Originally Posted by

**Wes Lachot**
This has been a lot about the 7 part of the 12 (Diatonic), but it's also worth mentioning that the negative image of Diatonic, which is of course Pentatonic, also seems to arise naturally from all ends of the earth as a sort of cross-cultural norm, or "fact of Nature". I'm running out of mojo right now, so I'll just leave it at that.

I found 5-tone ET tuning by ear, playing a DX-7 with microtuning capability years ago, and also discovered an interesting phenomenon concerning the numbers 7 and 5, which also happen to be the number of white and black keys on the piano keyboard. Seems the next ET tuning (after 5-tone) that sounded musical (in a primitive sense) was the 7-tone ET scale. Then of course there is the 12-tone scale, then the next two that work out reasonably well are the 17-tone and 19-tone scales, then the 29-tone and 31-tone scales, and so on. I began to see a pattern emerging (besides the fact that the last two are Mersenne pairs). The scales that come close to musical simple ratio consonances, 5; 7; 12; 17; 19; 29; 31; etc., can be broken down like this: 5; 7; 5+7; 5+7+5; 7+5+7; 5+7+5+7+5; 7+5+7+5+7; etc.