54edt

← 53edt

54edt

55edt →

Prime factorization	2 × 33
Step size	35.2214¢
Octave	34\54edt (1197.53¢) (→17\27edt)
Consistency limit	7
Distinct consistency limit	7

Division of the third harmonic into 54 equal parts (54EDT) is related to 34 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 2.4728 cents compressed and the step size is about 35.2214 cents. It is consistent to the 7-integer-limit, but not to the 8-integer-limit. In comparison, 34edo is only consistent up to the 6-integer-limit.

Intervals

degree	cents value	hekts	corresponding JI intervals	comments
0			exact 1/1
1	35.2214	24.0741	50/49, 49/48
2	70.4428	48.14815	25/24
3	105.6642	72.2222	17/16
4	140.8856	96.2963	13/12
5	176.1069	120.3704	10/9
6	211.3283	144.4444	26/23
7	246.5497	168.5185	15/13
8	281.7711	192.5926	20/17
9	316.9925	216.6667	6/5
10	352.2139	240.7407	11/9
11	387.4353	264.8148	5/4
12	422.6567	288.8889	23/18
13	457.8781	312.963	13/10
14	493.0994	337.037	4/3
15	528.3208	361.1111	19/14
16	563.5422	385.1852	18/13
17	598.7636	409.2593	41/29, 140/99
18	633.985	433.3333	13/9
19	669.2064	457.4074	28/19
20	704.4278	481.4815	3/2
21	739.6492	505.5559	20/13
22	774.8706	529.6296	36/23
23	810.0919	553.7037	8/5
24	845.3133	577.7778	44/27
25	880.5347	601.85185	5/3
26	915.7561	625.9259	17/10
27	950.9775	650	26/15
28	986.1989	674.074	23/13
29	1021.4203	698.14815	9/5
30	1056.6417	722.2222	81/44
31	1091.8631	746.2963	15/8
32	1127.0844	770.3704	23/12
33	1162.3058	794.4444	49/25, 96/49
34	1197.5272	818.5185	2/1
35	1232.7486	842.5926	100/49, 49/24
36	1267.97	866.6667	25/12
37	1303.1914	890.7407	17/8
38	1338.4128	914.8148	13/6
39	1373.6342	938.8889	20/9, 42/19
40	1408.8556	962.963	88/39
41	1444.0769	987.037	76/33
42	1479.2983	1011.1111	47/20
43	1514.5197	1035.1852	12/5
44	1549.7411	1059.2593	27/11
45	1584.9625	1083.3333	5/2
46	1620.1839	1107.4074	51/20
47	1655.4053	1131.4815	13/5
48	1690.6267	1155.5556	8/3
49	1725.8481	1179.6297	19/7
50	1761.0694	1203.7037	36/13
51	1796.2908	1227.7778	48/17
52	1831.5122	1251.85185	72/25
53	1866.7336	1275.5926	50/17
54	1901.9550	1300	exact 3/1	just perfect fifth plus an octave

Harmonics

Approximation of harmonics in 54edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.5	+0.0	-4.9	-3.8	-2.5	+12.4	-7.4	+0.0	-6.3	+4.8	-4.9
	Relative (%)	-7.0	+0.0	-14.0	-10.9	-7.0	+35.3	-21.1	+0.0	-17.9	+13.6	-14.0
Steps (reduced)		34 (34)	54 (0)	68 (14)	79 (25)	88 (34)	96 (42)	102 (48)	108 (0)	113 (5)	118 (10)	122 (14)

Approximation of harmonics in 54edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.6	+10.0	-3.8	-9.9	-9.2	-2.5	+9.6	-8.8	+12.4	+2.3	-4.2
	Relative (%)	-7.5	+28.3	-10.9	-28.1	-26.1	-7.0	+27.2	-24.9	+35.3	+6.6	-11.9
Steps (reduced)		126 (18)	130 (22)	133 (25)	136 (28)	139 (31)	142 (34)	145 (37)	147 (39)	150 (42)	152 (44)	154 (46)