Page 11 - Summer 2010

and brass.
Twentieth century electroacoustic music has also
employed circular effects. These occur, for example, in Risset’s Mutations 1; James Tenny’s For Ann (rising), Karlheinz Stockhousen’s Hymnen, and the Beatle’s A Day in the Life (Sergeant Pepper). Recently, Richard King, sound designer for the Batman movie The Dark Knight, employed an ever-ascending glide for the sound of Batman’s vehicle, the Batpod. Explaining his use of this sound in the Los Angeles Times, King wrote: “When played on a keyboard, it gives the illusion of greater and greater speed; the pod appears unstop- pable.”11
Towards circular banks of musical instrument tones
To achieve pitch circularity, must our choice of musical material be confined to highly artificial tones, or to several instrument tones playing simultaneously? Alternatively, might it be possible to create circular scales from sequences of single tones, with each tone comprising a full harmonic series? If this could be achieved, then the theoretical implica- tions of pitch circularity would be broadened. Furthermore, this would open the door to creating circular banks of tones derived from natural instruments, which would expand the scope of musical materials available to composers and per- formers.
Arthur Benade stated that a good flautist, while playing a sustained note, can smoothly vary the amplitudes of the odd numbered harmonics relative to the even-numbered
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ones, so as to produce an interesting effect. Suppose he
begins with a note at F0 = 440 Hz; the listener hears this as Concert A, well defined in both pitch class and pitch height. If the flautist then alters his manner of blowing so as to pro- gressively reduce the amplitudes of the odd harmonics rela- tive to the even ones, the listener will at some point realize that he is no longer hearing Concert A, but rather the A an octave higher (corresponding to F0 = 880 Hz). Yet the tran- sition from the lower to the higher octave can appear quite smooth. Based on this observation, one can surmise further that a tone consisting of a full harmonic series might be made to vary continuously in height between octaves without nec- essarily traversing the path specified by the helical model, but rather by traversing a straight path upwards or downwards in height—for example between D# and D#’ in Fig. 2. Pitch might then be represented as a solid cylinder rather than a helix. Sound Demonstration 3 presents a harmonic complex tone with F0 = 440 Hz, in which the odd harmonics are grad- ually reduced relative to the even ones, so that the perceived height of the tone moves smoothly up an octave.
In an experiment by Roy Patterson and his colleagues, a set of tones was employed, each of which consisted of the first 28 harmonics, and in which the relative amplitudes of the odd and even harmonics were varied. The subjects’ task was to judge the octave in which each tone occurred. Averaging the results across subjects, when the odd har- monics were 27 dB lower than the even ones, listeners judged the tones to be an octave higher; at smaller amplitude discrepancies, averaged judgments of height fell between the
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Given these findings, I surmised that one might be able
higher and lower octaves.
the direction opposite that of movement along the pitch class
5, 6
For example, the spectral envelope could be contin- uously rising, while the tones traverse the pitch class circle in counter-clockwise direction, so that the listener perceives a sequence that both ascends and descends at the same time. Risset has incorporated many of such glides into his compo- sitions, with striking artistic effect. For example, he employed an endlessly descending glissando in the incidental music to Pierre Halet’s Little Boy. This play portrays the nightmare of a pilot who took part in the destruction of Hiroshima, and the descending glide symbolizes the falling of the atomic bomb.
circle.
Circularities based on spectral proximity
For Shepard tones, there are two ways to interpret the perceptual tendency to form relationships based on pitch proximity. One possibility is that we invoke proximity along the pitch class circle, which is illustrated in Fig. 2. Another possibility is that we connect together the individual partials of the successive tones based on their proximity along the fre- quency continuum, as illustrated in Fig. 3. That spectral fac- tors alone can produce circularity effects was demonstrated by Jean-Claude Risset5, 6 when he produced endlessly ascend- ing and descending glissandi consisting of tone complexes whose partials stood in ratios other than an octave. An experimental demonstration of this spectral proximity effect was later produced by Edward Burns, who created banks of tones whose partials were separated by various ratios, rang- ing from 6 to 16 semitones. He found essentially no differ- ence in circularity judgments depending on whether octave
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ratios were involved. Other research demonstrating the con-
tribution of spectral proximity to pitch circularity has been carried out by Ryunen Teranishi,8 and by Yoshitaka Nakajima
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Pitch circularities in musical practice
Although stark pitch circularities were not created until
exact control of acoustic parameters became possible in the
mid-twentieth century, overall impressions of pitch circular-
ity have been generated by composers from the Renaissance
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In the early twentieth century, Alban Berg produced an effect that approached that of circularity generated by Shepard tones. In his 1925 opera Wozzeck, Berg employed a continuously rising scale that was orchestrated in such a way that the upper instruments faded out at the top of their range while the lower instruments faded in at the low end. Other twentieth century composers such as Bela Bartok and Gyorgy Ligeti orchestrated sequences that gave rise to circular impressions. In particular, Jean-Claude Risset has made extensive use of circular configurations in his orchestral works; for example in his piece Phases he orchestrated circu- lar configurations using harps, celesta, strings, percussion,
and his colleagues.
English keyboard music of the sixteenth century, such as composed by Orlando Gibbons, included clever manipulations of tone sequences in multiple octaves so as to create circular effects. In the eighteenth century, J. S. Bach was strikingly effective in devising passages that gave circular impressions, most famously in his organ Prelude and Fugue in E minor.
onward.
10 Acoustics Today, July 2010