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m Remove “the largest this can generate is n tone” because that’s self evident and doesn’t need to be said, remove all the “important to negative harmony” because that was on almost every entry and cluttered the table making it hard to read, remove the unsourced claims about history that contradict everything I’ve ever read, remove extra added EDOs because this is about n-comma, not about EDOs, EDOs can have their own different table, other similar cleanup
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{{Editable user page}}
{{Editable user page}}


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, 12, 17 and 19edo (to delineate MOS shapes), as well as a few other notable meantone tunings (e.g. 4/25-comma).
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]]).
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.
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.
Dozens of tunings on the table are significant to [[negative harmony temperaments|negative harmony temperament theory]], enough that labelling them all individually would clutter the table.


{| class="wikitable"
{| class="wikitable"
Line 12: Line 14:
|[[1/1-comma meantone]]||680.449||Close to [[30edo]]
|[[1/1-comma meantone]]||680.449||Close to [[30edo]]
|-
|-
|[[17/18-comma meantone]]
|[[15/16-comma meantone]]||681.793||  
|681.644
|
|-
|[[16/17-comma meantone]]
|681.714
|
|-
|[[15/16-comma meantone]]||681.793 ||Close to [[44edo]]
|-
|-
|[[14/15-comma meantone]]||681.883||
|[[14/15-comma meantone]]||681.883||Close to [[44edo]]
|-
|-
|[[13/14-comma meantone]]||681.985||
|[[13/14-comma meantone]]||681.985||  
|-
|-
|[[12/13-comma meantone]]||682.103||
|[[12/13-comma meantone]]||682.103||  
|-
|-
|[[11/12-comma meantone]]||682.241||
|[[11/12-comma meantone]]||682.241||  
|-
|-
|[[10/11-comma meantone]]||682.404||Close to [[51edo]]
|[[12/11-comma meantone]]||682.404||Close to [[51edo]]
|-
|-
|[[9/10-comma meantone]]||682.599||
|[[9/10-comma meantone]]||682.599||  
|-
|-
|[[8/9-comma meantone]]||682.838||Close to [[58edo]]
|[[8/9-comma meantone]]||682.838||Close to [[58edo]]
|-
|-
|[[15/17-comma meantone]]
|[[7/8-comma meantone]]||683.137||Close to [[65edo]]
|682.979
|
|-
|[[7/8-comma meantone]]||683.137|| Close to [[65edo]]
|-
|-
|[[13/15-comma meantone]]||683.316|| Close to [[72edo]]
|[[13/15-comma meantone]]||683.316||Close to [[72edo]]  
|-
|-
|[[6/7-comma meantone]]||683.521||Close to [[79edo]]
|[[6/7-comma meantone]]||683.521||Close to [[79edo]]
Line 48: Line 38:
|[[11/13-comma meantone]]||683.757||Close to [[86edo]]
|[[11/13-comma meantone]]||683.757||Close to [[86edo]]
|-
|-
|[[16/19-comma meantone]]
|[[5/6-comma meantone]]||684.033||  
|683.844
|
|-
|[[21/25-comma meantone]]
|683.890
|
|-
|-
|
|[[9/11-comma meantone]]||684.359||
|683.910
|As flat of [[Pythagorean tuning]] as [[5edo]] is sharp.
|-
|-
|[[5/6-comma meantone]]||684.033||
|[[13/16-comma meantone]]||684.481||  
|-
|-
|[[14/17-comma meantone]]
|[[4/5-comma meantone]]||684.75||  
|684.244
|
|-
|-
|[[9/11-comma meantone]]||684.359||
|[[11/14-comma meantone]]||685.057||  
|-
|-
|[[13/16-comma meantone]]||684.481||
|[[7/9-comma meantone]]||685.228||  
|-
|-
|[[4/5-comma meantone]]||684.750 ||
|[[10/13-comma meantone]]||685.412||Everything up to this point generates 9 and 16 tone MOS scales.
|-
|-
|[[11/14-comma meantone]]||685.057||
|[[7edo]]||685.714||The largest MOS scale this can generate is 7 tone. '''Lower boundary of 5-limit diamond monotone.'''
|-
|-
|[[7/9-comma meantone]]||685.228 ||
|[[3/4-comma meantone]]||685.825||Everything from this point onwards generates 12 and 19 tone MOS scales.
|-
|-
|[[10/13-comma meantone]]||685.412 ||
|[[11/15-comma meantone]]||686.184||
|-
|[[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 and 26 tone MOS scales.
|-
|[[11/15-comma meantone]]||686.184 ||
|-
|[[19/26-comma meantone]]
|686.239
|
|-
|-
|[[8/11-comma meantone]]||686.314||
|[[8/11-comma meantone]]||686.314||
|-
|-
|[[13/18-comma meantone]]
|[[5/7-comma meantone]]||686.593||  
|686.422
|
|-
|-
|[[5/7-comma meantone]]||686.593||
|[[7/10-comma meantone]]||686.901||  
|-
|-
|[[17/24-comma meantone|17/24- comma meantone]]
|[[9/13-comma meantone]]||687.066||  
|686.721
|
|-
|-
|[[12/17-comma meantone]]
|[[11/16-comma meantone]]||687.169||  
|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]]
|[[2/3-comma meantone]]||687.617||Close to [[89edo]]
|-
|-
|[[11/17-comma meantone]]
|[[9/14-comma meantone]]||688.129||Close to [[75edo]]
|688.039
|Close to [[75edo]]
|-
|[[9/14-comma meantone]]|| 688.129||
|-
|-
|[[7/11-comma meantone]]||688.269||Close to [[68edo]]
|[[7/11-comma meantone]]||688.269||Close to [[68edo]]
Line 126: Line 76:
|[[5/8-comma meantone]]||688.514||Close to [[61edo]]
|[[5/8-comma meantone]]||688.514||Close to [[61edo]]
|-
|-
|[[Golden ratio comma meantone]]
|[[8/13-comma meantone]]||688.720||Close to [[54edo]]
|688.663
|
|-
|[[8/13-comma meantone]]||688.720||
|-
|-
|[[11/18-comma meantone]]
|[[3/5-comma meantone]]||689.051||  
|688.812
|Close to [[54edo]]
|-
|-
|[[3/5-comma meantone]]||689.051||
|[[7/12-comma meantone]]||689.410||Close to [[47edo]]
|-
|-
|[[10/17-comma meantone]]
|[[4/7-comma meantone]]||689.666||Close to [[87edo]]
|689.304
|
|-
|-
|[[7/12-comma meantone]]||689.410|| Close to [[47edo]]
|[[9/16-comma meantone]]||689.858||  
|-
|-
|[[4/7-comma meantone]]|| 689.666||Close to [[87edo]]
|[[5/9-comma meantone]]||690.007||Close to [[40edo]]
|-
|-
|[[9/16-comma meantone]]||689.858 ||
|[[6/11-comma meantone]]||690.224||  
|-
|[[5/9-comma meantone]]||690.007 ||Close to [[40edo]]
|-
|[[6/11-comma meantone]]||690.224||
|-
|-
|[[7/13-comma meantone]]||690.375||Close to [[73edo]]
|[[7/13-comma meantone]]||690.375||Close to [[73edo]]
|-
|-
|[[8/15-comma meantone]]||690.485||
|[[8/15-comma meantone]]||690.485||Close to [[33edo]]
|-
|-
|[[9/17-comma meantone]]
|[[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).
|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]]
|[[7/15-comma meantone]]||691.919||Close to [[85edo]]
|-
|-
|[[6/13-comma meantone]]||692.029||
|[[6/13-comma meantone]]||692.029||  
|-
|[[5/11-comma meantone]]||692.179||
|-
|-
|[[26edo]]
|[[5/11-comma meantone]]||692.179||  
|692.308
|The largest MOS scale this can generate is 26 tone.
|-
|-
|[[4/9-comma meantone]]||692.397||
|[[4/9-comma meantone]]||692.397||Close to [[26edo]]
|-
|-
|[[7/16-comma meantone]]||692.546||
|[[7/16-comma meantone]]||692.546||  
|-
|-
|[[3/7-comma meantone]]||692.738||
|[[3/7-comma meantone]]||692.738||  
|-
|-
|[[5/12-comma meantone]]||692.994||Close to [[71edo]]
|[[5/12-comma meantone]]||692.994||Close to [[71edo]]
Line 188: Line 114:
|[[2/5-comma meantone]]||693.352||Close to [[45edo]]
|[[2/5-comma meantone]]||693.352||Close to [[45edo]]
|-
|-
|[[7/18-comma meantone]]||693.591||
|[[7/18-comma meantone]]||693.591||  
|-
|[[5/13-comma meantone]]||693.683||
|-
|-
|[[Split Golden ratio comma meantone]]
|[[5/13-comma meantone]]||693.683||Close to [[64edo]]
|693.740
|Close to [[64edo]]
|-
|-
|[[3/8-comma meantone]]||693.890||Close to [[83edo]]
|[[3/8-comma meantone]]||693.890||Close to [[83edo]]
|-
|-
|[[4/11-comma meantone]]|| 694.134||Almost exactly 1/3-''Pythagorean'' comma meantone
|[[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||Everything up to this point generates 12 and 19 and 26 tone MOS scales.
|-
|-
|[[19edo]]
|[[5/14-comma meantone]]||694.274||  
|694.737
|The largest MOS scale this can generate is 19 tone. Historically significant (see [[historical temperaments]]).
|-
|-
|[[1/3-comma meantone]]||694.786||Everything from this point onwards generates 12 and 19 and 31 tone MOS scales. Historically significant (see [[historical temperaments]]).
|[[6/17-comma meantone]]||694.365||
|-
|-
|
|[[1/3-comma meantone]]||694.786||Close to [[19edo]]. Historically significant (see [[historical temperaments]]).
|694.819
|As flat of [[Pythagorean tuning]] as [[22edo]] is sharp.
|-
|-
|[[5/16-comma meantone]]||695.234 ||
|[[5/16-comma meantone]]||695.234||  
|-
|-
|[[4/13-comma meantone]]||695.338||  
|[[4/13-comma meantone]]||695.338||  
|-
|-
|[[Lucy tuning]]
|[[3/10-comma meantone]]||695.503||Close to [[88edo]]
|695.493
|Historically significant (see [[historical temperaments]]). Close to [[88edo]].
|-
|[[3/10-comma meantone]]||695.503||
|-
|-
|[[5/17-comma meantone]]||695.630||
|[[5/17-comma meantone]]||695.630||
|-
|-
|[[7/24-comma meantone]]
|[[2/7-comma meantone]]||695.810||Close to [[69edo]]. Historically significant (see [[historical temperaments]]).
|695.682
|Close to [[69edo]].
|-
|-
|[[2/7-comma meantone]]||695.810||Historically significant (see [[historical temperaments]]).
|[[5/18-comma meantone]]||695.981||Close to [[50edo]]. Historically significant (see [[historical temperaments]]).
|-
|-
|[[5/18-comma meantone]]||695.981||Historically significant (see [[historical temperaments]]).
|[[3/11-comma meantone]]||696.090||Close to [[50edo]]
|-
|[[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]].
|[[7/26-comma meantone]]||696.165||Close to [[golden meantone]]. Historically significant (see [[historical temperaments]]).
|-
|-
|[[Quarter-comma meantone|1/4-comma meantone]]||696.578||Historically significant (see [[historical temperaments]]).
|[[4/15-comma meantone]]||696.220||Close to [[81edo]], close to [[golden meantone]]
|-
|-
|[[31edo]]
|[[Quarter-comma meantone|1/4-comma meantone]]||696.578||Close to [[31edo]]. Historically significant (see [[historical temperaments]]).
|696.774
|The largest MOS scale this can generate is 31 tone. Historically significant (see [[historical temperaments]]).
|-
|-
|[[4/17-comma meantone]]||696.895||
|[[4/17-comma meantone]]||696.895||
Line 264: Line 154:
|[[2/9-comma meantone]]||697.176||Close to 5-limit and undecimal CTE tunings. Historically significant (see [[historical temperaments]]).
|[[2/9-comma meantone]]||697.176||Close to 5-limit and undecimal CTE tunings. Historically significant (see [[historical temperaments]]).
|-
|-
|[[74edo]]
|[[3/14-comma meantone]]||697.346||Close to [[74edo]]. Historically significant (see [[historical temperaments]]).
|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||
|-
|-
|
|[[1/5-comma meantone]]||697.654||Close to [[43edo]]. Historically significant (see [[historical temperaments]]).
|698.023
|As flat of [[Pythagorean tuning]] as [[17edo]] is sharp.
|-
|-
|[[2/11-comma meantone]]||698.045||
|[[3/16-comma meantone]]||697.923||  
|-
|-
|[[55edo]]
|[[2/11-comma meantone]]||698.045||Close to [[55edo]]
|698.182
|The largest MOS scale this can generate is 55 tone. Historically significant (see [[historical temperaments]]).
|-
|-
|[[3/17-comma meantone]]||698.245||Negative harmonically significant tuning with flat fifth (see [[negative harmony temperaments]]).
|[[3/17-comma meantone]]||699.425||
|-
|-
|[[1/6-comma meantone]]||698.371||Historically significant (see [[historical temperaments]]).
|[[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]]).
|[[4/25-comma meantone]]||698.514||Close to [[67edo]]. Historically significant (see [[historical temperaments]]).
|-
|-
|[[3/19-comma meantone]]
|[[2/13-comma meantone]]||698.646||  
|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]]).
|[[1/7-comma meantone]]||698.883||Close to [[79edo]], [[91edo]]. Historically significant (see [[historical temperaments]]).
|-
|-
|[[2/15-comma meantone]]||699.088||
|[[2/15-comma meantone]]||699.088||  
|-
|-
|[[1/8-comma meantone]]||699.267||
|[[1/8-comma meantone]]||699.267||  
|-
|-
|[[2/17-comma meantone]]||699.425||
|[[2/17-comma meantone]]||699.425||  
|-
|-
|[[1/9-comma meantone]]||699.565||Negative harmonically significant tuning with flat fifth (see [[negative harmony temperaments]]).
|[[1/9-comma meantone]]||699.565||  
|-
|-
|[[1/10-comma meantone]]||699.804||
|[[1/10-comma meantone]]||699.804||  
|-
|-
|[[1/11-comma meantone]]||700.000||Everything up to this point generates 12 and 19 and 31 tone MOS scales.
|[[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]].)
|[[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 and 29 tone MOS scales.
|[[1/12-comma meantone]]||700.163||Everything from this point onwards generates 12 and 17 tone MOS scales.
|-
|-
|[[1/13-comma meantone]]||700.301||
|[[1/13-comma meantone]]||700.301||  
|-
|-
|[[1/14-comma meantone]]||700.419||Negative harmonically significant tuning with flat fifth (see [[negative harmony temperaments]]).
|[[1/14-comma meantone]]||700.419||  
|-
|-
|[[1/15-comma meantone]]||700.521||Negative harmonically significant tuning with flat fifth (see [[negative harmony temperaments]]).
|[[1/15-comma meantone]]||700.521||  
|-
|-
|[[1/16-comma meantone]]||700.611||
|[[1/16-comma meantone]]||700.611||  
|-
|-
|[[1/17-comma meantone]]||700.690||
|[[1/17-comma meantone]]||700.690||  
|-
|-
|[[1/18-comma meantone]]||700.760||
|[[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).
|0/1-comma meantone||701.955||[[Pythagorean tuning]]. Historically significant (see [[historical 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).
|-
|-
|[[-1/18-comma meantone]]
|[[-1/18-comma meantone]]
Line 336: Line 206:
|
|
|-
|-
| -[[-1/17-comma meantone|1/17-comma meantone]]
|[[-1/17-comma meantone]]
|703.220
|703.220
|
|
Line 346: Line 216:
|[[-1/15-comma meantone]]
|[[-1/15-comma meantone]]
|703.389
|703.389
|Close to 11/13 third-kleisma temperament. Historically significant tuning with sharp fifth (see [[historical temperaments]]).
|Close to 11/13 third-kleisma temperament.
|-
|-
|[[-1/14-comma meantone]]
|[[-1/14-comma meantone]]
|703.491
|703.491
|Close to [[29edo]]. Historically significant tuning with sharp fifth (see [[historical temperaments]]).
|Close to [[29edo]].
|-
|-
|[[-1/13-comma meantone]]
|[[-1/13-comma meantone]]
Line 358: Line 228:
|[[-1/12-comma meantone]]
|[[-1/12-comma meantone]]
|703.747
|703.747
|
|  
|-
|
|703.910
|As sharp of [[Pythagorean tuning]] as [[55edo|12edo]] is flat. Negative harmonically significant (see [[negative harmony temperaments]]).
|-
|-
|[[-1/11-comma meantone]]
|[[-1/11-comma meantone]]
|703.910
|703.910
|
|About as sharp of [[Pythagorean tuning]] as [[12edo]] is flat.
|-
|-
|[[-1/10-comma meantone]]
|[[-1/10-comma meantone]]
Line 374: Line 240:
|[[-1/9-comma meantone]]
|[[-1/9-comma meantone]]
|704.344
|704.344
|Close to [[46edo]], 11/7 quarter-kleisma temperament. Historically significant tuning with sharp fifth (see [[historical temperaments]]).
|Close to [[46edo]], 11/7 quarter-kleisma temperament.
|-
|-
|[[2/17-comma meantone|-2/17-comma meantone]]
|[[-2/17-comma meantone]]
|704.483
|704.483
|
|
Line 390: Line 256:
|[[-1/7-comma meantone]]
|[[-1/7-comma meantone]]
|705.027
|705.027
|Close to [[80edo]]. Negative harmonically significant (see [[negative harmony temperaments]]).
|Close to [[80edo]].
|-
|-
|[[-2/13-comma meantone]]
|[[-2/13-comma meantone]]
Line 400: Line 266:
|
|
|-
|-
| -[[-4/25-comma meantone|4/25-comma meantone]]
|[[-4/25-comma meantone]]
|705.396
|705.396
|Negative harmonically significant (see [[negative harmony temperaments]]).
|
|-
|-
|[[-1/6-comma meantone]]
|[[-1/6-comma meantone]]
|705.538
|705.538
|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]]
|[[-3/17-comma meantone]]
|705.750
|705.750
|Historically significant tuning with sharp fifth (see [[historical temperaments]].
|About as sharp of [[Pythagorean tuning]] as [[55edo]] is flat.
|-
|-
|[[-2/11-comma meantone]]
|[[-2/11-comma meantone]]
|705.865
|705.865
|Everything up to this point generates 12 and 17 and 29 tone MOS scales.
|Everything up to this point generates 17 and 29 tone MOS scales.
|-
|-
|[[17edo]]
|[[17edo]]
|705.882
|705.882
|Simplest tuning for Middle Eastern neutral third scales. The largest MOS scale this can generate is 17 tone.
|Vaguely resembles Middle Eastern neutral third scales.
|-
|-
|[[-3/16-comma meantone]]
|[[-3/16-comma meantone]]
|705.987
|705.987
|Everything from this point onwards generates 12 and 17 and 22 tone MOS scales.
|Everything from this point onwards generates 17 and 22 tone MOS scales.
|-
|
|706.236
|As sharp of [[Pythagorean tuning]] as [[43edo]] is flat. Negative harmonically significant (see [[negative harmony temperaments]]).
|-
|-
|[[-1/5-comma meantone]]
|[[-1/5-comma meantone]]
|706.256
|706.256
|Negative harmonically significant (see [[negative harmony temperaments]]).
|About as sharp of [[Pythagorean tuning]] as [[43edo]] is flat.
|-
|-
|[[-3/14-comma meantone]]
|[[-3/14-comma meantone]]
|706.563
|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]]
|[[-2/9-comma meantone]]
|706.734
|706.734
|Negative harmonically significant (see [[negative harmony temperaments]]).
|
|-
|-
|[[-3/13-comma meantone]]
|[[-3/13-comma meantone]]
Line 454: Line 308:
|[[-4/17-comma meantone]]
|[[-4/17-comma meantone]]
|707.015
|707.015
|
|About as sharp of [[Pythagorean tuning]] as [[74edo]] is flat.
|-
|-
|[[Negative Quarter-comma meantone]]
|707.332
|
|
|707.136
|As sharp of [[Pythagorean tuning]] as [[74edo]] is flat. Negative harmonically significant (see [[negative harmony temperaments]]).
|-
|-
|[[Negative Quarter-comma meantone|-1/4-comma meantone]]
|[[-4/15-comma meantone]]
|707.332
|Negative harmonically significant (see [[negative harmony temperaments]]).
|-
| -[[4/15-comma meantone]]
|707.690
|707.690
|
|About as sharp of [[Pythagorean tuning]] as [[Golden meantone]] is flat.
|-
|[[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 [[50edo|Golden meantone]] is flat. Negative harmonically significant (see [[negative harmony temperaments]]).
|-
|-
|[[-7/26-comma meantone]]
|[[-7/26-comma meantone]]
|707.745
|707.745
|Negative harmonically significant (see [[negative harmony temperaments]]).
|
|-
|-
|[[-3/11-comma meantone]]
|[[-3/11-comma meantone]]
|707.820
|707.820
|Almost exactly -1/4-''Pythagorean'' comma meantone
|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]]
|[[-5/18-comma meantone]]
|707.930
|707.930
|Negative harmonically significant (see [[negative harmony temperaments]]).
|About as sharp of [[Pythagorean tuning]] as [[50edo]] is flat.
|-
|-
|[[-2/7-comma meantone]]
|[[-2/7-comma meantone]]
|708.100
|708.100
|Negative harmonically significant (see [[negative harmony temperaments]]).
|
|-
|-
|[[-7/24-comma meantone]]
|[[-7/24-comma meantone]]
Line 506: Line 344:
|[[-3/10-comma meantone]]
|[[-3/10-comma meantone]]
|708.407
|708.407
|
|About sharp of [[Pythagorean tuning]] as [[19edo|Lucy tuning]] is flat. Nearly as sharp of [[Pythagorean tuning]] as [[88edo]] is flat.
|-
|
|708.417
|As sharp of [[Pythagorean tuning]] as [[19edo|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]]
|[[-4/13-comma meantone]]
Line 518: Line 352:
|[[-5/16-comma meantone]]
|[[-5/16-comma meantone]]
|708.675
|708.675
|
|  
|-
|[[22edo]]
|709.091
|Isomorphic to [[Indian music|Indian]] shrutis. The largest MOS scale this can generate is 22 tone.
|-
|-
|[[-1/3-comma meantone]]
|[[-1/3-comma meantone]]
|709.124
|709.124
|Negative harmonically significant (see [[negative harmony temperaments]]).
|Close to [[22edo]]. About as sharp of [[Pythagorean tuning]] as [[19edo]] is flat.
|-
|
|709.173
|As sharp of [[Pythagorean tuning]] as [[19edo]] is flat. Negative harmonically significant (see [[negative harmony temperaments]]).
|-
|-
|[[-6/17-comma meantone]]
|[[-6/17-comma meantone]]
Line 542: Line 368:
|[[-4/11-comma meantone]]
|[[-4/11-comma meantone]]
|709.775
|709.775
|Almost exactly -1/3-''Pythagorean'' comma meantone
|Almost exactly -1/3-''Pythagorean'' comma meantone.
|-
|-
|[[-3/8-comma meantone]]
|[[-3/8-comma meantone]]
Line 562: Line 388:
|[[-2/5-comma meantone]]
|[[-2/5-comma meantone]]
|710.558
|710.558
|Negative harmonically significant (see [[negative harmony temperaments]]).
|
|-
|-
|[[-7/17-comma meantone]]
|[[-7/17-comma meantone]]
Line 584: Line 410:
|
|
|-
|-
|
|[[-5/11-comma meantone]]
|711.602
|As sharp of [[Pythagorean tuning]] as [[26edo|19edo]] is flat.
|-
|[[5/11-comma meantone|-5/11-comma meantone]]
|711.731
|711.731
|
|
Line 606: Line 428:
|[[-1/2-comma meantone]]
|[[-1/2-comma meantone]]
|712.708
|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).
|Close to [[32edo]]. 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]]
|[[-9/17-comma meantone]]
|713.340
|713.340
|
|
|-
|-
| -[[-8/15-comma meantone|8/15-comma meantone]]
|[[-8/15-comma meantone]]
|713.425
|713.425
|
|
Line 664: Line 486:
|Close to [[52edo]].
|Close to [[52edo]].
|-
|-
| -[[-7/11-comma meantone|7/11-comma meantone]]
|[[-7/11-comma meantone]]
|715.641
|715.641
|
|
Line 700: Line 522:
|
|
|-
|-
|[[12/17-comma meantone|-12/17-comma meantone]]
|[[-12/17-comma meantone]]
|717.136
|717.136
|Close to [[82edo]].
|Close to [[82edo]].
Line 720: Line 542:
|
|
|-
|-
|[[19/26-comma meantone|-19/26-comma meantone]]
|[[-19/26-comma meantone]]
|717.671
|717.671
|
|
|-
|-
|[[11/15-comma meantone|-11/15-comma meantone]]
|[[-11/15-comma meantone]]
|717.726
|717.726
|
|
Line 730: Line 552:
|[[-3/4-comma meantone]]
|[[-3/4-comma meantone]]
|718.085
|718.085
|
|About as sharp of [[Pythagorean tuning]] as [[7edo]] is flat.
|-
|
|718.196
|As sharp of [[Pythagorean tuning]] as [[7edo]] is flat.
|-
|-
|[[-13/17-comma meantone]]
|[[-13/17-comma meantone]]
Line 770: Line 588:
|[[-5/6-comma meantone]]
|[[-5/6-comma meantone]]
|719.877
|719.877
|Everything up to this point generates 12 and 17 and 22 tone MOS scales.
|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.'''
|[[5edo]]||720.000||The largest MOS scale this can generate is 5 tone. '''Upper boundary of 5-limit diamond monotone.'''
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