An interesting theory about why the music scales take on the values they have.

• dissonance of two pure tone comes from the inaudible beats in the superposition
• the base frequency + the overtones determine the note and the timber
  • overtones are not necessarily harmonics. it depends on the musical instrument.
• adding up all the dissonance graph of all overtones of two notes, we can get a graph of dissonance, where the troughs have lowest dissonance.
  • do the same for three notes, we get a 3-d graph of dissonance.
  • the insight is that we should consider not only the dissonance of the base notes but also of all overtones
• it's found that many scales (relative to the base) and chords (relative to the lowest note) fall in the troughs of this graph
• conclusion: overtones in the instruments influence the musical scales used by a culture