1. New York University Adjunct Instructor Scott Burton
MSP
New York University
Adjunct Instructor Scott Burton

2. Let’s hear some songs
Play Pythagorean Dodecaphonic – 1 sec duration, 0 sec delay
Using “Nanafly” patterns
Pick any two patterns and call them “A” and “B”
Play pattern “AAAB” and repeat once
Tempo: 240 BPM

3. Interesting that a major third and a minor third = perfect fifth:
Harmony
Let’s start with two notes sounding simultaneously using pure “just” ratios
Unison 1:1 (we’ve been assigning 528Hz and calling C)
Octave 2:1
Fifth 3:2
Fourth 4:3
Third (major) 5:4 (M3)
Third (minor) 6:5 (m3)
Each pair has a unique sound...
Unison + Fifth
Unison + Fourth
Unison + M3 (happy or bright sounding)
Unison + m3 (sad or mysterious sounding)
Interesting that a major third and a minor third = perfect fifth:
5/4 * 6/5 = 3/2

4. Harmony ...
Two notes really define the character – especially unison + third
We can have more than two notes sounding simultaneously
To add color or richness let’s add a third note
“Triad” : unison + third + fifth
The third interval really defines the chord overall sound
Can add more intervals for color (e.g., “jazz chords”)
Next logical would be the 7th
We could add more:
9th (the 2nd up an octave)
11th (the 4th up an octave)
13th (the 6th up an octave)
Could add one of more of any of the above to add “color”

5. Medieval Harmony
Thirds were a problem thanks to Pythagoras (81:64 vs 5:4)
Thus Thirds were avoided in pre-15th century music
Harmony used the consonant 5th and/or it’s inversion the 4th
Very pure sounding but a little “sterile”
Supposedly singing in harmony using 4th and 5th intervals necessitated the creation of the first flat or accidental
Harmonizing in 3rds is quite nice but only if you don’t use the Pythag 3rd

6. Medieval Harmony Review first_flat.xlsx sheet
Singing in harmony using the 3rd was avoided at the time because the Pythag third (81/64) was dissonant.
We had to wait a few centuries for a better sounding 3rd to be engineered
Interesting to note that the Third would turn out to be a very sweet sounding and important interval - but only after it was adjusted from the pythag 81/64
It was further adjusted when ET was established...

7. Break

8. Chords and Keys
Modulation (changing key) requires altering notes to maintain interval spacings
Remember a different mode uses the same set of notes but has different order
Refer to sheet: sharps_flats_in_keys.xlsx (3 tabs)
For a three note chord starting on C
If we play the 1, 3rd, 5th intervals simultaneously we get the most basic chord in western music theory – a major C triad
C E G
We can build “triads” starting on every note in a scale.
Sequentially:
C E G, D F A, E G B, F A C, G B D, A C E, B D F, C E G
These are all 3 note chords that exist in a key which is the key of C in this case
All are composed of combinations of m3 and M3 intervals stacked on top of each other
The last chord (built on the B) is two m3’s and has a unique sound – “diminished”

9. Checkpoint
When the assignment for this week is complete next week you will have all the basic ingredients to make music:
Scales which are used to create Melodies
Harmony
Rhythm
Song structure – repetition, repose

10. Deliverables
Play the scale in the first_flat.xlsx sheet in this sequence:
play the first row (we’ll call the “base” scale)
play the "harmony 1" scale simultaneously with the base scale
play the "harmony 2" scale simultaneously with the base scale
Play 2,3) again after adjusting for the diminished interval by flattening the B
Play the 7 chords built on each scale degree starting with C (528Hz)
C E G, D F A, E G B, F A C, G B D, A C E, B D F
Play using Pythag Dodecaphonic
1 second duration, no silence between
Play using Pythagorean Dodecaphonic system
Parameterize so you can play either Pythag or ET