Introduction to the writings about early music

I was struck by Steve Reich's early discovery of "phasing", which occurs when two (or more) repeated events of unequal length are perceived simultaneously. At the beginning (and at certain subsequent) points they will coincide; in between one will be heard as increasingly delayed in relation to the other, then growing closer, until a moment of coincidence recurs. This is an instance of what Reich called "music as a gradual process". Recent conversations with composer Nicholas Pavkovic reminded me of my abiding interest in this and in what, for lack of a better name, I think of as an "algorithmic approach" to musical composition. I'm not sure what I find so attractive about this, as I am at heart an improviser, not a planner. Most systems seem to lead me astray, or end up as elaborate designs imperceptible to anyone including myself. Having said that, I admit that I have used systematic processes in a few pieces ("The Confines of Symmetry", "Marrying Music", "Calcululations", "War of Words").

I have studied such processes in other music. It has been suggested that I make available some of my research to others, in the hope that they will find it as remarkable and odd as I do. Most of this work depends upon secondary sources --- I make no claims to scholarship. Anyone with similar interests could presumably ferret out this information. I will provide a bibliography at some point.

And I invite corrections, contradictions, amendments, supplements, comments....

These analyses will fall into three categories: imitative designs (canon etc.); isorhythmic (i.e. phasing) designs; and other elaborate schemes not falling into either category. The works of interest are found at various points in music history, with greater concentrations in the late Middle Ages and in the 20th Century. Here is a list of the pieces I want to bring to your attention:

➁ Busnois "In hydraulis" isorhythmic motet

Score: http://imslp.org/wiki/In_hydraulis_%28Busnois,_Antoine%29

➂ Montpellier Codex

➃ Baude Cordier "tout par compas" imitative (graphic score)

http://www.youtube.com/watch?v=HeJXuqfhYDk

➄ Dufay "gloria ad modum tubae" "fuga duorum temporum"

http://www1.cpdl.org/wiki/images/sheet/duf-glor.pdf

➅ Ph. de Vitry "vos qui admiramini/Gratissima virginis" isorhythmic motet

➆ Ciconia "le ray au soleil" canon by diminution [several recorded performances exist; no web link found for the score]

➇ anon. "en la maison" canonic ballade (graphic score)

➈ Senleches "la harpe de melodie" canonic virelai (graphic score) ars subtilior

http://www.tradebit.com/filedetail.php/50075671-la-harpe-de-melodie

(the performance is less clear than that found here:

Album: "Masters, Monsters, and Mazes - Treading the Medieval Labyrinth"

Performers: Drew Minter, Mark Rimple, Marcia Young

Composers: Jacob De Senleches

Original Release Date: November 30, 2004

Label: MSR Classics