Pythagoras studies harmony

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Across
  1. 8. instrument made to study intervals
  2. 9. mathematical relationship making intervals
  3. 11. interval with ratio of 3:2
  4. 13. pleasing harmony
  5. 14. interval from twice the frequency
  6. 15. movable part of monochord
  7. 16. distance between 2 notes
  8. 17. the highness or lowness of a sound
Down
  1. 1. invented by Guido of Arezzo
  2. 2. first step in scientific method
  3. 3. instruments need ____________bodies
  4. 4. believed in cosmic harmony
  5. 5. intervals of 4th, 5th and octave are this
  6. 6. 2 or more notes sounding together
  7. 7. determines pitch
  8. 10. clashing harmony
  9. 12. Latin word meaning "ladder"