Music Software projects New york university Adjunct Instructor Scott Burton

“Mean-tone” tempered scale Transitional attempt to create a transposable scale based on simple integer ratios Partially tempered some degrees to irrational values Goal is to use pure M3 intervals (5/4) Tempers the whole tones (M2) Divide the M3 - take the mean (thus name) Not the arithmetic mean because pitch is exponential in frequency To add intervals we multiply their ratios Geometric mean or √5/4 – this is our new M2 We want 2 semi-tones and 5 whole-tones of √5/4 to comprise octave of 2/1 Pure M3s but now the fifths are no longer just 3/2 We’ve got a nice sounding third but it came at a price...

Deliverables Implement Mean-tone scale – use second tab of living spec sheet… Play first verse of Mary Had a Little Lamb Play that same song using the scales: 1. Pythagorean Dodecaphonic 2. Mean-tone 3. Even Tempered Play the same song on each of the 3 scales above Remember: key is a certain ordered interval set that is named by the note it starts on “Mode” is sequence that is note constrained “Key” is a sequence of intervals Build scales on base frequency of 528 Hz Adjust octaves as needed Happy coding!