User:BudjarnLambeth/Table of n-comma meantone generators: Difference between revisions

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|[[7/13-comma meantone]]||690.375||Whole tone not between 10/9 and 9/8
|[[7/13-comma meantone]]||690.375||Whole tone not between 10/9 and 9/8
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|-
|[[8/15-comma meantone]]||690.485||Whole tone not between 10/9 and 9/8
|[[8/15-comma meantone]]||690.485||Close to [[33edo]]. Whole tone not between 10/9 and 9/8
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|-
|[[1/2-comma meantone]]||691.202||Whole tone not between 10/9 and 9/8 (it’s exactly 10/9)
|[[1/2-comma meantone]]||691.202||Close to [[92edo]], [[59edo]]. Historically significant (see [[historical temperaments]]. Whole tone not between 10/9 and 9/8 (it’s exactly 10/9)
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|[[7/15-comma meantone]]||691.919||This is the first tuning on this list which is unambiguously meantone, since the whole tone is between 10/9 and 9/8.
|[[7/15-comma meantone]]||691.919||Close to [[85edo]]. This is the first tuning on this list which is unambiguously meantone, since the whole tone is between 10/9 and 9/8.
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|[[6/13-comma meantone]]||692.029||  
|[[6/13-comma meantone]]||692.029||  
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|[[5/11-comma meantone]]||692.179||  
|[[5/11-comma meantone]]||692.179||  
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|[[4/9-comma meantone]]||692.397||  
|[[4/9-comma meantone]]||692.397||Close to [[26edo]]
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|[[7/16-comma meantone]]||692.546||  
|[[7/16-comma meantone]]||692.546||  
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|[[3/7-comma meantone]]||692.738||  
|[[3/7-comma meantone]]||692.738||  
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|[[5/12-comma meantone]]||692.994||  
|[[5/12-comma meantone]]||692.994||Close to [[71edo]]
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|[[2/5-comma meantone]]||693.352||  
|[[2/5-comma meantone]]||693.352||Close to [[45edo]]
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|[[5/13-comma meantone]]||693.683||  
|[[5/13-comma meantone]]||693.683||Close to [[64edo]]
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|[[3/8-comma meantone]]||693.89||  
|[[3/8-comma meantone]]||693.890||Close to [[83edo]]
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|[[4/11-comma meantone]]||694.134||  
|[[4/11-comma meantone]]||694.134||Almost exactly 1/3 ''Pythagorean'' comma meantone
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|[[5/14-comma meantone]]||694.274||  
|[[5/14-comma meantone]]||694.274||  
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|[[1/3-comma meantone]]||694.786||  
|[[1/3-comma meantone]]||694.786||Close to [[19edo]]. Historically significant (see [[historical temperaments]].
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|[[5/16-comma meantone]]||695.234||  
|[[5/16-comma meantone]]||695.234||  
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|[[4/13-comma meantone]]||695.338||  
|[[4/13-comma meantone]]||695.338||  
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|[[3/10-comma meantone]]||695.503||  
|[[3/10-comma meantone]]||695.503||Close to [[88edo]]
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|[[2/7-comma meantone]]||695.81||  
|[[2/7-comma meantone]]||695.81||Close to [[69edo]]. Historically significant (see [[historical temperaments]].
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|[[3/11-comma meantone]]||696.09||  
|[[3/11-comma meantone]]||696.09||Close to [[50edo]]
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|[[4/15-comma meantone]]||696.22||  
|[[4/15-comma meantone]]||696.22||Close to [[81edo]], close to [[golden meantone]]
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|[[Quarter-comma meantone|1/4-comma meantone]]||696.578||  
|[[Quarter-comma meantone|1/4-comma meantone]]||696.578||Close to [[31edo]]. Historically significant (see [[historical temperaments]].
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|[[3/13-comma meantone]]||696.992||  
|[[3/13-comma meantone]]||696.992||  
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|[[2/9-comma meantone]]||697.176||  
|[[2/9-comma meantone]]||697.176|| Historically significant (see [[historical temperaments]].
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|[[3/14-comma meantone]]||697.346||  
|[[3/14-comma meantone]]||697.346||Close to [[74edo]]. Historically significant (see [[historical temperaments]].
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|[[1/5-comma meantone]]||697.654||  
|[[1/5-comma meantone]]||697.654||Close tp [[43edo]]. Historically significant (see [[historical temperaments]].
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|[[3/16-comma meantone]]||697.923||  
|[[3/16-comma meantone]]||697.923||  
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|[[2/11-comma meantone]]||698.045||  
|[[2/11-comma meantone]]||698.045||Close to [[55edo]].
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|[[1/6-comma meantone]]||698.371||  
|[[1/6-comma meantone]]||698.371||Close to [[67edo]]. Historically significant (see [[historical temperaments]].
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|[[2/13-comma meantone]]||698.646||  
|[[2/13-comma meantone]]||698.646||  
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|[[1/7-comma meantone]]||698.883||  
|[[1/7-comma meantone]]||698.883||Close to [[79edo]], [[91edo]]. Historically significant (see [[historical temperaments]].
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|[[2/15-comma meantone]]||699.088||  
|[[2/15-comma meantone]]||699.088||  

Revision as of 12:06, 1 March 2024

Temperament Generator (cents) Comments
1/1-comma “meantone” (actually mavila) 680.449 Not meantone but included for reference
7edo 685.714 Not meantone. It and anything flatter than it cannot generate a 12-tone MOS.
3/4-comma meantone 685.825 Whole tone is not between 10/9 and 9/8, so whether it counts as meantone is very questionable.
11/15-comma meantone 686.184 Whole tone not between 10/9 and 9/8
8/11-comma meantone 686.314 Whole tone not between 10/9 and 9/8
5/7-comma meantone 686.593 Whole tone not between 10/9 and 9/8
7/10-comma meantone 686.901 Whole tone not between 10/9 and 9/8
9/13-comma meantone 687.066 Whole tone not between 10/9 and 9/8
11/16-comma meantone 687.169 Whole tone not between 10/9 and 9/8
2/3-comma meantone 687.617 Whole tone not between 10/9 and 9/8
9/14-comma meantone 688.129 Whole tone not between 10/9 and 9/8
7/11-comma meantone 688.269 Whole tone not between 10/9 and 9/8
5/8-comma meantone 688.514 Whole tone not between 10/9 and 9/8
8/13-comma meantone 688.72 Whole tone not between 10/9 and 9/8
3/5-comma meantone 689.051 Whole tone not between 10/9 and 9/8
7/12-comma meantone 689.41 Whole tone not between 10/9 and 9/8
4/7-comma meantone 689.666 Whole tone not between 10/9 and 9/8
9/16-comma meantone 689.858 Whole tone not between 10/9 and 9/8
5/9-comma meantone 690.007 Whole tone not between 10/9 and 9/8
6/11-comma meantone 690.224 Whole tone not between 10/9 and 9/8
7/13-comma meantone 690.375 Whole tone not between 10/9 and 9/8
8/15-comma meantone 690.485 Close to 33edo. Whole tone not between 10/9 and 9/8
1/2-comma meantone 691.202 Close to 92edo, 59edo. Historically significant (see historical temperaments. Whole tone not between 10/9 and 9/8 (it’s exactly 10/9)
7/15-comma meantone 691.919 Close to 85edo. This is the first tuning on this list which is unambiguously meantone, since the whole tone is between 10/9 and 9/8.
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
2/5-comma meantone 693.352 Close to 45edo
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
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
2/7-comma meantone 695.81 Close to 69edo. Historically significant (see historical temperaments.
3/11-comma meantone 696.09 Close to 50edo
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.
3/13-comma meantone 696.992
2/9-comma meantone 697.176 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.
1/6-comma meantone 698.371 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
1/9-comma meantone 699.565
1/10-comma meantone 699.804
1/11-comma meantone 700.000 Effectively indistinguishable from 12edo. Does not generate a 19-tone MOS scale, so whether it counts as meantone is very questionable.
1/12-comma meantone 700.163 No 19-tone MOS
1/13-comma meantone 700.301 No 19-tone MOS
1/14-comma meantone 700.419 No 19-tone MOS
1/15-comma meantone 700.521 No 19-tone MOS
1/16-comma meantone 700.611 No 19-tone MOS
0/1-comma “meantone” (Pythagorean tuning) 701.955 Not meantone but included for reference. 9/8 is exact. Anything sharper will have whole tones not between 10/9 and 9/8, along with continuing to lack a 19-tone MOS.
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