715/714: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = | | Name = september comma, septembrisma | ||
| Color name = 17u3o1ory-2, sutholoruyo negative 2nd | |||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''715/714''', the ''' | '''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 superminor sixths [[21/13]] and [[55/34]] | |||
* the semitones [[68/65]] and [[22/21]]. | |||
== Commatic relations == | |||
This comma appears as the difference between the following superparticular pairs: | |||
* [[120/119]] and [[144/143]] | |||
* [[154/153]] and [[196/195]] | |||
* [[273/272]] and [[441/440]] | |||
* [[325/324]] and [[595/594]] | |||
* [[385/384]] and [[833/832]] | |||
* [[442/441]] and [[1156/1155]] | |||
* [[561/560]] and [[2601/2600]] | |||
* [[676/675]] and [[12376/12375]] | |||
not to mention some nonsuperparticular but useful relations: | |||
* [[375/374]] and [[1575/1573]] | |||
It factors into the following superparticular pairs: | |||
* [[1225/1224]] and [[1716/1715]] | |||
* [[1089/1088]] and [[2080/2079]] | |||
* [[1001/1000]] and [[2500/2499]] | |||
* [[936/935]] and [[3025/3024]] | |||
* [[729/728]] and [[37180/37179]] | |||
not to mention some nonsuperparticular but useful relations: | |||
* [[2025/2023]] and [[2431/2430]] | |||
* [[2200/2197]] and [[28561/28560]] | |||
== Temperaments == | |||
Tempering out this comma in the 17-limit gives the rank-6 '''september temperament''', and enables the [[September chords|related essentially tempered chords]]. | |||
=== September === | |||
[[Subgroup]]: Full 17-limit | |||
[[Comma basis]]: 715/714 | |||
[[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 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 | |||
[[Optimal ET sequence]]: {{Optimal ET sequence|19, 26, 31, 41, 46, 68, 72, 103, 111, 121, 140, 183, 224, 270, 364, 436, 547, 843}} | |||
== Etymology == | |||
The september comma was named by [[Scott Dakota]] in 2021; however, Scott Dakota has disavowed this name. | |||
[[Category:September]] | |||
[[Category:Commas named for the intervals they stack]] | |||
[[Category:Commas with names disavowed by the original namer]] | |||