36ed5

← 35ed5

36ed5

37ed5 →

Prime factorization	22 × 32
Step size	77.3976¢
Octave	16\36ed5 (1238.36¢) (→4\9ed5)
Twelfth	25\36ed5 (1934.94¢)
Consistency limit	3
Distinct consistency limit	3
Special properties	Highly composite

The 36 equal divisions of the fifth harmonic (5/1) is a tuning that divides the pentave into 36 equal steps. It combines Carlos Alpha scale with quarter-comma meantone. The step size is 77.3976 cents, thus making the tuning correspond to 15.5044 EDO. As a consequence of this, 36ed5 completely misses 2/1.

Theory

Selected intervals in 36ed5

Step	Just approximation	Size (cents)
1	23/22	77.3976
3	8/7	232.1928
5	5/4	386.9880
6	21/16	464.3856
9	3/2	696.5784
19	7/3	1470.554
28	7/2	2167.1329
31	4/1	2399.326
36	exact 5/1	2786.314

All intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	77.398	21/20, 22/21
2	154.795
3	232.193
4	309.59
5	386.988
6	464.386	17/13
7	541.783	15/11, 26/19
8	619.181	10/7
9	696.578	3/2
10	773.976
11	851.374
12	928.771	29/17
13	1006.169
14	1083.566
15	1160.964
16	1238.362
17	1315.759	15/7
18	1393.157	29/13
19	1470.554	7/3
20	1547.952	22/9
21	1625.35
22	1702.747
23	1780.145
24	1857.542
25	1934.94
26	2012.338
27	2089.735	10/3
28	2167.133	7/2
29	2244.53	11/3
30	2321.928
31	2399.326
32	2476.723
33	2554.121
34	2631.519
35	2708.916
36	2786.314	5/1

Harmonics

Approximation of harmonics in 36ed5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+38.4	+33.0	-0.7	+0.0	-6.1	+36.7	+37.7	-11.4	+38.4	+28.2	+32.3
	Relative (%)	+49.6	+42.6	-0.9	+0.0	-7.8	+47.4	+48.7	-14.8	+49.6	+36.4	+41.7
Steps (reduced)		16 (16)	25 (25)	31 (31)	36 (0)	40 (4)	44 (8)	47 (11)	49 (13)	52 (16)	54 (18)	56 (20)

Approximation of harmonics in 36ed5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-28.9	-2.4	+33.0	-1.3	-28.9	+26.9	+10.7	-0.7	-7.7	-10.9	-10.4
	Relative (%)	-37.3	-3.1	+42.6	-1.7	-37.3	+34.8	+13.9	-0.9	-10.0	-14.1	-13.5
Steps (reduced)		57 (21)	59 (23)	61 (25)	62 (26)	63 (27)	65 (29)	66 (30)	67 (31)	68 (32)	69 (33)	70 (34)