23ed7

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23ed7

24ed7 →

Prime factorization	23 (prime)
Step size	146.471¢
Octave	8\23ed7 (1171.77¢)
Twelfth	13\23ed7 (1904.12¢) (convergent)
Consistency limit	6
Distinct consistency limit	4

Division of the 7th harmonic into 23 equal parts (23ED7) is related to the Bohlen-Pierce scale, but with the 7/1 rather than the 3/1 being just. The step size is about 146.4707 cents, corresponding to 8.1928 EDO. It is almost identical to POTE generator for 7-limit bohpier temperament.

Intervals

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	146.4707	49/45
2	292.9414	13/11
3	439.4121	9/7
4	585.8828	7/5
5	732.3535	49/32
6	878.8241	5/3
7	1025.2948	9/5
8	1171.7655	63/32
9	1318.2362	15/7
10	1464.7069	7/3
11	1611.1776	28/11
12	1757.6483	11/4
13	1904.1190	3/1
14	2050.5897	49/15
15	2197.0604	32/9
16	2343.5311	35/9
17	2490.0018	21/5
18	2636.4724	32/7
19	2782.9431	5/1
20	2929.4138	49/9
21	3075.8845	77/13
22	3222.3552	45/7
23	3368.8259	exact 7/1	harmonic seventh plus two octaves

Harmonics

Approximation of prime harmonics in 23ed7

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-28.2	+2.2	-3.4	+0.0	-50.1	-46.4	-71.4	+29.0	-8.9	+29.3	+60.3
	Relative (%)	-19.3	+1.5	-2.3	+0.0	-34.2	-31.7	-48.8	+19.8	-6.0	+20.0	+41.1
Steps (reduced)		8 (8)	13 (13)	19 (19)	23 (0)	28 (5)	30 (7)	33 (10)	35 (12)	37 (14)	40 (17)	41 (18)

Approximation of prime harmonics in 23ed7

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+46.9	+15.6	-66.8	+72.1	+10.6	-28.6	+60.2	+44.2	-56.2	+42.2	+51.9
	Relative (%)	+32.0	+10.7	-45.6	+49.3	+7.2	-19.5	+41.1	+30.2	-38.3	+28.8	+35.5
Steps (reduced)		43 (20)	44 (21)	44 (21)	46 (0)	47 (1)	48 (2)	49 (3)	50 (4)	50 (4)	51 (5)	52 (6)

See also

• 13ED3: relative ED3 (Bohlen-Pierce scale)
• 19ED5: relative ED5

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