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| '''Nonprime prime power''': {{AFDOs|4, 8, 9, 16, 25, 27, 32, 49, 64, 81, 121, 125, 128, 169, 243, 256, 289, 343, 361, 512, 529, 625, 729, 841, 961, 1024, 1331, 1369, 1681, 1849, 2048}} | | '''Nonprime prime power''': {{AFDOs|4, 8, 9, 16, 25, 27, 32, 49, 64, 81, 121, 125, 128, 169, 243, 256, 289, 343, 361, 512, 529, 625, 729, 841, 961, 1024, 1331, 1369, 1681, 1849, 2048}} |
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| == Using AFDOs to make EDO interval tables ==
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| To make a quick and dirty table of intervals in an edo, you can go to [[Scale Workshop]] and do the following:
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| # Create a new Excel spreadsheet
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| # Make cell A1 = 1, A2 = 2 and so on. Flood-fill down to the size of your EDO
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| # Make cell B1 = (1200/EDO size)*A1 and flood-fill this formula all the way down column B
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| # Copy-paste column B into Scale Workshop
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| # Modify > approximate by harmonics > an afdo selected according to the table below (or choose your own)
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| # Modify > reduce
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| # Paste the result into the third (C) column in Excel
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| # Insert a row at the top of the spreadsheet to use as a header row
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| # Title the first column "Edo step", the second column “cents” and the third column "JI ratios"
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| Your table is now complete!
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| Do note that this is not a replacement for a manually curated table of intervals, nor is it even a replacement for a more cleverly computed table of intervals such as those generated by [[Template:Interval table]] or [[Template:Huge table]]. This method is very crude compared to those.
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| But it is very computationally light, so it can be helpful for really, really big edos that are difficult to document any other way.
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| Here is the table recommending what afdo to choose (i.e. what number to put for "approximate by harmonics"). The afdos recommended are the superior highly composite numbers (OEIS A002201):
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| {| class="wikitable"
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| |+
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| !EDO size
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| !Ideal AFDO to map to
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| !Included denominators
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| !Excluded denominators
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| |-
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| | 1edo to 20edo
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| | [[60afdo]]
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| | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30
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| | 7, 8, 9, 11, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32
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| |-
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| | 21edo to 40edo
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| | [[120afdo]]
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| | 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30
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| | 7, 9, 11, 13, 14, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32
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| |-
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| | 41edo to 120edo
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| | [[360afdo]]
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| | 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30
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| | 7, 11, 13, 14, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32
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| |-
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| | 121edo to 840edo
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| | [[2520afdo]]
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| | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30
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| | 11, 13, 16, 17, 19, 22, 23, 25, 26, 27, 29, 31, 32
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| |-
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| | 841edo to 1680edo
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| | [[5040afdo]]
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| | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30
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| | 11, 13, 17, 19, 22, 23, 25, 26, 27, 29, 31, 32
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| |-
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| | 1681edo to 18480edo
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| | [[55440afdo]]
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| | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 28, 30
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| | 13, 17, 19, 23, 25, 26, 27, 29, 31, 32
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| |-
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| | 18481edo to 240240edo
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| | [[720720afdo]]
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| | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 26, 28, 30
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| | 17, 19, 23, 25, 27, 29, 31, 32
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| |-
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| | 240241edo to 480480edo
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| | 1441440afdo
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| | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 26, 28, 30, 32
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| | 17, 19, 23, 29, 31
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| |-
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| | 480480edo to 1,441,440edo
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| | 4324320afdo
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| | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32
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| | 17, 19, 23, 29, 31
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| |-
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| | 1,441,441edo to 7,207,200edo
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| | 21621600afdo
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| | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32
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| | 17, 19, 23, 29, 31
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| |-
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| | 7,207,201edo to 122,522,400edo
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| | 367567200afdo
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| | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32
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| | 19, 23, 29, 31
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| |-
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| | 122,522,401edo to 2,327,925,600edo
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| | 6983776800afdo
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| | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32
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| | 23, 29, 31
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| |}
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| == See also == | | == See also == |