715/714: Difference between revisions

← Older edit

VisualWikitext

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = september comma, septembrisma
-| Ratio = 715/714
+| Color name = 17u3o1ory-2, sutholoruyo negative 2nd
-| Monzo = -1 -1 1 -1 1 1 -1
+| Comma = yes
-| Cents = 2.423
-| Name = September comma, <br> Septembrisma
-| Color name =
-| FJS name =
-| Sound =
 }}
+'''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:
+* the subfourths [[17/13]] and [[55/42]];
+* the superminor sixths [[21/13]] and [[55/34]];
+* the semitones [[68/65]] and [[22/21]].
-'''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.
+== 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]]
-[[Category:17-limit]]
+not to mention some nonsuperparticular but useful relations:
-[[Category:Unnoticeable comma]]
+* [[375/374]] and [[1575/1573]]
-[[Category:Superparticular]]
+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 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]]