music theory: "There are seven notes in this scale." me: ok music theory: "So we call it an 'octave.'" me, a mathematician: wait
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I forgot to mention base 8 was also invented slightly differently.
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aww

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it makes more sense aurally. Without the 8th note of the scale there's no resolution. It's also physics. End on 2:1 ratio
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I'd never really thought about this beforeThanks. Twitter will use this to make your timeline better. UndoUndo
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As a computing scientist you get used to count the 0 anyways
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right, but in this case the count goes from 1 to 7. She's absolutely right, and now I can't unsee it.
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the only way you get 8 notes is by including the same note from two adjacent octaves. It overlaps by 1.
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The equal-tempered scale is kind of a hack. Chords aren't perfectly tuned, but you can play chords in any key. 12 tones, with no overlap.
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If you put twelve dots equidistantly on a circle, and also score 7 equidistant notches so that one of them coincides with one of the dots...
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...then pick the dots closest to the notches, you'll get the same distance structure as in the major scale. Ditto for 5 and pentatonic
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