715/714: Difference between revisions

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{{Infobox Interval

| Name = september comma, septembrisma

| Color name = 17u3o1ory-2, sutholoruyo negative 2nd

| 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 ==

This comma ~~identifies itself~~ as the difference between the following superparticular pairs:

This comma appears as the difference between the following superparticular pairs:

* [[120/119]] and [[144/143]]

* [[154/153]] and [[196/195]]

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== 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.

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]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Name = september comma, septembrisma
+| Color name = 17u3o1ory-2, sutholoruyo negative 2nd
 | 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 ==
-This comma identifies itself as the difference between the following superparticular pairs:
+This comma appears as the difference between the following superparticular pairs:
 * [[120/119]] and [[144/143]]
 * [[154/153]] and [[196/195]]
@@ Line 33: / Line 37: @@
 == 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.
+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]]