32/27

Interval information

Ratio	32/27
Factorization	25 × 3-3
Monzo	[5 -3⟩
Size in cents	294.135¢
Name	Pythagorean minor third
Color name	w3, wa 3rd
FJS name	[math]\displaystyle{ \text{m3} }[/math]
Special properties	reduced, reduced subharmonic
Tenney norm (log2 nd)	9.75489
Weil norm (log2 max(n, d))	10
Wilson norm (sopfr(nd))	19
[sound info]
Open this interval in xen-calc

The Pythagorean minor third of 32/27 is the interval between 9/8 and 4/3 which arises naturally in 3-limit just intonation. Compared to the more typical 6/5- with which it is conflated in meantone- this interval is more dissonant, with a harmonic entropy level roughly on par with that of 9/8.

It is 352/351 sharp of 13/11, and tempering 352/351 out equates it with 13/11 and leads to minthmic chords.

Temperaments

32/27 is treated as a comma in edos 3 & 6, where the best approximation of a perfect 5th is the 800 cent interval that wraps around to the octave again after only three iterations, producing alteraugment. Temperaments it can be interpreted as if used as a generator include Kleiboh or Gariberttet.

Approximation

Edo approximations for 32/27 (294.13 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
4	1\4	300.00	+5.87	+1.96
8	2\8	300.00	+5.87	+3.91
12	3\12	300.00	+5.87	+5.87
16	4\16	300.00	+5.87	+7.82
20	5\20	300.00	+5.87	+9.78
33	8\33	290.91	-3.23	-8.87
37	9\37	291.89	-2.24	-6.92
41	10\41	292.68	-1.45	-4.96
45	11\45	293.33	-0.80	-3.01
49	12\49	293.88	-0.26	-1.05
53	13\53	294.34	+0.20	+0.90
57	14\57	294.74	+0.60	+2.86
61	15\61	295.08	+0.95	+4.81
65	16\65	295.38	+1.25	+6.77
69	17\69	295.65	+1.52	+8.72

See also

• 27/16 – its octave complement
• 81/64 – its fifth complement
• 9/8 – its fourth complement
• Gallery of just intervals
• Pythagorean tuning