23ed5

← 22ed5

23ed5

24ed5 →

Prime factorization	23 (prime)
Step size	121.144¢
Octave	10\23ed5 (1211.44¢) (semiconvergent)
Twelfth	16\23ed5 (1938.31¢)
Consistency limit	8
Distinct consistency limit	4

Division of the 5th harmonic into 23 equal parts (23ed5) is related to 10edo, but with the 5/1 rather than the 2/1 being just. The octave is stretched (about 11.4408 cents) and the step size is about 121.14407 cents.

Intervals

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	121.1441	15/14
2	242.2882	147/128
3	363.4322	16/13
4	484.5763	169/128
5	605.7204	17/12
6	726.8645	195/128
7	848.0085	80/49
8	969.1526	7/4
9	1090.2967	15/8
10	1211.4408	512/255	pseudo-octave
11	1332.5848	28/13
12	1453.7289	512/221
13	1574.8730
14	1696.0170	8/3
15	1817.1611	20/7
16	1938.3052	49/16
17	2059.4493	128/39
18	2180.5933	169/48
19	2301.7374	34/9
20	2422.8815	65/16	pseudo-4/1
21	2544.0256	352/81
22	2665.1696	14/3
23	2786.3137	exact 5/1	just major third plus two octaves

Harmonics

Approximation of harmonics in 23ed5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+11.4	+36.4	+22.9	+0.0	+47.8	+23.2	+34.3	-48.4	+11.4	-32.4	+59.2
	Relative (%)	+9.4	+30.0	+18.9	+0.0	+39.4	+19.2	+28.3	-40.0	+9.4	-26.8	+48.9
Steps (reduced)		10 (10)	16 (16)	20 (20)	23 (0)	26 (3)	28 (5)	30 (7)	31 (8)	33 (10)	34 (11)	36 (13)

Approximation of harmonics in 23ed5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+41.8	+34.6	+36.4	+45.8	-59.2	-37.0	-9.5	+22.9	+59.6	-21.0	+23.2
	Relative (%)	+34.5	+28.6	+30.0	+37.8	-48.9	-30.5	-7.8	+18.9	+49.2	-17.3	+19.2
Steps (reduced)		37 (14)	38 (15)	39 (16)	40 (17)	40 (17)	41 (18)	42 (19)	43 (20)	44 (21)	44 (21)	45 (22)

Music

• Aria Of A Ghost by Francium