Manheimisma
Ratio | 17545/17544 |
Factorization | 2-3 × 3-1 × 5 × 112 × 17-1 × 29 × 43-1 |
Monzo | [-3 -1 1 0 2 0 -1 0 0 1 0 0 0 -1⟩ |
Size in cents | 0.098676739¢ |
Name | manheimisma |
Color name | 43u29o17u1ooy-2 fothutwenosuloloyo negative 2nd |
FJS name | [math]\text{m}{-2}^{5,11,11,29}_{17,43}[/math] |
Special properties | superparticular, reduced |
Tenney height (log2 nd) | 28.1975 |
Weil height (log2 max(n, d)) | 28.1975 |
Wilson height (sopfr(nd)) | 125 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.1999 bits |
Comma size | unnoticeable |
open this interval in xen-calc |
17545/17544, the manheimisma, is a 43-limit superparticular comma of about 0.1 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
It can be factored into the following superparticular commas:
- 20125/20124 and 136851/136850
- 25025/25024 and 58696/58695
- 27951/27950 and 47125/47124
Temperaments
Tempering out this comma in the full 43-limit leads to the rank-13 temperament manheimismic. Using the 2.3.5.11.17.29.43 subgroup leads to the rank-6 temperament manheimic.
Manheimismic
Subgroup. 2.3.5.7.11.13.17.19.23.29.31.37.41.43
Comma list: 17545/17544
[⟨ | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 4 | ], |
⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | ], |
⟨ | 0 | 0 | 1 | 0 | 0 | 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 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | ], |
⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 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 | 0 | 0 | 1 | 0 | 0 | 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 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | ], |
⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 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 | 0 | 0 | 1 | 0 | ], |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.957, ~5/4 = 386.309, ~7/4 = 968.826, ~11/8 = 551.299, ~13/8 = 840.528, ~17/16 = 104.969, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.559, ~31/16 = 1145.036, ~37/32 = 251.344, ~41/32 = 429.062
Manheimic
Subgroup: 2.3.5.11.17.29.43
Comma list: 17545/17544
[⟨ | 1 | 1 | 2 | 3 | 4 | 4 | 4 | ], |
⟨ | 0 | 1 | 0 | 0 | 0 | 0 | -1 | ], |
⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 1 | ], |
⟨ | 0 | 0 | 0 | 1 | 0 | 0 | 2 | ], |
⟨ | 0 | 0 | 0 | 0 | 1 | 0 | -1 | ], |
⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.957, ~5/4 = 386.309, ~11/8 = 551.299, ~17/16 = 104.969, ~29/16 = 1029.559
Optimal ET sequence: 6j, 7gjjn, 7g, 10n, 12enn, 12gjn, 14cggjjn, 14cn, 15n, 16jn, 17cgn, 19egnn, 19, 22, 31gj, 31, 34n, 46j, 53gn, 56, 65, 118, 183, 414, 422, 487, 597, 605, 653, 677, 718, 764j, 836, 1019, 1513, 1600, 1783, 2000, 2231, 2349, 2414, 2836, 3737, 3920, 4197, 4436, 4619, 5520, 7033, 10139
Etymology
The manheimisma was named by Francium in 2024. It refers to the postal code of Manheim, Pennsylvania.