Comma pump examples
Contents
- 1 3-limit examples
- 2 5-limit examples
- 3 7-limit examples
- 3.1 126/125 (starling)
- 3.2 225/224 (marvel)
- 3.3 245/243 (sensamagic)
- 3.4 686/675 (sengic)
- 3.5 875/864 (keemic)
- 3.6 1029/1024 (gamelismic)
- 3.7 1728/1715 (orwellismic)
- 3.8 2401/2400 (breed)
- 3.9 3125/3087 (gariboh)
- 3.10 3136/3125 (hemimean)
- 3.11 4000/3969 (octagar)
- 3.12 4375/4374 (ragismic)
- 3.13 5120/5103 (hemifamity)
- 3.14 6144/6125 (porwell)
- 3.15 10976/10935 (hemimage)
- 3.16 64827/64000 (squalentine)
- 4 13-limit examples
3-limit examples
256/243 (blackwood)
battaglia-blackwood [dead link]
5-limit examples
81/80 (meantone)
These are very familiar from classical and popular music. See Meantone comma pump examples.
128/125 (augmented)
See 12edo comma pump examples.
250/243 (porcupine)
2048/2025 (diaschismic)
Also see 12edo comma pump examples.
3125/3072 (magic)
15625/15552 (hanson)
16875/16384 (negri)
20000/19683 (tetracot)
78732/78125 (sensi)
1600000/1594323 (amity)
2109375/2097152 (semicomma, 5-limit orwell)
7-limit examples
126/125 (starling)
| 1 | 5/4 | 3/2 | 7/4 | ~ | 125/126 | 625/504 | 125/84 | 125/72 |
| 21/20 | 21/16 | 3/2 | 7/4 | ~ | 25/24 | 125/96 | 125/84 | 125/72 |
| 21/20 | 6/5 | 3/2 | 9/5 | ~ | 25/24 | 25/21 | 125/84 | 25/14 |
| 36/35 | 6/5 | 36/25 | 9/5 | ~ | 50/49 | 25/21 | 10/7 | 25/14 |
| 27/25 | 63/50 | 36/25 | 9/5 | ~ | 15/14 | 5/4 | 10/7 | 25/14 |
| 126/125 | 63/50 | 189/125 | 441/250 | ~ | 1 | 5/4 | 3/2 | 7/4 |
| 1 | 5/4 | 3/2 | 7/4 | ~ | 125/126 | 625/504 | 125/84 | 125/72 |
| 21/20 | 6/5 | 3/2 | 9/5 | ~ | 25/24 | 25/21 | 125/84 | 25/14 |
| 27/25 | 63/50 | 36/25 | 9/5 | ~ | 15/14 | 5/4 | 10/7 | 25/14 |
| 126/125 | 63/50 | 189/125 | 441/250 | ~ | 1 | 5/4 | 3/2 | 7/4 |
225/224 (marvel)
| 1 | 5/4 | 3/2 | 7/4 | ~ | 225/224 | 1125/896 | 675/448 | 225/128 |
| 1 | 7/6 | 7/5 | 7/4 | ~ | 225/224 | 75/64 | 45/32 | 225/128 |
| 14/15 | 7/6 | 7/5 | 49/30 | ~ | 15/16 | 75/64 | 45/32 | 105/64 |
| 14/15 | 7/6 | 4/3 | 14/9 | ~ | 15/16 | 75/64 | 75/56 | 25/16 |
| 14/15 | 49/45 | 56/45 | 14/9 | ~ | 15/16 | 35/32 | 5/4 | 25/16 |
| 14/15 | 16/15 | 56/45 | 112/75 | ~ | 15/16 | 15/14 | 5/4 | 3/2 |
| 224/225 | 56/45 | 112/75 | 392/225 | ~ | 1 | 5/4 | 3/2 | 7/4 |
| 1 | 5/4 | 3/2 | 7/4 | ~ | 225/224 | 1125/896 | 675/448 | 225/128 |
| 1 | 7/6 | 7/5 | 7/4 | ~ | 225/224 | 75/64 | 45/32 | 225/128 |
| 14/15 | 7/6 | 4/3 | 14/9 | ~ | 15/16 | 75/64 | 75/56 | 25/16 |
| 14/15 | 16/15 | 56/45 | 112/75 | ~ | 15/16 | 15/14 | 5/4 | 3/2 |
| 224/225 | 56/45 | 112/75 | 392/225 | ~ | 1 | 5/4 | 3/2 | 7/4 |
245/243 (sensamagic)
| 1 | 5/4 | 3/2 | 7/4 | ~ | 245/243 | 1225/972 | 245/162 | 1715/972 |
| 15/14 | 9/7 | 3/2 | 12/7 | ~ | 175/162 | 35/27 | 245/162 | 140/81 |
| 27/28 | 9/8 | 9/7 | 45/28 | ~ | 35/36 | 245/216 | 35/27 | 175/108 |
| 27/28 | 54/49 | 135/98 | 81/49 | ~ | 35/36 | 10/9 | 25/18 | 5/3 |
| 405/392 | 243/196 | 81/56 | 81/49 | ~ | 25/24 | 5/4 | 35/24 | 5/3 |
| 243/245 | 243/196 | 729/490 | 243/140 | ~ | 1 | 5/4 | 3/2 | 7/4 |
| 1 | 5/4 | 3/2 | 7/4 | ~ | 245/243 | 1225/972 | 245/162 | 1715/972 |
| 27/28 | 9/8 | 9/7 | 45/28 | ~ | 35/36 | 245/216 | 35/27 | 175/108 |
| 405/392 | 243/196 | 81/56 | 81/49 | ~ | 25/24 | 5/4 | 35/24 | 5/3 |
| 243/245 | 243/196 | 729/490 | 243/140 | ~ | 1 | 5/4 | 3/2 | 7/4 |
1-5/4-3/2-7/4
15/14-9/7-3/2-12/7
27/28-9/8-9/7-45/28
27/28-54/49-135/98-81/49
405/392-243/196-81/56-81/49
243/245-243/196-729/490-243/140
1-5/4-3/2-7/4
27/28-9/8-9/7-45/28
405/392-243/196-81/56-81/49
243/245-243/196-729/490-243/140
686/675 (sengic)
875/864 (keemic)
1029/1024 (gamelismic)
1-5/4-3/2-7/4
1-5/4-10/7-5/3
1-8/7-10/7-12/7
20/21-8/7-10/7-80/49
48/49-8/7-64/49-80/49
48/49-384/343-64/49-384/245
384/343-64/49-512/343-640/343
256/245-64/49-512/343-256/147
1024/1029-1280/1029-512/343-256/147
1-5/4-3/2-7/4
1-8/7-10/7-12/7
48/49-8/7-64/49-80/49
384/343-64/49-512/343-640/343
1024/1029-1280/1029-512/343-256/147
1728/1715 (orwellismic)
1-5/4-3/2-7/4
1-7/6-7/5-7/4
49/48-7/6-35/24-7/4
49/48-7/6-49/36-49/30
49/48-343/288-49/36-245/144
343/288-49/36-343/216-343/180
1715/1728-343/288-2401/1728-343/216
1715/1728-343/288-1715/1152-245/144
1715/1728-8575/6912-1715/1152-12005/6912
1-5/4-3/2-7/4
49/48-7/6-35/24-7/4
49/48-343/288-49/36-245/144
1715/1728-343/288-2401/1728-343/216
1715/1728-8575/6912-1715/1152-12005/6912
2401/2400 (breed)
1-5/4-3/2-7/4
21/20-21/16-3/2-7/4
21/20-49/40-7/5-7/4
49/48-49/40-49/32-7/4
343/320-49/40-49/32-147/80
343/320-1029/800-1029/640-147/80
343/320-1029/800-2401/1600-343/200
343/320-2401/1920-2401/1600-2401/1280
7203/6400-16807/12800-2401/1600-2401/1280
16807/16000-16807/12800-2401/1600-16807/9600
2401/2400-2401/1920-2401/1600-16807/9600
1-5/4-3/2-7/4 21/20-49/40-7/5-7/4
343/320-49/40-49/32-147/80
2401/1600-343/200-343/160-1029/400
7203/6400-16807/12800-2401/1600-2401/1280
2401/2400-2401/1920-2401/1600-16807/9600
3125/3087 (gariboh)
3136/3125 (hemimean)
1-5/4-3/2-7/4
1-7/6-7/5-7/4
1-6/5-7/5-8/5
14/15,28/25-7/5-8/5
49/50-28/25-7/5-42/25
24/25-28/25-168/125-42/25
28/25-168/125-196/125-224/125
147/125-168/125-196/125-1176/625
686/625-784/625-196/125-1176/625
672/625-784/625-4704/3125-1176/625
3136/3125-784/625-4704/3125-5488/3125
1-5/4-3/2-7/4
1-6/5-7/5-8/5
28/25-7/5-42/25-49/25
28/25-168/125-196/125-224/125
686/625-784/625-196/125-1176/625
3136/3125-784/625-4704/3125-5488/3125
4000/3969 (octagar)
1-5/4-3/2-7/4
1-5/4-10/7-5/3
15/14-5/4-10/7-25/14
1-5/4-10/7-5/3
20/21-25/21-10/7-5/3
50/49-25/21-10/7-25/14
50/49-25/21-200/147-250/147
1000/1029-500/441-200/147-250/147
500/441-200/147-100/63-800/441
125/126-500/441-250/189-100/63
500/441-250/189-2000/1323-2500/1323
200/189-250/189-2000/1323-1000/567
4000/3969-5000/3969-2000/1323-1000/567
1-5/4-3/2-7/4
15/14-5/4-10/7-25/14
20/21-25/21-10/7-5/3
50/49-25/21-200/147-250/147
500/441-200/147-100/63-800/441
500/441-250/189-2000/1323-2500/1323
4000/3969-5000/3969-2000/1323-1000/567
4375/4374 (ragismic)
1-5/4-3/2-7/4
1-5/4-10/7-5/3
25/24-5/4-35/24-5/3
35/36-7/6-35/24-5/3
35/36-10/9-25/18-5/3
35/36-175/144-25/18-175/108
25/27-125/108-25/18-175/108
25/27-175/162-35/27-175/108
175/162-875/648-175/108-1225/648 ~ 27/25-27/20-81/50-189/100
175/162-875/648-125/81-875/486 ~ 27/25-27/20-54/35-9/5
4375/3888-875/648-6125/3888-875/486 ~ 9/8-27/20-63/40-9/5
4375/3888-625/486-4375/2916-875/486 ~ 9/8-9/7-3/2-9/5
6125/5832-875/729-4375/2916-875/486 ~ 21/20-6/5-3/2-9/5
4375/4374-875/729-4375/2916-1250/729 ~ 1-6/5-3/2-12/7
4375/4374-21875/17496-4375/2916-30625/17496 ~ 1-5/4-3/2-7/4
1-5/4-3/2-7/4
25/24-5/4-35/24-5/3
35/36-10/9-25/18-5/3
25/27-125/108-25/18-175/108
175/162-875/648-175/108-1225/648 ~ 27/25-27/20-81/50-189/100
4375/3888-875/648-6125/3888-875/486 ~ 9/8-27/20-63/40-9/5
6125/5832-875/729-4375/2916-875/486 ~ 21/20-6/5-3/2-9/5
4375/4374-21875/17496-4375/2916-30625/17496 ~ 1-5/4-3/2-7/4
5120/5103 (hemifamity)
1-5/4-3/2-7/4
35/32-5/4-35/24-7/4
25/24-5/4-35/24-5/3
25/24-25/21-25/18-5/3
35/36-10/9-25/18-5/3
20/21-10/9-4/3-5/3
20/21-10/9-80/63-100/63
400/441-200/189-80/63-100/63
200/189-80/63-40/27-320/189
80/81-32/27-40/27-320/189
80/81-640/567-800/567-320/189
80/81-640/567-320/243-128/81
1600/1701-640/567-320/243-2560/1701
256/243-320/243-2560/1701-1280/729
5120/5103-6400/5103-2560/1701-1280/729
1-5/4-3/2-7/4
25/24-5/4-35/24-5/3
35/36-10/9-25/18-5/3
20/21-10/9-80/63-100/63
200/189-80/63-40/27-320/189
80/81-640/567-800/567-320/189
1600/1701-640/567-320/243-2560/1701
256/243-320/243-2560/1701-1280/729
5120/5103-6400/5103-2560/1701-1280/729
6144/6125 (porwell)
1-5/4-3/2-7/4
35/32-5/4-35/24-7/4
35/32-5/4-25/16-15/8
35/32-21/16-105/64-15/8
35/32-175/128-105/64-245/128
525/512-175/128-75/64-105/64
525/512-1225/1024-175/128-875/512
6125/6144-1225/1024-6125/4096-875/512
8575/8192-1225/1024-6125/4096-3675/2048
18375/16384-2625/2048-6125/4096-3675/2048
18375/16384-42875/32768-6125/4096-30625/16384
4375/4096-30625/24576-6125/4096-30625/16384
6125/6144-30625/24576-6125/4096-42875/24576
1-5/4-3/2-7/4
35/32-5/4-25/16-15/8
35/32-175/128-105/64-245/128
525/512-1225/1024-175/128-875/512
8575/8192-1225/1024-6125/4096-3675/2048
18375/16384-42875/32768-6125/4096-30625/16384
6125/6144-30625/24576-6125/4096-42875/24576
