Canupisma

Interval information

Ratio	17836/17835
Factorization	22 × 3-1 × 5-1 × 73 × 13 × 29-1 × 41-1
Monzo	[2 -1 -1 3 0 1 0 0 0 -1 0 0 -1⟩
Size in cents	0.09706675¢
Name	Canupisma
Color name	41u29u3oz3g3 fowutwenuthotrizo-agu 3rd
FJS name	[math]\text{dd3}^{7,7,7,13}_{5,29,41}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	28.2449
Weil height (log2 max(n, d))	28.245
Wilson height (sopfr(nd))	116
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.1999 bits
Comma size	unnoticeable
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17836/17835, the canupisma is a 41-limit superparticular comma of about 0.097 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 616/615 and 638/637
• 3773/3772 and 4785/4784
• 7176/7175 and 12006/12005

It can be factored into following superparticular commas:

• 19344/19343 and 228781/228780
• 19551/19550 and 203320/203319
• 19845/19844 and 176176/176175
• 31213/31212 and 41616/41615

Temperaments

Tempering out this comma leads to the rank-12 canupismic temperament. Using the 2.3.5.7.13.29.41 subgroup leads to the rank-6 canupic temperament.

Canupismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41

Comma list: 17836/17835

Mapping:

[⟨	1	1	2	2	3	3	4	4	4	4	4	5	4	],
⟨	0	1	0	0	0	0	0	0	0	0	0	0	-1	],
⟨	0	0	1	0	0	0	0	0	0	0	0	0	-1	],
⟨	0	0	0	1	0	0	0	0	0	0	0	0	3	],
⟨	0	0	0	0	1	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	1	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	1	0	0	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	0	0	0	0	0	0	0	0	0	0	1	0	]]

Optimal tuning (CTE): ~2/1 = 1\1, ~3/2 = 701.957, ~5/4 = 386.317, ~7/4 = 968.810, ~11/8 = 551.318, ~13/8 = 840.518, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.593, ~31/16 = 1145.036, ~37/32 = 251.344

Canupic

Subgroup: 2.3.5.7.13.29.41

Comma list: 17836/17835

Mapping:

[⟨	1	1	2	2	3	4	4	],
⟨	0	1	0	0	0	0	-1	],
⟨	0	0	1	0	0	0	-1	],
⟨	0	0	0	1	0	0	3	],
⟨	0	0	0	0	1	0	1	],
⟨	0	0	0	0	0	1	-1	]]

Optimal tuning (CTE): ~2/1 = 1\1, ~3/2 = 701.957, ~5/4 = 386.317, ~7/4 = 968.810, ~13/8 = 840.518, ~29/16 = 1029.593

Optimal ET sequence: 5, 7dfjjmmm, 7djjm, 8dmm, 9j, 10m, 12fjm, 15, 17c, 19m, 27, 31, 39dfjmm, 41fm, 41, 53j, 58, 80, 94, 99, 103, 111j, 118, 121m, 140, 171, 198, 243, 251j, 292m, 301, 311, 354, 373, 441, 494, 513, 571, 711, 814, 954j, 1065, 1205, 1578, 1619, 1677, 1817, 2019, 2190, 3395, 5585, 8980

Etymology

This comma was named by Francium in 2024. It refers to the asteroid 17836 Canup, which in turn was named after the astrophysicist Robin Canup.

See also

• Unnoticeable comma
• List of superparticular intervals