# Gallery of CS Scales

This is a gallery of scales that have a constant structure. They are also epimorphic.

# Octave (2/1) span

## 11 tone

• 1/1 9/8 5/4 9/7 21/16 35/24 3/2 5/3 12/7 7/4 35/18 2/1

## 12 tone

• 1/1 15/14 9/8 15/13 5/4 15/11 11/8 3/2 13/8 5/3 7/4 15/8 2/1

## 18 tone

### Flippery CS's

The 31 flippery constant structures with step sizes 16/15, 25/24, 36/35, 49/48, modulo transposition and inversion! (to be checked):

• [1, 36/35, 15/14, 8/7, 7/6, 6/5, 5/4, 4/3, 48/35, 10/7, 35/24, 14/9, 8/5, 5/3, 12/7, 7/4, 28/15, 35/18, 2]
• [1, 36/35, 15/14, 8/7, 7/6, 6/5, 5/4, 4/3, 48/35, 10/7, 35/24, 14/9, 8/5, 5/3, 12/7, 7/4, 28/15, 48/25, 2]
• [1, 36/35, 15/14, 35/32, 7/6, 6/5, 5/4, 9/7, 48/35, 10/7, 35/24, 3/2, 8/5, 5/3, 12/7, 7/4, 9/5, 15/8, 2]
• [1, 36/35, 15/14, 8/7, 7/6, 6/5, 5/4, 9/7, 48/35, 10/7, 35/24, 3/2, 8/5, 5/3, 12/7, 7/4, 9/5, 15/8, 2]
• [1, 36/35, 15/14, 35/32, 7/6, 6/5, 5/4, 9/7, 48/35, 10/7, 35/24, 3/2, 8/5, 5/3, 12/7, 7/4, 9/5, 48/25, 2]
• [1, 36/35, 15/14, 8/7, 7/6, 6/5, 5/4, 9/7, 48/35, 10/7, 35/24, 3/2, 8/5, 5/3, 12/7, 7/4, 9/5, 48/25, 2]
• [1, 16/15, 10/9, 8/7, 7/6, 175/144, 35/27, 4/3, 48/35, 10/7, 35/24, 14/9, 8/5, 5/3, 12/7, 64/35, 40/21, 35/18, 2]
• [1, 36/35, 15/14, 35/32, 7/6, 6/5, 5/4, 9/7, 48/35, 10/7, 35/24, 3/2, 25/16, 5/3, 12/7, 7/4, 9/5, 15/8, 2]
• [1, 36/35, 15/14, 8/7, 7/6, 6/5, 5/4, 9/7, 48/35, 10/7, 35/24, 3/2, 25/16, 5/3, 12/7, 7/4, 9/5, 15/8, 2]
• [1, 25/24, 10/9, 8/7, 7/6, 175/144, 5/4, 4/3, 48/35, 10/7, 35/24, 14/9, 8/5, 5/3, 12/7, 64/35, 40/21, 35/18, 2]
• [1, 36/35, 15/14, 35/32, 9/8, 6/5, 5/4, 9/7, 48/35, 10/7, 35/24, 3/2, 25/16, 45/28, 12/7, 7/4, 9/5, 15/8, 2]
• [1, 25/24, 15/14, 8/7, 7/6, 175/144, 5/4, 4/3, 48/35, 10/7, 35/24, 3/2, 8/5, 5/3, 12/7, 64/35, 40/21, 35/18, 2]
• [1, 25/24, 15/14, 8/7, 7/6, 6/5, 5/4, 4/3, 48/35, 10/7, 35/24, 3/2, 8/5, 5/3, 12/7, 25/14, 40/21, 35/18, 2]
• [1, 25/24, 15/14, 8/7, 7/6, 6/5, 5/4, 4/3, 25/18, 10/7, 35/24, 3/2, 8/5, 5/3, 12/7, 25/14, 40/21, 35/18, 2]
• [1, 49/48, 21/20, 28/25, 7/6, 6/5, 5/4, 4/3, 48/35, 7/5, 35/24, 3/2, 8/5, 49/30, 42/25, 7/4, 28/15, 48/25, 2]
• [1, 25/24, 10/9, 8/7, 7/6, 6/5, 5/4, 4/3, 49/36, 7/5, 35/24, 14/9, 8/5, 5/3, 12/7, 7/4, 28/15, 35/18, 2]
• [1, 36/35, 15/14, 35/32, 7/6, 6/5, 5/4, 9/7, 21/16, 7/5, 35/24, 3/2, 25/16, 5/3, 12/7, 7/4, 9/5, 15/8, 2]
• [1, 49/48, 21/20, 35/32, 7/6, 6/5, 5/4, 4/3, 49/36, 7/5, 35/24, 3/2, 8/5, 5/3, 12/7, 7/4, 28/15, 35/18, 2]
• [1, 36/35, 15/14, 35/32, 7/6, 6/5, 5/4, 9/7, 21/16, 7/5, 35/24, 3/2, 8/5, 5/3, 12/7, 7/4, 9/5, 15/8, 2]
• [1, 16/15, 10/9, 8/7, 7/6, 6/5, 5/4, 4/3, 25/18, 10/7, 35/24, 14/9, 8/5, 5/3, 12/7, 7/4, 28/15, 35/18, 2]
• [1, 36/35, 15/14, 35/32, 7/6, 6/5, 5/4, 9/7, 21/16, 7/5, 36/25, 3/2, 25/16, 5/3, 12/7, 7/4, 9/5, 15/8, 2]
• [1, 36/35, 21/20, 35/32, 7/6, 6/5, 5/4, 9/7, 21/16, 7/5, 36/25, 3/2, 25/16, 5/3, 12/7, 7/4, 9/5, 15/8, 2]
• [1, 49/48, 21/20, 35/32, 7/6, 6/5, 5/4, 4/3, 48/35, 7/5, 35/24, 3/2, 8/5, 5/3, 12/7, 7/4, 28/15, 48/25, 2]
• [1, 49/48, 21/20, 35/32, 7/6, 6/5, 32/25, 4/3, 48/35, 7/5, 35/24, 3/2, 8/5, 5/3, 12/7, 7/4, 28/15, 48/25, 2]
• [1, 49/48, 21/20, 28/25, 7/6, 6/5, 32/25, 4/3, 48/35, 7/5, 35/24, 3/2, 8/5, 5/3, 12/7, 7/4, 28/15, 48/25, 2]
• [1, 36/35, 15/14, 35/32, 7/6, 6/5, 5/4, 9/7, 21/16, 7/5, 36/25, 3/2, 8/5, 5/3, 12/7, 7/4, 9/5, 15/8, 2]
• [1, 36/35, 21/20, 35/32, 7/6, 6/5, 5/4, 9/7, 21/16, 7/5, 36/25, 3/2, 8/5, 5/3, 12/7, 7/4, 9/5, 15/8, 2]
• [1, 16/15, 10/9, 8/7, 7/6, 6/5, 32/25, 4/3, 48/35, 7/5, 35/24, 14/9, 8/5, 5/3, 12/7, 7/4, 28/15, 48/25, 2]
• [1, 16/15, 49/45, 28/25, 7/6, 6/5, 32/25, 4/3, 48/35, 7/5, 35/24, 14/9, 8/5, 49/30, 42/25, 7/4, 28/15, 48/25, 2]
• [1, 36/35, 15/14, 35/32, 7/6, 6/5, 5/4, 9/7, 48/35, 7/5, 35/24, 3/2, 8/5, 5/3, 12/7, 7/4, 9/5, 15/8, 2]
• [1, 25/24, 15/14, 125/112, 25/21, 60/49, 5/4, 125/96, 75/56, 10/7, 72/49, 75/49, 25/16, 5/3, 12/7, 25/14, 90/49, 15/8, 2]

### Others

• 1/1 25/24 10/9 8/7 25/21 6/5 5/4 4/3 25/18 10/7 35/24 3/2 80/49 5/3 12/7 7/4 40/21 35/18 2/1 - notable for having 5 otonalities and 5 utonalities, the most that an 18 tone CS with the patent val can have
• 1/1 15/14 54/49 10/9 7/6 6/5 9/7 35/27 4/3 10/7 3/2 54/35 14/9 5/3 12/7 9/5 49/27 40/21 2/1

## 19 tone

• [1, 25/24, 35/32, 10/9, 7/6, 6/5, 5/4, 21/16, 4/3, 7/5, 35/24, 3/2, 14/9, 8/5, 5/3, 7/4, 9/5, 15/8, 35/18, 2]

### Non-patent val

• [1, 15/14, 10/9, 9/8, 7/6, 5/4, 80/63, 21/16, 4/3, 10/7, 40/27, 3/2, 45/28, 5/3, 27/16, 7/4, 15/8, 40/21, 63/32, 2]
• [1, 81/80, 21/20, 9/8, 8/7, 189/160, 6/5, 21/16, 4/3, 27/20, 7/5, 3/2, 32/21, 63/40, 8/5, 12/7, 16/9, 9/5, 28/15, 2]

## 20 tone

• [1, 21/20, 175/162, 10/9, 7/6, 6/5, 100/81, 35/27, 4/3, 7/5, 350/243, 40/27, 3/2, 8/5, 400/243, 5/3, 7/4, 9/5, 50/27, 35/18, 2]

## 22 tone

• 1/1 40/39 13/12 10/9 52/45 32/27 6/5 16/13 13/10 4/3 160/117 13/9 40/27 3/2 20/13 13/8 5/3 26/15 16/9 9/5 24/13 39/20 2/1

### Non-patent val

• [1, 64/63, 35/33, 35/32, 7/6, 32/27, 105/88, 175/144, 5/4, 4/3, 256/189, 140/99, 35/24, 3/2, 32/21, 35/22, 105/64, 7/4, 16/9, 315/176, 175/96, 35/18, 2]
• 1/1 875/864 25/24 21/20 27/25 35/32 9/8 175/144 5/4 4375/3456 125/96 21/16 27/20 35/24 3/2 175/108 5/3 42/25 125/72 7/4 9/5 35/18 2/1

## 24 tone

### Non-patent val

• 1/1 169/168 143/140 13/12 11/10 33/28 77/65 143/120 9/7 507/392 13/10 39/28 99/70 3/2 169/112 429/280 11/7 33/20 117/70 143/84 9/5 11/6 13/7 39/20 2/1 - one of the smallest CS's containing the 3 5 7 9 11 13 eikosany

## 28 tone

• 1/1 66/65 21/20 14/13 11/10 44/39 7/6 77/65 6/5 33/26 14/11 84/65 11/8 363/260 7/5 77/52 3/2 99/65 63/40 21/13 33/20 22/13 7/4 231/130 9/5 24/13 77/40 77/39 2/1 - one of the smallest CS's containing the 1 3 5 7 11 13 eikosany

## 29 tone

• 1/1 33/32 117/112 13/12 12/11 9/8 8/7 33/28 39/32 26/21 143/112 9/7 4/3 11/8 39/28 1287/896 143/96 3/2 99/64 11/7 13/8 429/256 143/84 1573/896 99/56 11/6 13/7 429/224 27/14 2/1 - one of the smallest CS's containing the 1 3 7 9 11 13 eikosany

## 31 tone

### Non-patent val

• 1/1 64/63 15/14 35/32 10/9 9/8 8/7 7/6 315/256 5/4 80/63 9/7 21/16 4/3 45/32 10/7 35/24 189/128 3/2 32/21 45/28 105/64 5/3 27/16 12/7 7/4 16/9 15/8 40/21 27/14 63/32 2/1

## 41 tone

• 1/1 49/48 28/27 21/20 15/14 35/32 10/9 9/8 8/7 7/6 189/160 6/5 49/40 5/4 81/64 9/7 21/16 4/3 49/36 112/81 7/5 10/7 35/24 40/27 3/2 49/32 14/9 63/40 8/5 49/30 5/3 27/16 12/7 7/4 16/9 9/5 147/80 28/15 40/21 35/18 160/81 2/1 - "Regulus"
• 1/1 45/44 25/24 21/20 15/14 12/11 10/9 9/8 8/7 7/6 25/21 6/5 11/9 5/4 14/11 9/7 21/16 4/3 15/11 11/8 7/5 10/7 16/11 22/15 3/2 32/21 14/9 11/7 8/5 18/11 5/3 27/16 12/7 7/4 16/9 9/5 11/6 15/8 21/11 27/14 49/25 2/1

## 46 tone

### Non-patent val

• 1/1 99/98 49/48 33/32 21/20 11/10 10/9 55/49 8/7 396/343 7/6 33/28 6/5 297/245 49/40 99/80 5/4 55/42 4/3 66/49 49/36 11/8 7/5 99/70 10/7 495/343 35/24 165/112 3/2 11/7 8/5 396/245 49/30 33/20 5/3 165/98 12/7 594/343 7/4 11/6 28/15 66/35 40/21 660/343 35/18 55/28 2/1

# Tritave (3/1) span

## 19 tone

• [1, 27/25, 55/49, 25/21, 9/7, 33/25, 7/5, 75/49, 11/7, 5/3, 9/5, 231/125, 49/25, 15/7, 11/5, 7/3, 63/25, 55/21, 25/9, 3]