Supplementary Sets and Regular Complementary Unending Canons (Part Four)

  title={Supplementary Sets and Regular Complementary Unending Canons (Part Four)},
  author={D. Vuza},
  journal={Perspectives of New Music},
  • D. Vuza
  • Published 1992
  • Art
  • Perspectives of New Music
Asymmetric Rhythms and Tiling Canons
The mathematics of some rhythmic structures common in popular and folk music are examined, including rhythms that cannot be aligned with other even divisions of the measure, and their results have a surprising application to rhythmic canons. Expand
Music in the pedagogy of mathematics
The popularization project concerning music and mathematics of the Royal Spanish Mathematical Society and its extension to an international level is proposed and some ideas and outlines for the creation of didactic material for mathematics courses within the framework of MMT are presented. Expand
Tiling the Musical Canon with Augmentations of the Ashanti Rhythmic Pattern
We discuss the problem of constructing a tiling of the musical time-line with a number of instruments (called voices) all of which are playing according to variations of a particular rhythmicExpand
Tiling the integers with aperiodic tiles
A finite subset A of integers tiles the discrete line ℤ if the integers can be written as a disjoint union of translates of A. In some cases, necessary and sufficient conditions for A to tile theExpand
Why rhythmic canons are interesting
The subject of rhythmic canons has been revivified by new concepts, coming from the field of music composition. The present article is a survey of the mathematical knowledge in this field, from theExpand
Michael Blake in Conversation with Tom Johnson in 2018
In the summer of 2011 Christine Lucia and I called on Tom Johnson at his home in Paris, and he invited us to two imminent events: the launch of Bernard Girard's Conversations avec Tom Johnson at theExpand
Perfect codes in Cayley sum graphs
A subset $C$ of the vertex set of a graph $\Gamma$ is called a perfect code of $\Gamma$ if every vertex of $\Gamma$ is at distance no more than one to exactly one vertex in $C$. Let $A$ be a finiteExpand
A Project Proposal for a Mathematical Study of Rhythm Tilings
  • 2019
The object of interest in this proposal is a two dimensional toroidal binary array constructed from a tiling of cyclic one dimensional binary arrays, here called a rhythm tiling. These rhythm tilingsExpand
Maximally Even Tilings
This paper investigates the construction of partial tiling canons in which the composite rhythm is maximally even, and compositions that feature more irregular/interesting rhythms. Expand
Maximally Even Tilings: Theory and Algorithms
This dissertation will investigate the existence, classification, and construction of rhythmic tiling canons in which the composite rhythm is maximally even. Expand


" Generalized Musical Intervals and Transjhnutions by David Lewin . " ( Review )
  • 1987
Generalized Musical Intervals and Transformations
  • D. Lewin
  • Psychology, Computer Science
  • 1987
This paper focuses on the development of knowledge structures in the context of discrete-time dynamical systems and their role in the history oftonal theory. Expand
On Formal Intervals between Time-Spans
There is in fact exactly one such FIS, up to isomorphism in the pertinent sense, of THINGS whose interval function is invariant under such transformations: int((au + m,xu), (bu - m,yu)) = int((a,x),(b,y)). Expand
Time-Point Sets and Meter
THE POSSIBILITY OF PERCEIVING any twelve-integer set as a succession of pitch classes or a succession of time-point classes and the possibility of applying the same systematic operations in theExpand
" Intervallic Relations between Two Collections of Notes " Some Investigations into Foreground Rhythrmc and Metric Patterning . "
  • In Music Theory - Special Topiw , edited by Richmond Browne , 101 - 37
  • 1959