35/32

Interval information

Ratio	35/32
Factorization	2-5 × 5 × 7
Monzo	[-5 0 1 1⟩
Size in cents	155.1396¢
Name	septimal neutral second
Color name	zy2, zoyo 2nd
FJS name	[math]\displaystyle{ \text{M2}^{5,7} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	10.1293
Weil norm (log2 max(n, d))	10.2586
Wilson norm (sopfr(nd))	22
Comma size	large
S-expression	S5⋅S6⋅S7
[sound info]
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35/32, the septimal neutral second, is approximately half of a 6/5 just minor third; (6/5)/(35/32)² = 6144/6125, the porwell comma. It is the interval between 8/7 and 5/4. It is 385/384 sharp of 12/11, and tempering it out makes the interval from 8/7 to 5/4 a 12/11, and leads to keenanismic chords, interpreting 48/35 as 11/8. It is also 176/175 flat of 11/10, and tempering that out instead leads to valinorsmic chords and interprets 48/35 as 15/11.

It is very closely approximated by 4\31, being just 0.3 cents sharp of that interval.

Approximation

Edo approximations for 35/32 (155.14 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
7	1\7	171.43	+16.29	+9.50
8	1\8	150.00	-5.14	-3.43
15	2\15	160.00	+4.86	+6.08
16	2\16	150.00	-5.14	-6.85
23	3\23	156.52	+1.38	+2.65
31	4\31	154.84	-0.30	-0.78
38	5\38	157.89	+2.76	+8.72
39	5\39	153.85	-1.29	-4.20
46	6\46	156.52	+1.38	+5.30
47	6\47	153.19	-1.95	-7.63
54	7\54	155.56	+0.42	+1.87
62	8\62	154.84	-0.30	-1.55
69	9\69	156.52	+1.38	+7.95
70	9\70	154.29	-0.85	-4.98
77	10\77	155.84	+0.70	+4.52
78	10\78	153.85	-1.29	-8.41

See also

• 64/35 – its octave complement
• Gallery of just intervals