715/714: Difference between revisions

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| Comma = yes

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'''715/714''', the '''september comma''' or '''septembrisma''' is an [[unnoticeable comma|unnoticeable]] [[17-limit]] [[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]].

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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]].

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 ===

[[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

[[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}}

{{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 }} *

<nowiki>*</nowiki> [[optimal patent val]]: [[843edo|843]]

[[Badness]] (Sintel): 0.292

== Etymology ==

The september comma was named by [[Scott Dakota]] in 2021; however, Scott Dakota has disavowed this name.

== See also ==

* [[List of superparticular intervals]]

[[Category:September]]

[[Category:Commas named for the intervals they stack]]

[[Category:Commas with names disavowed by the original namer]]

@@ Line 4: / Line 4: @@
 | Comma = yes
 }}
+'''715/714''', the '''september comma''' or '''septembrisma''' is an [[unnoticeable comma|unnoticeable]] [[17-limit]] [[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]].
@@ Line 36: / Line 35: @@
 == 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 ===
+[[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
+[[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}}
+{{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 }} *
+<nowiki>*</nowiki> [[optimal patent val]]: [[843edo|843]]
+[[Badness]] (Sintel): 0.292
 == Etymology ==
 The september comma was named by [[Scott Dakota]] in 2021; however, Scott Dakota has disavowed this name.
+== See also ==
+* [[List of superparticular intervals]]
 [[Category:September]]
 [[Category:Commas named for the intervals they stack]]
 [[Category:Commas with names disavowed by the original namer]]