Template:Interval edo approximation
- 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 | 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 | 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 | 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 |