Download MSP_lecture10

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.
2.
3.
Pythagorean Dodecaphonic
Mean-tone
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!