DESCRIPTION:
performed by members of Zeitkratzer Ensemble.

from the score:

'A "critical bandwidth" is a frequency range within which complex acoustic stimuli evoke auditory responses very different from those evoked by stimuli separated by a larger interval (in the same register). For example, two simple (sinusoidal) tones separated by an interval much smaller than the critical bandwidth are not heard as two tones at all, but rather as a single tone, with beats which produce a sensation of roughness, at a subjective loudness which is correlated with the sum of their individual amplitudes. Two simple tones separated by an interval larger than the critical bandwidth, on the other hand, are heard as two tones, smooth or "consonant" in quality, and at a loudness which approaches the sum of their (individual) loudnesses (rather than their amplitudes).

A performance of this work arises out of the normal process of the ensemble's tuning to A-440. After establishing a continuous unison on this A (the continuity enhanced by a tape-delay system), the players begin to expand the range of sounding pitches "geometrically", above and below the central pitch. That is, each successive interval in a given direction is twice the size of the preceding interval in that direction. Although these incremental intervals are always in strictly "harmonic" proportions (i.e., they can be represented by fairly low-integer frequency ratios), they are too small to be recognized as such (or even to be heard as "intervals") during the first half of the piece, in which the total pitch-range never exceeds the limits of the critical band (which, in this register, extends a major 2nd above and below the mid-point). Only after the expansion process has exceeded the critical bandwidth do the pitch-relations begin to be heard as "harmonic".'

- James Tenney