76384/76383

Interval information

Ratio	76384/76383
Factorization	25 × 3-4 × 7 × 11 × 23-1 × 31 × 41-1
Monzo	[5 -4 0 1 1 0 0 0 -1 0 1 0 -1⟩
Size in cents	0.02266503¢
Name	vernonisma
Color name	41u31o23u1oz1 fowuthiwotwethulozo unison
FJS name	[math]\displaystyle{ \text{d2}^{7,11,31}_{23,41} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	32.4419
Weil height (log2 max(n, d))	32.442
Wilson height (sopfr(nd))	135
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.19983 bits
Comma size	unnoticeable
Open this interval in xen-calc

76384/76383, the vernonisma, is a 41-limit superparticular comma of about 0.023 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 616/615 and 621/620
• 3773/3772 and 3969/3968
• 7750/7749 and 8625/8624
• 15376/15375 and 19251/19250

It can be factored into the following superparticular ratios:

• 76545/76544 and 36315136/36315135
• 134850/134849 and 176176/176175

Temperaments

Tempering out this comma in the full 41-limit leads to the rank-12 temperament vernonismic. Using the 2.3.7.11.23.31.41 subgroup leads to the rank-6 temperament vernonic.

Vernonic

Subgroup: 2.3.7.11.23.31.41

Comma list: 76384/76383

Mapping:

[⟨	1	1	2	3	4	4	6	],
⟨	0	1	0	0	0	0	-4	],
⟨	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 = 701.957, ~7/4 = 968.825, ~11/8 = 551.316, ~23/16 = 628.278, ~31/16 = 1145.031

Optimal ET sequence: 5ikm, 5i, 5e, 7dikm, 7, 9k, 10, 12ikm, 14, 17, 27e, 29, 31k, 41, 46, 58ik, 72, 77m, 89, 130m, 135, 166, 176, 265, 342, 518, 607, 701, 747, 836, 940, 954, 1012, 1219, 1354, 1776, 1983, 2248, 2819, 2995, 3337, 4366, 5067, 5585, 7185, 7361, 8404

Badness (Sintel): 0.082

Etymology

This comma was named by Francium in 2025. It refers to the postal code of Vernon, Texas.

See also

• Unnoticeable comma
• List of superparticular intervals