703/702

Interval information

Ratio	703/702
Factorization	2-1 × 3-3 × 13-1 × 19 × 37
Monzo	[-1 -3 0 0 0 -1 0 1 0 0 0 1⟩
Size in cents	2.464391¢
Name	noemisma
Color name	37o19o3u2 thisonothu 2nd
FJS name	[math]\text{P1}^{19,37}_{13}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	18.9127
Weil height (log2 max(n, d))	18.9148
Wilson height (sopfr(nd))	80
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.25561 bits
Comma size	unnoticeable
S-expression	S37 × S38
Open this interval in xen-calc

703/702, the noemisma, is a 37-limit superparticular comma of about 2.5 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 190/189 and 260/259
• 209/208 and 297/296
• 222/221 and 324/323

It can be factored into the following superparticular intervals:

• 704/703 and 494209/494208
• 729/728 and 19684/19683
• 741/740 and 13690/13689
• 760/759 and 9361/9360
• 925/924 and 2926/2925
• 1036/1035 and 2185/2184
• 1045/1044 and 2146/2145
• 1054/1053 and 2109/2108
• 1184/1183 and 1729/1728
• 1197/1196 and 1702/1701
• 1216/1215 and 1665/1664
• 1369/1368 and 1444/1443

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament noemismic. Using the 2.3.13.19.37 subgroup leads to the rank-4 temperament noemic.

Noemic

Subgroup: 2.3.13.19.37

Comma list: 703/702

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.183, ~13/8 = 840.942, ~19/16 = 296.967

Optimal ET sequence: 5f, 7, 9l, 10h, 12l, 15l, 17, 22fh, 24, 51, 53, 77, 130, 234, 258, 311, 441, 675, 752l, 1116hl

Badness (Sintel): 0.048

Etymology

This comma was named by Francium in 2025. It refers to 703 Noëmi, the asteroid, which in turn was named after Valentine Noëmi von Rothschild, presumed wife of the Baron Sigismund von Springer. Alternatively, Noemi is a Biblical heroine from the Book of Ruth.

See also

• Unnoticeable comma
• List of superparticular intervals