Group+Theory+and+Scales

Group Theory and Music Chris Deuchars Mus 175

I was both surprised and interested when we were introduced to the idea of looking at tonality through Group theory. For me, questions arise instantly: What Exactly is a Group again? Does Music Fit the definition? Does that lead us to new understanding, or anything else that we didn’t know before? I decided that I would take advantage of my procrastinating and research a subject that no one in the class has done yet.

In Short, in Math, a Group is something that comprises a set and an operation. The Set and Operation must satisfy some conditions in order to be a group. Groups have certain properties, that allow us to work with them; an Inverse, Identity, Homomorphism, Subgroups, Co-sets, etc. Groups are often used to represent. If you want to know more, read up: [] []
 * A Group:**


 * Math Set Theory vs. Music Set Theory:**

Wikipedia seems to play this down, saying ” musical set theory is often thought to involve the application of mathematical set to music, there are numerous differences between the methods and terminology of the two…”and “Musical set theory is best regarded as a field that is not so much related to mathematical set theory, as an application of combinatorics to music theory with its own vocabulary. The main connection to mathematical set theory is the use of the vocabulary of set theory to talk about finite sets.” []

On the other hand I found a page by John Baes, a mathematical physicist from UCR who definitely considers musical notes a to be the group of integers mod 12 or Z/12 He then does some proofs / derivations and talks about how since this works for notes, it will work for chords, and goes into other groups working on triads Major and minor. []. This guy’s page is pretty cool. I spent Way too much time here.

Generated collections, diatonic scales; scales can be formed by repeatedly adding a constant interval, in the case of the diatonic, the perfect fifth. [] There are other scales that can be generated from equal tempered scales with different modular bases. These scales could be new material for composers to use. []?
 * What does this lead to?**
 * Balzano and Zweifel: Another Look at Generalized Diatonic Scales.**

There is an entertaining page that I would like to share that claims that Music Group Theory allows groups whose music is substantially the same to be lumped together in and appraised and reviewed collectively. : []
 * And for that 90% of what’s on the internet that’s crap**.: