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How do these objects even out your ratios (or, I guess, what do you
mean by that)? Finding the difference between two frequencies after
converting them to a MIDI value allows you to work linearly instead of
logarithmically, which is just easier--well, for me anyway. For
example, after converting 912Hz and 1081Hz to MIDI and getting the
difference, you come up with 2.9431. Now you can just think of them as
2.9431 half-steps apart, and that one number will work starting from
any pitch. If you stick to the frequency realm, you'll have to consider
them a ratio of 912:1081, which is fine, but a little ugly and not as
easy. As far as filling in the gaps, I don't know if this will help at all or not, but it might be something to think about. When you look at how the major scale is constructed, it can be seen as taking advantage of the first few harmonics in the harmonic series. I'll use the C major scale to (try to) illustrate. Going up from C in the harmonic series, you get an octave, a fifth (G), another octave, a major third (E), and another fifth [1]. Those last three notes are a C major triad (C-E-G). Now, stepping back a bit, the first note other than C in the series is G, the fifth, or dominant, in the scale. If you go the other way, down a fifth, you get F, the subdominant. Now, taking the intervals from the C major chord and applying them to G and F, you get G-B-D and F-A-C, respectively. The notes in those chords are what is used to fill in the gaps, and now you have all of the notes of a C major scale: C-D-E-F-G-A-B. I mention all of that because you're already working with partials. So perhaps working with an interval or ratio between two of your partials and applying that to another of your partials to generate new frequencies might get you somewhere. Or it might suck, who the fuck knows :-). Either way, this sounds like an interesting project, and I'd be interested in seeing where you go with all of this. Best of luck, .mmb [1] http://en.wikipedia.org/wiki/Harmonic_series_(music) J bz wrote: Dear Mike and Andrew, |
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