Download MSP_lecture8 - New York University

Music Software Projects
New York University
Adjunct Instructor Scott Burton
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
Interesting that a
major third and a
 Third (major)
5:4 (M3)
minor third = perfect
 Third (minor)
6:5 (m3)
fifth:
5/4 * 6/5 = 3/2
 Each pair has a unique sound...
 Unison + Fifth
 Unison + Fourth
 Unison + M3 (happy or bright sounding)
 Unison + m3 (sad or mysterious sounding)
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
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
Medieval Harmony

Play the scale in the first_flat.xlsx sheet in this sequence:
1. play the first row (we’ll call the “base” scale)
2. play the "harmony 1" scale simultaneously with the base scale
3. play the "harmony 2" scale simultaneously with the base scale
*This is known as parallel motion

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...
Break
Modulation

Refer to sheet:

Play three note chord starting on C – the 1, 3rd, 5th intervals simultaneously

This is called a “Triad”.

Play a chord once for each key going around the circle of fifths.

The starting or “root” note for each Triad is each point around the circle
 Clockwise:
C G D A E B F#
 Counter-clockwise:
C F Bb Eb Ab Db Gb
 1 second duration
 no silence between chords

Play using:
sharps_flats_in_keys.xlsx
System
Third
Fifth
Just
5/4
3/2
Pythag
81/64
3/2
ET
=POWER(POWER(2,1/12),4)
=POWER(POWER(2,1/12),7)