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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 7edo and 12edo (to delineate MOS shapes), as well as a few other notable meantone tunings (e.g. 4/25-comma).
{{DISPLAYTITLE:User:BudjarnLambeth/Table of ''n''-comma meantone generators}}{{Editable user page}}


The comma being divided here is the syntonic comma ([[81/80]]).
Here are all [[meantone]] tunings that can be written in the form "n-comma meantone", where the syntonic comma ([[81/80]]) is being divided and n is a fraction between -1 and 1 with a denominator 22 or smaller.  


{| class="wikitable"
== Scope of table ==
 
=== Characteristics included ===
Some of the characteristics this table mentions for each temperament include:
* Whether it saw historical (pre-1950) use
* Whether it is close to (i.e. within 1/2 a degree of closing of) an [[edo]] smaller than 100
* Whether it is the closest on the table to the optimal [[CTE]] or [[POTE]] tuning of meantone or [[superpyth]] in any JI [[limit]]
* Whether it approximates a very simple n-[[Pythagorean comma]] meantone
* Whether it is about equally sharp of [[3/2]] as some other listed temperament is flat
* Whether it is close to exactly one [[just-noticeable difference]] away from 3/2
 
Occasional other comments may be included as well.
 
=== Characteristics omitted ===
Dozens of tunings on this table are significant to [[negative harmony temperaments|negative harmony temperament theory]], enough that labelling them all individually would clutter the table.
 
Every tuning on this table is close to some arbitrarily large edo, but labeling them beyond [[100edo]] would clutter the table.
 
=== Special cases included ===
A small number of additional temperaments are included. Not too many, to avoid clutter, just the bare minimum:
* {{EDOs|7, 12, 17 and 5}} edos (to delineate small [[MOS]] shapes and boundaries of [[diamond monotone]])
* any tunings listed under "[[historical temperaments]]" (e.g. 4/25-comma), ''but only the ones of the form "n-comma"''.
 
== Cautions ==
=== Preservation of meantone behavior ===
Temperaments that fall outside of the "[[Historical temperaments|historically-defined meantone]]" range will not possess most of the musical properties that meantone usually possesses, but they are included for completeness.
 
Temperaments that fall outside of the "diamond monotone" range preserve even fewer meantone properties, but they are also included for completeness.
 
== The table ==
 
=== Flatter than flattest historically-defined meantone ===
{| class="wikitable mw-collapsible"
|+Spectrum of meantone tunings 1/1-comma to 1/2-comma
!Meantone Temperament!!Generator (cents)!!Comments
|-
|[[1/1-comma meantone|1/1-comma]] ||680.449||Close to [[30edo]]
|-
|[[21/22-comma meantone|21/22-comma]]
|681.426
|Close to [[37edo]].
|-
|[[20/21-comma meantone|20/21-comma]]
|681.473
|
|-
|[[19/20-comma meantone|19/20-comma]]
|681.524
|
|-
|[[18/19-comma meantone|18/19-comma]]
|681.581
|
|-
|[[17/18-comma meantone|17/18-comma]]
|681.644
|
|-
|[[16/17-comma meantone|16/17-comma]]
|681.713
|
|-
|[[15/16-comma meantone|15/16-comma]] ||681.793|| Close to [[44edo]].
|-
|[[14/15-comma meantone|14/15-comma]] ||681.883||
|-
|[[13/14-comma meantone|13/14-comma]] ||681.985||
|-
|[[12/13-comma meantone|12/13-comma]] ||682.103||
|-
|[[11/12-comma meantone|11/12-comma]] ||682.241||
|-
|[[10/11-comma meantone|10/11-comma]] ||682.404||Close to [[51edo]].
|-
|[[19/21-comma meantone|19/21-comma]]
|682.497
|
|-
|[[9/10-comma meantone|9/10-comma]]||682.599||
|-
|[[17/19-comma meantone|17/19-comma]]
|682.713
|
|-
|[[8/9-comma meantone|8/9-comma]] ||682.838||Close to [[58edo]].
|-
|[[15/17-comma meantone|15/17-comma]]
|682.979
|
|-
|[[7/8-comma meantone|7/8-comma]] ||683.137||Close to [[65edo]].
|-
|[[13/15-comma meantone|13/15-comma]] ||683.316||Close to [[72edo]].
|-
|[[19/22-comma meantone|19/22-comma]]
|683.381
|
|-
|[[6/7-comma meantone|6/7-comma]] ||683.521||Close to [[79edo]].
|-
|[[17/20-comma meantone|17/20-comma]]
|683.675
|
|-
|[[11/13-comma meantone|11/13-comma]] ||683.757||Close to [[86edo]].
|-
|[[16/19-comma meantone|16/19-comma]]
|683.844
|
|-
|[[21/25-comma meantone|21/25-comma]]
|683.890
|Close to [[93edo]]
|-
|[[5/6-comma meantone|5/6-comma]] ||684.033|| Close to [[100edo]].
|-
|[[14/17-comma meantone|14/17-comma]]
|684.244
|
|-
|[[9/11-comma meantone|9/11-comma]] ||684.359||
|-
|[[13/16-comma meantone|13/16-comma]] ||684.481||
|-
|[[17/21-comma meantone|17/21-comma]]
|684.545
|
|-
|[[4/5-comma meantone|4/5-comma]] ||684.750||
|-
|[[15/19-comma meantone|15/19-comma]]
|684.976
|
|-
|[[11/14-comma meantone|11/14-comma]] ||685.057||
|-
|[[7/9-comma meantone|7/9-comma]] ||685.228||
|-
|[[17/22-comma meantone|17/22-comma]]
|685.337
|
|-
|[[10/13-comma meantone|10/13-comma]] ||685.412||
|-
|[[13/17-comma meantone|13/17-comma]]
|685.509
|
|-
|[[16/21-comma meantone|16/21-comma]]
|685.569
|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|3/4-comma]] ||685.825||Everything from this point onwards generates 12 and 19 tone MOS scales.
|-
|[[14/19-comma meantone|14/19-comma]]
|686.108
|
|-
|[[11/15-comma meantone|11/15-comma]] ||686.184||
|-
|[[19/26-comma meantone|19/26-comma]]
|686.239
|
|-
|[[8/11-comma meantone|8/11-comma]]||686.314||
|-
|[[13/18-comma meantone|13/18-comma]]
|686.423
|
|-
|[[5/7-comma meantone|5/7-comma]] ||686.593||
|-
|[[17/24-comma meantone|17/24-comma]]
|686.721
|
|-
|[[12/17-comma meantone|12/17-comma]]
|686.774
|
|-
|[[7/10-comma meantone|7/10-comma]] ||686.901||
|-
|[[9/13-comma meantone|9/13-comma]] ||687.066||
|-
|[[11/16-comma meantone|11/16-comma]] ||687.169||
|-
|[[13/19-comma meantone|13/19-comma]]
|687.240
|
|-
|[[15/22-comma meantone|15/22-comma]] 
|687.292
|
|-
|[[17/25-comma meantone|17/25-comma]]
|687.331
|
|-
|[[19/28-comma]]
|687.361
|
|-
|[[2/3-comma meantone|2/3-comma]] ||687.617||Close to [[89edo]].
|-
|[[17/26-comma meantone|17/26-comma]]
|687.893
|Close to [[82edo]].
|-
|[[15/23-comma meantone|15/23-comma]]
|687.929
|
|-
|[[13/20-comma meantone|13/20-comma]]
|687.976
|
|-
|[[11/17-comma  meantone|11/17-comma]] 
|688.039
|Close to [[75edo]]
|-
|[[9/14-comma meantone|9/14-comma]] ||688.129||
|-
|[[7/11-comma meantone|7/11-comma]] ||688.269||Close to [[68edo]].
|-
|[[12/19-comma meantone|12/19-comma]]
|688.372
|
|-
|[[5/8-comma meantone|5/8-comma]] ||688.514||Close to [[61edo]] and [[43/32]].
|-
|[[13/21-comma meantone|13/21-comma]]
|688.641
|
|-
|[[1/φ-comma meantone|1/ϕ-comma]]
|688.663
|
|-
|[[8/13-comma meantone|8/13-comma]] ||688.720||
|-
|[[11/18-comma meantone|11/18-comma]]
|688.812
|Close to [[54edo]].
|-
|[[14/23-comma meantone|14/23-comma]] 
|688.864
|
|-
|[[3/5-comma meantone|3/5-comma]] ||689.051||
|-
|[[13/22-comma meantone|13/22-comma]]
|689.247
|
|-
|[[10/17-comma meantone|10/17-comma]]
|689.304
|
|-
|[[7/12-comma meantone|7/12-comma]] ||689.410||Close to [[47edo]].
|-
|[[11/19-comma meantone|11/19-comma]]
|689.504
|
|-
|[[4/7-comma meantone|4/7-comma]] ||689.666||Close to [[87edo]].
|-
|[[9/16-comma meantone|9/16-comma]] ||689.858||
|-
|[[5/9-comma meantone|5/9-comma]] ||690.007||Close to [[40edo]].
|-
|[[11/20-comma meantone|11/20-comma]]
|690.127
|
|-
|[[6/11-comma meantone|6/11-comma]] ||690.224||
|-
|[[7/13-comma meantone|7/13-comma]] ||690.375||Close to [[73edo]].
|-
|[[8/15-comma meantone|8/15-comma]] ||690.485||
|-
|[[9/17-comma meantone|9/17-comma]]
|690.569
|
|-
|[[10/19-comma meantone|10/19-comma]]
|690.636
|
|-
|[[11/21-comma meantone|11/21-comma]]
|690.690
|Close to [[33edo]]
|-
|[[1/2-comma meantone|1/2-comma]] ||691.202||Close to [[92edo]], [[59edo]]. Historically significant (see [[historical temperaments]]). Everything up to this point does not have a whole tone between 10/9 and 9/8.
|}
 
=== Historically-defined meantone ===
{| class="wikitable mw-collapsible"
|+Spectrum of meantone tunings 10/21-comma to 1/22-comma
!Temperament!!Generator (cents)!!Comments
!Temperament!!Generator (cents)!!Comments
|-
|-
|[[1/1-comma meantone]]||680.449||  
|[[10/21-comma meantone|10/21-comma]]
|691.714
|
|-
|[[9/19-comma meantone|9/19-comma]]
|691.768
|Close to [[85edo]].
|-
|[[8/17-comma meantone|8/17-comma]]
|691.834
|
|-
|[[7/15-comma meantone|7/15-comma]] ||691.919||
|-
|[[6/13-comma meantone|6/13-comma]] ||692.029||
|-
|[[5/11-comma meantone|5/11-comma]] ||692.179||
|-
|[[9/20-comma meantone|9/20-comma]]
|692.277
|Close to [[26edo]].
|-
|[[4/9-comma meantone|4/9-comma]] ||692.397||
|-
|[[7/16-comma meantone|7/16-comma]] ||692.546||
|-
|[[3/7-comma meantone|3/7-comma]] ||692.738||
|-
|[[8/19-comma meantone|8/19-comma]]
|692.899
|
|-
|[[5/12-comma meantone|5/12-comma]] ||692.994||Close to [[71edo]].
|-
|[[7/17-comma meantone|7/17-comma]] ||693.099||
|-
|[[9/22-comma meantone|9/22-comma]]
|693.157
|
|-
|[[2/5-comma meantone|2/5-comma]] ||693.352||Close to [[45edo]].
|-
|[[9/23-comma meantone|9/23-comma]]
|693.539
|
|-
|[[7/18-comma meantone|7/18-comma]] ||693.591||
|-
|[[5/13-comma meantone|5/13-comma]] ||693.683||
|-
|[[1/(φ+1)-comma meantone|1/(ϕ+1)-comma]]
|693.740
|Close to [[64edo]].
|-
|[[8/21-comma meantone|8/21-comma]]
|693.762
|
|-
|[[3/8-comma meantone|3/8-comma]] ||693.890||Close to [[83edo]].
|-
|[[7/19-comma meantone|7/19-comma]]
|694.032
|
|-
|[[4/11-comma meantone|4/11-comma]] ||694.134||Almost exactly 1/3-''Pythagorean'' comma meantone.
|-
|[[5/14-comma meantone|5/14-comma]] ||694.274||
|-
|[[6/17-comma meantone|6/17-comma]] ||694.365||
|-
|[[7/20-comma meantone|7/20-comma]]
|694.428
|
|-
|[[8/23-comma meantone|8/23-comma]]
|694.475
|
|-
|[[9/26-comma meantone|9/26-comma]]
|694.511
|
|-
|[[1/3-comma meantone|1/3-comma]] ||694.786||Close to [[19edo]]. Historically significant (see [[historical temperaments]]).
|-
|[[9/28-comma meantone|9/28-comma]] 
|695.042
|
|-
|[[8/25-comma meantone|8/25-comma]] 
|695.073
|
|-
|[[7/22-comma meantone|7/22-comma]] 
|695.112
|
|-
|[[6/19-comma meantone|6/19-comma]]
|695.164
|
|-
|[[5/16-comma meantone|5/16-comma]] ||695.234||
|-
|[[4/13-comma meantone|4/13-comma]] ||695.338||
|-
|[[3/10-comma meantone|3/10-comma]] ||695.503||Close to [[88edo]] and [[Lucy tuning]]. Historically significant (see [[historical temperaments]]).
|-
|[[5/17-comma meantone|5/17-comma]] ||695.630||Close to [[69edo]].
|-
|[[7/24-comma meantone|7/24-comma]]
|695.682
|
|-
|[[2/7-comma meantone|2/7-comma]] ||695.810||Historically significant (see [[historical temperaments]]).
|-
|[[5/18-comma meantone|5/18-comma]] ||695.981||Close to [[50edo]].
|-
|[[3/11-comma meantone|3/11-comma]] ||696.090||
|-
|[[7/26-comma meantone|7/26-comma]] ||696.165||Close to [[golden meantone]]. Historically significant (see [[historical temperaments]]).
|-
|[[4/15-comma meantone|4/15-comma]] ||696.220||Close to [[5-limit]] meantone [[POTE]] tuning.
|-
|[[5/19-comma meantone|5/19-comma]]
|696.295
|Close to [[81edo]].
|-
|[[Quarter-comma meantone|1/4-comma]] ||696.578||Close to [[7-limit|septimal]] and [[tridecimal]] meantone POTE tunings. Historically significant (see [[historical temperaments]]).
|-
|[[5/21-comma meantone|5/21-comma]]
|696.834
|Close to [[31edo]].
|-
|[[4/17-comma meantone|4/17-comma]] ||696.895||
|-
|[[3/13-comma meantone|3/13-comma]] ||696.992||Close to [[7-limit|septimal]] & [[tridecimal]] meantone [[CTE]] tunings. Close to [[undecimal]] meantone POTE tuning.
|-
|[[5/22-comma meantone|5/22-comma]] 
|697.067
|
|-
|[[2/9-comma meantone|2/9-comma]] ||697.176||Close to [[5-limit]] and [[undecimal]] meantone CTE tunings. Historically significant (see [[historical temperaments]]).
|-
|[[3/14-comma meantone|3/14-comma]] ||697.346||Close to [[74edo]]. Historically significant (see [[historical temperaments]]).
|-
|[[4/19-comma meantone|4/19-comma]]
|697.427
|
|-
|[[1/5-comma meantone|1/5-comma]] ||697.654||Close to [[43edo]]. Historically significant (see [[historical temperaments]]).
|-
|[[4/21-comma meantone|4/21-comma]]
|697.859
|
|-
|[[3/16-comma meantone|3/16-comma]] ||697.923||
|-
|[[2/11-comma meantone|2/11-comma]] ||698.045||Close to [[55edo]]. Historically significant (see [[historical temperaments]]).
|-
|[[3/17-comma meantone|3/17-comma]] ||698.159||
|-
|[[4/23-comma meantone|4/23-comma]] 
|698.215
|
|-
|[[1/6-comma meantone|1/6-comma]] ||698.371||Historically significant (see [[historical temperaments]]). Everything up to this point has a fifth which is flat of [[Pythagorean tuning]] by at least the [[just-noticeable difference]].
|-
|[[4/25-comma meantone|4/25-comma]] ||698.514||Close to [[67edo]].
|-
|[[3/19-comma meantone|3/19-comma]]
|698.559
|
|-
|[[2/13-comma meantone|2/13-comma]] ||698.646|| Close to [[79edo]].
|-
|[[3/20-comma meantone|3/20-comma]]
|698.729
|
|-
|[[1/7-comma meantone|1/7-comma]] ||698.883||Close to [[91edo]]. Historically significant (see [[historical temperaments]]).
|-
|[[3/22-comma meantone|3/22-comma]] 
|699.022
|
|-
|[[2/15-comma meantone|2/15-comma]] ||699.088||
|-
|[[1/8-comma meantone|1/8-comma]] ||699.267||
|-
|[[2/17-comma meantone|2/17-comma]] ||699.425||  
|-
|-
|[[15/16-comma meantone]]||681.793||  
|[[1/9-comma meantone|1/9-comma]] ||699.565||  
|-
|-
|[[14/15-comma meantone]]||681.883||  
|[[2/19-comma meantone|2/19-comma]]  
|699.691
|
|-
|-
|[[13/14-comma meantone]]||681.985||  
|[[1/10-comma meantone|1/10-comma]] ||699.804||  
|-
|-
|[[12/13-comma meantone]]||682.103||  
|[[2/21-comma meantone|2/21-comma]]  
|699.907
|
|-
|-
|[[11/12-comma meantone]]||682.241||  
|[[1/11-comma meantone|1/11-comma]] ||700.000||Everything up to this point generates 12 and 19 tone MOS scales.
|-
|-
|[[12/11-comma meantone]]||682.404||  
|[[12edo]]||700.000||The largest MOS scale this can generate is 12 tone. Historically significant (see [[historical temperaments]].)
|-
|-
|[[9/10-comma meantone]]||682.599||  
|[[1/12-comma meantone|1/12-comma]] ||700.163||Everything from this point onwards generates 12 and 17 tone MOS scales.
|-
|-
|[[8/9-comma meantone]]||682.838||  
|[[1/13-comma meantone|1/13-comma]] ||700.301||  
|-
|-
|[[7/8-comma meantone]]||683.137||  
|[[1/14-comma meantone|1/14-comma]] ||700.419||  
|-
|-
|[[13/15-comma meantone]]||683.316||  
|[[1/15-comma meantone|1/15-comma]] ||700.521||  
|-
|-
|[[6/7-comma meantone]]||683.521||  
|[[1/16-comma meantone|1/16-comma]] ||700.611||  
|-
|-
|[[11/13-comma meantone]]||683.757||  
|[[1/17-comma meantone|1/17-comma]] ||700.690||  
|-
|-
|[[5/6-comma meantone]]||684.033||  
|[[1/18-comma meantone|1/18-comma]] ||700.760||  
|-
|-
|[[9/11-comma meantone]]||684.359||  
|[[1/19-comma meantone|1/19-comma]]  
|700.823
|
|-
|-
|[[13/16-comma meantone]]||684.481||  
|[[1/20-comma meantone|1/20-comma]]  
|700.879
|
|-
|-
|[[4/5-comma meantone]]||684.75||  
|[[1/21-comma meantone|1/21-comma]]  
|700.931
|
|-
|-
|[[11/14-comma meantone]]||685.057||  
|[[1/22-comma meantone|1/22-comma]]  
|700.977
|
|}
 
=== Negative harmony theory-defined meantone (most often approached as [[superpyth]]) ===
{| class="wikitable mw-collapsible"
|+Spectrum of meantone tunings 0/1-comma to -10/21-comma
!Meantone Temperament!!Generator (cents)!!Comments
|-
|-
|[[7/9-comma meantone]]||685.228||  
|[[Pythagorean tuning]]
|701.955||Historically significant (see [[historical temperaments]].)  Everything from this point onwards does not have a whole tone between 10/9 and 9/8.
|-
|-
|[[10/13-comma meantone]]||685.412||Everything up to this point generates 9 and 16 tone MOS scales.
|[[-1/22-comma meantone|-1/22-comma]]  
|702.933
|
|-
|-
|[[7edo]]||695.714||The largest MOS scale this can generate is 7 tone.
|[[-1/21-comma meantone|-1/21-comma]]  
|702.979
|
|-
|-
|[[3/4-comma meantone]]||685.825||Everything from this point onwards generates 12 and 19 tone MOS scales.
|[[-1/20-comma meantone|-1/20-comma]]  
|703.030
|
|-
|-
|[[11/15-comma meantone]]||686.184||
|[[-1/19-comma meantone|-1/19-comma]]  
|703.087
|
|-
|-
|[[8/11-comma meantone]]||686.314||
|[[-1/18-comma meantone|-1/18-comma]]  
|703.150
|
|-
|-
|[[5/7-comma meantone]]||686.593||  
|[[-1/17-comma meantone|-1/17-comma]]  
|703.220
|
|-
|-
|[[7/10-comma meantone]]||686.901||  
|[[-1/16-comma meantone|-1/16-comma]]  
|703.299
|
|-
|-
|[[9/13-comma meantone]]||687.066||
|[[-1/15-comma meantone|-1/15-comma]]  
|703.389
|Close to 11/13 third-[[kleisma]] temperament.
|-
|-
|[[11/16-comma meantone]]||687.169||
|[[-1/14-comma meantone|-1/14-comma]]  
|703.491
|Close to [[29edo]].
|-
|-
|[[2/3-comma meantone]]||687.617||Close to [[89edo]]
|[[-1/13-comma meantone|-1/13-comma]]  
|703.609
|
|-
|-
|[[9/14-comma meantone]]||688.129||Close to [[75edo]]
|[[-1/12-comma meantone|-1/12-comma]]  
|703.747
|  
|-
|-
|[[7/11-comma meantone]]||688.269||Close to [[68edo]]
|[[-1/11-comma meantone|-1/11-comma]]  
|703.910
|About as sharp of [[Pythagorean tuning]] as [[12edo]] is flat.
|-
|-
|[[5/8-comma meantone]]||688.514||Close to [[61edo]]
|[[-2/21-comma meantone|-2/21-comma]]  
|704.003
|Close to [[75edo]].
|-
|-
|[[8/13-comma meantone]]||688.720||Close to [[54edo]]
|[[-1/10-comma meantone|-1/10-comma]]  
|704.105
|
|-
|-
|[[3/5-comma meantone]]||689.051||  
|[[-2/19-comma meantone|-2/19-comma]]  
|704.219
|
|-
|-
|[[7/12-comma meantone]]||689.410||Close to [[47edo]]
|[[-1/9-comma meantone|-1/9-comma]]  
|704.344
|Close to [[46edo]], 11/7 quarter-kleisma temperament.
|-
|-
|[[4/7-comma meantone]]||689.666||Close to [[87edo]]
|[[-2/17-comma meantone|-2/17-comma]]  
|704.483
|
|-
|-
|[[9/16-comma meantone]]||689.858||  
|[[-1/8-comma meantone|-1/8-comma]]  
|704.643
|
|-
|-
|[[5/9-comma meantone]]||690.007||Close to [[40edo]]
|[[-2/15-comma meantone|-2/15-comma]]  
|704.823
|Close to [[63edo]].
|-
|-
|[[6/11-comma meantone]]||690.224||  
|[[-3/22-comma meantone|-3/22-comma]]  
|704.888
|
|-
|-
|[[7/13-comma meantone]]||690.375||Close to [[73edo]]
|[[-1/7-comma meantone|-1/7-comma]]
|705.027
|Close to [[80edo]].
|-
|-
|[[8/15-comma meantone]]||690.485||Close to [[33edo]]
|[[-3/20-comma meantone|-3/20-comma]]  
|705.181
|
|-
|-
|[[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).
|[[-2/13-comma meantone|-2/13-comma]]  
|705.350
|
|-
|-
|[[7/15-comma meantone]]||691.919||Close to [[85edo]]
|[[-3/19-comma meantone|-3/19-comma]]  
|705.350
|
|-
|-
|[[6/13-comma meantone]]||692.029||  
|[[-4/25-comma meantone|-4/25-comma]]  
|705.396
|
|-
|-
|[[5/11-comma meantone]]||692.179||
|[[-1/6-comma meantone|-1/6-comma]]  
|705.538
| Everything from this point onwards has a fifth which is sharp of [[Pythagorean tuning]] by at least the [[just-noticeable difference]].
|-
|-
|[[4/9-comma meantone]]||692.397||Close to [[26edo]]
|[[-4/23-comma meantone|-4/23-comma]]
|705.695
|
|-
|-
|[[7/16-comma meantone]]||692.546||
|[[-3/17-comma meantone|-3/17-comma]]  
|705.750
|About as sharp of [[Pythagorean tuning]] as [[55edo]] is flat.
|-
|-
|[[3/7-comma meantone]]||692.738||
|[[-2/11-comma meantone|-2/11-comma]]  
|705.865
|Everything up to this point generates 17 and 29 tone MOS scales.
|-
|-
|[[5/12-comma meantone]]||692.994||Close to [[71edo]]
|[[17edo]]
|705.882
|The largest MOS scale this can generate is 17 tone. Vaguely resembles Middle Eastern [[neutral third scale]]s.
|-
|-
|[[7/17-comma meantone]]||693.099||
|[[-3/16-comma meantone|-3/16-comma]]  
|705.987
|Everything from this point onwards generates 17 and 22 tone MOS scales.
|-
|-
|[[2/5-comma meantone]]||693.352||Close to [[45edo]]
|[[-4/21-comma meantone|-4/21-comma]]  
|706.051
|
|-
|-
|[[7/18-comma meantone]]||693.591||
|[[-1/5-comma meantone|-1/5-comma]]  
|706.256
|About as sharp of [[Pythagorean tuning]] as [[43edo]] is flat.
|-
|-
|[[5/13-comma meantone]]||693.683||Close to [[64edo]]
|[[-4/19 comma meantone|-4/19 comma]]  
|706.483
|
|-
|-
|[[3/8-comma meantone]]||693.890||Close to [[83edo]]
|[[-3/14-comma meantone|-3/14-comma]]  
|706.563
| About as sharp of [[Pythagorean tuning]] as [[74edo]] is flat.
|-
|-
|[[4/11-comma meantone]]||694.134||Almost exactly 1/3 ''Pythagorean'' comma meantone
|[[-2/9-comma meantone|-2/9-comma]]  
|706.734
|
|-
|-
|[[5/14-comma meantone]]||694.274||  
|[[-5/22-comma meantone|-5/22-comma]]
|706.843
|
|-
|-
|[[6/17-comma meantone]]||694.365||
|[[-3/13-comma meantone|-3/13-comma]]  
|706.918
|Close to [[39edo]].
|-
|-
|[[1/3-comma meantone]]||694.786||Close to [[19edo]]. Historically significant (see [[historical temperaments]]).
|[[-4/17-comma meantone|-4/17-comma]]  
|707.015
|
|-
|-
|[[5/16-comma meantone]]||695.234||
|[[-5/21-comma meantone|-5/21-comma]]  
|707.076
|About as sharp of [[Pythagorean tuning]] as [[31edo]] is flat.
|-
|-
|[[4/13-comma meantone]]||695.338||  
|[[-1/4-comma meantone|-1/4-comma]]
|707.332
|
|-
|-
|[[3/10-comma meantone]]||695.503||Close to [[88edo]]
|[[-5/19-comma meantone|-5/19-comma]]  
|707.615
|
|-
|-
|[[5/17-comma meantone]]||695.630||
|[[-4/15-comma meantone|-4/15-comma]]  
|707.690
|About as sharp of [[Pythagorean tuning]] as [[golden meantone]] is flat.
|-
|-
|[[2/7-comma meantone]]||695.810||Close to [[69edo]]. Historically significant (see [[historical temperaments]]).
|[[-7/26-comma meantone|-7/26-comma]]  
|707.745
|
|-
|-
|[[5/18-comma meantone]]||695.981||Close to [[50edo]]. Historically significant (see [[historical temperaments]]).
|[[-3/11-comma meantone|-3/11-comma]]  
|707.820
|Almost exactly -1/4-''Pythagorean'' comma meantone
|-
|-
|[[3/11-comma meantone]]||696.090||Close to [[50edo]]
|[[-5/18-comma meantone|-5/18-comma]]  
|707.930
|About as sharp of [[Pythagorean tuning]] as [[50edo]] is flat. Close to [[100edo]].
|-
|-
|[[7/26-comma meantone]]||696.165||Close to [[golden meantone]]. Historically significant (see [[historical temperaments]]).
|[[-2/7-comma meantone|-2/7-comma]]  
|708.100
|
|-
|-
|[[4/15-comma meantone]]||696.22||Close to [[81edo]], close to [[golden meantone]]
|[[-7/24-comma meantone|-7/24-comma]]  
|708.227
|
|-
|-
|[[Quarter-comma meantone|1/4-comma meantone]]||696.578||Close to [[31edo]]. Historically significant (see [[historical temperaments]]).
|[[-5/17-comma meantone|-5/17-comma]]  
|708.280
|
|-
|-
|[[4/17-comma meantone]]||696.895||
|[[-3/10-comma meantone|-3/10-comma]]  
|708.407
|Nearly as sharp of [[Pythagorean tuning]] as [[Lucy tuning]] is flat. Nearly as sharp of [[Pythagorean tuning]] as [[88edo]] is flat.
|-
|-
|[[3/13-comma meantone]]||696.992||Close to septimal & tridecimal CTE tunings.
|[[-4/13-comma meantone|-4/13-comma]]  
|708.572
|
|-
|-
|[[2/9-comma meantone]]||697.176||Close to 5-limit and undecimal CTE tunings. Historically significant (see [[historical temperaments]]).
|[[-5/16-comma meantone|-5/16-comma]]  
|708.675
|
|-
|-
|[[3/14-comma meantone]]||697.346||Close to [[74edo]]. Historically significant (see [[historical temperaments]]).
|[[-6/19-comma meantone|-6/19-comma]]  
|708.746
|
|-
|-
|[[1/5-comma meantone]]||697.654||Close tp [[43edo]]. Historically significant (see [[historical temperaments]]).
|[[-7/22-comma meantone|-7/22-comma]]  
|708.800
|
|-
|-
|[[3/16-comma meantone]]||697.923||  
|[[-8/25-comma meantone|-8/25-comma]]  
|708.837
|
|-
|-
|[[2/11-comma meantone]]||698.045||Close to [[55edo]]
|[[-9/28-comma meantone|-9/28-comma]]  
|708.867
|
|-
|-
|[[3/17-comma meantone]]||699.425||
|[[-1/3-comma meantone|-1/3-comma]]  
|709.124
|Close to [[22edo]]. About as sharp of [[Pythagorean tuning]] as [[19edo]] is flat.
|-
|-
|[[1/6-comma meantone]]||698.371||Close to [[67edo]]. Historically significant (see [[historical temperaments]]).
|[[-9/26-comma meantone|-9/26-comma]]  
|709.399
|Close to [[2.3.7-limit]] superpyth [[POTE]] tuning.
|-
|-
|[[4/25-comma meantone]]||698.514||Close to [[67edo]]. Historically significant (see [[historical temperaments]]).
|[[-8/23-comma meantone|-8/23-comma]]  
|709.435
|
|-
|-
|[[2/13-comma meantone]]||698.646||  
|[[-7/20-comma meantone|-7/20-comma]]  
|709.482
|
|-
|-
|[[1/7-comma meantone]]||698.883||Close to [[79edo]], [[91edo]]. Historically significant (see [[historical temperaments]]).
|[[-6/17-comma meantone|-6/17-comma]]  
|709.545
|Close to [[11-limit]] superpyth [[CTE]] tuning.
|-
|-
|[[2/15-comma meantone]]||699.088||
|[[-5/14-comma meantone|-5/14-comma]]  
|709.636
|Close to [[93edo]]. Close to [[2.3.7-limit]] and [[7-limit]] superpyth CTE tunings.
|-
|-
|[[1/8-comma meantone]]||699.267||
|[[-4/11-comma meantone|-4/11-comma]]  
|709.775
|Almost exactly -1/3-''Pythagorean'' comma meantone.
|-
|-
|[[2/17-comma meantone]]||699.425||
|[[-7/19-comma meantone|-7/19-comma]]  
|709.878
|Close to [[13-limit]] superpyth CTE tuning.
|-
|-
|[[1/9-comma meantone]]||699.565||  
|[[-3/8-comma meantone|-3/8-comma]]  
|710.019
|
|-
|-
|[[1/10-comma meantone]]||699.804||  
|[[-8/21-comma meantone|-8/21-comma]]  
|710.148
|
|-
|-
|[[1/11-comma meantone]]||700.000||Everything up to this point generates 12 and 19 tone MOS scales.
|[[-1/(φ+1)-comma meantone|-1/(ϕ+1)-comma]]
|710.170
|Close to [[11-limit]] superpyth POTE tuning.
|-
|-
|[[12edo]]||700.000||The largest MOS scale this can generate is 12 tone. Historically significant (see [[historical temperaments]].  
|[[-5/13-comma meantone|-5/13-comma]]  
|710.227
|Close to [[49edo]]. Close to [[7-limit]] superpyth POTE tuning.
|-
|-
|[[1/12-comma meantone]]||700.163||Everything from this point onwards generates 12 and 17 tone MOS scales.
|[[-7/18-comma meantone|-7/18-comma]]  
|710.319
|
|-
|-
|[[1/13-comma meantone]]||700.301||  
|[[-9/23-comma meantone|-9/23-comma]]
|710.371
|
|-
|-
|[[1/14-comma meantone]]||700.419||
|[[-2/5-comma meantone|-2/5-comma]]  
|710.558
|Close to [[13-limit]] superpyth POTE tuning.
|-
|-
|[[1/15-comma meantone]]||700.521||  
|[[-9/22-comma meantone|-9/22-comma]]  
|710.753
|
|-
|-
|[[1/16-comma meantone]]||700.611||  
|[[-7/17-comma meantone|-7/17-comma]]  
|710.810
|
|-
|-
|[[1/17-comma meantone]]||700.690||  
|[[-5/12-comma meantone|-5/12-comma]]  
|710.915
|
|-
|-
|[[1/18-comma meantone]]||700.760||  
|[[-8/19-comma meantone|-8/19-comma]]  
|711.010
|
|-
|-
|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).
|[[-3/7-comma meantone|-3/7-comma]]
|711.172
|Close to [[27edo]].
|-
|[[-7/16-comma meantone|-7/16-comma]]  
|711.364
|
|-
|[[-4/9-comma meantone|-4/9-comma]]
|711.513
|
|-
|[[-9/20-comma meantone|-9/20-comma]]
|711.633
|
|-
|[[-5/11-comma meantone|-5/11-comma]]
|711.731
|
|-
|[[-6/13-comma meantone|-6/13-comma]]
|711.880
|Close to [[59edo]].
|-
|[[-7/15-comma meantone|-7/15-comma]]
|711.991
|
|-
|[[-8/17-comma meantone|-8/17-comma]]
|712.075
|
|-
|[[-9/19-comma meantone|-9/19-comma]]
|712.142
|
|-
|[[-10/21-comma meantone|-10/21-comma]]
|712.196
|
|}
|}
[[Category:Tables]][[Category:Meantone]]
 
=== Sharper than sharpest negative harmonic-defined meantone ===
{| class="wikitable mw-collapsible"
|+ Spectrum of meantone tunings -1/2-comma to -1/1-comma
!Meantone Temperament!!Generator (cents)!!Comments
|-
|[[-1/2-comma meantone|-1/2-comma]]
|712.708
|Close to [[32edo]]. Everything from this point onwards does not have a whole tone being between 9/8 and 729/640.
|-
|[[-11/21-comma meantone|-11/21-comma]]
|713.220
|
|-
|[[-10/19-comma meantone|-10/19-comma]]
|713.274
|
|-
|[[-9/17-comma meantone|-9/17-comma]]
|713.340
|
|-
|[[-8/15-comma meantone|-8/15-comma]]
|713.425
|
|-
|[[-7/13-comma meantone|-7/13-comma]]
|713.535
|Close to [[37edo]].
|-
|[[-6/11-comma meantone|-6/11-comma]]
|713.686
|
|-
|[[-11/20-comma meantone|-11/20-comma]]
|713.783
|
|-
|[[-5/9-comma meantone|-5/9-comma]]
|713.903
|
|-
|[[-9/16-comma meantone|-9/16-comma]]
|714.052
|
|-
|[[-4/7-comma meantone|-4/7-comma]]
|714.244
|Close to [[42edo]].
|-
|[[-11/19-comma meantone|-11/19-comma]]
|714.406
|
|-
|[[-7/12-comma meantone|-7/12-comma]]
|714.500
|
|-
|[[-10/17-comma meantone|-10/17-comma]]
|714.606
|
|-
|[[-13/22-comma meantone|-13/22-comma]]
|714.663
|
|-
|[[-3/5-comma meantone|-3/5-comma]]
|714.859
|Close to [[47edo]].
|-
|[[-14/23-comma meantone|-14/23-comma]]
|715.046
|
|-
|[[-11/18-comma meantone|-11/18-comma]]
|715.098
|
|-
|[[-8/13-comma meantone|-8/13-comma]]
|715.190
|
|-
|[[-1/φ-comma meantone|-1/ϕ-comma]]
|715.247
|
|-
|[[-13/21-comma meantone|-13/21-comma]]
|715.268
|
|-
|[[-5/8-comma meantone|-5/8-comma]]
|715.396
|Close to [[52edo]] and 387/256.
|-
|[[-12/19-comma meantone|-12/19-comma]]
|715.538
|
|-
|[[-7/11-comma meantone|-7/11-comma]]
|715.641
|
|-
|[[-9/14-comma meantone|-9/14-comma]]
|715.780
|Close to [[57edo]].
|-
|[[-11/17-comma meantone|-11/17-comma]]
|715.871
|
|-
|[[-13/20-comma meantone|-13/20-comma]] 
|715.934
|
|-
|[[-2/3-comma meantone|-2/3-comma]]
|716.293
|Close to [[62edo]].
|-
|[[-15/22 comma meantone|-15/22 comma]]
|716.618
|Close to [[67edo]].
|-
|[[-13/19 comma meantone|-13/19 comma]]
|716.669
|Close to [[72edo]].
|-
|[[-11/16-comma meantone|-11/16-comma]]
|716.741
|
|-
|[[-9/13-comma meantone|-9/13-comma]]
|716.844
|Close to [[77edo]].
|-
|[[-7/10-comma meantone|-7/10-comma]]
|717.009
|
|-
|[[-12/17-comma meantone|-12/17-comma]]
|717.136
|Close to [[82edo]].
|-
|[[-17/24-comma meantone|-17/24-comma]]
|717.188
|Close to [[87edo]].
|-
|[[-5/7-comma meantone|-5/7-comma]]
|717.317
|Close to [[92edo]].
|-
|[[-13/18-comma meantone|-13/18-comma]]
|717.487
|Close to [[97edo]].
|-
|[[-8/11-comma meantone|-8/11-comma]]
|717.596
|
|-
|[[-19/26-comma meantone|-19/26-comma]]
|717.671
|
|-
|[[-11/15-comma meantone|-11/15-comma]]
|717.726
|
|-
|[[-14/19-comma meantone|-14/19-comma]]
|717.802
|
|-
|[[-3/4-comma meantone|-3/4-comma]]
|718.085
|About as sharp of [[Pythagorean tuning]] as [[7edo]] is flat.
|-
|[[-21/26-comma meantone|-21/26-comma]] 
|718.325
|
|-
|[[-16/21-comma meantone|-16/21-comma]]
|718.341
|
|-
|[[-13/17-comma meantone|-13/17-comma]]
|718.401
|
|-
|[[-10/13-comma meantone|-10/13-comma]]
|718.498
|
|-
|[[-17/22-comma meantone|-17/22-comma]]
|718.574
|
|-
|[[-7/9-comma meantone|-7/9-comma]]
|718.682
|
|-
|[[-11/14-comma meantone|-11/14-comma]]
|718.853
|
|-
|[[-15/19-comma meantone|-15/19-comma]]
|718.934
|
|-
|[[-4/5-comma meantone|-4/5-comma]]
|719.160
|
|-
|[[-17/21-comma meantone|-17/21-comma]]
|719.365
|
|-
|[[-13/16-comma meantone|-13/16-comma]]
|719.429
|
|-
|[[-9/11-comma meantone|-9/11-comma]]
|719.551
|
|-
|[[-14/17-comma meantone|-14/17-comma]]
|719.666
|
|-
|[[-5/6-comma meantone|-5/6-comma]]
|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|-21/25-comma]]
|720.020
|Everything from this point onwards generates 13 and 18 tone MOS scales.
|-
|[[-16/19-comma meantone|-16/19-comma]]
|720.066
|
|-
|[[-11/13-comma meantone|-11/13-comma]]
|720.153
|
|-
|[[-17/20-comma meantone|-17/20-comma]]
|720.235
|
|-
|[[-6/7-comma meantone|-6/7-comma]]
|720.399
|
|-
|[[-19/22-comma meantone|-19/22-comma]]
|720.529
|
|-
|[[-13/15-comma meantone|-13/15-comma]]
|720.594
|
|-
|  -[[7/8-comma meantone|7/8-comma]]
|720.773
|
|-
|[[-15/17-comma meantone|-15/17-comma]]
|720.931
|
|-
|[[-8/9-comma meantone|-8/9-comma]]
|721.017
|
|-
|[[-17/19-comma meantone|-17/19-comma]]
|721.197
|
|-
|[[-9/10-comma meantone|-9/10-comma]]
|721.311
|
|-
|[[-19/21-comma meantone|-19/21-comma]]
|721.413
|
|-
|[[-10/11-comma meantone|-10/11-comma]]
|721.506
|
|-
|[[-11/12-comma meantone|-11/12-comma]]
|721.669
|
|-
|[[-12/13-comma meantone|-12/13-comma]]
|721.807
|
|-
|[[-13/14-comma meantone|-13/14-comma]]
|721.925
|
|-
|[[-14/15-comma meantone|-14/15-comma]]
|722.028
|
|-
|[[-15/16-comma meantone|-15/16-comma]]
|722.117
|
|-
|[[-16/17-comma meantone|-16/17-comma]]
|722.196
|
|-
|[[-17/18-comma meantone|-17/18-comma]]
|722.266
|
|-
|[[-18/19-comma meantone|-18/19-comma]]
|722.329
|
|-
|[[-19/20-comma meantone|-19/20-comma]]
|722.386
|
|-
|[[-20/21-comma meantone|-20/21-comma]]
|722.437
|
|-
|[[-21/22-comma meantone|-21/22-comma]]
|722.484
|
|-
|[[-1/1-comma meantone|-1/1-comma]]
|723.461
|Close to [[68edo]].
|-
|}
 
[[Category:Tables]]
[[Category:Meantone]]
Retrieved from "https://en.xen.wiki/w/User:BudjarnLambeth/Table_of_n-comma_meantone_generators"