| DoubleHexachordalThm | The
hexachordal theorem is twice true for general topologic compact groups…
Since there are two kinds of intervals (left and right), there are two
versions of the theorem, not one ! But only one way to compare the
interval contents of a subset and its complement. |
| Generators of a scale | The
major scale is generated either by ascending fifths or by descending
fourths. But some scales may have more than two generators. I explain
among other things while the number of generators can never be 14...
Other results include infinite generated scales, e.g. {n x mod 1 }. |
| Finite groupes of rational spectral units. |
These esoteric beings, spectral units, are bridges between homometric
sets (like the famous (0 1 4 6) and (0 1 3 7) pc-sets). A little part
of the mystery is unveiled as the finite groups of rational spectral
units are hereby described and classified. |
| DFT vs JSB | On Music Theory Online, june 2009.
How Discrete Fourier Transform enables to compare transpositional
qualities of temperaments among major scales, thus perhaps settling the
dispute over which was the "good temperament" favored by JS Bach. |
| Fourier again | A round up of applications of the DFT in musical analysis. Given for the SMT metting, Nashville 2008. |
| More Vuza canons | Following
recent ideas by Matolcsi, all Vuza canons for n=120 and n=144 have been
found. Given in Pisa in 2008, published since in JMM's special issue on
Tiling Problems. |
| Berlin 2007 |
A
talk on Discrete
Fourier Transform and how it encapsulates most of the musically
relevant information about subsets of Z/cZ; developing an idea of Ian
Quinn, pursuing David Lewin's work. |
| Fourier Oracles for Computer-Aided Improvisation |
About Fourier transform and real-time grooving of scales or rhythms. ICMC
2006, New Orleans. A real-time implementation was shown by Thomas Noll at the 2009 SMCM congress in Yale. |
| vulgarisation.nb
|
Vulgarisation talk about rhythmic canons. Close to presentationCanons.nb |
| Autosimilar melodies |
A fascinating
notion discovered by Tom Johnson: autosimilar melodies,
as shown during the colloque Mélodie
organized by the SFAM (october 2006). In french. |
| Autosimilar melodies |
Same thing in more detail (MaMuX, october 2006). |
|
|
| typeIIIMEsets |
Solution of a conjecture by Norman Carey about type III ME
sets (some kind of generated scales). With a pretty
movie alongside the notebook. |
| Chicago
|
A conference for the
'Fall session 2004' of AMS, in Evanston (Illinois) with previously unknown correlations between Vuza
canons and Fuglede's conjecture. No paper, but the slideShow
(Keynote format, zipped, for MacOS only) is fine. There is a Powerpoint version too. |
| Cyclotomic canons |
Talk
for ICMC, Barcelona 2005: applications of
cyclotomic polynomials for musicians, in software OpenMusic. |
| simpleVuzaAlgo.nb
|
Implementation of a recent and simple algorithm by Frank
Jszederewsky, building acyclic canons (aka RCMC, or Vuza canons).
Included in canonCrawler. |
| Wild.nb
|
Another (glutton) algorithm, very simple, yet effective, from canadian
Jonathan Wild, for tiling with a 3 note motif and its retrograde version. |
| canonsJuly05.pdf |
Conference for musicians: DIY rhythmic canons. Little or no maths. |
| canonsForGeeks.pdf |
The other side of the
coin: all out on mathematical
properties (Galoisian theory of finite fields,
spectral
conjecture). |
| GrazSlideShow.nb
|
A large file (1608 ko)
of a talk (slideShow) in Graz
colloquium, may 2004. MathReader required. |
| Graz.pdf
|
Paper from the same
conference in Graz. Mostly mathematic
stuff. |
| IrcamDiapo.nb
|
(in french) Slideshow of
a recent conference (january 2004)
in Ircam, about
computing new canons and especially Vuza canons not obtainable by
Vuza's algorithm. MathReader required. |
| nouveaux
Vuza canons |
(in french)
An abstract of above item, but in html (about new Vuza canons). |
| someNewCanons.nb
|
Same in english.
MathReader. |
| someNewCanons.pdf
|
idem, in .pdf |
| midiFiles
|
Midi files for diverse
canons. |
| frenchRésumé |
A paper for la
Gazette des
Mathématiciens, a
good specialized revue. Summarizing all
the connections I have found between canons and mathematics of tiling
the line. |
| Musica.m |
Mathematica package for
exporting Midi files. Required for
some
of my routines, for instance canonToMidi.
|
| Musica.nb |
A file explaining the
above package Musica.m. |
| presentationCanons.nb |
An elementary (I hope
;) ) slideShow about rhythmic canons.
MathReader. |
| prezZürich.bin
|
Perhaps an unusual file
format for this slideShow
(AppleWorks…) of
a conference in Zürich. Right-click (or control-click sous
MacOS)
for download.
I promise I'll translate to another format should anyone ask nicely ;-)
|
| zurichepos.pdf
|
Paper after MaMuTh
colloquium in Zürich (november 2003).
Published by Epos
in a valuable reference book. |
| Tiling problems in Music Composition |
Presented
in ICMC 2002, Göteborg. |
|
|
| vuzaAlgoproduced.nb |
All acyclic canons
produced by Vuza's algorithm with period
less than 216. |
| canonCrawler.nb
|
This
precious notebook includes most of the
routines I have developed for computing with and about rhythmic canons.
|
| JohnsonConjecture.htm |
Proof of Johnson's
conjecture about tilings (canons) with
augmentation. Where
Galois theory over finite fields unexpectedly arises about rhythmic
canons. |
| exposéIrcam |
(in french)
Web page retracing my first steps in the wonderful world of rhythmic
canons.
Better stuff since but any browser will read this. |
| canonToMidi.nb.
|
Procedures for turning
some canons into Midi files. Not necessary in Mathematica 6.0 |
| ircam012003.nb
|
(in french) A conference
(Ircam 2003) with some simple ideas
about rhythmic canons. |
| ircam2003
|
Same thing, as a .html
file. |
|
|