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Filled in missing regular meantone tunings and created rows for remaining historical equal temperaments. Created most of “negative harmony” section.
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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).
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).


The comma being divided here is the syntonic comma ([[81/80]]).
The comma being divided here is the syntonic comma ([[81/80]]).
Line 84: Line 84:
|[[7edo]]|| 685.714|| The largest MOS scale this can generate is 7 tone. '''Lower boundary of 5-limit diamond monotone.'''
|[[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.
|[[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 ||
|[[11/15-comma meantone]]||686.184 ||
Line 125: Line 125:
|-
|-
|[[5/8-comma meantone]]||688.514||Close to [[61edo]]
|[[5/8-comma meantone]]||688.514||Close to [[61edo]]
|-
|[[Golden ratio comma meantone]]
|688.663
|
|-
|-
|[[8/13-comma meantone]]||688.720||
|[[8/13-comma meantone]]||688.720||
Line 186: Line 190:
|[[7/18-comma meantone]]||693.591||
|[[7/18-comma meantone]]||693.591||
|-
|-
|[[5/13-comma meantone]]||693.683||Close to [[64edo]]
|[[5/13-comma meantone]]||693.683||
|-
|[[Split Golden ratio comma meantone]]
|693.740
|Close to [[64edo]]
|-
|-
|[[3/8-comma meantone]]||693.890||Close to [[83edo]]
|[[3/8-comma meantone]]||693.890||Close to [[83edo]]
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|[[5/14-comma meantone]]||694.274 ||
|[[5/14-comma meantone]]||694.274 ||
|-
|-
|[[6/17-comma meantone]]||694.365||
|[[6/17-comma meantone]]||694.365||Everything up to this point generates 12 and 19 and 26 tone MOS scales.
|-
|-
|[[19edo]]
|[[19edo]]
Line 200: Line 208:
|The largest MOS scale this can generate is 19 tone. Historically significant (see [[historical temperaments]]).
|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]]).
|[[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]]).
|-
|-
|
|
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|The largest MOS scale this can generate is 55 tone. Historically significant (see [[historical temperaments]]).
|The largest MOS scale this can generate is 55 tone. Historically significant (see [[historical temperaments]]).
|-
|-
|[[3/17-comma meantone]]||698.245||
|[[3/17-comma meantone]]||698.245||Negative harmonically significant tuning with flat fifth (see [[negative harmony temperaments]]).
|-
|-
|[[1/6-comma meantone]]||698.371||Historically significant (see [[historical temperaments]]).
|[[1/6-comma meantone]]||698.371||Historically significant (see [[historical temperaments]]).
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|[[2/17-comma meantone]]||699.425||
|[[2/17-comma meantone]]||699.425||
|-
|-
|[[1/9-comma meantone]]||699.565||
|[[1/9-comma meantone]]||699.565||Negative harmonically significant tuning with flat fifth (see [[negative harmony temperaments]]).
|-
|-
|[[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 tone MOS scales.
|[[1/11-comma meantone]]||700.000||Everything up to this point generates 12 and 19 and 31 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 tone MOS scales.
|[[1/12-comma meantone]]||700.163||Everything from this point onwards generates 12 and 17 and 29 tone MOS scales.
|-
|-
|[[1/13-comma meantone]]||700.301||
|[[1/13-comma meantone]]||700.301||
|-
|-
|[[1/14-comma meantone]]||700.419||
|[[1/14-comma meantone]]||700.419||Negative harmonically significant tuning with flat fifth (see [[negative harmony temperaments]]).
|-
|-
|[[1/15-comma meantone]]||700.521||
|[[1/15-comma meantone]]||700.521||Negative harmonically significant tuning with flat fifth (see [[negative harmony temperaments]]).
|-
|-
|[[1/16-comma meantone]]||700.611||
|[[1/16-comma meantone]]||700.611||
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|-
|-
|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]].) 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).
|-
|[[-1/18-comma meantone]]
|703.150
|
|-
| -[[-1/17-comma meantone|1/17-comma meantone]]
|703.220
|
|-
|[[-1/16-comma meantone]]
|703.299
|
|-
|[[-1/15-comma meantone]]
|703.389
|Close to 11/13 third-kleisma temperament. Historically significant tuning with sharp fifth (see [[historical temperaments]]).
|-
|[[-1/14-comma meantone]]
|703.491
|Close to [[29edo]]. Historically significant tuning with sharp fifth (see [[historical temperaments]]).
|-
|[[-1/13-comma meantone]]
|703.609
|
|-
|[[-1/12-comma meantone]]
|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]]
|703.910
|
|-
|[[-1/10-comma meantone]]
|704.105
|
|-
|[[-1/9-comma meantone]]
|704.344
|Close to [[46edo]], 11/7 quarter-kleisma temperament. Historically significant tuning with sharp fifth (see [[historical temperaments]]).
|-
|[[2/17-comma meantone|-2/17-comma meantone]]
|704.483
|
|-
|[[-1/8-comma meantone]]
|704.643
|
|-
|[[-2/15-comma meantone]]
|704.823
|Close to [[63edo]].
|-
|[[-1/7-comma meantone]]
|705.027
|Close to [[80edo]]. Negative harmonically significant (see [[negative harmony temperaments]]).
|-
|[[-2/13-comma meantone]]
|705.350
|
|-
|[[-3/19-comma meantone]]
|705.350
|
|-
| -[[-4/25-comma meantone|4/25-comma meantone]]
|705.396
|Negative harmonically significant (see [[negative harmony temperaments]]).
|-
|-
|[[-1/6-comma meantone]]
|[[-1/6-comma meantone]]
|705.027
|705.538
|Negative harmonically significant (see [[negative harmony temperaments]]).
|Negative harmonically significant (see [[negative harmony temperaments]]).
|-
|-
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|[[-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.
|-
|-
|[[17edo]]
|[[17edo]]
Line 346: Line 426:
|[[-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.
|-
|-
|
|
Line 466: Line 546:
|[[-3/8-comma meantone]]
|[[-3/8-comma meantone]]
|710.019
|710.019
|
|-
|[[Negative Split Golden ratio comma meantone]]
|710.170
|
|
|-
|-
Line 570: Line 654:
|[[-8/13-comma meantone]]
|[[-8/13-comma meantone]]
|715.190
|715.190
|
|-
|[[Negative Golden ratio comma meantone]]
|
|
|
|-
|-
Line 682: Line 770:
|[[-5/6-comma meantone]]
|[[-5/6-comma meantone]]
|719.877
|719.877
|Everything up to this point generates 12 and 17 tone MOS scales.
|Everything up to this point generates 12 and 17 and 22 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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