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 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]].
* 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 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 ===
=== September ===
[[Subgroup]]: Full 17-limit
[[Subgroup]]: 2.3.5.7.11.13.17


[[Comma basis]]: 715/714
[[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


[[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]]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 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|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 }} *


[[Optimal ET sequence]]: {{Optimal ET sequence|19, 26, 31, 41, 46, 68, 72, 103, 111, 121, 140, 183, 224, 270, 364, 436, 547, 843}}
<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 named for the intervals they stack]]
[[Category:Commas with names disavowed by the original namer]]
[[Category:Commas with names disavowed by the original namer]]

Latest revision as of 15:05, 22 March 2026

Interval information
Ratio 715/714
Factorization 2-1 × 3-1 × 5 × 7-1 × 11 × 13 × 17-1
Monzo [-1 -1 1 -1 1 1 -1⟩
Size in cents 2.423001¢
Names september comma,
septembrisma
Color name 17u3o1ory-2, sutholoruyo negative 2nd
FJS name [math]\displaystyle{ \text{m}{-2}^{5,11,13}_{7,17} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 18.9616
Weil norm (log2 max(n, d)) 18.9636
Wilson norm (sopfr(nd)) 58
Comma size unnoticeable
Open this interval in xen-calc

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:

Commatic relations

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

not to mention some nonsuperparticular but useful relations:

It factors into the following superparticular pairs:

not to mention some nonsuperparticular but useful relations:

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

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 ]]
mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

Optimal tunings:

  • 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 *

* optimal patent val: 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

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