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Escher chord progressions

Mauritz Escher like Chord progressions in puredata

This is part of a series of PureData patches that generate music all by themselves, using mathematical
rules that apply quite nicely to music theory.

Screenshot: escher-screenshot.gif

Mp3: escher-zenpho.mp3
Patch: escher.pd - you'll also need adsr.pd

First some basic music theory:
(skip this if you're comfortable with chords, 7ths, and inversions)

A major scale is constructed of 8 notes, with the "root" note doubled at the 8th note.
For the key of C major (all the "white" notes on a piano) the names and numbers of the notes in
the scale of C-major are:

Name, Number:
C, 1st (root)
D, 2nd
E, 3rd
F, 4th
G, 5th
A, 6th
B, 7th
C, 8th (remember the root is doubled at the octave)

A triad is constructed of the 1st, the 3rd, and the 5th notes in the scale.
A SEVENTH chord is constructed of a triad (notes 1,3 and 5) PLUS the 7th note in the
scale. So a C major 7th is note 1,3,5,7 or C,E,G,B.

Up until now we've been describing "standard" voicings of the chords, in other words, the notes
are played so that the root is the lowest pitched note, the 3rd is higher, the 5th is higher
still, and the 7th is the note just below the octave of the root.

At the risk of sounding redundant, "octave numbers" after the note name help clarify which octave
the note is to be played in. To play a C major 7th on the third octave, we would write:
C3,E3,G3,B3. To play it an octave higher we would write: C4,E4,G4,B4.

"Inversions" of chords re-order the pitches of the notes, but still play notes with the same
"name" as the 3rd, 5th, 7th etc. For example:

C3,E3,G3,B3 is a standard C major 7th...

...and G2,C3,E3,B3 is an inversion. All the notes are there (C,E,G,B) but they are in a different
order to the normal "Root, Third, Fifth, Seventh" arrangement. In this case, we say that "the
fifth is in the root".


Okay so now we know what a major 7th chord is. Lets deal with chord progressions.

Now imagine playing C3,E3,G3,B3 and removing the "root" (the C3) from the notes played,
we have a chord that reads "E3,G3,B3" - we were playing C major 7th and now we're playing E minor.

*THIS IS A VERY IMPORTANT STEP* Moving from C major 7 to E minor sounds "natrual" because the
notes that occour in C major 7 ALSO occour in the E minor.

Now lets make this E minor chord a 7th...

We've said before that a 7th chord can be constructed by playing the 1st, 3rd, and 5th notes, PLUS
the 7th note in the scale.

The scale of E minor (a flavour of minor) is:

Name, Number
E, 1st (root)
F#, 2nd
G, 3rd
E, 4th
B, 5th
C, 6th
D, 7th
E, 8th (octave)

The 7th note is "D" so we add the D note to our E minor triad to make E minor 7th.
E minor 7th is therefore: "E3,G3,B3,D4".

We can extend this E minor again, removing the root, working out the new scale for G major, adding
the 7th to make G major 7th, and again, and again, and again... but if we do - we keep moving
*UP IN PITCH* and spiral off the end of the keyboard.


Okay, so what my patch does is to take the idea of generating new 7th chords over and over,
but to play inversions of these chords so that the notes stay inside a single octave. If the
"root" note is in the 3rd octave, C3 for example. Then when I move to E minor, the D4 is
transposed to be a D3, to keep within this octave range.

Due to the fact that there are 12 semitones in an octave, and notes that fall outside the octave
range will wrap around to be an octave lower. The maths for generating the new chords basically
involves taking each note in the current major 7th chord and adding two semitones to each note in

Now our terminology could cause confusion here, because there are "notes in a scale" and "notes in a chord"... So I'm going to define some notation to show when i'm talking about the notes in a

For example:

A C major 7th has the notes C3,E3,G3,B3.
Note-1-in-the-chord is to be defined as chord_note_1.
Note-2-in-the-chord is defined as chord_note_2.
Note-3-in-the-chord is defined as chord_note_3.
Note-4-in-the-chord is defined as chord_note_4.

chord_note_1 has the pitch C3.
chord_note_2 has the pitch E3.
chord_note_3 has the pitch G3.
chord_note_4 has the pitch B3.

It is important to be clear about the idea of "pitch", "chord_notes" and "scale_notes" because
because chord_note_3 has the pitch "G3" and scale_note_3 of C major which is the pitch "E3".


Back to the procedure for generating new seventh chords.

We generate a major 7th to begin with.

We add 2 semitones to chord_note_1 to get "D3", and we leave the other notes alone.
Our chord now reads: D3,E3,G3,B3.
Which is an "inversion" of E minor 7th.

This time we add 2 semitones to chord_note_2 to get "F#3", and we leave the other notes alone as
Our chord now reads: D3,F#3,G3,B3
This is an inversion of G major 7th.

This time we add 2 semitones to chord_note_3 to get "A3", we leave the other notes.
Our chord now reads: D3,F#3,A3,B3
This is an inversion of B minor 7th.

This time we add 2 semitones to chord_note_4 to get C#4...

Our chord now reads: D#3,F#3,A3,C#3
This is an inversion of D major 7th.

After my patch modifies all 4 chord_notes, it moves back to chord_note_1, and adds another
2 semitones... over and over.

Eventually we get back to C major 7th again, but on the way we move through a variety of different
chords that evokes very interesting changes of moods.

Want to try playing with it?
Mp3: escher-zenpho.mp3
Patch: escher.pd - you'll also need adsr.pd

(c)2009 zenpho@zenpho.co.uk - Phill Phelps