 0 -1 2], ⟨0 2 4 1]]

POTE generator: ~7/6 = 213.117

Optimal ET sequence: 5c, 6, 11bc, 17bb

Badness: 0.059070

## Geryon

*See also: Dicot family*

Subgroup: 2.3.5.7

Comma list: 8/7, 25/21

Mapping: [⟨1 1 2 3], ⟨0 2 1 0]]

POTE generator: ~5/4 = 385.440

Optimal ET sequence: 3d, ⟨16 26 37 48], ⟨19 31 44 57], ⟨22 36 51 66]

Badness: 0.051009

## Malacoda

Subgroup: 2.3.5.7

Comma list: 15/14, 35/32

Mapping: [⟨1 0 3 2], ⟨0 2 -1 1]]

POTE generator: ~7/6 = 276.283

Optimal ET sequence: 1, 4, 9c, 13bcc

Badness: 0.037207

## Ugolino

*See also: Bug family*

Subgroup: 2.3.5.7

Comma list: 15/14, 27/25

Mapping: [⟨1 0 0 -1], ⟨0 2 3 5]]

POTE generator: ~6/5 = 278.360

Optimal ET sequence: 4, 9d, 13bd

Badness: 0.043758

## Medusa

*See also: Pelogic family*

Subgroup: 2.3.5.7

Comma list: 15/14, 64/63

Mapping: [⟨1 0 7 6], ⟨0 1 -3 -2]]

POTE generator: ~3/2 = 685.632

Optimal ET sequence: 2, 5c, 7

Badness: 0.042712

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 15/14, 22/21, 33/32

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

POTE generator: ~3/2 = 685.809

Optimal ET sequence: 2, 5c, 7

Badness: 0.026828

## Plutus

*See also: Meantone family*

Subgroup: 2.3.5.7

Comma list: 15/14, 81/80

Mapping: [⟨1 0 -4 -5], ⟨0 1 4 5]]

POTE generator: ~3/2 = 682.895

Optimal ET sequence: 2cd, 5d, 7

Badness: 0.045275

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 15/14, 22/21, 81/80

Mapping: [⟨1 0 -4 -5 -6], ⟨0 1 4 5 6]]

POTE generator: ~3/2 = 685.234

Optimal ET sequence: 2cde, 5de, 7

Badness: 0.032521

## Involution

Subgroup: 2.3.5

Mapping: [⟨1 1 3], ⟨0 1 -2]]

CTE generator: ~3/2 = 509.892

Optimal ET sequence: None aside from extremely absurd alternative ETs

Badness: 0.133021

### 7-limit

Subgroup: 2.3.5.7

Comma list: 45/28, 8/7

Mapping: [⟨1 1 3 3], ⟨0 1 -2 0]]

CTE generator: ~3/2 = 509.892

Optimal ET sequence: None aside from extremely absurd alternative ETs

Badness: 0.118764

## Devolution

Subgroup: 3.5.7

Mapping: [⟨1 1 2], ⟨0 1 -1]]

CTE generator: ~5/3 = 701.863

Optimal ET sequence: 8cdd, otherwise none aside from extremely absurd alternative ETs

Badness (Sintel): 0.751