zapnspark

Musical Geometry
« on: April 17, 2008, 06:53:26 PM »


bcarso

Musical Geometry
« Reply #1 on: April 17, 2008, 09:05:11 PM »
Yeah, I was just reading the Science article.  This is the second major general-science-mag article of Tymoczko's in the last couple of years I believe.

Just posting the link wouldn't work as you have to be a subscriber, but if anyone has a burning desire to read such inspiring passages as this one:

"Geometrically, a musical object can be represented as a point in  . The four OPTI equivalences create quotient spaces by identifying (or "gluing together") points in  (fig. S3). Octave equivalence identifies pitches p and p + 12, transforming  into the n-torus  . Transpositional equivalence identifies points in  with their (Euclidean) orthogonal projections onto the hyperplane containing chords summing to 0. This transforms  into  , creating a barycentric coordinate system in the quotient (basis vectors pointing from the barycenter of a regular n-simplex to its vertices). Permutation equivalence identifies points in  with their reflections in the hyperplanes containing chords with duplicate notes. Musical inversion is represented by geometric inversion through the origin. Permutation and inversion create singular quotient spaces (orbifolds) not locally Euclidean at their fixed points. C equivalence associates points in spaces of different dimension: The result is the infinite-dimensional union of a series of finite subset spaces (6–8)."

...they are welcome to contact me. (note, some funny symbols that should show above are not reproduced when pasting from Word).

Freq Band

Musical Geometry
« Reply #2 on: April 17, 2008, 10:22:29 PM »
Quote from: "bcarso"


"Geometrically, a musical object can be represented as a point in  . The four OPTI equivalences create quotient spaces by identifying (or "gluing together") points in  (fig. S3). Octave equivalence identifies pitches p and p + 12, transforming  into the n-torus  . Transpositional equivalence identifies points in  with their (Euclidean) orthogonal projections onto the hyperplane containing chords summing to 0. This transforms  into  , creating a barycentric coordinate system in the quotient (basis vectors pointing from the barycenter of a regular n-simplex to its vertices). Permutation equivalence identifies points in  with their reflections in the hyperplanes containing chords with duplicate notes. Musical inversion is represented by geometric inversion through the origin. Permutation and inversion create singular quotient spaces (orbifolds) not locally Euclidean at their fixed points. C equivalence associates points in spaces of different dimension: The result is the infinite-dimensional union of a series of finite subset spaces (6–8)."


This old news. Everything in RED... .I've known since high school.


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bcarso

Musical Geometry
« Reply #3 on: April 18, 2008, 12:11:16 AM »
I am tempted to say "but how does it sound??"  At least one part of me would want to say that.

But I also love math.

Svart

Musical Geometry
« Reply #4 on: April 18, 2008, 11:06:56 AM »
all that math makes me glad I got into EE instead of something that actually uses it..  :green:
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Mbira

Musical Geometry
« Reply #5 on: April 18, 2008, 12:49:37 PM »
That's just what I needed to finally figure out that turnaround to "All the Things You Are"!  Thanks!
Joel Laviolette

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bcarso

Musical Geometry
« Reply #6 on: April 18, 2008, 01:14:14 PM »
Quote from: "Mbira"
That's just what I needed to finally figure out that turnaround to "All the Things You Are"!  Thanks!


 :green:

(helpful as well for blowing on the changes to Stella by Starlight on a single-line instrument without accompaniment and not unwittingly changing key early in the third phrase) :grin:



Yeah, the thing I like* about stuff like this is the omnipresent push to codify and in some cases eviscerate the ability that separates real musicians from wannabes... the ones who wind up writing about the hermeneutics and sociology bla bla of music ("so-and-so whom we've never heard should have been as famous as Beethoven were it not for the power elite of the day" kind of stuff).  The deficiency of which Charles Rosen always uses to skewer and slow-roast the hapless but richly deserving subjects in his reviews.  Namely, he points out that THEY CAN'T HEAR!!


*the sarcasm light is on there

bcarso

Musical Geometry
« Reply #7 on: April 18, 2008, 01:40:04 PM »
Quote from: "Svart"
all that math makes me glad I got into EE instead of something that actually uses it..  :green:


I know a lot of composers.  I even are one sometimes.  Almost all* have expressed an indifference to or outright distaste for math, and some have wondered why in the world a supposedly close relationship between music and math is heard about so often.  Although I have some ideas about it, I don't think I'll be citing the work above in support anytime soon, other than in jest.  Not that it lacks merit.

There are books that are attempting to explore the relationship without quite descending into the maelstrom of orbifolds and such, and they are probably worth reading.  One that I thought might be more explanatory, Ed Rothstein's Emblems of Mind, turns out IIRC to be mostly a paean to the aesthetic beauty of really good maths.

I seem to be about the only person less than thrilled with another of the latest directions, the neurological approach, such as Levitin's This Is Your Brain on Music, or Sacks' more recent Musicophilia.**  But so it goes.


*I don't know many of the dwindling number of academic and likely near-senile serialists, still maintaining that they are avant-garde and Their Way will ultimately prevail.

** Fodor's TLS review expresses some misgivings: http://tls.timesonline.co.uk/article/0,,25364-2650389_1,00.html

zebra50

Musical Geometry
« Reply #8 on: April 18, 2008, 01:44:13 PM »
Quote

Geometrically, a musical object can be represented as a point in  . The four OPTI equivalences create quotient spaces by identifying (or "gluing together") points in  (fig. S3). Octave equivalence identifies pitches p and p + 12, transforming  into the n-torus  . Transpositional equivalence identifies points in  with their (Euclidean) orthogonal projections onto the hyperplane containing chords summing to 0. This transforms  into  , creating a barycentric coordinate system in the quotient (basis vectors pointing from the barycenter of a regular n-simplex to its vertices). Permutation equivalence identifies points in  with their reflections in the hyperplanes containing chords with duplicate notes. Musical inversion is represented by geometric inversion through the origin. Permutation and inversion create singular quotient spaces (orbifolds) not locally Euclidean at their fixed points. C equivalence associates points in spaces of different dimension: The result is the infinite-dimensional union of a series of finite subset spaces (6–8).


Yeah, we were talking about this in the pub on the way from work tonight. Glad it's all sorted out now. I was wondering about the barycentric toroidal Euclidean stuff.

I have to confess, I set off to the studio at 11.30, via lunch at the pub. I just got in. The studio didn't happen!
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bcarso

Musical Geometry
« Reply #9 on: April 18, 2008, 03:09:55 PM »
Since grousing so much I wanted to actually recommend something.

The latest issue of Ploughshares, vol. 33 No. 4, a quarterly out of Emerson College in Boston, has a lot of great stuff.  One standout that is at least peripherally related to this thread is a piece by trombonist James Leigh, "Jazz Below the Water Line", which starts off like this:

"Fifty-six years ago I picked up a musical instrument for the first time with intent to commit jazz."


rafafredd

Musical Geometry
« Reply #10 on: April 19, 2008, 04:42:00 PM »
oh, funy.. Now they want to say they discovered something that freely goes on in the mind of musicians since music is music and man is man. Most good musicians with great ears works synergetically. Now they won´t be able to make it with computer graphics any closer to what goes on in my mind when I close my eyes. And it´s infinite resolution graphics, with infinite resolution 3d axis, and infinite number of collors. One way or another, anyone can see it with a little happy helping hand, if you know what I mean. Or by training, hard training. And I say, it´s much more fun than a cinema display in a concert room will ever be.

What about Scriabin?

If you consider all musical variants, there are infinite equations that could be aplyed to create 3d graphics. I don´t even find their graphics impressive, really. Boring graphics. Most music looks much better, and it´s never the same in one´s mind.

jdbakker

Musical Geometry
« Reply #11 on: April 20, 2008, 01:39:12 PM »
Quote from: "bcarso"
Yeah, the thing I like* about stuff like this is the omnipresent push to codify and in some cases eviscerate the ability that separates real musicians from wannabes... the ones who wind up writing about the hermeneutics and sociology bla bla of music ("so-and-so whom we've never heard should have been as famous as Beethoven were it not for the power elite of the day" kind of stuff).  The deficiency of which Charles Rosen always uses to skewer and slow-roast the hapless but richly deserving subjects in his reviews.  Namely, he points out that THEY CAN'T HEAR!!

*the sarcasm light is on there

In a somewhat similar vein (although in a different field), you may want to read this rant. A touch on the long side, but I suspect many here can sympathize with the point he's making.

JDB.

bcarso

Musical Geometry
« Reply #12 on: April 20, 2008, 02:58:28 PM »
I like that a lot!  What a great teacher the writer must be.

His comments about teaching math can be applied to so many subjects.  His introductory examples using music and painting are good ones.  But I decided I didn't want to do physics for a while after some exceptionally bad teaching late in grade school, which gave the clear impression that all was said and done, and at best one could look forward to just more of the same.

Another friend who had slogged through to get a PhD in physics was actually quite a creative circuit designer.  But he was horrified that he was being an engineer when designing circuits, and that this was somehow just too mundane.

He then determined that he wanted to get way better at music.  How to do this?  Well, go back to school!  He actually re-enrolled at another school as an undergrad, and fought through to get a music degree.  He had to abandon a composition major when it became clear he wasn't gong to cut it, and wound up finishing up with Voice.  At the end of all he confessed to me that his primary motivation was to get better than me (a sad thing to hear).  

I had warned him that an early start in music helped a lot---but he evidently thought that meant an early exposure to rules and codifications, rather than listening and playing and hearing.  He apparently assumed that to be able to play and write you had to have thoroughly embraced music theory, harmony, counterpoint etc., which although I'd done a bit of self-study on, had very little to do with what I wrote or improvised.

Once, at the end of a lengthy and excessive evening, behind substantial alcohol and other herbs and spices, I lapsed and misidentified a simple musical structure in a piece that we were listening to.  I was corrected, and apologized for the lapse---but this guy had a huge Gedankenblitz, a veritable epiphany, and declared me to be a musical idiot savant.  I was too reticent in those days to say F*#$ you!---I'm not an idiot to begin with!  But it was clear he had permanently registered and classified me, on the basis of this rather anomalous evidence, and took great comfort in thinking that his admitted mediocrity and my seeming superiority were not the results of anything over which one had control---it was something genetic, neurological.  He was absolved.


 

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