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{nd}[/math]) |
~1.22077 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.
Quadrantonic
Subgroup: 2.3.5.7.11.17
[⟨ | 1 | 0 | 0 | 0 | 0 | -1 | ], |
⟨ | 0 | 1 | 0 | 0 | 1 | 1 | ], |
⟨ | 0 | 0 | 1 | 0 | 1 | 1 | ], |
⟨ | 0 | 0 | 0 | 1 | 1 | 1 | ], |
⟨ | 0 | 0 | 0 | 0 | -2 | -1 | ]] |
- sval mapping generators: ~2, ~3, ~5, ~7, ~34/11
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9948, ~5/4 = 386.3991, ~7/4 = 968.9508, ~17/11 = 752.9186
Optimal ET sequence: 17cg, 19eg, 22, 27eg, 39dg, 43, 46, 65d, 68, 72, 118, 171, 183, 239, 282, 301, 311, 400, 422, 472, 494, 894, 1012g, 1205, 1388
Quadrantonismic
Subgroup: 2.3.5.7.11.13.17
[⟨ | 1 | 0 | 0 | 0 | 0 | 0 | -1 | ], |
⟨ | 0 | 1 | 0 | 0 | 1 | 0 | 1 | ], |
⟨ | 0 | 0 | 1 | 0 | 1 | 0 | 1 | ], |
⟨ | 0 | 0 | 0 | 1 | 1 | 0 | 1 | ], |
⟨ | 0 | 0 | 0 | 0 | -2 | 0 | -1 | ], |
⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ]] |
- mapping generators: ~2, ~3, ~5, ~7, ~34/11, ~13
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9948, ~5/4 = 386.3991, ~7/4 = 968.9508, ~17/11 = 752.9186, ~13/8
Optimal ET sequence: 17cg, 19eg, 22, 26, 27eg, 29g, 39dfg, 43, 46, 65d, 68, 72, 111, 121, 140, 171, 183, 217, 282, 301, 311, 354, 400, 422, 494, 894, 1012g, 1133, 1205, 1506g, 1627e
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").