42edf

← 41edf

42edf

43edf →

Prime factorization	2 × 3 × 7
Step size	16.7132 ¢
Octave	72\42edf (1203.35 ¢) (→ 12\7edf)
Twelfth	114\42edf (1905.31 ¢) (→ 19\7edf)
Consistency limit	7
Distinct consistency limit	7

42 equal divisions of the perfect fifth (abbreviated 42edf or 42ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 42 equal parts of about 16.7 ¢ each. Each step represents a frequency ratio of (3/2)^1/42, or the 42nd root of 3/2.

42EDF is related to 72edo, but with the 3/2 rather than the 2/1 being just, which results in octaves being stretched by about 3.3514 ¢. This corresponds to 71.7995 edo, practically identical to every fifth step of 359edo. Unlike 72edo, it is only consistent up to the 7-integer-limit, with discrepancy for the 8th harmonic (three octaves).

Lookalikes: 72edo, 114edt, 186ed6

Harmonics

Approximation of prime harmonics in 42edf

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3.35	+3.35	+4.79	+7.24	-6.44	+5.19	-7.98	+0.02	+3.52	+3.33	+4.87
	Relative (%)	+20.1	+20.1	+28.7	+43.3	-38.5	+31.0	-47.8	+0.1	+21.1	+20.0	+29.1
Steps (reduced)		72 (30)	114 (30)	167 (41)	202 (34)	248 (38)	266 (14)	293 (41)	305 (11)	325 (31)	349 (13)	356 (20)

Approximation of prime harmonics in 42edf

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-0.60	+5.53	+6.64	+3.07	-4.37	-6.20	+2.94	+7.65	+7.54	-7.12	+6.55
	Relative (%)	-3.6	+33.1	+39.7	+18.3	-26.2	-37.1	+17.6	+45.8	+45.1	-42.6	+39.2
Steps (reduced)		374 (38)	385 (7)	390 (12)	399 (21)	411 (33)	422 (2)	426 (6)	436 (16)	442 (22)	444 (24)	453 (33)

Intervals

Degrees	Cents value	Approximate ratios (11-limit)
0		1/1
1	16.7132	81/80
2	33.4264	45/44
3	50.1396	33/32
4	66.8529	25/24
5	83.5661	21/20
6	100.2793	35/33
7	116.9925	15/14
8	133.7057	27/25
9	150.4189	12/11
10	167.1321	11/10
11	183.8454	10/9
12	200.5586	9/8
13	217.2717	25/22
14	233.985	8/7
15	250.6982	81/70
16	267.4114	7/6
17	284.1246	33/28
18	300.8379	25/21
19	317.5511	6/5
20	334.2643	40/33
21	350.9775	11/9
22	367.6907	99/80
23	384.4039	5/4
24	401.1171	44/35
25	417.8304	14/11
26	434.5436	9/7
27	451.2568	35/27
28	467.97	21/16
29	484.6832	33/25
30	501.3964	4/3
31	518.1096	27/20
32	534.8229	15/11
33	551.536	11/8
34	568.2493	25/18
35	584.9625	7/5
36	601.6757	99/70
37	618.3889	10/7
38	635.1021	36/25
39	651.8154	16/11
40	668.5286	22/15
41	685.2418	40/27
42	701.955	3/2
43	718.6682	50/33
44	735.3814	32/21
45	752.0946	54/35
46	768.8079	14/9
47	785.5211	11/7
48	802.2343	35/22
49	818.9475	8/5
50	835.6607	81/50
51	852.3739	18/11
52	869.0871	33/20
53	885.8004	5/3
54	902.5136	27/16
55	919.2268	56/33
56	935.94	12/7
57	952.6532	121/70
58	969.3664	7/4
59	986.0796	44/25
60	1002.7929	16/9
61	1019.506	9/5
62	1036.2193	20/11
63	1052.9235	11/6
64	1069.6457	50/27
65	1086.3589	15/8
66	1103.0721	66/35
67	1119.7854	21/11
68	1136.4986	27/14
69	1153.2118	35/18
70	1169.925	49/25
71	1186.6382	99/50
72	1203.3514	2/1
73	1220.0646	81/40
74	1236.7779	45/22
75	1253.4911	33/16
76	1270.2043	56/27
77	1286.9175	21/10
78	1303.6307	70/33
79	1320.3439	15/7
80	1337.05715	54/25
81	1353.7704	24/11
82	1370.4836	11/5
83	1387.1968	20/9
84	1403.91	9/4