25/22

Interval information

Ratio	25/22
Factorization	2-1 × 52 × 11-1
Monzo	[-1 0 2 0 -1⟩
Size in cents	221.3095¢
Names	ptolemismic whole tone, undecimal acute whole tone
Color name	1uyy2, luyoyo 2nd
FJS name	[math]\displaystyle{ \text{A2}^{5,5}_{11} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	9.10329
Weil norm (log2 max(n, d))	9.28771
Wilson norm (sopfr(nd))	23
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25/22, the ptolemismic whole tone or undecimal acute whole tone, is an 11-limit interval. It is sharp of 9/8, the Pythagorean whole tone, by 100/99, the ptolemisma, hence the name. It is also flat of 8/7, the septimal major second, by 176/175, the valinorsma. Another interval close to it but simpler is 17/15, from which it is separated by 375/374.

Approximation

Edo approximations for 25/22 (221.31 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
5	1\5	240.00	+18.69	+7.79
11	2\11	218.18	-3.13	-2.87
16	3\16	225.00	+3.69	+4.92
22	4\22	218.18	-3.13	-5.73
27	5\27	222.22	+0.91	+2.05
32	6\32	225.00	+3.69	+9.84
33	6\33	218.18	-3.13	-8.60
38	7\38	221.05	-0.26	-0.81
43	8\43	223.26	+1.95	+6.97
49	9\49	220.41	-0.90	-3.68
54	10\54	222.22	+0.91	+4.11
60	11\60	220.00	-1.31	-6.55
65	12\65	221.54	+0.23	+1.24
70	13\70	222.86	+1.55	+9.03
71	13\71	219.72	-1.59	-9.41
76	14\76	221.05	-0.26	-1.63

See also

• 44/25 – its octave complement
• 33/25 – its fifth complement
• 25/11 – one octave higher
• Gallery of just intervals
• File:Ji-25-22-csound-foscil-220hz.mp3