Pitch Class Theory for Ableton Live

[Bagatell]

Someone on another forum asked if there were any music theory books for people that use piano rolls and don't read standard notation. Here's what I came up with to turn this chord progression


I7 I7 IVM7 IVM7 II7 II7 V7 V7
Vm7 I7 IVM7 IVM7 VIm7 II7 IIm7 V7

or this

C7 C7 Fmaj7 Fmaj7 D7 D7 G7 G7
Gm7 C7 Fmaj7 Fmaj7 Am7 D7 Dm7 G7

into noise on a computer using the Ableton Live piano roll.


Set up Live like this


Using the chordhouse online tool

convert the above chord progression into this

CEGBb CEGBb FACE FACE DF#AC DF#AC GCEF GCEF
GBEF CEGB FACE FACE ACEG DF#AC DFAC GBDF

using this

(C)=(0)

(C C# D D# E F F# G G# A A# B)
(0 1 2 3 4 5 6 7 8 9 T E)

turn the above note sets into pitch sets like this


(047E) (047E) (5904) (5904) (2690) (2690) (7056) (7056)
(7E56) (047E) (5904) (5904 (9057) (2690) (2590) (7E25)

arrange the above pitch sets vertically like this



(047E) |
(047E) |
(5904) |
(5904) |
(2690) |
(2690) |
(7056) |
(7056) |
(7E56) |____{unordered chord sets}
(047E) |
(5904) |
(5904) |
(9057) |
(2690) |
(2590) |
(7E25) |

now order the sets like this (5904) becomes (0459), (756E) becomes (567E) etc.

(047E) |
(047E) |
(0459) |
(0459) |_______(0 2 4 5 6 7 9 E) {subset}
(0269) |
(0269) |
(0567) |
(0567) |
(567E) | (0 2 4 5 6 7 9 T E) {superset} {pitch axis}
(047E) |
(0459) |
(0459) |
(0579) |________________________(0 2 4 5 7 9 T) {subset}
(0269) |
(0259) |
(257E) *


Download Paul Nelsons 15 page guide to Pitch class sets here and you're all set.



"Pitch Class Sets are a method for describing harmonies in 20th century music.
These notations and methods can describe and manipulate any type of chord that can be created within a 12-tone (equally tempered) scale
It is an extremely useful technique for composers to help understand and control the harmonies which make up their music. Pitch class sets are the chemistry of harmonic color."

Its main advantage over standard notation is that it doesn't use acccident(als) or keys and clefs, you might say it's free and open-source

[Bagatell]

Some introductory stuff on Pitch Class Theory

http://en.wikipedia.org/wiki/Pitch_class

Joe Satriani and PC theory

http://en.wikipedia.org/wiki/Pitch_axis_theory

[Bagatell]

Trust me. This is not as complicated as it looks.

[crumhorn]

^^^ That is good because it looks really complicated.

Full marks for the work you put in on this.

I'm used to naming pitch classes with Letters A to G modified with sharps and Flats, so this is an alien world to me. but it's fascinating stuff, and I need to study it further. Thanks for the lead.

The trouble with the system of traditional Letter names is that it places the Major Scale and it's modes at centre stage and treats all other scales as altered forms of that. But this can also be a very good thing for traditional western music where the major scale is dominant and musical notation and even instruments to some extent are designed around it.

One big problem with traditional notation is when it comes to naming chords. eg the notes C E G A. Is that a C6 chord or an Am7 in it's 2nd inversion? With the pitch class system it just becomes 0479. But then you loose information about how it relates to the key of the music.

Also I think it ignores the importance of different inversions of the same chord. Like the change from a minor to a major character for minor seven chord in it's 2nd inversion. This is really important for more complex chords - eg 13th chords which contain every note in the scale... C13, Am13, Em13b9, etc are all spelled 024579E but they have quite different characters when played in their root inversion

I guess no system is perfect.

[Bagatell]

^^^ That is good because it looks really complicated.

Full marks for the work you put in on this.

Thank you sir.

One big problem with traditional notation is when it comes to naming chords. eg the notes C E G A. Is that a C6 chord or an Am7 in it's 2nd inversion? With the pitch class system it just becomes 0479. But then you loose information about how it relates to the key of the music.

Also I think it ignores the importance of different inversions of the same chord. Like the change from a minor to a major character for minor seven chord in it's 2nd inversion. This is really important for more complex chords - eg 13th chords which contain every note in the scale... C13, Am13, Em13b9, etc are all spelled 024579E but they have quite different characters when played in their root inversion

Forget about modes, scales and keys for the moment and try thinking polychromatically for a while.

[salatspinatra]

Looking forward to dive into this; I'll ask some more questions once I do. I've been raised on Roman Numerals, having been a family friend of John Mehegan. And for my own nitpickyness, I've often looked at all the clip color options and wondered "how will this many colors help me organize anything?" Maybe this approach will win out.

[Bagatell]

Some musical numbers and sets.

() {silence}
(0) {single note}
(0,1) {a half step}
(0,2) {a whole step}
3 Number of diatonic scale classes
7 Number of note names (A-G); number of notes in a common scale; number of white keys per octave on a piano;number of scale classes (= 7-note interval sets).
9 Number of scales one note different from the Major scale.
12 Number of notes in the most common equal-tempered scale.
13 Number of common musical keys (C + 1-6 flats/sharps).
21 Number of 7-note diatonic scales (= 7 x 3).
23 Number of elementary 2-fold polychords.
55 Number of chords with a single "1" interval (= F9).
66 Number of 7-note chords (= 7-note scale types).
77 Number of distinct interval sets (= partitions of 12).
245 Number of 7-note triatonic scales (= 7 x 35).
273 Number of notationally-distinct diatonic scales (= 13 x 21).
351 Number of distinct chord types (= JV(12)-1).
462 Number of (7-note) musical scales (= 7 x 66).
2048 Number of «-note scales for all n (= 2 ) .
4095 Number of chords without rotational isomorphism (= 212-1).
6006 Number of notationally-distinct scales (= 13 x 462).


The chart on the PC Relationships Calculator (N.B. calculator not just a chart) is in two columns.
I love the fact that () {silence} is directly opposite (0,1,2,3,4,5,6,7,8,9,T,E) {the chromatic scale}
What's opposite (0,2,4,7,9) {the pentatonic scale} ? (0,1,3,5,6,8,T) {the diatonic scale}

[stringtapper]

Trust me. This is not as complicated as it looks.

No, it's not. But it is more complicated than simply learning traditional tonal theory.

While there are some theorists who have used pitch-class set theory to analyze tonal music (David Lewin and other Neo-Riemannians in particular) the system really is most useful in dealing with non-tonal usage, whether from a compositional or analytical standpoint. One of the main criticisms of using pcs theory in tonal music is that you lose the representation of function between and among chords in a diatonic system. Allen Forte developed pcs theory precisely because of the lack of discernible functions in atonal music. A very comprehensible and relatively generalized system for understanding diatonic theory already exists and has been used successfully for quite a while now and it really isn't as complicated as it looks.

But as a way in for people who have not been exposed to non-tonal music I think it's a good effort.

As a related aside I'm soon going to be releasing an algorithmic polysynth as a M4L device that lets you choose between chords, scales, and pitch-class sets as the underlying pitch collection which can then be automated to create progressions or transformations.

One big problem with traditional notation is when it comes to naming chords. eg the notes C E G A. Is that a C6 chord or an Am7 in it's 2nd inversion?

You mean 1st inversion.

[Bagatell]

Trust me. This is not as complicated as it looks.

No, it's not. But it is more complicated than simply learning traditional tonal theory.

Which is all very well if you are happy with traditional tonal harmony. I'm not trying to sell anything here. Take it or leave.


All I know is that when I saw that line of (0)s down the left hand side of the page I knew where Rameaus fundemenatal bass and George Russells Lydian Chromatic Tonic came from.

[stringtapper]

Which is all very well if you are happy with traditional tonal harmony. I'm not trying to sell anything here. Take it or leave.

I'm just going by the examples you've given in your first post, which are "traditional tonal harmony" and not atonal by any stretch.

All I know is that when I saw that line of (0)s down the left hand side of the page I knew where Rameaus fundemenatal bass and George Russells Lydian Chromatic Tonic came from.

You got Rameau's contention that the most fundamental of progressions is that which moves by fifth and that any other bass progression is merely an abbreviation of such fundamental bass motion all from a line of 0s going down a page? Good for you. I had to read the treatise.

[doghouse]

[Bagatell]

Which is all very well if you are happy with traditional tonal harmony. I'm not trying to sell anything here. Take it or leave.

I'm just going by the examples you've given in your first post, which are "traditional tonal harmony" and not atonal by any stretch.

All I know is that when I saw that line of (0)s down the left hand side of the page I knew where Rameaus fundemenatal bass and George Russells Lydian Chromatic Tonic came from.

You got Rameau's contention that the most fundamental of progressions is that which moves by fifth and that any other bass progression is merely an abbreviation of such fundamental bass motion all from a line of 0s going down a page? Good for you. I had to read the treatise.

We've come a ways from merely trying to help a newbie understand music without reading standard notation haven't we?

Your points are all well taken and if you see no benefit in pitch classes, so be it, but I think I'll be taking a closer look at it.

[crumhorn]

You mean 1st inversion.

Indeed I do and that is what I put originally. Then I got all confused and changerd it for some reason - oh hum.

Some musical numbers and sets.

3 Number of diatonic scale classes

I'd be interested to know the definition of "diatonic scale class"

I always think of diatonic scales as being all the different modes of the major scale.

[Bagatell]

Some musical numbers and sets.

3 Number of diatonic scale classes

I'd be interested to know the definition of "diatonic scale class"

I always think of diatonic scales as being all the different modes of the major scale.

That's what I thought as well.

However in "From Polychords to Polya" Michael Keith defines the term like so -

Quote:
K-atonic interval sets. An interesting type of interval set is one in
which all intervals between 1 and k (inclusive) are represented, for some
k. Such a set is referred to as K-atonic, after the musical term diatonic
which is used for the case k = 2. We refer to k = 3, 4,... as triatonic,
quadratonic, etc.


So diatonic has uses two intervals - half and whole step, whilst triatonic uses three intervals - half step, whole step and minor third. But I suppose as long as we know what the set, scale, mode, chord etc. contains, we can call it what we like.

[The Leveller]

It is nice work, but certainly over complex if you understand basic music theory.