1. Music Software Projects New York University Adjunct Instructor Scott Burton

2. Submission for today Let’s hear some triads... ET Pythag Just Team names

3. Pythag Dodecaphonic is Better It has more useable “accidentals” However the major third still clashes with the harmonic series closest interval (5/4) There are two Diminished Fifths To evolve towards the 12 tone chromatic scale of today we first have to get 12 tones instead of 13 – which means 1 diminished fifth not 2 Also we want to adjust some of the intervals to be closer to harmonic series… Which brings us to the scale of Ptolemy See living spec spreadsheet: pythag_ptolemy_sheet_phase6.xlsx

4. Creating a nice sounding third In Pythagorean tuning, the only perfectly consonant intervals were the 5 th and the 4 th (the inversion of the 5 th ). Depending on your definition of “perfect” the 2 nd and 6 th were pretty good too (they appear in the harmonic series). The 3 rd was a rich interval that variable pitch instruments (vocals, strings, etc.) could naturally adjust to away from the Pythagorean 3 rd and towards the harmonic series third… The Pythagorean Third (81/64) was dissonant. This limited the use of harmony – specifically sweet sounding 3-note chords (triads). Tempering the thirds to be more consonant was a logical evolution and was the key innovation with Ptolemy’s system

5. Creating a nice sounding third... The “Syntonic Comma” is the difference between the Pythagorean Third and the Harmonic Series (closest) “Third” of 5/4: Pythagorean Third minus harmonic series third results is this “comma”: 81/80 = 81/64 / 5/4 For ex., in the key of C: If you decrease E by the syntonic comma (81:80) then: Major Third C -> E is flattened : 81/64 x 80/81 = 5/4 Minor Third E -> G is sharpened: 32/27 x 81/80 = 6/5 Minor Third + Major Third = Fifth ( 6/5 x 5/4 = 3/2 ) Notice also that this “more pure” minor third of 6/5 is closer but still does not exist as a harmonic in the harmonic series – the closest harmonic series interval is 19/16. However the interval appears in a sense because it’s the difference between the harmonics 3/2 and 5/4... The Major Third interval of 5/4 is represented exactly in the harmonic series

6. Break Then the “Wheel of Bembe” Play beat cycles to metronome rhythm_sheet_bembe_wheel.xlsx

7. Programming Phase Assignment covers lecture 9 and 10 on the class page Implement the scale of Ptolemy Play the sorted 12 note scale 1 second duration no rest between notes Implement the Bembe wheel rhythm sheet: rhythm_sheet_bembe_wheel.xlsx Choose sounds for each pattern so they sound good to your ears. Some high, some mid, some low Play the Bembe wheel for 2 12 beat cycles Play to tempo of 180bpm