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Challenges, Puzzles, and Exercises => Exercises => Topic started by: whitebark on December 17, 2017, 12:14:53 PM

Title: Pitch Class Sets
Post by: whitebark 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
Title: Re: Pitch Class Sets
Post by: Jerry Engelbach 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
Title: Re: Pitch Class Sets
Post by: RJB54 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.
Title: Re: Pitch Class Sets
Post by: whitebark 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
Title: Re: Pitch Class Sets
Post by: Jerry Engelbach 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
Title: Re: Pitch Class Sets
Post by: whitebark 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
Title: Re: Pitch Class Sets
Post by: RJB54 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 (http://www.composeforums.com/index.php?topic=1115.0)
Title: Re: Pitch Class Sets
Post by: Jerry Engelbach on December 21, 2017, 08:22:31 AM
Robert,
 
Outstanding! Thanks for providing a link back to that.
 
Cheers,
Jer
Title: Re: Pitch Class Sets
Post by: Jerry Engelbach 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
Title: Re: Pitch Class Sets
Post by: whitebark 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
Title: Re: Pitch Class Sets
Post by: Patrick O'Keefe 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.

Title: Re: Pitch Class Sets
Post by: RJB54 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.
Title: Re: Pitch Class Sets
Post by: RJB54 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.
Title: Re: Pitch Class Sets
Post by: RJB54 on December 21, 2017, 06:13:50 PM
Robert,
 
Outstanding! Thanks for providing a link back to that.
 
Cheers,
Jer

Thanks.
Title: Re: Pitch Class Sets
Post by: Jerry Engelbach 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.
Title: Re: Pitch Class Sets
Post by: RJB54 on December 22, 2017, 11:08:29 AM
Forte came up with his system to address a real need in analyzing non-diatonic music. There were all kinds of terminology in play often using variants of diatonic terminology. As I said, the Forte names are nice and abstract and the rules for merging pitches into set classes are objective and not subjective. There are those, myself included, who feel that his method is a little too objective in that some feel that musical ramifications are ignored in his formulas.

The classic example is set class 3-11 ( I think) where Forte's theory merges the pitch set for the major and minor triads into the same set class, thus saying that these two pitch collections are exactly the same, which, of course, is not really true. My way of dealing with this issue is by incorporating the concept of a subclass within Forte's class, one subclass for the prime form and one for the inversion. Thus, one can, when desired, refer to entities with differing musical purposes using my extension to Forte's naming scheme.
Title: Re: Pitch Class Sets
Post by: Jerry Engelbach on December 22, 2017, 01:52:26 PM

I appreciate the explanation.

No question, I get the impression from your music that you know exactly what you're doing.
 
I know of course that theory is what explains the music rather than creates it. One can use what one needs from the theory without obeying it as a set of preordained rules.
 
For the purpose of learning, however, one does exercises that treat it as if it were just that.
Title: Re: Pitch Class Sets
Post by: EdSharpe on March 10, 2020, 11:14:24 PM
I apologize for being late to the party.  I was reading through some of the older posts when I came across this one.  And I though; this was a kool exercise/challenge and though I would give it a ago.  So I lookup Forte numbers and found that Wikipedia  has a list of pitch-class sets (https://en.wikipedia.org/wiki/List_of_pitch-class_sets (https://en.wikipedia.org/wiki/List_of_pitch-class_sets)) so I start looking through them to find an interesting one to use when I remembered I had serendipitously written a piece using the Forte 5-3B pitch-class back in 2005.   And in fact I was not even thinking out things like pitch class when I wrote it, only some time afterwards I realized it fit into a single pitch class.

Unlike the previous examples in this thread I did not use any transpositions of the pitch-class, the entire piece consists of just the five notes {A Bb C Db D} and in face the D natural only occurs once at the end of the piece.  So up until then the piece is based on the 4-3 Forte pitch-class.  But I said, this was all in hind sight.     

Being thee and half minutes long the piece is a bit longer than your constant.  It also has no bar lines or time signature and rhythms are not precisely notated. 

The piece: Heath Death of the Universe is for a solo Bass Clarinet. 

Score:  https://www.scoreexchange.com/scores/38070.html (https://www.scoreexchange.com/scores/38070.html)

MP3: https://soundcloud.com/ed-w-sharpe/the-heat-death-of-the-universe (https://soundcloud.com/ed-w-sharpe/the-heat-death-of-the-universe)

Video:  https://www.youtube.com/watch?v=--4Fs9ZEkaE (https://www.youtube.com/watch?v=--4Fs9ZEkaE)

The recording is of bass clarinet part being feed through a tape-echo plug-in causing notes to be repeated, elongated, and sounding together even though they were not played at the same time.  If you do listen to it I would recommend head phones or a system with good stereo separation as the echos and repeats are moved around the sound field. 

EWS
Title: Re: Pitch Class Sets
Post by: RJB54 on May 02, 2020, 10:30:08 AM
Ed, a very interesting piece. I really enjoyed the sonic landscape.