Author Topic: Pitch Class Sets  (Read 5971 times)

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whitebark

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Pitch Class Sets
« on: December 17, 2017, 12:14:53 PM »
A Pitch Class Set is a generalization of the idea of a chord, expanding it to include all octave transpositions and inversions. Tables of PC Sets provide an efficient way to classify chords of all types in a clear and efficient way.  Composers find PC Sets useful because using notes within a PC Set can give the resulting music a distinct sound.  For a good intro on PC Sets, be sure to watch Alan Belkin's Youtube videos on the topic (Modern Harmony 8b).

For this exercise, write a short work (16 measures or so) using a small PC Set, one with a "normal form" of 3 or 4 notes.

Here's my exercise using a 4 note PC Set with a Forte Number 4-16:

https://www.dropbox.com/s/dipy1o8kja9vuc6/Pitch%20Class%20Set%20Exercise.mp3?dl=0
https://www.dropbox.com/s/746qr3d1jjo2riz/Pitch%20Class%20Set%20Exercise.pdf?dl=0

In my example score, I have indicated the lowest note of the transposed Normal Form used in various spots in the music. This note is not necessarily the root note of the associated chord.

Have Fun!
Jay
« Last Edit: December 17, 2017, 02:25:41 PM by whitebark »

Jerry Engelbach

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Re: Pitch Class Sets
« Reply #1 on: December 17, 2017, 02:45:48 PM »
Whew, that's a tough one, Jay. Nice exercise.
 
You managed to get in 11 of 12 pitch classes. Why not go the extra measure and include "D"?
 
Cheers,
Jer
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RJB54

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Re: Pitch Class Sets
« Reply #2 on: December 18, 2017, 10:33:21 AM »
This is an interesting challenge that I hope others will explore. I won't because this is one of the components used in most of my compositions. In particular I refer you to my String Quartet #1 which is particularly germane as the vast majority of the content is based similar pitch cells.
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whitebark

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Re: Pitch Class Sets
« Reply #3 on: December 18, 2017, 11:18:06 AM »
Whew, that's a tough one, Jay. Nice exercise.
 
You managed to get in 11 of 12 pitch classes. Why not go the extra measure and include "D"?
 

Sorry I missed D, Jer!  If you can get past the terminology, this exercise isn't all that tough.

-Jay

Jerry Engelbach

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Re: Pitch Class Sets
« Reply #4 on: December 18, 2017, 04:23:16 PM »
Sorry I missed D, Jer!  If you can get past the terminology, this exercise isn't all that tough.

-Jay
Yeah, I did have to do a bit of Googling for "4 note PC Set with a Forte Number 4-16."

Not part of my normal vocabulary.

Cheers,
Jer
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whitebark

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Re: Pitch Class Sets
« Reply #5 on: December 19, 2017, 04:34:46 PM »
In particular I refer you to my String Quartet #1 which is particularly germane as the vast majority of the content is based similar pitch cells.

Interesting!  I'd like to listen to your string quartet, but can't find any links to it.

Jay

RJB54

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Re: Pitch Class Sets
« Reply #6 on: December 19, 2017, 04:56:01 PM »
Currently it's in Page 5 of Works In Progress Senior named String_Quartet_01(For Real). I really should do a final review and move it into the completed works section  ;D.

Here is a link to it: http://www.composeforums.com/index.php?topic=1115.0
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Jerry Engelbach

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Re: Pitch Class Sets
« Reply #7 on: December 21, 2017, 08:22:31 AM »
Robert,
 
Outstanding! Thanks for providing a link back to that.
 
Cheers,
Jer
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Jerry Engelbach

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Re: Pitch Class Sets
« Reply #8 on: December 21, 2017, 08:30:58 AM »
Jay,
 
I like your exercises. I hope I got this right.
 
I used Forte 4-17: 0347. For structure I did an 8-bar pattern in strings with four pitch classes, then appended it in retrograde and repeated the whole thing a few times, then added a freeform clarinet solo and tweaked the whole thing a little.
 
It's pretty rough, but I enjoyed being restricted by the notes available.
 
Score:
https://www.dropbox.com/s/4alsky111v7wdih/Pitch%20Class%20Exercise%2001a%20with%20Strings.pdf?dl=0
 
Audio:
https://www.dropbox.com/s/g9ti2izafupnkev/Pitch%20Class%20Exercise%2001a%20with%20Strings.mp3?dl=0
 
Cheers,
Jer
Finale 26
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whitebark

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Re: Pitch Class Sets
« Reply #9 on: December 21, 2017, 04:09:02 PM »
That was a fun little exercise with a "bluesy" pc set, Jer! Looks like you did it right. 

-Jay

Patrick O'Keefe

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Re: Pitch Class Sets
« Reply #10 on: December 21, 2017, 04:17:48 PM »
A few years ago my teacher had me playing around with pitch-class sets.  I suspect I missed the a lot of the theoretical significance, but it seemed like a handy way to organize a cell of notes - horizontally or vertically - without need for harmonic implications.  I'm sure the interval vector has value beyond measuring "how interesting" a specific pitch-class set is but I never got into it.  And I'm sure analyzing the sequence of applied transformations provides some kind of useful information but I've always been guilty of relying on my ears instead.  And I never understood the musical significance of the Forte numbers even in those rare cases when I know the Forte number.

I wrote a set of 4 piano pieces using the pitch-class set [0,1,3,4,8].  (I know that 3 and 4 note sets are more typical.)  For anybody that really cares, that's the Forte number 5-z17 (according to Wikipedia).  I've unfortunately lost all my notes (so to speak) on those pieces. 

Since I am basically a tonal composer I then took the very tonal pitch-class set [0,2,5,8] and wrote a couple pieces.  If I did my homework correctly, [0,2,5,8] is the "best normal order" for a diminished 7 chord so I called these "Diminished Expectations" or in full "Amber Sets of Diminished Expectations" (because amber is fossilized pitch).  The pieces are for vibraphone, bassoon, bongos, and conga drums.
https://app.box.com/s/q5sshuir9a7ztj73d8ndohg275uz9k03

Some day I will rewrite the 2nd and complete the collection with a 3rd piece.


RJB54

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Re: Pitch Class Sets
« Reply #11 on: December 21, 2017, 06:03:54 PM »
There's no musical significance to the Forte numbers. They are organizational only. The number before the dash indicates the cardinality (the number of pitches) in the set-class. The number after the dash is a sequentially assigned number given to each set-class of that cardinality based upon a formula established by Forte. The Z in some class names indicates that this class has the same interval vector as another class.

It is a convenient, objective, method of identifying all possible pitch collections allowing for theoretical discussion and compositional use in an organized and controlled manner.

The Forte numbers can also be used in a discussion of tonal entities as well since the Forte numbers label all possible pitch collections including diatonic ones.

An excellent example of using the Forte numbers for analysis of atonal music is Janet Schmallfeldt's book on Wozzeck where melodic and harmonic relationships are identified and discussed using the Forte numbers.
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RJB54

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Re: Pitch Class Sets
« Reply #12 on: December 21, 2017, 06:13:30 PM »
Jay,
 
I like your exercises. I hope I got this right.
 
I used Forte 4-17: 0347. For structure I did an 8-bar pattern in strings with four pitch classes, then appended it in retrograde and repeated the whole thing a few times, then added a freeform clarinet solo and tweaked the whole thing a little.
 
It's pretty rough, but I enjoyed being restricted by the notes available.
 
Score:
https://www.dropbox.com/s/4alsky111v7wdih/Pitch%20Class%20Exercise%2001a%20with%20Strings.pdf?dl=0
 
Audio:
https://www.dropbox.com/s/g9ti2izafupnkev/Pitch%20Class%20Exercise%2001a%20with%20Strings.mp3?dl=0
 
Cheers,
Jer

Nice work exercising the pitch set.
Information is not knowledge. Knowledge is not wisdom. Wisdom is not truth. Truth is not beauty. Beauty is not love. Love is not music. Music is THE BEST.
Frank Zappa

RJB54

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Re: Pitch Class Sets
« Reply #13 on: December 21, 2017, 06:13:50 PM »
Robert,
 
Outstanding! Thanks for providing a link back to that.
 
Cheers,
Jer

Thanks.
Information is not knowledge. Knowledge is not wisdom. Wisdom is not truth. Truth is not beauty. Beauty is not love. Love is not music. Music is THE BEST.
Frank Zappa

Jerry Engelbach

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Re: Pitch Class Sets
« Reply #14 on: December 22, 2017, 04:04:15 AM »
Nice work exercising the pitch set.
Thank you, Robert.
 
I'd never heard of Forte numbers before. Obviously, in playing tonal jazz I'm restricted by the underlying chord structure (although I can choose to play "inside" or "outside"). The Forte method of organization seems to me another interesting way to limit the notes and give an overall coherence to the music, especially if it's atonal.
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