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	77.4	21/20, 22/21
2	154.8
3	232.2
4	309.6
5	387
6	464.4	17/13
7	541.8	15/11, 26/19
8	619.2	10/7
9	696.6	3/2
10	774
11	851.4
12	928.8	29/17
13	1006.2
14	1083.6
15	1161
16	1238.4
17	1315.8	15/7
18	1393.2	29/13
19	1470.6	7/3
20	1548	22/9
21	1625.3
22	1702.7
23	1780.1
24	1857.5
25	1934.9
26	2012.3
27	2089.7	10/3
28	2167.1	7/2
29	2244.5	11/3
30	2321.9
31	2399.3
32	2476.7
33	2554.1
34	2631.5
35	2708.9
36	2786.3	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)