32edt

← 31edt

32edt

33edt →

Prime factorization	25
Step size	59.4361¢
Octave	20\32edt (1188.72¢) (→5\8edt)
Consistency limit	4
Distinct consistency limit	4

32EDT is the equal division of the third harmonic into 32 parts of 59.4361 cents each, corresponding to 20.1898 edo. It has a distinct sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13, 17, and 19 are all sharp. It tempers out 3125/3087 and 885735/823543 in the 7-limit; 891/875, 1331/1323, and 2475/2401 in the 11-limit; 275/273, 351/343, 729/715, and 847/845 in the 13-limit; 121/119, 189/187, 225/221, 459/455, and 845/833 in the 17-limit; 135/133, 171/169, 247/245, 325/323, and 363/361 in the 19-limit (no-twos subgroup). It is the eighth zeta peak tritave division.

Harmonics

Approximation of prime harmonics in 32edt

Harmonic		2	3	5	7	11	13	17	19	23
Error	Absolute (¢)	-11.3	+0.0	+7.2	+19.0	+9.2	+17.2	+28.2	+14.0	-19.6
	Relative (%)	-19.0	+0.0	+12.1	+32.0	+15.5	+28.9	+47.5	+23.5	-33.0
Steps (reduced)		20 (20)	32 (0)	47 (15)	57 (25)	70 (6)	75 (11)	83 (19)	86 (22)	91 (27)

Approximation of odd harmonics in 32edt

Harmonic		25	27	29	31	33	35	37	39	41	43	45
Error	Absolute (¢)	+14.4	+0.0	-4.8	-1.4	+9.2	+26.2	-10.6	+17.2	-10.0	+26.5	+7.2
	Relative (%)	+24.2	+0.0	-8.1	-2.4	+15.5	+44.1	-17.8	+28.9	-16.8	+44.5	+12.1
Steps (reduced)		94 (30)	96 (0)	98 (2)	100 (4)	102 (6)	104 (8)	105 (9)	107 (11)	108 (12)	110 (14)	111 (15)

Intervals

step	cents	hekts
1	59.436	40.625
2	118.872	81.25
3	178.308	121.875
4	237.744	162.5
5	297.180	203.125
6	356.617	243.75
7	416.053	284.375
8	475.489	325
9	534.925	365.625
10	594.361	406.25
11	653.797	446.875
12	713.233	487.5
13	772.669	528.125
14	832.105	568.75
15	891.541	609.375
16	950.978	650
17	1010.414	690.625
18	1069.85	731.25
19	1129.286	774.875
20	1188.722	812.5
21	1248.158	853.125.
22	1307.594	893.75
23	1367.03	934.375
24	1426.466	975
25	1485.902	1015.625
26	1545.338	1056.25
27	1604.775	1096.875
28	1664.211	1137.5
29	1723.647	1178.125
30	1783.083	1218.75
31	1842.519	1259.375
32	1901.955	1300