715/714: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = september comma, septembrisma | | Name = september comma, septembrisma | ||
| Color name = 17u3o1ory-2, sutholoruyo negative 2nd | |||
| 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''. | '''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 == | == Commatic relations == | ||
This comma | This comma appears as the difference between the following superparticular pairs: | ||
* [[120/119]] and [[144/143]] | * [[120/119]] and [[144/143]] | ||
* [[154/153]] and [[196/195]] | * [[154/153]] and [[196/195]] | ||
| Line 32: | Line 36: | ||
== Temperaments == | == Temperaments == | ||
Tempering out this comma in the 17-limit gives the rank-6 '''september temperament''', and enables the related essentially tempered chords. | 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 == | == Etymology == | ||
The september comma was named by [[Scott Dakota]] in 2021. | The september comma was named by [[Scott Dakota]] in 2021; however, Scott Dakota has disavowed this name. | ||
[[Category:September]] | [[Category:September]] | ||
[[Category:Commas named for the intervals they stack]] | |||
[[Category:Commas with names disavowed by the original namer]] | |||
Latest revision as of 09:51, 23 March 2025
| Interval information |
septembrisma
reduced
715/714, the september comma or septembrisma is a 17-limit unnoticeable superparticular comma with a size of approximately 2.42 cents. It is also described as the septendecimal bridge comma. It is the gap between:
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:
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 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: 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.