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Some of the fun of this project has centered around replacing the broad, fuzzy, harmonics of the primordial sound by single pure tones. This renders the sound more musical to our ears, and opens a new avenue for some playful analysis. Now, replacing each harmonic by its central frequency does not necessarily yield a note which belongs on one of our musical scales. For this reason, I've generated two versions of the harmonic sounds, one with the exact frequencies, and one with each frequency adjusted slightly to match the nearest note on our "tempered" scale.
There are several types of musical scale, the two most famous being Pythagorean (pentatonic) and tempered. The Pythagorean scale uses notes with frequencies in simple whole number ratios, while the tempered scale divides each octave into twelve "semitones", with equal consecutive frequency ratios. Since an octave separates notes with frequency ratio 2, then a note which is "n" semitones above f0 has frequency fn = f0 × 2n/12 = f0 × (1.05946)n ; (e.g. if n=12, f12 = f0 × 2). By adjusting the harmonics to match this particular set of frequencies brings them into our normal musical framework, and one can discuss the nature of the intervals using familiar terms, such as major or minor third, etc. This kind of transformation is one of "mode", in this case from "microtonal" (i.e. infinitely variable) to even tempered.
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