Thanks for the tip. I was also waiting for this to come out. I'm off to Amazon....

Victor

----- Original Message -----
From: Anthony Palomba <apalomba@austin.rr.com>
Date: Wednesday, March 9, 2011 2:16 am
Subject: Re: [Csnd] Recommended book: A Geometry of Music
To: csound@lists.bath.ac.uk

> I gotta say I am super excited to finally be getting this book too.
> I found some articles about Tymoczko's work years ago but they 
> were lacking in specifics. I can't wait to really start digging into more details. 
 > 
> I agree, it is a truly ground breaking way of representing tonal
> spaces. What I am really excited about is exploring the ability to 
> take other computational geometric forms and project/map them into 
> these chord spaces.
 > 
> I plan on implementing my own python version as soon as I get it.
> 
> 
> 
> 
> Anthony
> 
> 
> 
> 
> On Tue, Mar 8, 2011 at 7:52 PM, Michael Gogins <michael.gogins@gmail.com> wrote:
 > I've received my copy of Dmitri Tymoczko's new book, _A Geometry of
>  Music: Harmony and Counterpoint in the Extended Common Practice_
>  (Oxford and New York: Oxford University Press, 2011).
 > 
>  In my view, this is a very important book in music theory, and I
>  highly recommend it to any computer music person with any sort of
>  interest in anything like chords, scales, and voice-leading.
 > 
>  I find that the work of Tymoczko (and his colleagues Clifton
>  Callender, Rachel Hall, Adrian Childs, etc.) in elaborating a
>  geometric theory of chords and voice-leadings facilitates generative
>  composition in ways that other formal or mathematical approaches to
>  music theory, such as the generative grammar of Jackendoff and
>  Lerdahl, simply do not (at least, not for me). I have composed a
>  number of works based on generating movements in chord spaces, either
>  directly moving chords as points in multi-dimensional spaces, or
>  applying neo-Riemannian operations such as the Generalized Contextual
>  Group of Fiore and Satyendra as implemented in such chord spaces, and
>  I presented a paper on this work of mine at the 2006 ICMC.
 > 
>  The great thing about the geometric approach is its ability to greatly
>  simplify and easily automate operations upon pitches and chords,
>  across various scales of musical structure, and including recursive
>  operations. It helps a great deal that the mathematics involved is not
>  very complicated once some quite basic principles of group theory and
>  quotient spaces are assimilated -- no need to learn category theory or
>  differential geometry! The required principles are presented with
>  exemplary clarity in Tymoczko's book. Furthermore, operations can be
>  efficiently implemented (for example, finding a well-formed
>  voice-leading by selecting the shortest of multiple paths through
>  multi-octave chord space is of O(log N) complexity and can be
>  implemented in a page or so of Python, whereas voice-leading by
>  formalizing the rules of _Gradus ad Parnassum_ is I guess of O(C^N)
>  complexity and takes multiple pages of code).
 > 
>  Just as Hiller and Isaacson, and Xenakis' sieves, opened up the use of
>  stochastic processes for algorithmic composition on various scales of
>  musical structure, and thus brought considerable variety and power
>  into atonal algorithmic composition, so operations in music spaces of
>  varying degrees of abstraction open up a good chunk of the resources
>  of tonality and extended tonality for algorithmic composition.
 > 
>  --
>  Michael Gogins
>  Irreducible Productions
 > http://www.michael-gogins.com
>  Michael dot Gogins at gmail dot com
 > 
 > 
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 > 
 > 
 

Dr Victor Lazzarini, Senior Lecturer, Dept. of Music,
National University of Ireland, Maynooth



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