31edf

← 30edf

31edf

32edf →

Prime factorization	31 (prime)
Step size	22.6437 ¢
Octave	53\31edf (1200.12 ¢) (convergent)
Twelfth	84\31edf (1902.07 ¢) (convergent)
Consistency limit	10
Distinct consistency limit	10

31 equal divisions of the perfect fifth (abbreviated 31edf or 31ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 31 equal parts of about 22.6 ¢ each. Each step represents a frequency ratio of (3/2)^1/31, or the 31st root of 3/2.

Theory

31edf is almost identical to 53edo, but with the 3/2 rather than the 2/1 being just. The octave is stretched by about 0.1166 cents. Like 53edo, 31edf is consistent to the 10-integer-limit.

Harmonics

Approximation of harmonics in 31edf

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.12	+0.12	+0.23	-1.14	+0.23	+5.09	+0.35	+0.23	-1.02	-7.52	+0.35
	Relative (%)	+0.5	+0.5	+1.0	-5.0	+1.0	+22.5	+1.5	+1.0	-4.5	-33.2	+1.5
Steps (reduced)		53 (22)	84 (22)	106 (13)	123 (30)	137 (13)	149 (25)	159 (4)	168 (13)	176 (21)	183 (28)	190 (4)

Approximation of harmonics in 31edf (continued)

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	-2.36	+5.20	-1.02	+0.47	+8.73	+0.35	-2.68	-0.90	+5.20	-7.40	+6.22	+0.47
	Relative (%)	-10.4	+23.0	-4.5	+2.1	+38.6	+1.5	-11.8	-4.0	+23.0	-32.7	+27.5	+2.1
Steps (reduced)		196 (10)	202 (16)	207 (21)	212 (26)	217 (0)	221 (4)	225 (8)	229 (12)	233 (16)	236 (19)	240 (23)	243 (26)

Subsets and supersets

31edf is the 11th prime edf, following 29edf and coming before 37edf. It does not contain any nontrivial subset edfs.

See also

• 9ed9/8 – relative ed9/8
• 53edo – relative edo
• 84edt – relative edt
• 137ed6 – relative ed6