715/714: Difference between revisions

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{{Infobox Interval
{{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, <br> Septendecimal bridge comma
| Color name =
| FJS name =
| Sound =  
}}
}}


'''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 known 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]].


[[Category:17-limit]]
== Commatic relations ==
[[Category:Unnoticeable commas]]
This comma appears as the difference between the following superparticular pairs:
[[Category:Superparticular]]
* [[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:
* [[375/374]] and [[1575/1573]]
 
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 [[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; 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]]

Latest revision as of 09:51, 23 March 2025

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 height (log2 nd) 18.9616
Weil height (log2 max(n, d)) 18.9636
Wilson height (sopfr(nd)) 58
Comma size unnoticeable
Open this interval in xen-calc

715/714, the september comma or septembrisma is a 17-limit unnoticeable 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

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: 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; however, Scott Dakota has disavowed this name.

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