29/16

Interval information

Ratio	29/16
Subgroup monzo	2.29 [-4 1⟩
Size in cents	1029.577¢
Names	vicesimononal supraminor seventh, octave-reduced 29th harmonic
Color name	29o7, tweno 7th
FJS name	[math]\displaystyle{ \text{m7}^{29} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	8.85798
Weil norm (log2 max(n, d))	9.71596
Wilson norm (sopfr(nd))	37
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In 29-limit just intonation, 29/16 is the vicesimononal supraminor seventh, which is also the octave-reduced 29th harmonic. It is sharp of the Pythagorean minor seventh (16/9) by 261/256 (~33 ¢), and sharp of the classic minor seventh (9/5) by 145/144 (~12 ¢).

Approximation

This interval is very accurately approximated by 7edo (6\7). It is approximately a cent away from it, the difference being 1/7 of the jackpot comma, 17249876309/17179869184.

Edo approximations for 29/16 (1029.58 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
7	6\7	1028.57	-1.01	-0.59
14	12\14	1028.57	-1.01	-1.17
21	18\21	1028.57	-1.01	-1.76
28	24\28	1028.57	-1.01	-2.35
35	30\35	1028.57	-1.01	-2.93
42	36\42	1028.57	-1.01	-3.52
49	42\49	1028.57	-1.01	-4.11
56	48\56	1028.57	-1.01	-4.69
57	49\57	1031.58	+2.00	+9.51
63	54\63	1028.57	-1.01	-5.28
64	55\64	1031.25	+1.67	+8.92
70	60\70	1028.57	-1.01	-5.87
71	61\71	1030.99	+1.41	+8.33
77	66\77	1028.57	-1.01	-6.45
78	67\78	1030.77	+1.19	+7.75

See also

• 32/29 – its octave complement
• 48/29 – its twelfth complement