273/272

Interval information

Ratio	273/272
Factorization	2-4 × 3 × 7 × 13 × 17-1
Monzo	[-4 1 0 1 0 1 -1⟩
Size in cents	6.35316¢
Name	tannisma
Color name	17u3oz1, suthozo 1sn, Suthozo comma
FJS name	[math]\displaystyle{ \text{P1}^{7,13}_{17} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	16.1802
Weil height (log2 max(n, d))	16.1855
Wilson height (sopfr(nd))	48
Comma size	small
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273/272, the tannisma, is a small 17-limit (also 2.3.7.13.17 subgroup) comma with a value of roughly 6.35 cents. It forms the difference between 21/17 and 16/13, and the difference between 39/32 and 17/14, as well as the difference between 17/13 and 21/16.

Commatic relations

This comma is the difference between the following superparticular pairs:

• 35/34 and 40/39
• 52/51 and 64/63
• 65/64 and 85/84
• 91/90 and 136/135
• 154/153 and 352/351
• 169/168 and 442/441
• 221/220 and 1156/1155
• 225/224 and 1275/1274
• 256/255 and 4096/4095

It factors into the following superparticular pairs:

• 441/440 and 715/714
• 385/384 and 936/935
• 375/374 and 1001/1000
• 364/363 and 1089/1088
• 351/350 and 1225/1224
• 325/324 and 1701/1700
• 289/288 and 4914/4913

Temperaments

Tempering out this comma in the 17-limit leads to the rank-6 tannismic temperament, or in the 2.3.7.13.17 subgroup, the rank-4 tannic temperament, both characterized by the equivalences introduced above, and lead to a type of essentially tempered chord called the tannismic chord. However, that is not all, as according to Scott Dakota, the tannic temperament is actually of similar overall utility to those that temper out the marvel comma.