Genzelisma
| Ratio | 18241/18240 |
| Factorization | 2-6 × 3-1 × 5-1 × 17 × 19-1 × 29 × 37 |
| Monzo | [-6 -1 -1 0 0 0 1 -1 0 1 0 1⟩ |
| Size in cents | 0.094911546¢ |
| Name | Genzelisma |
| Color name | 37o29o19u17og2 thisotwenonusogu 2nd |
| FJS name | [math]\text{d1}^{17,29,37}_{5,19}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 28.3097 |
| Weil height (log2 max(n, d)) | 28.3098 |
| Wilson height (sopfr(nd)) | 122 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.1999 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
18241/18240, the genzelisma, is a 37-limit superparticular comma of about 0.095 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 481/480 and 494/493
- 2146/2145 and 2432/2431
- 6993/6992 and 11340/11339
- 7696/7695 and 13312/13311
It can be factored into following superparticular intervals:
- 21505/21504 and 120176/120175
- 23409/23408 and 82621/82620
- 23751/23750 and 78625/78624
Temperaments
Tempering out this comma in the full 37-limit leads to the rank-11 temperament genzelismic. Using the 2.3.5.17.19.29.37 subgroup leads to the rank-6 temperament genzelic.
Genzelismic
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
Comma list: 18241/18240
| [⟨ | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 5 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 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 | 0 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ], |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.958, ~5/4 = 386.319, ~7/4 = 968.826, ~11/8 = 551.318, ~13/8 = 840.528, ~17/16 = 104.938, ~19/16 = 297.531, ~23/16 = 628.274, ~29/16 = 1029.553, ~31/16 = 1145.036
Genzelic
Subgroup: 2.3.5.17.19.29.37
Comma list: 18241/18240
| [⟨ | 1 | 1 | 2 | 4 | 4 | 4 | 5 | ], |
| ⟨ | 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 (CTE): ~2 = 1\1, ~3/2 = 701.958, ~5/4 = 386.319, ~17/16 = 104.938, ~19/16 = 297.531, ~29/16 = 1029.553
Optimal ET sequence: 5g, 5ghj, 7gh, 10j, 10h, 12, 19gh, 19, 22h, 24, 26, 34, 38j, 43, 46hj, 53, 56, 65l, 72, 77, 80, 99, 106, 149, 183, 205, 388, 472, 513, 559, 593, 631, 677, 730, 836, 1041, 1190, 1395, 1718, 1795, 2000, 2836, 3190, 4026, 6026, 8257, 8934, 10052
Etymology
This comma was named by Francium in 2024. It refers to 18241 Genzel, the asteroid, which in turn was named after the German astronomer Reinhard Genzel.