Why and how mathematical concepts and tools often used for
harmony and melodic structures may prove useful towards
a rhythmic language. A contribution to the
Mathematics and Computation in Music
We survey several occurrences of combinatorics of words and morphisms in the pieces of Tom Johnson, showing in particular that some of the sequences of notes that he used intuitively can be interpreted or constructed through combinatorial objects such as morphisms. Furthermore some of these sequences have an independent interest in number theory and theoretical computer science.
A rather detailed
asks Tom Johnson about his trajectory, tastes and influences. First
published in Serbian and English in the New Sound international
journal of music.
As a contribution to the
2016 Symmetry Festival
in Vienna, Tom Johnson elaborates upon some concepts introduced
in his recent book Other Harmony.
PDF file; a video recording of this lecture is also available online.
`Anyone interested in the seismic changes that new music underwent in early 1970s New York City (and that should include most of you) will sooner or later come across the name of Tom Johnson, if only because his collected reviews for the Village Voice remain a historical reference document of seminal importance. But Tom Johnson's career as a music journalist is only part of the story: since relocating to France in the mid 1980s he's pursued his first love, composition. While many of the minimalists whose work he enthusiastically championed back in the early glory days of the Kitchen have now moved back into the material comfort of the mainstream, Tom Johnson is one of the few first generation minimalists who's "kept on going"; in Johnson's case exploring the precision and pure beauty of mathematics and translating it into music.’
Abstract: Finite automata occupy only one chapter in my book Self-Similar Melodies (1996), but in 1997 I wanted to study sequences of this kind in a more rigorous manner. I ended up compos¡ng a collection of Automatic Music for six percussionists. The first seven movements were premiered in Moscow by the ensemble of Marc Pekarsky, and simultaneously in Munich as part of Klang Aktionen, and there are now 18 movements. I analyze here three of these pieces, two of which seem “twisted” to me.
Automatic Music as part of the Illustrated Music video series available in YouTube:
Lecture delivered in MaMuX seminra, IRCAM, Paris, April 1, 2011
A detailed article by French mathematician Emmanuel Amiot, featuring some of Tom Johnson’s theories and musical objects. Also from Emmanuel, numerous other papers and documents are available; particularly his book Music Through Fourier Space (Springer, 2016).
The idea is simple. Find an object, any object, declare it a work of art, and it is a work of art. (...) A generation of Fluxus artists developed this point of view, John Cage adapted it to compose music through chance operations, and it is now quite natural that a composer or artist might choose to work with a found mathematical object.
Séminaire Entretemps, Musique, mathématiques et philosophie.
Remarks read at the März Musik festival in Berlin in March 2004.
“Today most music education takes place in institutions, and often it is of very high quality, but some things can only happen in the private sector, where there is no institutional structure.”
PDF file (in English).
Lecture presented Dec. 13, 2003 in a colloquium on Arts and Sciences sponsored by the association La Métive in La Creuse (France)
Written for the review KunstMusik number 2, 2004
A text presented for participants of the MaMuX seminar at IRCAM, Nov. 20, 2004
Lecture for Section I in the Conference on “Mathematics and Computation in Music,” Berlin, May 18 – 20, 2007. Revised with additions, August 2007.
Lecture delivered at MaMuX meeting, IRCAM, January 24, 2004.
Abstract: Self-replicating melodic loops have already been discussed in the last section of the author’s book Self-Replicating Melodies, and in a more mathematical article by David Feldman, and employed in several compositions by Johnson and other composers. This presentation is an introduction to the idea, along with computer output of orbit structures, and some other more recent observations.
“I was 32 years old when The Four Note Opera was premiered, and that was 32 years ago. Now, with the wisdom one is expect to have at the age of 64, I should know everything about this early work, but I really don’t know much more than before.”
Abstract: Rhythmic canons and other one-dimensional tiling techniques dominated my composing for two or three years, and a number of instrumental pieces, both solo and ensemble, evolved during this time. With numerous examples, I have put together a little survey of different ways in which I have done this, often leaving holes and using other procedures not normally considered correct.
Abstract: Covering two- and three-dimensional spaces with repeated tiles has been extensively studied for 2000 years, but tiling in one dimension is much less explored. How can one cover the points of a line with repeated patterns? How does one string beads so that the colors fall in repeating formations? How can a melody be written that contains overlapping canons of other melodies? Continuing from my general presentation of the subject at the Journées d’informatique musicale (Bourges, June 2001), I want to define Tiling the Line more rigorously on a theoretical level, as well as showing some applications in recent musical compositions.
Résumé : On a étudié les pavages en deux et trois dimensions depuis 2000 ans, mais les pavages d’une seule dimension sont beaucoup moins explorées. Comment couvrir les points d’une ligne avec des formes répétées ? Comment enfiler les perles de manière que chaque couleur ait sa propre forme répétée? Comment écrire une mélodie qui contient des canons d’autres mélodies qui se chevauchent ? Suivant une présentation générale du sujet au Journées d’informatique musicale (Bourges, juin 2001) je veux définir Pavage de la ligne plus rigoureusement au niveau théorique, et montrer comment je l’applique musicalement dans quelques compositions récents.
Presented at the meeting “Pavages et problèmes de combinatoire en théorie et composition musicale”, Ircam (Paris).