Mathematics and Music

[Robert M]

Tonight, while following links for DX-7 presets, I stumbled across this page:


http://www.maths.abdn.ac.uk/~bensond...ths-music.html


Once there, you will find a link to a book called Mathematics and Music, written by David J. Benson. The author is offering it online as a pdf file, and he says a hard-copy version will be published sometime in 2006.

My own math skills are woefully inadequate for grasping the full measure of this book, but I thought it was be something that other folks on the forum might be interested in (assuming this link hasn't previously been shared, of course).

[Robert P]

Robert,

That's a great link.
Thanks!!

R.

[musical.matthew]

So did you come across some good DX7 presets? I would be interested in those links also...

[newmewzikboy]

wonderful stuff.

I'll let you know more about the section on symetries which is my area of expertise. It appears only a survey.

Mathematics is VERY helpful for me. But I found you need to make your own choices on what is actually useful. And how that fits into your other techniques.

The acoustic math stuff here is nice to look over

[Robert M]

So did you come across some good DX7 presets? I would be interested in those links also...

Yep!

http://www.maths.abdn.ac.uk/~bensondj/html/dx7.html

Go down the page to the Patches section, and there are a few options to choose from.

[Robert M]

Mathematics is VERY helpful for me. But I found you need to make your own choices on what is actually useful. And how that fits into your other techniques.

I tell myself if I had a better grasp of higher math, it would help with understanding music. I'll still read the book (as much as I can manage) for the basic ideas presented.

[newmewzikboy]

Most of the math related to composition has been devoted to set theoretics. It's been worked to death. And it's easy to take it on face value, w/o thought that musical and cognitive understanding isn't necessarily based on being mathematically perfect. In fact, it may be the opposite, in that people are using generalizations when they listen to music not perfect details.

The mathematics for set theory is rather simple. Don't believe what you hear when people talk about how dogmatic and ~~~~like composers of the 60-70's were and those that use it are out of date blabla...Like anything...keep an open mind as gems are found where fools tend to tread. There are aspects that are truly astonishing and useful. And there are more specific parts that are useless and impractical. You can take parts of it in your own way. Finding books on these theories is very hard to do. And most of them are out of date or never get beyond an old school understanding. When you get into the advanced stuff, there is a lot of very powerful - some useful and some not so useful - materials. It just takes self discipline to read through it and filter out what was there for peer review and what is there that is practical from a composers perspective. University dissertations are another great place to get information. Dont believe everything you read. And dont discard everything you read.

[chet reinhardt]

I've been meaning to post something here for a while but the topic has its quirks. I would conjecture that there are more types of mathematics than there are types of music. And the treatments of the different topics are subject to a great deal of variation. So here is a short list of books you might (or might not) want to look at.

Two good qualitative discussions of math and the pursuit of mathematics that have musical applications are: Chaos by James Glieck and Digital Mantras: The Languages of Abstract and Virtual Worlds by Steven Holtzman. Really quite nice.

I like the recreational mathematics of Smullyan and Martin Gardner. Lots of fun.
( see http://en.wikipedia.org/wiki/Raymond_Smullyan) .

Logic programming and automated reasoning might be of interest to some (Automated Reasoning: Introduction and Applications by Wos, Overbeek, Lusk, and Bolye or perhaps Logic for Problem Solving by Kowalski). I personally liked this stuff a lot.

Cliff Jones wrote an interesting book called Software Development: A Rigorous Approach which provides some interesting ideas on denotational semantics influenced methods that can also be used to specify complex systems such as compositions. Or you might find Object-oriented Modelling and Design to be more interesting or useful (Rumbaugh et al) or perhaps Object-oriented Analysis and Design by Booch. Some might say that this is not really math but there is a lot of math that is less clearly specified.

If this stuff is too elementary for you take a look at Topoi: The Categorial Analysis of Logic by Goldblatt. Categorical purists prefer Categories for the Working Mathematician by Maclaine but I like the fact that Goldblatt defines his notations and starts out at set theory. Category theory was constructed to provide an alternative to set theory for the foundation for mathematics.

There is of course a great deal more math of varying sorts and a great many ways of using it to assist in composition (or to using music as a way of understanding mathematics).

Best wishes

Chet

[newmewzikboy]

I have read most of the books you post here. I would say nothing really demonstrates any practical use...including OOD or OOPLA..which isn't so much mathematical but "crisp" logical.

Some of the theories of sets as described by Cone, Morris, Starr, Forte, Rahn, Babbitt would be a good place to start, and probably end too. I'd say there are only a few practical abstracts that are there.

http://faculty.washington.edu/jrahn/w2002musicmath.htm
http://faculty.washington.edu/jrahn/


The problem with mathematical approaches is that is not necessarily how the brain "generalizes" when it understands musical abstraction. Fuzzy based systems and expert systems gear toward this world, but fall short. Ambiguity is a very nice thing when it comes to music...which is why mathematics, with all its discreteness is an impedance mismatch.

Lerdahl is worth reading....although difficult

http://www.amazon.com/exec/obidos/tg...books&n=507846

[chet reinhardt]

Newmewzikboy

To each his or her own.

I''ve made extensive use of scale-invariant self-similarity with respect to the large scale structure of compositions and the Glieck book is certainly sufficient to be the catalyst for that realization.

And even if one skips the equations and just reads the text Goldblatt provides a way of freeing the mind to see relations between structures (considered quite abstractly) that I think has helped me see analogies between quite disparate compositions that I've found useful. And generally I find it more fruitful to think in terms of categories and morphisms between them than in terms of sets.

It is true that I never got around to constructing the system for generating compositions from compact specifications that I once envisioned. But the hard part of that for me was reading and writing midi-files. If I had something that could translate between Prolog clauses and midi I might brush the Cantor dust off some of my old files and see what I can do with the idea.

But generally I think that for a great many people what Herb Simon called the laws of qualitative structure (the ontology of the domain and some general ideas about what sort of things one can do with these ontological objects) is quite sufficient to spark new approaches.

It is true that the approach reflected in my references veers towards the logical and the qualitative rather than in the numerical quantitative direction but I find it to be the more fruitful direction for me. And of course one important aspect of foundational studies is that one can be translated into the other.

As I said before to each his own.

By the way, I've been following your latest set of posts with great interest. You are making a great contribution to the discussion. Keep up the good work.

Best wishes

Chet