221/220

Interval information

Ratio	221/220
Factorization	2-2 × 5-1 × 11-1 × 13 × 17
Monzo	[-2 0 -1 0 -1 1 1⟩
Size in cents	7.851415¢
Name	minor naiadma
Color name	17o3o1ug2, Sotholugu 2nd Sotholugu comma
FJS name	[math]\text{d2}^{13,17}_{5,11}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	15.5693
Weil height (log2 max(n, d))	15.5758
Wilson height (sopfr(nd))	50
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.75473 bits
Comma size	small
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221/220, the minor naiadma, is a small 17-limit superparticular comma about 7.9 cents in size. It forms the difference between 13/10 (tridecimal semisixth) and 22/17 (small septendecimal semisixth). It is also the amount by which a stack consisting of 13/10 and 17/10 exceeds 11/5 (11/10 plus an octave). The name minor naiadma is contrast to the major naiadma, 170/169, measuring about 10.2¢, which is the difference between 13/10 and 17/13 (large septendecimal semisixth). They are so named because 13/10, 17/13 and 22/17 are naiadic interseptimal intervals, and 221/220 is smaller than 170/169 by a 13-limit unnoticeable comma, 2200/2197 (petrma).

Commatic relations

This comma identifies itself as the difference between the following superparticular pairs:

• 34/33 and 40/39
• 51/50 and 66/65
• 78/77 and 120/119
• 91/90 and 154/153
• 136/135 and 352/351
• 169/168 and 715/714

It factors into the following superparticular pairs:

• 225/224 and 12376/12375
• 243/242 and 2431/2430
• 273/272 and 1156/1155
• 289/288 and 936/935
• 351/350 and 595/594
• 364/363 and 561/560
• 441/440 and 442/441

See also

• Small comma
• List of superparticular intervals