58edf

← 57edf

58edf

59edf →

Prime factorization	2 × 29
Step size	12.1027¢
Octave	99\58edf (1198.16¢)
Twelfth	157\58edf (1900.12¢)
Consistency limit	12
Distinct consistency limit	9

Division of the just perfect fifth into 58 equal parts (58EDF) is related to 99edo, but with the 3/2 rather than the 2/1 being just. The octave is about 1.8354 cents compressed and the step size is about 12.1027 cents (corresponding to 99.1517 edo). It is consistent to the 12-integer-limit. In comparison, 99edo is only consistent up to the 10-integer-limit.

Harmonics

Approximation of prime harmonics in 58edf

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-1.84	-1.84	-2.70	-4.28	-0.10	+1.15	-3.37	-2.29	+5.83	+3.91	-2.62
	Relative (%)	-15.2	-15.2	-22.3	-35.4	-0.8	+9.5	-27.9	-18.9	+48.1	+32.3	-21.7
Steps (reduced)		99 (41)	157 (41)	230 (56)	278 (46)	343 (53)	367 (19)	405 (57)	421 (15)	449 (43)	482 (18)	491 (27)

Intervals

Todo: complete table The mapping for 11 and 13 should differ from 99edo.

Degrees	Cents Value	Five limit	Seven limit	Eleven limit	Thirteen limit
1	12.1027	2048/2025	126/125	99/98	91/90
2	24.2053	81/80	64/63	55/54
3	36.308	128/125	49/48
4	48.4107	250/243	36/35	33/32
5	60.5134	648/625	28/27		26/25
6	72.616	25/24		22/21
7	84.7187	256/243	21/20
8	96.8214	135/128		81/77	52/49
9	108.92405	16/15
10	121.0267	2187/2048	15/14
11	133.1294	27/25			13/12
12	145.2321	625/576	49/45
13	157.3347	800/729	35/32	11/10
14	169.4374	1125/1024	54/49
15	181.54	10/9	10/9
16	193.6428	4096/3645	28/25
17	205.7454	9/8
18	217.8481	256/225	245/216	112/99	91/80
19	229.9508	729/640	8/7
20	242.05345	144/125		63/55	52/45
21	254.1561	125/108	81/70		15/13
22	266.2587	729/625	7/6
23	278.3615	75/64		33/28
24	290.4641	32/27	32/27		13/11
25	302.5668	1215/1024	25/21
26	314.6695	6/5
27	326.7722	3125/2592	98/81		91/75
28	338.8748	243/200	128/105	11/9
29	350.9775	625/512	49/40
30	363.0802	100/81		27/22	16/13
31	375.18285	3888/3125	56/45
32	387.2855	5/4
33	399.3882	512/405	63/50		49/39
34	411.4909	81/64	80/63		33/26
35	423.5935	32/25		14/11
36	435.6962	625/486	9/7
37	447.7989	162/125	35/27		13/10
38	459.90155	125/96	64/49	55/42
39	472.0042	320/243	21/16
40	484.1069	675/512	250/189		65/49
41	469.2096	4/3
42	508.3122	8192/6075	75/56	66/49
43	520.4149	27/20
44	532.5176	512/375	49/36
45	544.6203	1000/729	48/35	11/8
46	556.7229	864/625	112/81		91/66
47	568.8256	25/18			18/13
48	580.9283	1024/729	7/5
49	593.03095	45/32
50	605.1336	64/45
51	617.2362	729/512	10/7
52	629.339	36/25			13/9
53	641.4416	625/432	81/56		75/52
54	653.5443	729/500	35/24	16/11
55	665.647	375/256	72/49
56	677.7497	40/27
57	689.8523	6075/4096	112/75	49/33
58	701.955	3/2
59	714.0577	1024/675	189/125		91/60
60	726.16035	243/160	32/21
61	738.263	192/125	49/32
62	750.3657	125/81	54/35		20/13
63	762.4684	972/625	14/9
64	774.571	25/16		11/7
65	786.6737	128/81	63/40		52/33
66	798.7764	405/256	100/63		78/49
67	810.87905	8/5
68	822.9817	3125/1944	45/28
69	835.0844	81/50		44/27	13/8
70	847.1871	625/384	49/30
71	859.2897	400/243	105/64	18/11
72	871.3924	3375/2048	81/49
73	883.4951	5/3
74	895.5978	2048/1215	42/25
75	907.7004	27/16			22/13
76	919.8031	128/75		56/33	56/33
77	931.9058	1250/729	12/7
78	944.00845	216/125	140/81		26/15
79	956.1111	125/72		110/63	45/26
80	968.2138	1280/729	7/4
81	980.3165	225/128	225/128	99/56
82	992.4191	16/9
83	1004.5218	3645/2048	25/14
84	1016.6245	9/5
85	1028.7272	2048/1125	49/27
86	1040.8298	729/400	64/35	11/6
87	1052.9325	1152/625	90/49
88	1065.0352	50/27
89	1077.13785	4096/2187	28/15
90	1089.2405	15/8
91	1101.3432	256/135	189/100	154/81	49/26
92	1113.4459	243/128	40/21
93	1125.5485	48/25
94	1137.6512	625/324	27/14		25/13
95	1149.7539	243/125	35/18		35/18
96	1161.8566	125/64	49/25		49/25
97	1173.9592	160/81	63/32
98	1186.0619	2025/1024	125/63
99	1198.1646	2/1
100	1210.2672	4096/2025	252/125	99/49	91/45
101	1222.3699	81/40	128/63	55/27
102	1234.4726	256/125	49/24
103	1246.5753	500/243	72/35	33/16
104	1258.6779	1296/625	56/27		52/25
105	1270.7806	25/12		44/21
106	1282.8833	512/243	21/10
107	1294.98595	135/64		162/77	104/49
108	1307.0886	32/15
109	1319.1913	2187/1024	15/7
110	1331.294	54/25			13/6
111	1343.3966	625/288	98/45
112	1355.4993	1600/729	35/16	11/5
113	1367.602	1125/512	108/49
114	1379.7047	20/9
115	1391.8073	8192/3645	56/25
116	1403.91	9/4

See also

• 99edo
• 157edt