1156/1155
Ratio | 1156/1155 |
Factorization | 2^{2} × 3^{-1} × 5^{-1} × 7^{-1} × 11^{-1} × 17^{2} |
Monzo | [2 -1 -1 -1 -1 0 2⟩ |
Size in cents | 1.4982554¢ |
Name | quadrantonisma |
Color name | 17oo1urg2, sosolurugu 2nd, Sosolurugu comma |
FJS name | [math]\text{d2}^{17,17}_{5,7,11}[/math] |
Special properties | square superparticular, reduced |
Tenney height (log_{2} nd) | 20.3486 |
Weil height (log_{2} max(n, d)) | 20.3499 |
Wilson height (sopfr (nd)) | 64 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.4085 bits |
Comma size | unnoticeable |
S-expression | S34 |
open this interval in xen-calc |
1156/1155, the quadrantonisma, is a 17-limit no-13 superparticular comma measuring about 1.41 cents. It may be properly described as the septendecimal quartertones comma, since it is the difference between 34/33 and 35/34, the two 17-limit quartertones.
Commatic relations
In terms of commas, it is the difference between the following pairs:
- 289/288 and 385/384
- 442/441 and 715/714
- 561/560 and 1089/1088
- 595/594 and 1225/1224
- 936/935 and 4914/4913
It factors into the following pairs:
- 2080/2079 and 2601/2600
- 1275/1274 and 12376/12375
Temperaments
Tempering out this comma in the 17-limit results in the rank-6 quadrantonismic temperament, or in the 2.3.5.7.11.17 subgroup, the rank-5 quadrantonic temperament. In either case 35/33 is split into two equal parts, each representing 34/33~35/34, and enables quadrantonismic chords. If 9801/9800 is also added to the comma list, the quartertone above becomes literally a quarter of 9/8 and is tuned exactly middle of 33/32, the undecimal quartertone, and 36/35, the septimal quartertone.
Etymology
The quadrantonisma was named by Flora Canou in 2023. It is a contraction of septendecimal quartertones comma into a single word consisting of Latin quadrans ("fourth") and tonus ("tone").