Music 680: Special Topics in Music Theory - Electronics in Performance (Fall 2006) Class 8: October 30, 2006 Karlheinz Stockhausen Mantra (1970) formula composition as the final elaboration of serial technique fractal expansion: each element of the row is expanded into a section of music with the row divided into four "limbs" to create larger-scale formal divisions dependence of musical parameters rather than independence each pitch is associated with a characteristic gesture/motive/ornament, duration, dynamic and a characteristic ring modulation (can be understood as a kind of electronic harmony) the rehabilitation of ornament the characteristic (sub-)motive is the perceptible form-defining element ring modulation as the imposition of tonality for each each frequency in the first signal, the ring modulated output has two frequencies original frequency + sine oscillator frequency original frequency - sine oscillator frequency (these new frequencies are referred to as sidebands: they bracket the original on both sides) possibility of negative frequencies in the lower sidebands these reflect "off" zero (with a phase shift) the absolute value is the easy way to calculate their frequency sidebands can be relatively harmonic or relatively inharmonic which produces the sensation of consonance or dissonance central to Mantra's conception ring modulation in Pd multiplying any two signals together produces ring modulation but by convention, the second signal is a sine oscillator amplitude modulation adds a DC component to the modulating signal complex ring modulation any two signals can be multiplied together but each (source, modulator) pair of frequencies produces sidebands so a complex modulating signal will produce many, many sidebands which rapidly tends towards noise.... continuing with algorithmic techniques in Pd arrays as gestural data; repeatable resource build a patch which produces some kind of prolation canon from array data parametric coherence vs. parametric independence - common timebase or independent? preview of next week: Crumb Black Angels, Ferneyhough Time and Motion Study II (scores on reserve)