Zangarisma
| Ratio | 10693/10692 |
| Subgroup monzo | 2.3.11.17.37 [-2 -5 -1 2 1⟩ |
| Size in cents | 0.16191106¢ |
| Name | Zangarisma |
| Color name | 37o17oo1u3 thisososolu 3rd |
| FJS name | [math]\text{d2}^{17,17,37}_{11}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 26.7686 |
| Weil height (log2 max(n, d)) | 26.7688 |
| Wilson height (sopfr(nd)) | 101 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.19846 bits |
| Comma size | unnoticeable |
| S-expression | S34 / S36 |
| open this interval in xen-calc | |
10693/10692, the zangarisma, is a 37-limit superparticular comma of about 0.16 cents.
Commatic relationships
This comma is the difference between the following superparticular ratios:
It can be factored into following superparticular commas:
- 11271/11270 and 208495/208494
- 11914/11913 and 104329/104328
- 12376/12375 and 78625/78624
- 18241/18240 and 25840/25839
- 19684/19683 and 23409/23408
Temperaments
Tempering out this comma in the full 37-limit leads to the rank-11 temperament zangarismic. Using the 2.3.11.17.37 subgroup leads to the rank-4 temperament zangaric.
Zangarismic
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
Comma list: 10693/10692
| [⟨ | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 2 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | -2 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.967, ~5/4 = 386.314, ~7/4 = 968.826, ~11/8 = 551.329, ~13/8 = 840.528, ~17/16 = 104.923, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036
Zangaric
Subgroup: 2.3.11.17.37
Comma list: 10693/10692
| [⟨ | 1 | 1 | 3 | 4 | 2 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 5 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | -2 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.967, ~11/8 = 551.329, ~17/16 = 104.923
Optimal ET sequence: 5eg, 8ll, 9g, 10e, 10l, 12el, 14l, 21eg, 22, 24, 111, 135, 159, 183, 207, 253, 277, 328, 352, 376, 535, 559, 583, 605, 629, 764, 788, 812, 1648, 2000, 2024, 2812, 2836, 3672, 6508
Etymology
This comma was named by Francium in 2024. It refers to 10693 Zangari, the asteroid, which in turn was named after a postdoctoral researcher.