32/21

32/21, the septimal superfifth, is the interval between 9/8 and 12/7. It is 64/63 sharp of 3/2, and so is equated to 3/2 in temperaments such as pajara, superpyth or augene which tempers out 64/63.

Interval information

Ratio	32/21
Factorization	25 × 3-1 × 7-1
Monzo	[5 -1 0 -1⟩
Size in cents	729.2191¢
Names	septimal superfifth, wide fifth, octave-reduced 21st subharmonic
Color name	r5, ru 5th
FJS name	[math]\displaystyle{ \text{P5}_{7} }[/math]
Special properties	reduced, reduced subharmonic
Tenney norm (log2 nd)	9.39232
Weil norm (log2 max(n, d))	10
Wilson norm (sopfr(nd))	20
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In septimal meantone, this interval is represented by the diminished sixth.

Approximation

Edo approximations for 32/21 (729.22 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
5	3\5	720.00	-9.22	-3.84
10	6\10	720.00	-9.22	-7.68
18	11\18	733.33	+4.11	+6.17
23	14\23	730.43	+1.22	+2.33
28	17\28	728.57	-0.65	-1.51
33	20\33	727.27	-1.95	-5.35
38	23\38	726.32	-2.90	-9.19
41	25\41	731.71	+2.49	+8.50
46	28\46	730.43	+1.22	+4.66
51	31\51	729.41	+0.19	+0.82
56	34\56	728.57	-0.65	-3.02
61	37\61	727.87	-1.35	-6.86
69	42\69	730.43	+1.22	+6.99
74	45\74	729.73	+0.51	+3.15
79	48\79	729.11	-0.11	-0.69

See also

• Gallery of just intervals
• 21/16, its inverse interval