17/15

Interval information

Ratio	17/15
Factorization	3-1 × 5-1 × 17
Monzo	[0 -1 -1 0 0 0 1⟩
Size in cents	216.6867¢
Name	diatismic whole tone
Color name	17og3, sogu 3rd
FJS name	[math]\displaystyle{ \text{d3}^{17}_{5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	7.99435
Weil norm (log2 max(n, d))	8.17493
Wilson norm (sopfr(nd))	25
[sound info]
Open this interval in xen-calc

In 17-limit just intonation, 17/15 is the diatismic whole tone measuring about 216.7 ¢. It exceeds the Pythagorean whole tone (9/8) by a diatisma (136/135), hence the name. It is the mediant of 9/8 and 8/7, as it is (9 + 8)/(8 + 7). It is found in the harmonic series between the 17th and 15th harmonics. 11edo's second degree, measuring approximately 218.2¢, is close in size to 17/15 – indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo.

√2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for wizard and its various relatives (lizard, gizzard, etc.).

Approximation

Edo approximations for 17/15 (216.69 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
5	1\5	240.00	+23.31	+9.71
6	1\6	200.00	-16.69	-8.34
11	2\11	218.18	+1.50	+1.37
17	3\17	211.76	-4.92	-6.97
22	4\22	218.18	+1.50	+2.74
28	5\28	214.29	-2.40	-5.60
33	6\33	218.18	+1.50	+4.11
39	7\39	215.38	-1.30	-4.23
44	8\44	218.18	+1.50	+5.48
50	9\50	216.00	-0.69	-2.86
55	10\55	218.18	+1.50	+6.85
61	11\61	216.39	-0.29	-1.49
66	12\66	218.18	+1.50	+8.22
67	12\67	214.93	-1.76	-9.83
72	13\72	216.67	-0.02	-0.12
77	14\77	218.18	+1.50	+9.59
78	14\78	215.38	-1.30	-8.46

See also

• 30/17 – its octave complement
• 20/17 – its fourth complement
• Gallery of just intervals