User:BudjarnLambeth/Table of n-comma meantone generators
Here are all meantone tunings that can be written in the form "n-comma meantone", where n is a fraction between 0 and 1 with a denominator 18 or smaller. Also included are 7edo and 12edo (to delineate MOS shapes), as well as a few other notable meantone tunings (e.g. 4/25-comma).
| Temperament | Generator (cents) | Comments |
|---|---|---|
| 1/1-comma meantone | 680.449 | |
| 15/16-comma meantone | 681.793 | |
| 14/15-comma meantone | 681.883 | |
| 13/14-comma meantone | 681.985 | |
| 12/13-comma meantone | 682.103 | |
| 11/12-comma meantone | 682.241 | |
| 12/11-comma meantone | 682.404 | |
| 9/10-comma meantone | 682.599 | |
| 8/9-comma meantone | 682.838 | |
| 7/8-comma meantone | 683.137 | |
| 13/15-comma meantone | 683.316 | |
| 6/7-comma meantone | 683.521 | |
| 11/13-comma meantone | 683.757 | |
| 5/6-comma meantone | 684.033 | |
| 9/11-comma meantone | 684.359 | |
| 13/16-comma meantone | 684.481 | |
| 4/5-comma meantone | 684.75 | |
| 11/14-comma meantone | 685.057 | |
| 7/9-comma meantone | 685.228 | |
| 10/13-comma meantone | 685.412 | Everything up to this point generates 9 and 16 tone MOS scales. |
| 7edo | 695.714 | The largest MOS scale this can generate is 7 tone. |
| 3/4-comma meantone | 685.825 | Everything from this point onwards generates 12 and 19 tone MOS scales. |
| 11/15-comma meantone | 686.184 | |
| 8/11-comma meantone | 686.314 | |
| 5/7-comma meantone | 686.593 | |
| 7/10-comma meantone | 686.901 | |
| 9/13-comma meantone | 687.066 | |
| 11/16-comma meantone | 687.169 | |
| 2/3-comma meantone | 687.617 | |
| 9/14-comma meantone | 688.129 | |
| 7/11-comma meantone | 688.269 | |
| 5/8-comma meantone | 688.514 | |
| 8/13-comma meantone | 688.72 | |
| 3/5-comma meantone | 689.051 | |
| 7/12-comma meantone | 689.41 | |
| 4/7-comma meantone | 689.666 | |
| 9/16-comma meantone | 689.858 | |
| 5/9-comma meantone | 690.007 | |
| 6/11-comma meantone | 690.224 | |
| 7/13-comma meantone | 690.375 | |
| 8/15-comma meantone | 690.485 | Close to 33edo |
| 1/2-comma meantone | 691.202 | Close to 92edo, 59edo. Historically significant (see historical temperaments. Everything up to this point does not meet the original historical definition of meantone (the whole tone being between 10/9 and 9/8). |
| 7/15-comma meantone | 691.919 | Close to 85edo |
| 6/13-comma meantone | 692.029 | |
| 5/11-comma meantone | 692.179 | |
| 4/9-comma meantone | 692.397 | Close to 26edo |
| 7/16-comma meantone | 692.546 | |
| 3/7-comma meantone | 692.738 | |
| 5/12-comma meantone | 692.994 | Close to 71edo |
| 7/17-comma meantone | 693.099 | |
| 2/5-comma meantone | 693.352 | Close to 45edo |
| 7/18-comma meantone | 693.591 | |
| 5/13-comma meantone | 693.683 | Close to 64edo |
| 3/8-comma meantone | 693.890 | Close to 83edo |
| 4/11-comma meantone | 694.134 | Almost exactly 1/3 Pythagorean comma meantone |
| 5/14-comma meantone | 694.274 | |
| 6/17-comma meantone | 694.365 | |
| 1/3-comma meantone | 694.786 | Close to 19edo. Historically significant (see historical temperaments). |
| 5/16-comma meantone | 695.234 | |
| 4/13-comma meantone | 695.338 | |
| 3/10-comma meantone | 695.503 | Close to 88edo |
| 5/17-comma meantone | 695.630 | |
| 2/7-comma meantone | 695.810 | Close to 69edo. Historically significant (see historical temperaments). |
| 5/18-comma meantone | 695.981 | Close to 50edo. Historically significant (see historical temperaments). |
| 3/11-comma meantone | 696.090 | Close to 50edo |
| 7/26-comma meantone | 696.165 | Close to golden meantone. Historically significant (see historical temperaments). |
| 4/15-comma meantone | 696.22 | Close to 81edo, close to golden meantone |
| 1/4-comma meantone | 696.578 | Close to 31edo. Historically significant (see historical temperaments). |
| 4/17-comma meantone | 696.895 | |
| 3/13-comma meantone | 696.992 | Close to septimal & tridecimal CTE tunings. |
| 2/9-comma meantone | 697.176 | Close to 5-limit and undecimal CTE tunings. Historically significant (see historical temperaments). |
| 3/14-comma meantone | 697.346 | Close to 74edo. Historically significant (see historical temperaments). |
| 1/5-comma meantone | 697.654 | Close tp 43edo. Historically significant (see historical temperaments). |
| 3/16-comma meantone | 697.923 | |
| 2/11-comma meantone | 698.045 | Close to 55edo |
| 3/17-comma meantone | 699.425 | |
| 1/6-comma meantone | 698.371 | Close to 67edo. Historically significant (see historical temperaments). |
| 4/25-comma meantone | 698.514 | Close to 67edo. Historically significant (see historical temperaments). |
| 2/13-comma meantone | 698.646 | |
| 1/7-comma meantone | 698.883 | Close to 79edo, 91edo. Historically significant (see historical temperaments). |
| 2/15-comma meantone | 699.088 | |
| 1/8-comma meantone | 699.267 | |
| 2/17-comma meantone | 699.425 | |
| 1/9-comma meantone | 699.565 | |
| 1/10-comma meantone | 699.804 | |
| 1/11-comma meantone | 700.000 | Everything up to this point generates 12 and 19 tone MOS scales. |
| 12edo | 700.000 | The largest MOS scale this can generate is 12 tone. |
| 1/12-comma meantone | 700.163 | Everything from this point onwards generates 12 and 17 tone MOS scales. |
| 1/13-comma meantone | 700.301 | |
| 1/14-comma meantone | 700.419 | |
| 1/15-comma meantone | 700.521 | |
| 1/16-comma meantone | 700.611 | |
| 1/17-comma meantone | 700.690 | |
| 1/18-comma meantone | 700.760 | |
| 0/1-comma meantone | 701.955 | Pythagorean tuning. Everything from this point onwards does not meet the original historical definition of meantone (the whole tone being between 10/9 and 9/8). |