715/714: Difference between revisions
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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 | * 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]]. | * the semitones [[68/65]] and [[22/21]]. | ||
| Line 36: | Line 35: | ||
== Temperaments == | == Temperaments == | ||
Tempering out this comma in the 17-limit gives the rank-6 '''september | 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 == | == Etymology == | ||
The september comma was named by [[Scott Dakota]] in 2021; however, Scott Dakota has disavowed this name. | 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:September]] | ||
[[Category:Commas named for the intervals they stack]] | |||
[[Category:Commas with names disavowed by the original namer]] | |||
Latest revision as of 15:05, 22 March 2026
| Interval information |
septembrisma
reduced
715/714, the september comma or septembrisma is an unnoticeable 17-limit superparticular comma with a size of approximately 2.42 cents. 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 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 chords.
September
Subgroup: 2.3.5.7.11.13.17
| [⟨ | 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
- WE: ~2 = 1200.0409 ¢, ~3/2 = 702.0169 ¢, ~5/4 = 386.0109 ¢, ~7/4 = 969.0667 ¢, ~11/8 = 550.7048 ¢, ~13/8 = 839.8438 ¢
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.0260 ¢, ~5/4 = 385.0429 ¢, ~7/4 = 969.0934 ¢, ~11/8 = 550.7520 ¢, ~13/8 = 839.8854 ¢
Optimal ET sequence: 22f, 26, 27eg, 29g, 31, 38df, 41, 46, 60e, 65d, 68, 72, 103, 111, 121, 140, 183, 224, 270, 364, 436, 547, 634g, 706f *
Badness (Sintel): 0.292
Etymology
The september comma was named by Scott Dakota in 2021; however, Scott Dakota has disavowed this name.