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{{DISPLAYTITLE:User:BudjarnLambeth/Table of ''n''-comma meantone generators}}{{Editable user page}}


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.  
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.  


== Overview of table ==
== Scope of table ==


=== Characteristics included ===
=== Characteristics included ===
Line 9: Line 9:
* Whether it saw historical (pre-1950) use
* 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 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 an optimized tuning of meantone (e.g. 7-limit [[CTE]])
* 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 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 about equally sharp of [[3/2]] as some other listed temperament is flat
Line 233: Line 233:
|
|
|-
|-
|[[5/8-comma meantone|5/8-comma]] ||688.514||Close to [[61edo]].
|[[5/8-comma meantone|5/8-comma]] ||688.514||Close to [[61edo]] and [[43/32]].
|-
|-
|[[13/21-comma meantone|13/21-comma]]  
|[[13/21-comma meantone|13/21-comma]]  
Line 239: Line 239:
|
|
|-
|-
|[[Golden ratio-comma meantone|Golden ratio-comma]]  
|[[1/φ-comma meantone|1/ϕ-comma]]
|688.663
|688.663
|
|
Line 355: Line 355:
|[[5/13-comma meantone|5/13-comma]] ||693.683||
|[[5/13-comma meantone|5/13-comma]] ||693.683||
|-
|-
|[[Split Golden ratio-comma meantone|Split Golden ratio-comma]]  
|[[1/(φ+1)-comma meantone|1/(ϕ+1)-comma]]
|693.740
|693.740
|Close to [[64edo]].
|Close to [[64edo]].
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|[[7/26-comma meantone|7/26-comma]] ||696.165||Close to [[golden meantone]]. Historically significant (see [[historical temperaments]]).
|[[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||
|[[4/15-comma meantone|4/15-comma]] ||696.220||Close to [[5-limit]] meantone [[POTE]] tuning.
|-
|-
|[[5/19-comma meantone|5/19-comma]]  
|[[5/19-comma meantone|5/19-comma]]  
Line 431: Line 431:
|Close to [[81edo]].
|Close to [[81edo]].
|-
|-
|[[Quarter-comma meantone|1/4-comma]] ||696.578||Historically significant (see [[historical temperaments]]).
|[[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]]  
|[[5/21-comma meantone|5/21-comma]]  
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|[[4/17-comma meantone|4/17-comma]] ||696.895||
|[[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.
|[[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]]   
|[[5/22-comma meantone|5/22-comma]]   
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|
|
|-
|-
|[[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 distance]].
|[[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]].
|[[4/25-comma meantone|4/25-comma]] ||698.514||Close to [[67edo]].
Line 668: Line 668:
|[[17edo]]
|[[17edo]]
|705.882
|705.882
|Vaguely resembles Middle Eastern neutral third scales.
|The largest MOS scale this can generate is 17 tone. Vaguely resembles Middle Eastern [[neutral third scale]]s.
|-
|-
|[[-3/16-comma meantone|-3/16-comma]]  
|[[-3/16-comma meantone|-3/16-comma]]  
Line 710: Line 710:
|About as sharp of [[Pythagorean tuning]] as [[31edo]] is flat.
|About as sharp of [[Pythagorean tuning]] as [[31edo]] is flat.
|-
|-
|[[Negative Quarter-comma meantone|Negative Quarter-comma]]  
|[[-1/4-comma meantone|-1/4-comma]]
|707.332
|707.332
|
|
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|[[-4/15-comma meantone|-4/15-comma]]  
|[[-4/15-comma meantone|-4/15-comma]]  
|707.690
|707.690
|About as sharp of [[Pythagorean tuning]] as [[Golden meantone]] is flat.
|About as sharp of [[Pythagorean tuning]] as [[golden meantone]] is flat.
|-
|-
|[[-7/26-comma meantone|-7/26-comma]]  
|[[-7/26-comma meantone|-7/26-comma]]  
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|[[-9/26-comma meantone|-9/26-comma]]  
|[[-9/26-comma meantone|-9/26-comma]]  
|709.399
|709.399
|
|Close to [[2.3.7-limit]] superpyth [[POTE]] tuning.
|-
|-
|[[-8/23-comma meantone|-8/23-comma]]  
|[[-8/23-comma meantone|-8/23-comma]]  
Line 792: Line 792:
|[[-6/17-comma meantone|-6/17-comma]]  
|[[-6/17-comma meantone|-6/17-comma]]  
|709.545
|709.545
|
|Close to [[11-limit]] superpyth [[CTE]] tuning.
|-
|-
|[[-5/14-comma meantone|-5/14-comma]]  
|[[-5/14-comma meantone|-5/14-comma]]  
|709.636
|709.636
|Close to [[93edo]]
|Close to [[93edo]]. Close to [[2.3.7-limit]] and [[7-limit]] superpyth CTE tunings.
|-
|-
|[[-4/11-comma meantone|-4/11-comma]]  
|[[-4/11-comma meantone|-4/11-comma]]  
Line 804: Line 804:
|[[-7/19-comma meantone|-7/19-comma]]  
|[[-7/19-comma meantone|-7/19-comma]]  
|709.878
|709.878
|
|Close to [[13-limit]] superpyth CTE tuning.
|-
|-
|[[-3/8-comma meantone|-3/8-comma]]  
|[[-3/8-comma meantone|-3/8-comma]]  
Line 814: Line 814:
|
|
|-
|-
|[[Negative Split Golden ratio-comma meantone|Negative Split Golden ratio-comma]]  
|[[-1/(φ+1)-comma meantone|-1/(ϕ+1)-comma]]
|710.170
|710.170
|
|Close to [[11-limit]] superpyth POTE tuning.
|-
|-
|[[-5/13-comma meantone|-5/13-comma]]  
|[[-5/13-comma meantone|-5/13-comma]]  
|710.227
|710.227
|Close to [[49edo]].
|Close to [[49edo]]. Close to [[7-limit]] superpyth POTE tuning.
|-
|-
|[[-7/18-comma meantone|-7/18-comma]]  
|[[-7/18-comma meantone|-7/18-comma]]  
Line 832: Line 832:
|[[-2/5-comma meantone|-2/5-comma]]  
|[[-2/5-comma meantone|-2/5-comma]]  
|710.558
|710.558
|
|Close to [[13-limit]] superpyth POTE tuning.
|-
|-
|[[-9/22-comma meantone|-9/22-comma]]  
|[[-9/22-comma meantone|-9/22-comma]]  
Line 972: Line 972:
|
|
|-
|-
|[[Negative Golden ratio-comma meantone|Negative Golden ratio-comma]]  
|[[-1/φ-comma meantone|-1/ϕ-comma]]
|715.247
|715.247
|
|
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|[[-5/8-comma meantone|-5/8-comma]]  
|[[-5/8-comma meantone|-5/8-comma]]  
|715.396
|715.396
|Close to [[52edo]].
|Close to [[52edo]] and 387/256.
|-
|-
|[[-12/19-comma meantone|-12/19-comma]]  
|[[-12/19-comma meantone|-12/19-comma]]  
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