Still not entirely sure I know what you're after, so at the risk of repeating myself, use the (just intoned) intervals here:
1, 1:1-unison; 2, 135:128-major_chroma; 3, 9:8-major_second; 4, 6:5-minor_third; 5, 5:4-major_third; 6, 4:3-perfect_fourth; 7, 45:32-diatonic_fourth; 8, 3:2-perfect_fifth; 9, 8:5-minor_sixth; 10, 27:16-pyth_major_sixth; 11, 9:5-minor_seventh; 12, 15:8-major_seventh; 13, 2:1-octave;
I.e. major third = 6:5, and 6 divided by 5 is 1.2, so to transpose up a major third, multiply original frequency by 1.2.
Or, 5 divided by 6 is 0.83333333, so multiply by that to transpose down a major third. Or cook up something with [expr] that does the job more precisely, like [expr f$1 * (5/6)] etc etc...
All of these should "sound good" across the whole musical spectrum so long as you don't plan on changing key ;-)
D.
J bz wrote:
If I'm saying that these frequencies are 'good' to my ear, is there a way of creating equally 'good' sounding notes to fill in the gaps in, say for example, a 12 note scale based on these notes scaling from the lowest to the highest without doing the whole thing 'by ear'?