Template:Interval edo approximation: Difference between revisions

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<includeonly>{{#invoke:Interval_Edo_Approximation|main
<includeonly>{{#invoke: Interval edo approximation|main
|interval={{{interval|{{{1}}}}}}
| interval = {{{interval|{{{1}}}}}}
|tolerance={{{tolerance|10}}}
| tolerance = {{{tolerance|10}}}
|min_edo={{{min_edo|2}}}
| min_edo = {{{min_edo|2}}}
|max_edo={{{max_edo|80}}}
| max_edo = {{{max_edo|80}}}
}}</includeonly><noinclude>
}}</includeonly><noinclude>
{{Dochead}}
== Usage ==
== Usage ==
 
This template generates edo approximation tables for just intervals.  
This template generates EDO approximation tables for just intervals. [https://en.xen.wiki/w/Module:Interval_Edo_Approximation | source code here]


=== Basic syntax ===
=== Basic syntax ===
<pre>
<pre>
{{Interval_Edo_Approximation|3/2}}
{{Interval edo approximation|3/2}}
</pre>
</pre>
if the name of the page is the interval you're trying to create a table of, use  
if the name of the page is the interval you are trying to create a table of, use  
<pre>
<pre>
{{Interval_Edo_Approximation | {{PAGENAME}}}}
{{Interval edo approximation|{{PAGENAME}}}}
</pre>
</pre>
=== With named parameter ===
=== With named parameter ===
<pre>
<pre>
{{Interval_Edo_Approximation|interval=5/4}}
{{Interval edo approximation|interval=5/4}}
</pre>
</pre>


=== With custom parameters ===
=== With custom parameters ===
<pre>
<pre>
{{Interval_Edo_Approximation|interval=7/6|tolerance=10|min_edo=12|max_edo=72}}
{{Interval edo approximation|interval=7/6|tolerance=10|min_edo=12|max_edo=72}}
</pre>
</pre>


=== Parameters ===
=== Parameters ===
 
; <code>interval</code> (or first unnamed parameter)
* '''interval''' (or first unnamed parameter) - The just interval ratio (required). Format: "numerator/denominator" (e.g., "3/2", "5/4", "7/6")
: 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)
; <code>tolerance</code>
* '''min_edo''' - Minimum EDO to check (optional, default: 5)
: relative error tolerance in percent (optional, default: 9)
* '''max_edo''' - Maximum EDO to check (optional, default: 60)
; <code>min_edo</code>
: minimum edo to check (optional, default: 5)
; <code>max_edo</code>
: maximum edo to check (optional, default: 60)


=== Examples ===
=== Examples ===
; Perfect fifth (3/2)
{{Interval edo approximation|3/2}}


==== Perfect fifth (3/2) ====
; Major third (5/4) with custom tolerance (20%)
{{Interval_Edo_Approximation|3/2}}
{{Interval edo approximation|5/4|tolerance=20}}
 
==== Major third (5/4) with custom tolerance (20%) ====
{{Interval_Edo_Approximation|5/4|tolerance=20}}


==== Septimal minor third (7/6) with extended range (up to 80EDO) ====
; Septimal minor third (7/6) with extended range (up to 80edo)
{{Interval_Edo_Approximation|7/6|min_edo=5|max_edo=80}}
{{Interval edo approximation|7/6|min_edo=5|max_edo=80}}


[[Category:Music theory templates]]
[[Category:Music theory templates]]
[[Category:EDO templates]]
[[Category:EDO templates]]
</noinclude>
</noinclude>

Revision as of 12:28, 3 November 2025


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.

Basic syntax

{{Interval edo approximation|3/2}}

if the name of the page is the interval you are trying to create a table of, use 

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

With named parameter

{{Interval edo approximation|interval=5/4}}

With custom parameters

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

Parameters

interval (or first unnamed parameter)
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)

Examples

Perfect fifth (3/2)
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
Major third (5/4) with custom tolerance (20%)
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
Septimal minor third (7/6) with extended range (up to 80edo)
Edo approximations for 7/6 (266.87 ¢)
≤ 80edo, 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
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