ABSTRACT:
In the Renaissance, boys were taught to sing an improvised line against a liturgical cantus firmus. In this presentation, the authors model that process of improvisation. They show how each factor that the improviser must take into account can be represented as an independent variable in a formula that determines legal and illegal note choices. The choice of which of several legal notes the improviser can make is refined with the use of preference rules, from which a "one-day forecast" (i.e., from one note to the next) is made. The predictive skill of this forecast is improved by the preference rules when compared with the reality of two of Zarlino's compositions. Then a "long-range forecast" is made using the "random walk" principle, and the authors show that their success over 26 notes is greater than the predictive skill of the best model of the ten-day weather forecast. Finally they show how imitation is a limiting case of improvised counterpoint, and provides an "El Nino" effect when used in improvisation.
ABOUT PETER SCHUBERT & AYRTON ZADRA:
Peter Schubert teaches music theory at the Schulich School of Music. Ayrton Zadra is a research scientist at Environment Canada.
Peter Schubert came to Montreal from New York City, where he founded and directed Opera Uptown and The New Calliope Singers, a group renowned for its commitment to modern music during its fifteen-year career. The group presented over fifty premieres and released a critically acclaimed CD entitled "New Cantatas and Madrigals."
Since 1991, he has conducted the highly respected Montreal-based group, The Orpheus Singers. Under his direction, the group has placed as a finalist several times the CBC Competition for Amateur Choruses, winning first prize in the chamber chorus category in 1996. The Orpheus Singers has presented premieres of several new Canadian works and participated in a CD of the musical compositions of Freidrich Nietzsche.
In 1998, Peter Schubert founded VivaVoce, a professional vocal ensemble, to stimulate interest in choral chamber music ranging from the Renaissance to the day before yesterday. By presenting unique, interactive "commentated concerts" in schools and concert halls, VivaVoce delights and entertains it audiences of all ages, instilling in them a deeper understanding of their musical heritage.
Schubert holds a Ph.D. in musicology from Columbia University. Currently an Associate Professor at the McGill University Faculty of Music, Schubert is the author of a groundbreaking and highly regarded textbook, Modal Counterpoint, Renaissance Style (Oxford University Press, 1999). With colleague Christoph Neidhoefer he also co-authored Baroque Counterpoint (Prentice-Hall, 2005).
Peter Schubert studied conducting with Nadia Boulanger, Helmuth Rilling, Jacques-Louis Monod and David Gilbert and has been assistant to Gregg Smith and Agnes Grossman. He has published an edition of Renaissance Noels as well as his own innovative arrangements of five popular Christmas carols with C.F. Peters.