User:BudjarnLambeth/Table of n-comma meantone generators
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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 5, 7 and 12edo (to delineate MOS shapes), as well as a few other notable meantone tunings (e.g. 4/25-comma).
The comma being divided here is the syntonic comma (81/80).
Temperaments that fall outside of the diamond monotone range will not provide most of the advantages that meantone usually provides, but they are included for completeness.
| Temperament | Generator (cents) | Comments |
|---|---|---|
| 1/1-comma meantone | 680.449 | Close to 30edo |
| 17/18-comma meantone | 681.644 | |
| 16/17-comma meantone | 681.714 | |
| 15/16-comma meantone | 681.793 | Close to 44edo |
| 14/15-comma meantone | 681.883 | |
| 13/14-comma meantone | 681.985 | |
| 12/13-comma meantone | 682.103 | |
| 11/12-comma meantone | 682.241 | |
| 10/11-comma meantone | 682.404 | Close to 51edo |
| 9/10-comma meantone | 682.599 | |
| 8/9-comma meantone | 682.838 | Close to 58edo |
| 15/17-comma meantone | 682.979 | |
| 7/8-comma meantone | 683.137 | Close to 65edo |
| 13/15-comma meantone | 683.316 | Close to 72edo |
| 6/7-comma meantone | 683.521 | Close to 79edo |
| 11/13-comma meantone | 683.757 | Close to 86edo |
| 16/19-comma meantone | 683.844 | |
| 21/25-comma meantone | 683.890 | |
| 683.910 | As flat of Pythagorean tuning as 5edo is sharp. | |
| 5/6-comma meantone | 684.033 | |
| 14/17-comma meantone | 684.244 | |
| 9/11-comma meantone | 684.359 | |
| 13/16-comma meantone | 684.481 | |
| 4/5-comma meantone | 684.750 | |
| 11/14-comma meantone | 685.057 | |
| 7/9-comma meantone | 685.228 | |
| 10/13-comma meantone | 685.412 | |
| 13/17-comma meantone | 685.509 | Everything up to this point generates 9 and 16 tone MOS scales. |
| 7edo | 685.714 | The largest MOS scale this can generate is 7 tone. Lower boundary of 5-limit diamond monotone. |
| 3/4-comma meantone | 685.825 | Everything from this point onwards generates 12 and 19 tone MOS scales. |
| 11/15-comma meantone | 686.184 | |
| 19/26-comma meantone | 686.239 | |
| 8/11-comma meantone | 686.314 | |
| 13/18-comma meantone | 686.422 | |
| 5/7-comma meantone | 686.593 | |
| 17/24- comma meantone | 686.721 | |
| 12/17-comma meantone | 686.774 | |
| 7/10-comma meantone | 686.901 | |
| 9/13-comma meantone | 687.066 | |
| 11/16-comma meantone | 687.169 | |
| 2/3-comma meantone | 687.617 | Close to 89edo |
| 11/17-comma meantone | 688.039 | Close to 75edo |
| 9/14-comma meantone | 688.129 | |
| 7/11-comma meantone | 688.269 | Close to 68edo |
| 5/8-comma meantone | 688.514 | Close to 61edo |
| 8/13-comma meantone | 688.720 | |
| 11/18-comma meantone | 688.812 | Close to 54edo |
| 3/5-comma meantone | 689.051 | |
| 10/17-comma meantone | 689.304 | |
| 7/12-comma meantone | 689.410 | Close to 47edo |
| 4/7-comma meantone | 689.666 | Close to 87edo |
| 9/16-comma meantone | 689.858 | |
| 5/9-comma meantone | 690.007 | Close to 40edo |
| 6/11-comma meantone | 690.224 | |
| 7/13-comma meantone | 690.375 | Close to 73edo |
| 8/15-comma meantone | 690.485 | |
| 9/17-comma meantone | 690.569 | Close to 33edo |
| 1/2-comma meantone | 691.202 | Close to 92edo. 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). |
| 8/17-comma meantone | 691.834 | Close to 59edo. |
| 7/15-comma meantone | 691.919 | Close to 85edo |
| 6/13-comma meantone | 692.029 | |
| 5/11-comma meantone | 692.179 | |
| 26edo | 692.308 | The largest MOS scale this can generate is 26 tone. |
| 4/9-comma meantone | 692.397 | |
| 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 | |
| 19edo | 694.737 | The largest MOS scale this can generate is 19 tone. Historically significant (see historical temperaments). |
| 1/3-comma meantone | 694.786 | Historically significant (see historical temperaments). |
| 694.819 | As flat of Pythagorean tuning as 22edo is sharp. | |
| 5/16-comma meantone | 695.234 | |
| 4/13-comma meantone | 695.338 | |
| Lucy tuning | 695.493 | Historically significant (see historical temperaments). Close to 88edo. |
| 3/10-comma meantone | 695.503 | |
| 5/17-comma meantone | 695.630 | |
| 7/24-comma meantone | 695.682 | Close to 69edo. |
| 2/7-comma meantone | 695.810 | Historically significant (see historical temperaments). |
| 5/18-comma meantone | 695.981 | Historically significant (see historical temperaments). |
| 50edo | 696.000 | The largest MOS scale this can generate is 50 tone. Historically significant (see historical temperaments). |
| 3/11-comma meantone | 696.090 | Almost exactly 1/4-Pythagorean comma meantone |
| 7/26-comma meantone | 696.165 | Historically significant (see historical temperaments). |
| Golden meantone | 696.214 | Historically significant (see historical temperaments). |
| 696.218 | As flat of Pythagorean tuning as 39edo is sharp. Negative harmonically significant tuning with flat fifth (see negative harmony temperaments). | |
| 4/15-comma meantone | 696.220 | Close to 81edo. |
| 1/4-comma meantone | 696.578 | Historically significant (see historical temperaments). |
| 31edo | 696.774 | The largest MOS scale this can generate is 31 tone. 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). |
| 74edo | 697.297 | The largest MOS scale this can generate is 74 tone. Historically significant (see historical temperaments). |
| 3/14-comma meantone | 697.346 | Historically significant (see historical temperaments). |
| 1/5-comma meantone | 697.654 | Historically significant (see historical temperaments). |
| 43edo | 697.654 | The largest MOS scale this can generate is 43 tone. Historically significant (see historical temperaments). |
| 3/16-comma meantone | 697.923 | |
| 698.023 | As flat of Pythagorean tuning as 17edo is sharp. | |
| 2/11-comma meantone | 698.045 | |
| 55edo | 698.182 | The largest MOS scale this can generate is 55 tone. Historically significant (see historical temperaments). |
| 3/17-comma meantone | 698.245 | |
| 1/6-comma meantone | 698.371 | Historically significant (see historical temperaments). |
| 4/25-comma meantone | 698.514 | Close to 67edo. Historically significant (see historical temperaments). |
| 3/19-comma meantone | 698.559 | |
| 2/13-comma meantone | 698.646 | Close to 79edo. |
| 1/7-comma meantone | 698.883 | Close to 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. Historically significant (see historical temperaments.) |
| 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. Historically significant (see historical temperaments.) Negative harmonically significant (see negative harmony temperaments). Everything from this point onwards does not meet the original historical definition of meantone (the whole tone being between 10/9 and 9/8). |
| -1/6-comma meantone | 705.027 | Negative harmonically significant (see negative harmony temperaments). |
| 705.728 | As sharp of Pythagorean tuning as 55edo is flat. Negative harmonically significant (see negative harmony temperaments). | |
| -3/17-comma meantone | 705.750 | Historically significant tuning with sharp fifth (see historical temperaments. |
| -2/11-comma meantone | 705.865 | |
| 17edo | 705.882 | Simplest tuning for Middle Eastern neutral third scales. The largest MOS scale this can generate is 17 tone. |
| -3/16-comma meantone | 705.987 | |
| 706.236 | As sharp of Pythagorean tuning as 43edo is flat. Negative harmonically significant (see negative harmony temperaments). | |
| -1/5-comma meantone | 706.256 | Negative harmonically significant (see negative harmony temperaments). |
| -3/14-comma meantone | 706.563 | Negative harmonically significant (see negative harmony temperaments). |
| 706.613 | As sharp of Pythagorean tuning as 74edo is flat. Negative harmonically significant (see negative harmony temperaments). | |
| -2/9-comma meantone | 706.734 | Negative harmonically significant (see negative harmony temperaments). |
| -3/13-comma meantone | 706.918 | |
| -4/17-comma meantone | 707.015 | |
| 707.136 | As sharp of Pythagorean tuning as 74edo is flat. Negative harmonically significant (see negative harmony temperaments). | |
| -1/4-comma meantone | 707.332 | Negative harmonically significant (see negative harmony temperaments). |
| -4/15-comma meantone | 707.690 | |
| 39edo | 707.692 | Historically significant tuning with sharp fifth (see historical temperaments.) The largest MOS scale this can generate is 39 tone. |
| 707.696 | As sharp of Pythagorean tuning as Golden meantone is flat. Negative harmonically significant (see negative harmony temperaments). | |
| -7/26-comma meantone | 707.745 | Negative harmonically significant (see negative harmony temperaments). |
| -3/11-comma meantone | 707.820 | Almost exactly -1/4-Pythagorean comma meantone |
| 707.910 | As sharp of Pythagorean tuning as 50edo is flat. Negative harmonically significant (see negative harmony temperaments). | |
| -5/18-comma meantone | 707.930 | Negative harmonically significant (see negative harmony temperaments). |
| -2/7-comma meantone | 708.100 | Negative harmonically significant (see negative harmony temperaments). |
| -7/24-comma meantone | 708.227 | |
| -5/17-comma meantone | 708.280 | |
| -3/10-comma meantone | 708.407 | |
| 708.417 | As sharp of Pythagorean tuning as Lucy tuning is flat. Nearly as sharp of Pythagorean tuning as 88edo is flat. Negative harmonically significant (see negative harmony temperaments). | |
| -4/13-comma meantone | 708.572 | |
| -5/16-comma meantone | 708.675 | |
| 22edo | 709.091 | Isomorphic to Indian shrutis. The largest MOS scale this can generate is 22 tone. |
| -1/3-comma meantone | 709.124 | Negative harmonically significant (see negative harmony temperaments). |
| 709.173 | As sharp of Pythagorean tuning as 19edo is flat. Negative harmonically significant (see negative harmony temperaments). | |
| -6/17-comma meantone | 709.545 | |
| -5/14-comma meantone | 709.636 | |
| -4/11-comma meantone | 709.775 | Almost exactly -1/3-Pythagorean comma meantone |
| -3/8-comma meantone | 710.019 | |
| -5/13-comma meantone | 710.227 | Close to 49edo. |
| -7/18-comma meantone | 710.319 | |
| -2/5-comma meantone | 710.558 | Negative harmonically significant (see negative harmony temperaments). |
| -7/17-comma meantone | 710.810 | |
| -5/12-comma meantone | 710.915 | |
| -3/7-comma meantone | 711.172 | Close to 27edo. |
| -7/16-comma meantone | 711.364 | |
| -4/9-comma meantone | 711.513 | |
| 711.602 | As sharp of Pythagorean tuning as 19edo is flat. | |
| -5/11-comma meantone | 711.731 | |
| -6/13-comma meantone | 711.880 | Close to 59edo. |
| -7/15-comma meantone | 711.991 | |
| -8/17-comma meantone | 712.075 | |
| -1/2-comma meantone | 712.708 | Close to 32edo. Negative harmonically significant (see negative harmony temperaments). Everything from this point onwards does not meet the negative harmonic definition of meantone (the whole tone being between 9/8 and 729/640). |
| -9/17-comma meantone | 713.340 | |
| -8/15-comma meantone | 713.425 | |
| -7/13-comma meantone | 713.535 | Close to 37edo. |
| -6/11-comma meantone | 713.686 | |
| -5/9-comma meantone | 713.903 | |
| -9/16-comma meantone | 714.052 | |
| -4/7-comma meantone | 714.244 | Close to 42edo. |
| -7/12-comma meantone | 714.500 | |
| -10/17-comma meantone | 714.606 | |
| -3/5-comma meantone | 714.859 | Close to 47edo. |
| -11/18-comma meantone | 715.098 | |
| -8/13-comma meantone | 715.190 | |
| -5/8-comma meantone | 715.396 | Close to 52edo. |
| -7/11-comma meantone | 715.641 | |
| -9/14-comma meantone | 715.780 | Close to 57edo. |
| -11/17-comma meantone | 715.871 | |
| -2/3-comma meantone | 716.293 | Close to 62edo. |
| -15/22 comma meantone | 716.618 | Close to 67edo. |
| -13/19 comma meantone | 716.669 | Close to 72edo. |
| -11/16-comma meantone | 716.741 | |
| -9/13-comma meantone | 716.844 | Close to 77edo. |
| -7/10-comma meantone | 717.009 | |
| -12/17-comma meantone | 717.136 | Close to 82edo. |
| -17/24-comma meantone | 717.188 | Close to 87edo. |
| -5/7-comma meantone | 717.317 | Close to 92edo. |
| -13/18-comma meantone | 717.487 | Close to 97edo. |
| -8/11-comma meantone | 717.596 | |
| -19/26-comma meantone | 717.671 | |
| -11/15-comma meantone | 717.726 | |
| -3/4-comma meantone | 718.085 | |
| 718.196 | As sharp of Pythagorean tuning as 7edo is flat. | |
| -13/17-comma meantone | 718.401 | |
| -10/13-comma meantone | 718.498 | |
| -7/9-comma meantone | 718.682 | |
| -11/14-comma meantone | 718.853 | |
| -4/5-comma meantone | 719.160 | |
| -13/16-comma meantone | 719.429 | |
| -9/11-comma meantone | 719.551 | |
| -14/17-comma meantone | 719.666 | |
| -5/6-comma meantone | 719.877 | Everything up to this point generates 12 and 17 tone MOS scales. |
| 5edo | 720.000 | The largest MOS scale this can generate is 5 tone. Upper boundary of 5-limit diamond monotone. |
| -21/25-comma meantone | 720.020 | Everything from this point onwards generates 13 and 18 tone MOS scales. |
| -16/19-comma meantone | 720.066 | |
| -11/13-comma meantone | 720.153 | |
| -6/7-comma meantone | 720.399 | |
| -13/15-comma meantone | 720.594 | |
| -7/8-comma meantone | 720.773 | |
| -15/17-comma meantone | 720.931 | |
| -8/9-comma meantone | 721.017 | |
| -9/10-comma meantone | 721.311 | |
| -10/11-comma meantone | 721.506 | |
| -11/12-comma meantone | 721.669 | |
| -12/13-comma meantone | 721.807 | |
| -13/14-comma meantone | 721.925 | |
| -14/15-comma meantone | 722.028 | |
| -15/16-comma meantone | 722.117 | |
| -16/17-comma meantone | 722.196 | |
| -17/18-comma meantone | 722.266 | |
| -1/1-comma meantone | 723.461 | Close to 68edo |