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).

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
15/16-comma meantone	681.793
14/15-comma meantone	681.883	Close to 44edo
13/14-comma meantone	681.985
12/13-comma meantone	682.103
11/12-comma meantone	682.241
12/11-comma meantone	682.404	Close to 51edo
9/10-comma meantone	682.599
8/9-comma meantone	682.838	Close to 58edo
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
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	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
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	Close to 89edo
9/14-comma meantone	688.129	Close to 75edo
7/11-comma meantone	688.269	Close to 68edo
5/8-comma meantone	688.514	Close to 61edo
8/13-comma meantone	688.720	Close to 54edo
3/5-comma meantone	689.051
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	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	696.220	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 to 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. 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. Everything from this point onwards does not meet the original historical definition of meantone (the whole tone being between 10/9 and 9/8).
5edo	720.000	Upper boundary of 5-limit diamond monotone.