715/714
Jump to navigation
Jump to search
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 | 2.4230012¢ |
Names | september comma, septembrisma |
FJS name | [math]\text{m}{-2}^{5,11,13}_{7,17}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 18.9616 |
Weil height (log_{2} max(n, d)) | 18.9636 |
Wilson height (sopfr (nd)) | 58 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.42389 bits |
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.
Commatic relations
This comma identifies itself 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.
Etymology
The september comma was named by Scott Dakota in 2021.