random thoughts on classifying chords

I’m going to attempt to classify chords from first principles, forgetting about the restrictions imposed by existing terminology. Chords are essentially a partial harmonic series. Therefore, they can be indicated as a series of ascending integers indicating ratios of frequencies of elements in the chord, such as 1:2 (octave), 2:3 (fifth), 4:5:6 (major triad), and so on. This is for pure tone combinations. Real instruments contain overtones in each note, so the total effect is more complicated (or collapsed, depending on the view). We will just deal with pure tones for now.
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