View Full Version : Set Theory -- Accidental Discoveries

Bongo Boy
10-30-2002, 11:38 PM
Elsewhere at iBreathe szulc (James) casually mentioned 'set theory' while talking another topic. At the time I just thought this was a general reference to mathematical set theory, and moved on.

But, while rooting around the 'net to find something totally unrelated, I ran into Set Theory as a music topic--who da thunk?

If you're interested, please visit the following URL:


Without even getting into set theory at all, you may find some interesting music-related factoids here.

11-04-2002, 10:05 AM
Hi Bongo,

I can't seem to load this page. I tried it a few times .... well, I give it another shot later on.


Bongo Boy
11-05-2002, 12:41 AM
I tried it again just now, using the link above. It worked, eventually--it was very, very slow coming up. Perhaps the site is having some troubles. The following site has some of its own material plus many other links.


11-05-2002, 09:02 AM
wow, cool, very interesting - lot's of information on this page. This will keep me busy for a while :D



Bongo Boy
11-07-2002, 04:27 AM
Originally posted by Guni
This will keep me busy for a while :D

Good. Several of us were getting concerned that you might be slacking off a bit. :)

12-04-2002, 10:15 PM
I just spent about 40 minutes in that link.
It's covers a lot.
Great link, Bongo.

12-04-2002, 10:38 PM
When I speak of set theory I am usually referring to it in the strict mathematical sense. I also am thinking in terms of Unions Intersections, Universal sets and Subsets. The other thing I am thinking of is Combinatorics permutations of sets and combinations of sets.
For instance the Universal Set of Notes (in western Music) is the Chromatic Scale, a Sub set of this is The C major Scale, a Sub Set of this is the C Major Chord a Sub Set of this is the Note C. C is a member of the Universal Set (By definition) it is also a member of the Set Called the C Major Chord. The intersection of the C Major Scale and The F Major Scale is the Hexatonic Scale with the Following Notes (C D E F G A ). The intersection of the C Major G Major and F Major Scales is the C Major Pentatonic Scale (C D E G A). I could ramble on about this for hours... but you get the idea.

Bongo Boy
12-04-2002, 11:22 PM
Okay, so my first impression was right, then, and not a mistake at all. This is intriguing. The obvious implication then is for key changes, at the very least, and the consequent implications for chord progressions.

Where you have a scale that is the intersection of two others, for example, have you seen examples where it looks like that fact was actually used in a composition--that is, where the music moves from A to A-intersection-B to B as a transitional device?

It seems like being able to determine if this was actually happening would be hard--determining that it was intentional would be nearly impossible.

12-04-2002, 11:58 PM
Don't get hung up on this one example I have shown. Set Theory can be applied to almost every facet of music.

12-06-2002, 02:38 AM
Here is a very good site for music theory, and you can download this little program that can help u with recognition of intervals, chords, and scales etc, and many more things...


12-08-2002, 03:29 PM
This link has some incredible information, I could spend years assimilating all of this information. I especially like the Bach Anaylsis. This is a great link and set of links. For anyone intereested in studying the mathematical basis for composition this is the 'Holy Grail'.

12-08-2002, 07:00 PM

yeah - some amazing resource! Bach analysis is really good. I'll take my time to dig into that to grasp the point in detail.