Zangarisma

Interval information

Ratio	10693/10692
Subgroup monzo	2.3.11.17.37 [-2 -5 -1 2 1⟩
Size in cents	0.1619111¢
Name	Zangarisma
Color name	37o17oo1u3 thisososolu 3rd
FJS name	[math]\text{d2}^{17,17,37}_{11}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	26.7686
Weil height (log2 max(n, d))	26.7688
Wilson height (sopfr(nd))	101
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19846 bits
Comma size	unnoticeable
S-expression	S34 / S36
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10693/10692, the zangarisma, is a 37-limit superparticular comma of about 0.16 cents.

Commatic relationships

This comma is the difference between the following superparticular ratios:

• 289/288 and 297/296
• 1156/1155 and 1296/1295
• 3367/3366 and 4914/4913
• 3774/3773 and 5832/5831

It can be factored into following superparticular commas:

• 11271/11270 and 208495/208494
• 11914/11913 and 104329/104328
• 12376/12375 and 78625/78624
• 18241/18240 and 25840/25839
• 19684/19683 and 23409/23408

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament zangarismic. Using the 2.3.11.17.37 subgroup leads to the rank-4 temperament zangaric.

Zangarismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 10693/10692

Mapping:

[⟨	1	1	2	2	3	3	4	4	4	4	4	2	],
⟨	0	1	0	0	0	0	0	0	0	0	0	5	],
⟨	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	1	],
⟨	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 = 701.967, ~5/4 = 386.314, ~7/4 = 968.826, ~11/8 = 551.329, ~13/8 = 840.528, ~17/16 = 104.923, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036

Zangaric

Subgroup: 2.3.11.17.37

Comma list: 10693/10692

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.967, ~11/8 = 551.329, ~17/16 = 104.923

Optimal ET sequence: 5eg, 8ll, 9g, 10e, 10l, 12el, 14l, 21eg, 22, 24, 111, 135, 159, 183, 207, 253, 277, 328, 352, 376, 535, 559, 583, 605, 629, 764, 788, 812, 1648, 2000, 2024, 2812, 2836, 3672, 6508

Etymology

This comma was named by Francium in 2024. It refers to 10693 Zangari, the asteroid, which in turn was named after a postdoctoral researcher.

See also

• Unnoticeable comma
• List of superparticular intervals