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| Comma = yes
| Comma = yes
}}
}}
'''715/714''', the '''september comma''' or '''septembrisma''' is a [[17-limit]] [[unnoticeable comma|unnoticeable]] [[superparticular]] comma with a size of approximately 2.42 [[cent]]s. It is also described as the ''septendecimal bridge comma''. It is the gap between:
'''715/714''', the '''september comma''' or '''septembrisma''' is a [[17-limit]] [[unnoticeable comma|unnoticeable]] [[superparticular]] comma with a size of approximately 2.42 [[cent]]s. It is also described as the ''septendecimal bridge comma''. It is the gap between:
* the subfourths [[17/13]] and [[55/42]]
* the subfourths [[17/13]] and [[55/42]];
* the superminor sixths [[21/13]] and [[55/34]]
* the superminor sixths [[21/13]] and [[55/34]];
* the semitones [[68/65]] and [[22/21]].
* the semitones [[68/65]] and [[22/21]].


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== Temperaments ==
== Temperaments ==
Tempering out this comma in the 17-limit gives the rank-6 '''september temperament''', and enables the [[September chords|related essentially tempered chords]].  
Tempering out this comma in the 17-limit gives the rank-6 '''september''' temperament, and enables the related [[essentially tempered chord]]s – [[september chords]].  


=== September ===
=== September ===
[[Subgroup]]: Full 17-limit
[[Subgroup]]: 2.3.5.7.11.13.17
 
[[Mapping]]:
{| class="right-all"
|-
| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 1 || ]]
|}
: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13


[[Comma basis]]: 715/714
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.0409{{c}}, ~3/2 = 702.0169{{c}}, ~5/4 = 386.0109{{c}}, ~7/4 = 969.0667{{c}}, ~11/8 = 550.7048{{c}}, ~13/8 = 839.8438{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0260{{c}}, ~5/4 = 385.0429{{c}}, ~7/4 = 969.0934{{c}}, ~11/8 = 550.7520{{c}}, ~13/8 = 839.8854{{c}}


[[Mapping]]: [⟨1 0 0 0 0 0 -1], ⟨0 1 0 0 0 0 -1], ⟨0 0 1 0 0 0 1], ⟨0 0 0 1 0 0 -1], ⟨0 0 0 0 1 0 1], ⟨0 0 0 0 0 1 1]]
{{Optimal ET sequence|legend=1| 22f, 26, 27eg, 29g, 31, 38df, 41, 46, 60e, 65d, 68, 72, 103, 111, 121, 140, 183, 224, 270, 364, 436, 547, 634g, 706f }} *


[[Optimal tuning]] (POTE): ~2 = 1＼1, ~3/2 = 701.9930, ~5/4 = 385.9978, ~7/4 = 969.0337, ~11/8 = 550.6860, ~13/8 = 839.8152
<nowiki>*</nowiki> [[optimal patent val]]: [[843edo|843]]


[[Optimal ET sequence]]: {{Optimal ET sequence|19, 26, 31, 41, 46, 68, 72, 103, 111, 121, 140, 183, 224, 270, 364, 436, 547, 843}}
[[Badness]] (Sintel): 0.292


== Etymology ==
== Etymology ==
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