# Dicot family

(Redirected from Dichotic)

The 5-limit parent comma for the dicot family is 25/24, the classical chromatic semitone. Its monzo is [-3 -1 2, and flipping that yields ⟨⟨2 1 -3]] for the wedgie. This tells us the generator is a classical third (major and minor mean the same thing), and that two such thirds give a fifth. In fact, (5/4)2 = (3/2)(25/24).

Possible tunings for dicot are 7edo, 17edo, 24edo using the val 24 38 55] (24c) and 31edo using the val 31 49 71] (31c). In a sense, what dicot is all about is using neutral thirds and pretending that is 5-limit, and like any temperament which seems to involve pretending, dicot is at the edge of what can sensibly be called a temperament at all. In other words, it is an exotemperament.

## Dicot

Subgroup: 2.3.5

Comma list: 25/24

Mapping[1 1 2], 0 2 1]]

mapping generators: ~2, ~5/4

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 348.594

• 5-odd-limit diamond monotone: ~5/4 = [300.000, 400.000] (1\4 to 1\3)
• 5-odd-limit diamond tradeoff: ~5/4 = [315.641, 386.314] (full comma to untempered)
• 5-odd-limit diamond monotone and tradeoff: ~5/4 = [315.641, 386.314]

### Overview to extensions

The second comma of the normal comma list defines which 7-limit family member we are looking at. Septimal dicot, with wedgie ⟨⟨2 1 3 -3 -1 4]] adds 36/35, sharp with wedgie ⟨⟨2 1 6 -3 4 11]] adds 28/27, and dichotic with wedgie ⟨⟨2 1 -4 -3 -12 -12]] adds 64/63, all retaining the same period and generator.

Decimal with wedgie ⟨⟨4 2 2 -6 -8 -1]] adds 49/48, sidi with wedgie ⟨⟨4 2 9 -3 6 15]] adds 245/243, and jamesbond with wedgie ⟨⟨0 0 7 0 11 16]] adds 81/80. Here decimal divides the period to 1/2 octave, and sidi uses 9/7 as a generator, with two of them making up the combined 5/3 and 8/5 neutral sixth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator.

## Septimal dicot

Subgroup: 2.3.5.7

Comma list: 15/14, 25/24

Mapping[1 1 2 2], 0 2 1 3]]

Wedgie⟨⟨2 1 3 -3 -1 4]]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 336.381

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 15/14, 22/21, 25/24

Mapping: [1 1 2 2 2], 0 2 1 3 5]]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 342.125

### Eudicot

Subgroup: 2.3.5.7.11

Comma list: 15/14, 25/24, 33/32

Mapping: [1 1 2 2 4], 0 2 1 3 -2]]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 336.051

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 15/14, 25/24, 33/32, 40/39

Mapping: [1 1 2 2 4 4], 0 2 1 3 -2 -1]]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 338.846

## Flat

Subgroup: 2.3.5.7

Comma list: 21/20, 25/24

Mapping[1 1 2 3], 0 2 1 -1]]

Wedgie⟨⟨2 1 -1 -3 -7 -5]]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 331.916

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 21/20, 25/24, 33/32

Mapping: [1 1 2 3 4], 0 2 1 -1 -2]]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 337.532

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 14/13, 21/20, 25/24, 33/32

Mapping: [1 1 2 3 4 4], 0 2 1 -1 -2 -1]]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 341.023

## Sharp

Subgroup: 2.3.5.7

Comma list: 25/24, 28/27

Mapping[1 1 2 1], 0 2 1 6]]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 357.938

Wedgie⟨⟨2 1 6 -3 4 11]]

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 25/24, 28/27, 35/33

Mapping: [1 1 2 1 2], 0 2 1 6 5]]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 356.106

## Dichotic

Subgroup: 2.3.5.7

Comma list: 25/24, 64/63

Mapping[1 1 2 4], 0 2 1 -4]]

Wedgie⟨⟨2 1 -4 -3 -12 -12]]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 356.264

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 25/24, 45/44, 64/63

Mapping: [1 1 2 4 2], 0 2 1 -4 5]]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 354.262

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 25/24, 40/39, 45/44, 64/63

Mapping: [1 1 2 4 2 4], 0 2 1 -4 5 -1]]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 354.365

### Dichotomic

Subgroup: 2.3.5.7.11

Comma list: 22/21, 25/24, 33/32

Mapping: [1 1 2 4 4], 0 2 1 -4 -2]]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 354.073

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 22/21, 25/24, 33/32, 40/39

Mapping: [1 1 2 4 4 4], 0 2 1 -4 -2 -1]]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 354.313

### Dichosis

Subgroup: 2.3.5.7.11

Comma list: 25/24, 35/33, 64/63

Mapping: [1 1 2 4 5], 0 2 1 -4 -5]]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 360.659

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 25/24, 35/33, 40/39, 64/63

Mapping: [1 1 2 4 5 4], 0 2 1 -4 -5 -1]]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 360.646

## Decimal

Subgroup: 2.3.5.7

Comma list: 25/24, 49/48

Mapping[2 0 3 4], 0 2 1 1]]

mapping generators: ~7/5, ~7/4

Wedgie⟨⟨4 2 2 -6 -8 -1]]

Optimal tuning (POTE): ~7/5 = 1\2, ~7/4 = 948.443 (~7/6 = 251.557)

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 25/24, 45/44, 49/48

Mapping: [2 0 3 4 -1], 0 2 1 1 5]]

Optimal tuning (POTE): ~7/5 = 1\2, ~7/4 = 946.507 (~7/6 = 253.493)

### Decimated

Subgroup: 2.3.5.7.11

Comma list: 25/24, 33/32, 49/48

Mapping: [2 0 3 4 10], 0 2 1 1 -2]]

Optimal tuning (POTE): ~7/5 = 1\2, ~7/4 = 944.934 (~7/6 = 255.066)

### Decibel

Subgroup: 2.3.5.7.11

Comma list: 25/24, 35/33, 49/48

Mapping: [2 0 3 4 7], 0 2 1 1 0]]

Optimal tuning (POTE): ~7/5 = 1\2, ~7/4 = 956.507 (~8/7 = 243.493)

## Sidi

Subgroup: 2.3.5.7

Comma list: 25/24, 245/243

Mapping[1 3 3 6], 0 -4 -2 -9]]

mapping generators: ~2, ~9/7

Wedgie⟨⟨4 2 9 -12 3 15]]

Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 427.208

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 25/24, 45/44, 99/98

Mapping: [1 3 3 6 7], 0 -4 -2 -9 -10]]

Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 427.273

Subgroup: 2.3.5.7

Comma list: 9/8, 25/24

Mapping[4 6 9 0], 0 0 0 1]]

Wedgie⟨⟨0 0 4 0 6 9]]

Optimal tuning (POTE): ~6/5 = 1\4, ~8/7 = 324.482

## Jamesbond

Subgroup: 2.3.5.7

Comma list: 25/24, 81/80

Mapping[7 11 16 0], 0 0 0 1]]

Wedgie⟨⟨0 0 7 0 11 16]]

Optimal tuning (POTE): ~10/9 = 1\7, ~7/4 = 941.861

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 25/24, 33/32, 45/44

Mapping: [7 11 16 0 24], 0 0 0 1 0]]

Optimal tuning (POTE): ~10/9 = 1\7, ~7/4 = 941.090

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 25/24, 27/26, 33/32, 40/39

Mapping: [7 11 16 0 24 26], 0 0 0 1 0 0]]

Optimal tuning (POTE): ~10/9 = 1\7, ~7/4 = 949.236