The Mathematics of Tibetan Rol Mo

Abstract

by lineages of carefully trained and selected professional leader-directors (dbu mdzad, umdze), it had developed by the middle of the 20th century into a vast repertoire of named and notated compositions. Many of the hundreds of pieces that once existed are still played today in the Tibetan refugee monasteries of India and Nepal. Yet, rol mo remains a strangely unexplored form of musical art. Some Western writers deny altogether that much of it is music, claiming rather that it is magical sound created for (usually unspecified) reasons. Tibetan musicians and educated listeners, with detailed standards of musical esthetics used to support their judgments, reject such ethnocentric speculations. Rol mo is indeed performed in a ritual context, in order to make a sensually pleasing offering (mchod pa) to the Buddhist (Buddhas, Bodhisattvas, Protectors, Yi dam). For precisely this reason, it must be both skillfully executed (mkhas pa) and aurally pleasant (snyan pa). If such considerations suggest an of the alien, designed to please the ears of gods rather than of men, it must be remembered that the themselves are visualized by Tibetans as idealized representations of human qualities. Rol mo esthetics simply represent human esthetics in an extreme form. Music appropriate to such an esthetic will have both extremely heightened emotional effect and extremely elaborated formal structures, to please the emotional and cognitive faculties of its idealized audience. This paper focuses on the latter aspect, that of the extreme elaboration of formal structure in rol mo. We will deal with one aspect of this subject: the complex mathematical organization of rhythmic structures. If it is possible to generalize about rhythmic structure in different world musical systems, we might say that most music is rhythmically organized in one of two ways: 1) cyclically, with groups of a specific number of beats recurring in regular cycles (Western measures, Indian tdla, Java-