View Full Version : Sets and composition

01-26-2007, 08:30 AM
I studied composition a long, long time ago and have just come back to music. In reading analysis of some compositions, I've finding a description that I am not familiar with - a description of sets. For instance, a referral to Bartok as set {0,1,4} and set {}.

What does this mean? I suspect that it's describing intervals, but does it, in the first example, describe the tonic, major second, subdominant? The tonic, minor second, minor third? Or something else entirely? I hate being so ignorant.

Thanks in advance,

01-26-2007, 09:02 AM
I have not heard of this either. What is the source of your analyses? It would be easier to understand what "set" means in your question if we could read it in context.

The only music that I know that is described in sets would be serialism (twelve-tone). It was devised as a mathematical language to write music. It had specific rules which included sets and subsets (both tonal as well as rhythmic). Bartok is early 20th century and most probably the analyses would have been on a piece he wrote in that style. I'm only conjecturing here since I don't know the context of your question.

Maybe some of the forums other members will know the answer better than I.

You might move this question over to the General Discussion Area where more of the members would see it!

01-26-2007, 09:15 AM
Of course I've already lost the link to the Bartok reference, but here's one to Chinese composer Luo Zhongrong:

Luo tries to maximize the use of different pentatonic pitch-class sets--i.e., the three pentatonic tetrachords [0247], [0257], and [0358] and four pentatonic trichords [024], [025], [027], and [037]

(quoted material is from http://goliath.ecnext.com/coms2/summary_0199-1832542_ITM)

It is all in reference to serial music. I'm assuming that the first reference is to tonic, major second, fourth and seventh, but I don't know for sure.

01-26-2007, 12:19 PM
It could be the notes of a chromatic scale. Assuming it is in serial form a matrix is set up with notes assigned thus:

C C# D D# E F F# G G# A A# B
0 1 2 3 4 5 6 7 8 9 10 11

Then [0247] would be C, D, E, G respectively. I will look at the link you put in and if I see anything that rings a bell for me, I will respond again.

01-26-2007, 12:32 PM
For a good description of how Chinese scales were crafted mathematically, check ou this web page:


It compares the tempered scale of western culture with that of the chinese.

01-26-2007, 02:43 PM
Maybe this
"Set Theory Primer for Music"
can be of some help:


Could recommend some books if you are interested.


01-26-2007, 02:52 PM
Thank you - the sets theory page seems to answer the question - they're counting semitones.

Yes, I'd like to know of some books.

01-27-2007, 08:17 PM
I would recommend the following books (in this order)

1. Introduction to Post-Tonal Theory Third ed. by Joseph N. Straus
Very good primer, contains a lot more than pitch class theory.

2. Basic Atonal Theory by John Rahn
Out of print. Find it at www.bookfinder.com (http://www.bookfinder.com)

3. The Structure of Atonal Music by Allen Forte
Advanced, best to read the other books first.


01-27-2007, 08:43 PM
Allen Forte's "The Structure of Atonal Music" (Yale, 1973) is
pretty much a classic in books on Pitch-Class Theory.

The basic idea is that if you can label every possible combination
of the 12 chromatic pitches (pitch-classes), you are then in a position
to start analyzing the relationships between the sets, and hopefully
to gain insight into the inner workings of compositions that had previously
been difficult to analyze using traditional methods.

It was sort of a musical version of the Human Genome Project and was
very popular in the 60's and 70's. It's very rational (some would say too
much so) and therefore very teachable. However, it's not for the faint of heart.

Here's a random sentence from a 1970's music theory magazine (Perspectives
of New Music)....make sure you're seated....

"If S={(t,x),(t=x),(t+1,Y),(t+2,z),(t+3,x),(t+4,y),(t+ 5,z)} where for each member (t,x) of S, (t,x) is a quale-complex in which t is a time-order position and x is a pitch quale, and there exist pitch functions A, B, and C such that x is a member of A, y is a member of B, and x is a member of C (no commitment is made to their identity or non-identity), the we can define a subset-predicate R such that......[sentence goes on another 5 lines]"

- k

01-28-2007, 02:05 PM
Ha. I finished music school in 1971, and I remember my professors saying that what was then called New Math (sets) was beginning to be used in musical analysis. I guess I just missed it. In fact, we referred to tone rows as sets, but wrote them down as note names, not numbers.

I'll see if I can find the books through a library - there may be more than I really want to know. It strikes me that people who analyze works of art
sometimes take their analysis to levels never considered by the artist.