[Dixielandjazz] Prettiest Melody

Stephen G Barbone barbonestreet at earthlink.net
Mon Mar 2 19:16:58 PST 2009

> John McClernan <mcclernan1 at comcast.net> wrote:
> ... or was the chord progression of the first part of "New Orleans"
> stolen from the bridge of "You Took Advantage Of Me" or "Wrap Your
> Troubles In Dreams" ?  Is this a "chicken-or-egg" quandary?

Hey John (who is a good music teacher as well as a good OKOM tubist)

You and other curious minds may be interested in the theory, or is it  
now fact, that we've all been stealing the same small set of chord  
progressions from the classical composers circa 1700 to 1900,  
according to Princeton music professor Dmitri Tymoczko. Surf his web  
site listed in the below article for a fascinating look at how just  
about all Western music genres have used a small fraction of all the  
chords available. Complete with examples to click on.

That's why tunes like "New Orleans", and say, "Fly Me To The Moon",   
can be made to sound almost exactly like a Bach two part invention  
between solo horn and piano, or a three part Bach invention if you add  
the bass, in the hands of improvising jazz musicians. And if it's  
Bach, I sure like it.

Rio Clemente and I had a fling with that on "New Orleans" at a jam  
session a couple of years ago.


Friday, Jan. 26, 2007 - TIME MAGAZINE - by Michael D. Lemonick
The Geometry of Music

When you first hear them, a Gregorian chant, a Debussy prelude and a  
John Coltrane improvisation might seem to have almost nothing in  
common--except that they all include chord progressions and something  
you could plausibly call a melody. But music theorists have long known  
that there's something else that ties these disparate musical forms  
together. The composers of these and virtually every other style of  
Western music over the past millennium tend to draw from a tiny  
fraction of the set of all possible chords. And their chord  
progressions tend to be efficient, changing as few notes, by as little  
as possible, from one chord to the next.
Exactly how one style relates to another, however, has remained a  
mystery--except over one brief stretch of musical history. That, says  
Princeton University composer Dmitri Tymoczko, "is why, no matter  
where you go to school, you learn almost exclusively about classical  
music from about 1700 to 1900. It's kind of ridiculous."

But Tymoczko may have changed all that. Borrowing some of the  
mathematics that string theorists invented to plumb the secrets of the  
physical universe, he has found a way to represent the universe of all  
possible musical chords in graphic form. "He's not the first to try,"  
says Yale music theorist Richard Cohn. "But he's the first to come up  
with a compelling answer."

Tymoczko's answer, which led last summer to the first paper on music  
theory ever published in the journal Science, is that the cosmos of  
chords consists of weird, multidimensional spaces, known as orbifolds,  
that turn back on themselves with a twist, like the Möbius strips math  
teachers love to trot out to prove to students that a two-dimensional  
figure can have only one side. Indeed, the simplest chords, which  
consist of just two notes, live on an actual Möbius strip. Three-note  
chords reside in spaces that look like prisms--except that opposing  
faces connect to each other. And more complex chords inhabit spaces  
that are as hard to visualize as the multidimensional universes of  
string theory.

But if you go to Tymoczko's website http://www.music.princeton.edu/~dmitri/ 
   you can see exactly what he's getting at by looking at movies he  
has created to represent tunes by Chopin and, of all things, Deep  
Purple. In both cases, as the music progresses, one chord after  
another lights up in patterns that occupy a surprisingly small stretch  
of musical real estate. According to Tymoczko, most pieces of chord- 
based music tend to do the same, although they may live in a different  
part of the orbifold space. Indeed, any conceivable chord lies  
somewhere in that space, although most of them would sound  
screechingly harsh to human ears.

The discovery is useful for at least a couple of reasons, says  
Tymoczko. "One is that composers have been exploring the geometrical  
structure of these maps since the beginning of Western music without  
really knowing what they were doing." It's as though you figured out  
your way around a city like Boston, for example, without realizing  
that some of your routes intersect. "If someone then showed you a  
map," he says, "you might say, 'Wow, I didn't realize the Safeway was  
close to the disco.' We can now go back and look at hundreds of years  
of this intuitive musical pathmaking and realize that there are some  
very simple principles that describe the process."

That's likely to help both scholars and teachers, he argues. By  
showing how compositions of various styles move through his orbifold  
spaces, says Tymoczko, you can see how different styles of Western  
music relate to each other and evolve. Tymoczko's maps can also be an  
aid to composers, says Cohn. Most have a favorite corner in orbifold  
space, a set of related chord types that they tend to explore over and  
over in different ways. Venturing into a different part of space can  
be tough; you have to learn your way around a whole new auditory  
neighborhood. You can do that intuitively by wandering around and  
seeing where you get to. But with the maps, you can plot a route that  
you know in advance will make some sort of sense.

That doesn't mean you can program a computer with Tymoczko's orbifold  
maps and have it spit out beautiful compositions. "I don't want to  
sell these maps as the royal road to composition," he warns. "They  
don't substitute for the hard work of learning how to move notes  
around." But they can help show when a new idea is promising and when  
it will probably lead to a dead end. "They might make an O.K. composer  
good," says Tymoczko, "but they won't make a good composer great."

More information about the Dixielandjazz mailing list