1702/1701

Interval information

Ratio	1702/1701
Subgroup monzo	2.3.7.23.37 [1 -5 -1 1 1⟩
Size in cents	1.017475¢
Name	kalaharisma
Color name	s37o23or2 sathisotwethoru 2nd
FJS name	[math]\text{m}{-2}^{23,37}_{7}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	21.4652
Weil height (log2 max(n, d))	21.466
Wilson height (sopfr(nd))	84
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.20877 bits
Comma size	unnoticeable
Open this interval in xen-calc

1702/1701, the kalaharisma, is a 37-limit superparticular comma of about 1.02 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 148/147 and 162/161
• 253/252 and 297/296
• 703/702 and 1197/1196
• 736/735 and 1296/1295

It can be factored into the following superparticular intervals:

• 1716/1715 and 208495/208494
• 1729/1728 and 108928/108927
• 1863/1862 and 19684/19683
• 2024/2023 and 10693/10692
• 2080/2079 and 9361/9360
• 2185/2184 and 7696/7695
• 2553/2552 and 5104/5103
• 3256/3255 and 3565/3564

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament kalaharismic. Using the 2.3.7.23.37 subgroup leads to the rank-4 temperament kalaharic.

Kalaharic

Subgroup: 2.3.7.23.37

Comma list: 1702/1701

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.063, ~7/4 = 968.894, ~23/16 = 628.098

Optimal ET sequence: 5, 9il, 12, 14l, 17, 22, 31, 46, 48, 53, 77, 99, 130, 176, 207, 229, 306, 535, 1381, 1610, 1687, 1817l, 1916, 2451, 2986

Badness (Sintel): 0.051

Etymology

This comma was named by Francium in 2025. It refers to 1702 Kalahari, the asteroid, which in turn was named after the Kalahari Desert.

See also

• Unnoticeable comma
• List of superparticular intervals