45edf

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45edf

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Prime factorization	32 × 5
Step size	15.599¢
Octave	77\45edf (1201.12¢)
Twelfth	122\45edf (1903.08¢)
Consistency limit	10
Distinct consistency limit	10

Division of the just perfect fifth into 45 equal parts (45EDF) is related to 77edo, but with the 3/2 rather than the 2/1 being just. The octave is stretched by about 1.123 cents and the step size is about 15.599 cents.

The patent val has a generally sharp tendency for harmonics up to 16, with the exception for 11.

Lookalikes: 77edo, 122edt

Harmonics

Approximation of prime harmonics in 45edf

Harmonic		2	3	5	7	11	13	17	19	23
Error	Absolute (¢)	+1.12	+1.12	+5.91	+0.56	-1.98	+5.19	-6.87	+3.36	+0.18
	Relative (%)	+7.2	+7.2	+37.9	+3.6	-12.7	+33.3	-44.0	+21.5	+1.1
Steps (reduced)		77 (32)	122 (32)	179 (44)	216 (36)	266 (41)	285 (15)	314 (44)	327 (12)	348 (33)

Approximation of prime harmonics in 45edf

Harmonic		29	31	37	41	43	47	53	59	61
Error	Absolute (¢)	+4.45	-1.82	+3.85	-2.27	-6.73	-4.73	+5.65	+7.18	-3.74
	Relative (%)	+28.5	-11.6	+24.7	-14.6	-43.2	-30.3	+36.2	+46.0	-24.0
Steps (reduced)		374 (14)	381 (21)	401 (41)	412 (7)	417 (12)	427 (22)	441 (36)	453 (3)	456 (6)

Intervals

Degree	Cents Value	Approximate Ratios in the 13-limit
0		1/1
1	15.599	81/80, 99/98
2	31.198	64/63, 49/48
3	46.797	33/32, 36/35
4	62.396	28/27, 27/26, 26/25
5	77.995	21/20, 22/21, 25/24
6	93.594	135/128
7	109.193	16/15
8	124.792	15/14, 14/13
9	140.391	13/12
10	155.99	12/11, 11/10
11	171.589	72/65
12	187.188	10/9
13	202.787	9/8
14	218.386	256/225
15	233.985	8/7
16	249.584	15/13
17	265.183	7/6
18	280.782	33/28
19	296.381	32/27, 13/11
20	311.98	6/5
21	327.579	98/81
22	343.178	11/9, 39/32
23	358.777	16/13
24	374.376	56/45, 26/21
25	389.975	5/4
26	405.574	33/26, 81/64
27	420.173	14/11, 32/25
28	436.772	9/7
29	452.371	13/10
30	467.97	21/16
31	483.569	120/91
32	499.168	4/3
33	514.767	27/20
34	530.366	49/36
35	545.965	11/8, 15/11
36	561.564	18/13
37	577.163	7/5
38	592.762	45/32
39	608.361	64/45
40	623.96	10/7
41	639.559	13/9
42	655.158	16/11, 22/15
43	670.757	72/49
44	686.356	40/27
45	701.955	3/2
46	717.554	91/60
47	733.153	32/21
48	748.752	20/13
49	764.351	14/9
50	779.95	11/7, 25/16
51	795.549	52/33, 128/81
52	818.148	8/5
53	826.747	45/28, 21/13
54	842.346	13/8
55	857.945	18/11, 64/39
56	873.544	81/49
57	889.143	5/3
58	904.742	27/16, 22/13
59	920.341	56/33
60	935.84	12/7
61	951.539	26/15
62	967.138	7/4
63	982.737	225/128
64	998.336	16/9
65	1013.935	9/5
66	1029.534	65/36
67	1045.133	11/6, 20/11
68	1060.732	24/13
69	1076.331	28/15
70	1091.93	15/8
71	1107.529	256/135
72	1123.128	40/21, 48/25
73	1138.727	27/14, 25/13
74	1154.326	64/33, 35/18
75	1169.925	63/32, 96/49
76	1185.524	160/81, 196/99
77	1201.123	/1
78	1216.722	81/40, 99/49
79	1232.321	128/63, 49/24
80	1247.92	33/16, 72/35
81	1263.519	56/27, 27/13, 52/25
82	1279.118	21/10, 44/21,25/12
83	1294.717	135/64
84	1310.316	32/15
85	1325.915	15/7, 28/13
86	1341.514	13/6
87	1357.113	24/11, 11/5
88	1372.712	144/65
89	1388.311	20/9
90	1403.91	9/4