Genzelisma

Interval information

Ratio	18241/18240
Factorization	2-6 × 3-1 × 5-1 × 17 × 19-1 × 29 × 37
Monzo	[-6 -1 -1 0 0 0 1 -1 0 1 0 1⟩
Size in cents	0.09491155¢
Name	Genzelisma
Color name	37o29o19u17og2 thisotwenonusogu 2nd
FJS name	[math]\text{d1}^{17,29,37}_{5,19}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	28.3097
Weil height (log2 max(n, d))	28.3098
Wilson height (sopfr(nd))	122
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.1999 bits
Comma size	unnoticeable
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18241/18240, the genzelisma, is a 37-limit superparticular comma of about 0.095 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 481/480 and 494/493
• 2146/2145 and 2432/2431
• 6993/6992 and 11340/11339
• 7696/7695 and 13312/13311

It can be factored into following superparticular intervals:

• 21505/21504 and 120176/120175
• 23409/23408 and 82621/82620
• 23751/23750 and 78625/78624

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament genzelismic. Using the 2.3.5.17.19.29.37 subgroup leads to the rank-6 temperament genzelic.

Genzelismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 18241/18240

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.958, ~5/4 = 386.319, ~7/4 = 968.826, ~11/8 = 551.318, ~13/8 = 840.528, ~17/16 = 104.938, ~19/16 = 297.531, ~23/16 = 628.274, ~29/16 = 1029.553, ~31/16 = 1145.036

Genzelic

Subgroup: 2.3.5.17.19.29.37

Comma list: 18241/18240

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.958, ~5/4 = 386.319, ~17/16 = 104.938, ~19/16 = 297.531, ~29/16 = 1029.553

Optimal ET sequence: 5g, 5ghj, 7gh, 10j, 10h, 12, 19gh, 19, 22h, 24, 26, 34, 38j, 43, 46hj, 53, 56, 65l, 72, 77, 80, 99, 106, 149, 183, 205, 388, 472, 513, 559, 593, 631, 677, 730, 836, 1041, 1190, 1395, 1718, 1795, 2000, 2836, 3190, 4026, 6026, 8257, 8934, 10052

Etymology

This comma was named by Francium in 2024. It refers to 18241 Genzel, the asteroid, which in turn was named after the German astronomer Reinhard Genzel.

See also

• Unnoticeable comma
• List of superparticular intervals