715/714: Difference between revisions
Added MC- and HCJI intervals related by this comma. |
No edit summary |
||
| (5 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox Interval | {{Infobox Interval | ||
| Name = september comma, septembrisma | | Name = september comma, septembrisma | ||
| Color name = 17u3o1ory-2, sutholoruyo negative 2nd | |||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
| Line 6: | Line 7: | ||
'''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 | * the superminor sixths [[21/13]] and [[55/34]] | ||
* the semitones [[68/65]] and [[22/21]]. | * the semitones [[68/65]] and [[22/21]]. | ||
| Line 36: | Line 37: | ||
== 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 [[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]] | |||