Manheimisma

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	0.09867674¢
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
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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:

• 1463/1462 and 1596/1595
• 1936/1935 and 2176/2175
• 2925/2924 and 3510/3509
• 7569/7568 and 13311/13310

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

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 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.

See also

• Unnoticeable comma
• List of superparticular intervals