27edf

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27edf

28edf →

Prime factorization	33
Step size	25.9983 ¢
Octave	46\27edf (1195.92 ¢)
Twelfth	73\27edf (1897.88 ¢)
Consistency limit	6
Distinct consistency limit	6

Division of the just perfect fifth into 27 equal parts (27EDF) is related to 46 edo, but with the 3/2 rather than the 2/1 being just. The octave is about 4.0767 cents compressed and the step size is about 25.9983 cents. Unlike 46edo, it is only consistent up to the 6-integer-limit, with discrepancy for the 7th harmonic.

It is related to the regular temperament which tempers out 4375/4374 and 2199023255552/2188322577315 in the 7-limit, which is supported by 46, 323, 369, 415, and 692 EDOs.

Lookalikes: 46edo, 73edt

Harmonics

Approximation of prime harmonics in 27edf

Harmonic		2	3	5	7	11	13	17	19
Error	Absolute (¢)	-4.1	-4.1	-4.5	+11.0	+8.4	+5.2	+8.7	-1.8
	Relative (%)	-15.7	-15.7	-17.3	+42.1	+32.4	+20.0	+33.6	-7.1
Steps (reduced)		46 (19)	73 (19)	107 (26)	130 (22)	160 (25)	171 (9)	189 (0)	196 (7)

(contd.)

Harmonic		23	29	31	37	41	43	47	53
Error	Absolute (¢)	+5.4	-6.0	+8.6	-11.7	-7.5	-11.9	-9.9	-9.9
	Relative (%)	+20.7	-22.9	+33.0	-45.2	-28.7	-45.9	-38.2	-38.3
Steps (reduced)		209 (20)	224 (8)	229 (13)	240 (24)	247 (4)	250 (7)	256 (13)	264 (21)

Intervals

Intervals of 27edf

degree	cents value	corresponding JI intervals	comments
0		exact 1/1
1	25.9983
2	51.9967
3	77.9950
4	103.9933
5	129.9917	69/64
6	155.9900
7	181.9883	10/9
8	207.9867		pseudo-9/8
9	233.9850		pseudo-8/7
10	259.9833		pseudo-7/6
11	285.9817
12	311.9800		pseudo-6/5
13	337.9783	175/144
14	363.9767	216/175
15	389.9750		pseudo-5/4
16	415.9733
17	441.9717		pseudo-9/7
18	467.9700
19	493.9683		pseudo-4/3
20	519.9667	27/20
21	545.9650
22	571.9633	32/23
23	597.9617
24	623.9600
25	649.9583
26	675.9567
27	701.9550	exact 3/2	just perfect fifth