Template:Interval edo approximation

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This template is implemented by the Lua module Module:Interval edo approximation.

This template invokes the following functions: main from Interval edo approximation.

Usage

This template generates edo approximation tables for just intervals.

{{Interval edo approximation|interval = 3/2 | interval_name = 3/2}}

if the name of the page is the interval you are trying to create a table of, it will by default use the pagename as the interval.

{{Interval edo approximation|{{PAGENAME}}}}

{{Interval edo approximation|interval=7/6|tolerance=10|min_edo=12|max_edo=72 | interval_name = Septimal Minor third}}

interval: the just interval ratio (required). Format: "numerator/denominator" (e.g., "3/2", "5/4", "7/6")
tolerance: relative error tolerance in percent (optional, default: 9)
min_edo: minimum edo to check (optional, default: 5)
max_edo: maximum edo to check (optional, default: 60)
interval_name: the name of the interval you would like to label it. best case for when approximating irrational numbers; e.g. acoustic phi would be approximated with a large fracton. where interval = 1618/1000 | interval_name = ϕ

Edo approximations for 3/2 (701.96 ¢)
*≤ 80edo, relative error ≤ 10%*
Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
5	3\5	720.00	+18.04	+7.52
7	4\7	685.71	-16.24	-9.47
12	7\12	700.00	-1.96	-1.96
17	10\17	705.88	+3.93	+5.56
24	14\24	700.00	-1.96	-3.91
29	17\29	703.45	+1.49	+3.61
36	21\36	700.00	-1.96	-5.87
41	24\41	702.44	+0.48	+1.65
46	27\46	704.35	+2.39	+9.17
48	28\48	700.00	-1.96	-7.82
53	31\53	701.89	-0.07	-0.30
58	34\58	703.45	+1.49	+7.22
60	35\60	700.00	-1.96	-9.78
65	38\65	701.54	-0.42	-2.26
70	41\70	702.86	+0.90	+5.26
77	45\77	701.30	-0.66	-4.21

Edo approximations for 5/4 (386.31 ¢)
*≤ 80edo, relative error ≤ 20%*
Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
3	1\3	400.00	+13.69	+3.42
6	2\6	400.00	+13.69	+6.84
9	3\9	400.00	+13.69	+10.26
12	4\12	400.00	+13.69	+13.69
13	4\13	369.23	-17.08	-18.51
15	5\15	400.00	+13.69	+17.11
16	5\16	375.00	-11.31	-15.08
19	6\19	378.95	-7.37	-11.66
22	7\22	381.82	-4.50	-8.24
25	8\25	384.00	-2.31	-4.82
28	9\28	385.71	-0.60	-1.40
31	10\31	387.10	+0.78	+2.02
34	11\34	388.24	+1.92	+5.44
37	12\37	389.19	+2.88	+8.87
40	13\40	390.00	+3.69	+12.29
41	13\41	380.49	-5.83	-19.91
43	14\43	390.70	+4.38	+15.71
44	14\44	381.82	-4.50	-16.48
46	15\46	391.30	+4.99	+19.13
47	15\47	382.98	-3.33	-13.06
50	16\50	384.00	-2.31	-9.64
53	17\53	384.91	-1.41	-6.22
56	18\56	385.71	-0.60	-2.80
59	19\59	386.44	+0.13	+0.62
62	20\62	387.10	+0.78	+4.05
65	21\65	387.69	+1.38	+7.47
68	22\68	388.24	+1.92	+10.89
71	23\71	388.73	+2.42	+14.31
72	23\72	383.33	-2.98	-17.88
74	24\74	389.19	+2.88	+17.73
75	24\75	384.00	-2.31	-14.46
78	25\78	384.62	-1.70	-11.04

Edo approximations for 7/6 (266.87 ¢)
*≤ 150edo, relative error ≤ 10%*
Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
9	2\9	266.67	-0.20	-0.15
18	4\18	266.67	-0.20	-0.31
27	6\27	266.67	-0.20	-0.46
36	8\36	266.67	-0.20	-0.61
45	10\45	266.67	-0.20	-0.77
54	12\54	266.67	-0.20	-0.92
63	14\63	266.67	-0.20	-1.07
67	15\67	268.66	+1.79	+9.97
72	16\72	266.67	-0.20	-1.23
76	17\76	268.42	+1.55	+9.82
81	18\81	266.67	-0.20	-1.38
85	19\85	268.24	+1.36	+9.66
90	20\90	266.67	-0.20	-1.53
94	21\94	268.09	+1.21	+9.51
99	22\99	266.67	-0.20	-1.68
103	23\103	267.96	+1.09	+9.36
108	24\108	266.67	-0.20	-1.84
112	25\112	267.86	+0.99	+9.20
117	26\117	266.67	-0.20	-1.99
121	27\121	267.77	+0.90	+9.05
126	28\126	266.67	-0.20	-2.14
130	29\130	267.69	+0.82	+8.90
135	30\135	266.67	-0.20	-2.30
139	31\139	267.63	+0.75	+8.75
144	32\144	266.67	-0.20	-2.45
148	33\148	267.57	+0.70	+8.59