Transcript MSP_lecture6x

Music Software Projects
New York University
Adjunct Instructor Scott Burton
Comparing ET / Pythag / Harmonic Series
 Pythagoras established the number of steps per octave in western
music which we still use today but…
 The 7-note natural scale third was dissonant
 12 tone chromatic scale degrees were unusable
 The Sixth and Seventh intervals were also dissonant
 Goals of scale engineering after Pythagoras:
 Adjust dissonant intervals to be closer to harmonic series
 Adjust ratios to be super-particular
 Make them sound better 
 For ex., Ptolemy adjusted the 3rd, 6th and 7th degrees
 Irony is that ET adjusted ALL intervals away from the series...
Comparing Scale Intervals
 The primary measure we will use to compare is “Cents”
 100 cents per smallest interval in the 12 ET tones scale
 Cents = (1200/LOG(2,10)) * LOG(IntervalFactor,10)
 Example: Let IntervalFactor = 1.5 (the 3/2 or “Fifth”)
 701.995 = (1200/LOG(2,10)) * LOG(1.5,10)
 By Definition the Fifth in ET is 700 cents
 ET is 1.995 different than the Just or “pure” fifth of 3/2
 Cents are very handy when comparing intervals across tuning systems.
Programming Phase
 Add Cents calculation parameterized by either:
1. Any two intervals (e.g, “m2” and “5”)
2. Interval factor (e.g., 1.059)
 Store letter names in your note/interval object
 You can assume our base frequency stays the same at 528hz and
we’ll call that “C”
 But you still have to parameterize by starting frequency 
 Using letter note names will be useful for us as we build more
tuning systems and compare them
 Add Interval string names
 “m3”, “M3”, etc.
 See column F in DegreeNaming.xlsx
Programming Phase cont...
 Produce three output rows per scale to stdout
 ET, Harmonic Series and Pythagorean
 Use first 7 notes only from the Pythagorean scale
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No accidentals from ET
No sharps/flats
 Use the 5th octave of the Harmonic Series
 Using the Major Third – the “M3” interval
 Print out the frequencies and cents of the just that interval from:
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ET scale
Harmonic series
Pythagorean scale (7 note, 8 including the octave)
 Output format:
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Units IntervalName ET HarmonicSeries Pythagorean
HZ
M3
XXX YYY
ZZZ
Cents
M3
XXX YYY
ZZZ
After the break:
 Prepare for Rhythm
 Learn how to read the “Riddim” sheet
 “Nanofly” by Billy Martin