33ed5

← 32ed5

33ed5

34ed5 →

Prime factorization	3 × 11
Step size	84.4337¢
Octave	14\33ed5 (1182.07¢)
Twelfth	23\33ed5 (1941.98¢)
Consistency limit	2
Distinct consistency limit	2

33ED5 is the equal division of the 5th harmonic into 33 parts of 84.4337 cents each (very close to the minor septimal semitone, 21/20, 84.4672 cents). It is related to the 128&270 temperament (Septisemitonic temperament, named by Xenllium), which tempers out 102760448/102515625 and 200120949/200000000 in the 7-limit, supported by 128, 142, 270, 398, 412, 668, and 682 EDOs.

Related regular temperaments

7-limit 128&270

Commas: 102760448/102515625, 200120949/200000000

POTE generator: ~21/20 = 84.4463

Mapping: [<2 5 0 -1|, <0 -13 33 47|]

EDOs: 128, 142, 270, 398, 412, 668, 682

Badness: 0.1661

11-limit 128&270

Commas: 3025/3024, 131072/130977, 422576/421875

POTE generator: ~21/20 = 84.4430

Mapping: [<2 5 0 -1 11|, <0 -13 33 47 -29|]

EDOs: 128, 142, 270, 398, 412, 668, 682

Badness: 0.0583

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	84.434	20/19, 23/22
2	168.867	11/10
3	253.301	15/13, 22/19
4	337.735	17/14, 23/19, 28/23
5	422.169	14/11
6	506.602
7	591.036	7/5, 24/17
8	675.47	25/17, 28/19
9	759.904	17/11
10	844.337
11	928.771	12/7
12	1013.205
13	1097.639
14	1182.072
15	1266.506	25/12
16	1350.94	24/11
17	1435.374	23/10
18	1519.807	12/5
19	1604.241
20	1688.675
21	1773.109
22	1857.542
23	1941.976
24	2026.41
25	2110.844	17/5
26	2195.277	25/7
27	2279.711	26/7
28	2364.145
29	2448.579
30	2533.012	13/3
31	2617.446
32	2701.88	19/4
33	2786.314	5/1

Harmonics

Approximation of harmonics in 33ed5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-17.9	+40.0	-35.9	+0.0	+22.1	+8.5	+30.7	-4.4	-17.9	-14.1	+4.2
	Relative (%)	-21.2	+47.4	-42.5	+0.0	+26.2	+10.1	+36.3	-5.2	-21.2	-16.7	+4.9
Steps (reduced)		14 (14)	23 (23)	28 (28)	33 (0)	37 (4)	40 (7)	43 (10)	45 (12)	47 (14)	49 (16)	51 (18)

Approximation of harmonics in 33ed5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+34.5	-9.4	+40.0	+12.7	-7.8	-22.3	-31.5	-35.9	-35.9	-32.0	-24.5
	Relative (%)	+40.8	-11.1	+47.4	+15.1	-9.2	-26.4	-37.3	-42.5	-42.5	-37.9	-29.0
Steps (reduced)		53 (20)	54 (21)	56 (23)	57 (24)	58 (25)	59 (26)	60 (27)	61 (28)	62 (29)	63 (30)	64 (31)