55edt

← 54edt

55edt

56edt →

Prime factorization	5 × 11
Step size	34.581 ¢
Octave	35\55edt (1210.34 ¢) (→ 7\11edt)
Consistency limit	3
Distinct consistency limit	3

55EDT is the equal division of the third harmonic into 55 parts of 34.5810 cents each, corresponding to 34.7011 edo. It is related to the regular temperament which tempers out 420175/419904 and 205891132094649/204800000000000 in the 7-limit, which is supported by 243, 347, and 590 EDOs among others.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	34.6	23.6
2	69.2	47.3	25/24, 27/26
3	103.7	70.9	18/17, 33/31
4	138.3	94.5
5	172.9	118.2	21/19, 31/28
6	207.5	141.8	26/23
7	242.1	165.5	31/27
8	276.6	189.1	27/23
9	311.2	212.7	6/5
10	345.8	236.4	11/9
11	380.4	260
12	415	283.6	14/11, 33/26
13	449.6	307.3	22/17
14	484.1	330.9
15	518.7	354.5	23/17, 31/23
16	553.3	378.2
17	587.9	401.8
18	622.5	425.5	33/23
19	657	449.1	19/13
20	691.6	472.7
21	726.2	496.4
22	760.8	520	14/9
23	795.4	543.6
24	829.9	567.3	21/13, 29/18
25	864.5	590.9	28/17
26	899.1	614.5
27	933.7	638.2
28	968.3	661.8
29	1002.8	685.5
30	1037.4	709.1	31/17
31	1072	732.7	13/7
32	1106.6	756.4
33	1141.2	780	27/14, 29/15
34	1175.8	803.6
35	1210.3	827.3
36	1244.9	850.9
37	1279.5	874.5	23/11
38	1314.1	898.2
39	1348.7	921.8
40	1383.2	945.5
41	1417.8	969.1
42	1452.4	992.7
43	1487	1016.4	26/11, 33/14
44	1521.6	1040
45	1556.1	1063.6	27/11
46	1590.7	1087.3	5/2
47	1625.3	1110.9	23/9
48	1659.9	1134.5
49	1694.5	1158.2
50	1729.1	1181.8	19/7
51	1763.6	1205.5
52	1798.2	1229.1	17/6, 31/11
53	1832.8	1252.7	26/9
54	1867.4	1276.4
55	1902	1300	3/1

Harmonics

Approximation of harmonics in 55edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+10.3	+0.0	-13.9	+14.7	+10.3	-14.5	-3.6	+0.0	-9.5	-1.6	-13.9
	Relative (%)	+29.9	+0.0	-40.2	+42.6	+29.9	-41.8	-10.3	+0.0	-27.5	-4.6	-40.2
Steps (reduced)		35 (35)	55 (0)	69 (14)	81 (26)	90 (35)	97 (42)	104 (49)	110 (0)	115 (5)	120 (10)	124 (14)

Approximation of harmonics in 55edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-14.2	-4.1	+14.7	+6.8	+5.5	+10.3	-14.1	+0.8	-14.5	+8.7	+0.9
	Relative (%)	-40.9	-12.0	+42.6	+19.5	+16.0	+29.9	-40.8	+2.4	-41.8	+25.3	+2.7
Steps (reduced)		128 (18)	132 (22)	136 (26)	139 (29)	142 (32)	145 (35)	147 (37)	150 (40)	152 (42)	155 (45)	157 (47)

Related regular temperaments

243&347 temperament

7-limit

Commas: 420175/419904, |-22 30 -11>

POTE generator: ~49/48 = 34.5742

Map: [<1 0 -2 2|, <0 55 150 28|]

EDOs: 243, 347, 590

11-limit

Commas: 137781/137500, 352947/352000, 16808715/16777216

POTE generator: ~49/48 = 34.5761

Map: [<1 0 -2 2 10|, <0 55 150 28 -227|]

EDOs: 243, 347, 590

13-limit

Commas: 4459/4455, 15379/15360, 67392/67375, 83349/83200

POTE generator: ~49/48 = 34.5762

Map: [<1 0 -2 2 10 2|, <0 55 150 28 -227 59|]

EDOs: 243, 347, 590