2 pianos, 1 ring modulator
Tonight marked the close of the Urban Alchemy concert series at the Pulitzer Foundation for the Arts in conjuction with the exhibition of collected works of Gordon Matta-Clark. The program featured Karlheinz Stockhausen's 1970 work Mantra, written for two pianos, electronics, and sparse percussion. The crux of the work is perhaps what ties it most closely to the exhibition in the surrounding space. As Matta-Clark re-envisioned spaces and interior-exterior relationships, Stockhausen here reformulates the two-piano classical form by addition of a novel element: the ring-modulator circuit.
It was popular in the 19th century, before recorded media, to reduce orchestral works to two-piano versions that could be played in your luxe foyer at the mercy of your caprice, bypassing the need to round up your cadre of orchestra-types (heavy drinkers they are). Here Stockhausen not only reworks an established form, but in my opinion he makes a parodic jab at the idea of 'reducing' musical works. Near the close of the lengthy Mantra, Stockhausen notates a lightspeed summary of everything that occurred in the piece up to that point.
But back to the new element: the ring-modulator. Though the 'ring' in the name is often erroneously traced to the bell-like tones that the circuit is able to produce, it derives from the typical structure of the analog circuit: a ring of diodes. (Pull out your Schaum's physics outline) SLSO Music Director David Robertson started to explain the operation of the device in the pre-concert lecture and a way that was totally understandable and almost fun, which I will try to replicate. The ring-modulator multiplies the input signal (piano) by a 'carrier' signal [that's convolution in the frequency domain] so that the resulting output contains tones at the sum and the difference of the input and carrier frequencies. For you acoustics buffs that means that the ratios between these new processed signals can be very un-harmonic. This is the means by which many ring-modulator outputs sound like bells (metallic overtones are often not harmonic). See also: Arvo Part's 'tintinnabular' period of composition, where he explicitly notates such overtones played on other instruments to create this rare quality.
The result is a vast continuum of timbre from the very limited starting material of two pianos and a circuit. For example, there is one segment of the piece where piano chords seem to waver in an out of audibility, like a tremolo effect on a surf guitar (awful analogy). I am fairly sure this is acheived if the carrier frequency is set very low, so that sum and difference tones generated are relatively close, creating the pulsating 'beat' heard here. When high-register tones are played with this carrier frequency, the beat is so fast that it generates its own buzzing 'undertone'.
Why doesn't every Steinway come with a little ring modulator and internal speaker? Listen to about 20 of the 70-ish minutes of Mantra and you'll understand how this component fell out of present-day favor from its heyday in electronic/computer music composition of the 60s-70s. The ring-modulator is now that guitar effect you never use, or more scathingly, it is a textbook space-age noise used for creating specific imagery. During one segment of the piece where a single chord is sustained while the ring-modulator's carrier freq. knob is turned up and back down again, I had to cover my mouth to keep from shouting "BLAST OFF!!!!!!!!!!!!!!"
Such is the fate of a "new" sound -- in an effort to subvert the expectations associated with 'traditional' music eventually it, too, lends itself to imitation and overuse.
If you are unfamiliar with the music of Stockhausen, Mantra is an excellent place to begin, since new listeners might find his prior chance-inspired works aimless or boring, and his early serialist pieces overcomplicated.