1665/1664

Interval information
Ratio	1665/1664
Subgroup monzo	2.3.5.13.37 [-7 2 1 -1 1⟩
Size in cents	1.040093 ¢
Name	gabisma
Color name	37o3uy1 ; thisothuyo unison
FJS name	[math]\displaystyle{ \text{d}{-2}^{5,37}_{13} }[/math]
Special properties	superparticular,; reduced
Tenney norm (log2 nd)	21.4017
Weil norm (log2 max(n, d))	21.4026
Wilson norm (sopfr(nd))	75
Comma size	unnoticeable
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1665/1664, the gabisma, is a 37-limit superparticular comma of about 1.0 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

It can be factored into the following superparticular intervals:

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament gabismic. Using the 2.3.5.13.37 subgroup leads to the rank-4 temperament gabic.

Gabismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list. 1665/1664

Mapping:

[⟨	1	1	2	2	3	3	4	4	4	4	4	6	],
⟨	0	1	0	0	0	0	0	0	0	0	0	-2	],
⟨	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	1	],
⟨	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	0	],
⟨	0	0	0	0	0	0	0	0	0	0	1	0	]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.862, ~5/4 = 386.214, ~7/4 = 968.826, ~11/8 = 551.318, ~13/8 = 840.781, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036

Gabic

Subgroup: 2.3.5.13.37

Comma list: 1665/1664

Mapping:

[⟨	1	1	2	3	6	],
⟨	0	1	0	0	-2	],
⟨	0	0	1	0	-1	],
⟨	0	0	0	1	1	]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.862, ~5/4 = 386.214, ~13/8 = 840.781

Optimal ET sequence: 5, 7f, 7l, 9, 10, 12l, 12f, 15, 19, 34, 53, 171, 224, 277, 354, 407, 631, 684, 1038, 1091l, 1532l, 1756l, 1809l, 2163ll, 2216ll

Etymology

This comma was named by Francium in 2025. It refers to 1665 Gaby, the asteroid, which in turn was named after Gaby Reinmuth, the daughter-in-law of discoverer Karl Wilhelm Reinmuth.