9251/9250

Interval information

Ratio	9251/9250
Subgroup monzo	2.5.11.29.37 [-1 -3 1 2 -1⟩
Size in cents	0.1871503¢
Name	harchisma
Color name	37u29oo1og31 thisubitweno-alotrigu unison
FJS name	[math]\displaystyle{ \text{dd2}^{11,29,29}_{5,5,5,37} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	26.3506
Weil height (log2 max(n, d))	26.3508
Wilson height (sopfr(nd))	123
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.19855 bits
Comma size	unnoticeable
Open this interval in xen-calc

9251/9250, the harchisma, is a 37-limit superparticular comma of about 0.19 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 841/840 and 925/924
• 1276/1275 and 1480/1479
• 2001/2000 and 2553/2552

It can be factored into the following superparticular ratios:

• 9361/9360 and 787176/787175
• 9801/9800 and 164836/164835
• 10626/10625 and 71485/71484
• 13456/13455 and 29601/29600

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament harchismic. Using the 2.5.11.29.37 subgroup leads to the rank-4 temperament harchic.

Harchic

Subgroup: 2.5.11.29.37

Comma list: 9251/9250

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 386.330, ~11/8 = 551.306, 29/16 = 1029.529

Optimal ET sequence: 5ejl, 6, 9, 13, 15, 22, 28, 37, 65, 103l, 108, 131, 140, 159, 168, 196, 233, 364, 379, 401, 407, 444, 640, 1084, 1724, 2873, 3041, 3513, 4153, 4597, 5237

Badness (Sintel): 0.011

Etymology

This comma was named by Francium in 2025. It refers to 9251 Harch, the asteroid, which in turn was named after Ann P. Harch, an scientist at the Cornell University.

See also

• Unnoticeable comma
• List of superparticular intervals