Shchedrinisma
| Ratio | 4625/4624 |
| Subgroup monzo | 2.5.17.37 [-4 3 -2 1⟩ |
| Size in cents | 0.37436135¢ |
| Name | shchedrinisma |
| Color name | 37o17uuy3-2 thisosusutriyo negative 2nd |
| FJS name | [math]\text{ddd}{-3}^{5,5,5,37}_{17,17}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 24.3502 |
| Weil height (log2 max(n, d)) | 24.3505 |
| Wilson height (sopfr(nd)) | 94 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.20041 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
4625/4624, the shchedrinisma, is a 37-limit superparticular comma of about 0.37 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
It can be factored into following superparticular commas:
- 4693/4692 and 319125/319124
- 4761/4760 and 161875/161874
- 5985/5984 and 20350/20349
- 6325/6324 and 17205/17204
Temperaments
Tempering out this comma in the full 37-limit leads to the rank-11 temperament shchedrinismic. Using the 2.5.17.37 subgroup leads to the rank-3 temperament shchedrinic.
Shchedrinismic
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
Comma list: 4625/4624
| [⟨ | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 6 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -3 | ], |
| ⟨ | 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 | 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 = 701.955, ~5/4 = 386.271, ~7/4 = 968.826, ~11/8 = 551.318, ~13/8 = 840.528, ~17/16 = 105.043, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036
Shchedrinic
Subgroup: 2.5.17.37
Comma list: 4625/4624
| [⟨ | 1 | 2 | 4 | 6 | ], |
| ⟨ | 0 | 1 | 0 | 3 | ], |
| ⟨ | 0 | 0 | 1 | 2 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 386.271, ~17/16 = 105.043
Optimal ET sequence: 4, 5g, 6l, 7g, 9, 16, 22, 25, 34, 56, 81, 90, 115, 205, 320, 3315, 3635, 3955, 4275, 4595, 4915, 5235, 5555l, 5875l, 6195l, 6754l, 7074l, 7394l, 7714l
Etymology
The shchedrinisma was named by Francium in 2024. It refers to 4625 Shchedrin, the asteroid. Which was in turn named after a Russian composer.