Manheimisma

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Interval information
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:

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

Mapping:

[⟨ 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

Mapping:

[⟨ 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 sequence6j, 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.

See also