Program notes by Evan Ziporyn
Sulvasutra (2006) is based on an ancient Sanskrit treatise, probably dating from 800 BC. An appendix to the Vedas proper, it gives rules for the proper construction of religious altars. Vedic ritual sacrifice required precisely proportioned fire altars, which themselves took on highly symbolic, intricately designed shapes, such as the famous syena-cita (‘great eagle’) altar diagrammed below. The text contains all that is known of ancient Indian mathematics, presented as applied math, as formulae without proofs. Included among these, among other things, is the method for determining lengths in right triangles, i.e., the Pythagorean Theorem.
The Sulvasutra suggests that devotion is linked to order, that the spiritual agni (‘fire’) is enabled by knowledge. This brings us to music, another meeting point of body and mind. Music is a physical force that touches our emotions, this is probably why it matters to us, but it is also pure number made manifest. The master musicians for whom I wrote this piece all speak different musical languages, but all are built from the same building blocks. China’s elegant huang chung (‘yellow bell’) tuning system, India’s microtonal sruti, and Pythagorean tuning itself (the starting point for western tuning) are all derived from the geometric ratios of the overtone series. The results have little in common on the surface: the same materials can make many different altars. As listeners, we don’t need to be conscious of the numbers: the rigor is present whether we know it or not. Wu Man tuning her pipa, or Sandeep Das playing the tabla – both are forms of applied mathematics. The music doesn’t work, the fire can’t burn, without it. So in this piece I go back to these principles, deriving both form and content from these shared fundamentals.
Sulvasutra is in three continuous movements, built around rhythmic cycles of 4, 5 and 3, that is, the sides of a right triangle. “Ka” (literally, ‘who,’ also the first consonant in the Sanskrit alphabet) is the secret name of Prajapati, the self-existing one who creates the universe. His story here mingles with our own creation myth, the Big Bang. String harmonics are floating particles, regarded as waves by the ‘one seer,’ who dreams the pipa melody. The particles accrue to singularity, then explode and take shape, creating space for the tintal meter of the tabla.
“Agni” is the sacrificial fire, Prajapati’s second creation, itself a god. There is evidence that elements of Vedic culture spread to Georgia and Greece; this movement represents that wildfire-like diffusion. Its modal harmonies wind their way through Georgia to the west; its meter begins as strict jhap (a 5 beat tal) and end in an additive feel closer to the Balkans.
In “Letter to Pythagoras (3/4/5)”, we remain in Greece, where the Mystical Order learned its math from someone (who?). Over a simple drone, the violins build a melody on the same 3-4-5 triangle. Mathematical formulae are infinitely expandable, and what follows is a door opening to that expansion, all burning steadily over a strict 3-beat tal.