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)