AFDO: Difference between revisions
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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}} | ||
== Using afdos to make edo interval tables == | |||
To make a quick and dirty table of intervals in an edo, you can go to Scale Workshop and use "approximate by harmonics" to make a list of JI ratios for each interval. Copy-paste it into Excel to make a table. | |||
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. This method is very crude. | |||
Here is a 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): | |||
{| class="wikitable" | |||
|+ | |||
!EDO size | |||
!Ideal AFDO to map to | |||
!Smallest denominators excluded | |||
|- | |||
| 1edo to 20edo | |||
| [[60afdo]] | |||
| 7, 8, 9 | |||
|- | |||
| 21edo to 40edo | |||
| [[120afdo]] | |||
| 7, 9, 11 | |||
|- | |||
| 41edo to 120edo | |||
| [[360afdo]] | |||
| 7, 11, 13 | |||
|- | |||
| 121edo to 840edo | |||
| [[2520afdo]] | |||
| 11, 13, 16 | |||
|- | |||
| 841edo to 1680edo | |||
| [[5040afdo]] | |||
| 11, 13, 17 | |||
|- | |||
| 1681edo to 18480edo | |||
| [[55440afdo]] | |||
| 13, 17, 19 | |||
|- | |||
| 18481edo to 240240edo | |||
| [[720720afdo]] | |||
| 17, 19, 23 | |||
|- | |||
| 240241edo to 480480edo | |||
| 1441440afdo | |||
| 17, 19, 23 | |||
|- | |||
| 480480edo to 1,441,440edo | |||
| 4324320afdo | |||
| 17, 19, 23 | |||
|- | |||
| 1,441,441edo to 7,207,200edo | |||
| 21621600afdo | |||
| 17, 19, 23 | |||
|- | |||
| 7,207,201edo to 122,522,400edo | |||
| 367567200afdo | |||
| 19, 23, 29 | |||
|- | |||
| 122,522,401edo to 2,327,925,600edo | |||
| 6983776800afdo | |||
| 23, 29, 31 | |||
|} | |||
== See also == | == See also == | ||