55edt

← 54edt

55edt

56edt →

Prime factorization	5 × 11
Step size	34.581¢
Octave	35\55edt (1210.34¢) (→7\11edt)
Consistency limit	2
Distinct consistency limit	2

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	Approximate ratios
0	0	1/1
1	34.581
2	69.162	25/24, 27/26
3	103.743	18/17, 33/31
4	138.324
5	172.905	21/19, 31/28
6	207.486	26/23
7	242.067	31/27
8	276.648	27/23
9	311.229	6/5
10	345.81	11/9
11	380.391
12	414.972	14/11, 33/26
13	449.553	22/17
14	484.134
15	518.715	23/17, 31/23
16	553.296
17	587.877
18	622.458	33/23
19	657.039	19/13
20	691.62
21	726.201
22	760.782	14/9
23	795.363
24	829.944	21/13, 29/18
25	864.525	28/17
26	899.106
27	933.687
28	968.268
29	1002.849
30	1037.43	31/17
31	1072.011	13/7
32	1106.592
33	1141.173	27/14, 29/15
34	1175.754
35	1210.335
36	1244.916
37	1279.497	23/11
38	1314.078
39	1348.659
40	1383.24
41	1417.821
42	1452.402
43	1486.983	26/11, 33/14
44	1521.564
45	1556.145	27/11
46	1590.726	5/2
47	1625.307	23/9
48	1659.888
49	1694.469
50	1729.05	19/7
51	1763.631
52	1798.212	17/6, 31/11
53	1832.793	26/9
54	1867.374
55	1901.955	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