“I have retained melodic lines in the process of composition, they are governed by rules as strict as Palestrina’s or those of the Flemish school, but…  polyphonic structure does not come through, you cannot hear it; it remains hidden in a microscopic, underwater world, to us inaudible.”
–György Ligeti, 1983
Particular arrangements of musical objects exhibiting some kind of local rhythmic activity or density often give rise to a feeling of global stasis. Our tendency to integrate extremely complex, dynamic musical surfaces into globally static precepts—to hear local activity astexture—has been exploited by the European post-war sound mass composers (e.g. Ligeti, Xenakis, Penderecki) and composers of electronic music through various compositional techniques (e.g. micropolyphony, stochastic methods, granular synthesis, etc.)
What are the variables/parameters and corresponding thresholds governing the feeling of either stasis or activity? This study will aim investigate the effects of rhythmic complexity or density, defined as and measured by the number of voices present in a texture or by the average IOI between musical events, on the feeling of stasis vs. activity. A related question might ask whether there are certain types of microstructures (e.g. micropolyphony) which alter the perception of stasis vs. activity in some systematic way.
I also hope to understand how this phenomenon relates to brute perceptual thresholds (i.e., 2 ms for the perception of distinct tones) and Albert Bregman’s theories of auditory segmentation, integration and segregation. The concluding discussion might consider the salience of this phenomenon in extramusical contexts.
MacKay, J. (1984). On the perception of density and stratification in granular sonic textures: An exploratory study. Interface 13, pp. 171-186.
Madsen, S.T. & Widmer, G. (2006). Music complexity measures predicting the listening experience. Proceedings of the 9th International Conference on Music Perception & Cognition (ICMPC9).
Barrington, L, Chan, A.B. & Lanckriet, G (2010). Modeling Music as a Dynamic Texture. IEEE Transactions on Audio, Speech and Language Processing 18:3, pp. 602-612.
Particular arrangements of musical objects exhibiting some kind of local rhythmic activity or density often give rise to a feeling of global stasis. Our tendency to integrate extremely complex, dynamic musical surfaces into globally static percepts—to hear local activity astexture—has been exploited by the European post-war sound mass composers (e.g. Ligeti, Xenakis, Penderecki) and composers of electronic music through various compositional techniques (e.g. micropolyphony, stochastic methods, granular synthesis, etc.)
What are the variables (or parameters) and corresponding thresholds that governs the feeling of either stasis or activity, in the music of the aforementioned composers and in general? This study aims to investigate the effects of rhythmic complexity or density on the feeling of stasis versus activity. A related question might be whether there are certain types of microstructures (e.g. micropolyphony) which alter the perception of stasis vs. activity in some systematic way.
In Western music before the 20th century, texture typically falls into the following categories: monophonic, polyphonic, homophonic, or heterophonic. The 1950s and 1960s saw a great expansion in the use and definition of musical texture: Ligeti introduced micropolyphony and Xenakis introduced granular textures to the postwar avant-garde. Ligeti used traditional contrapuntal principles to craft intricate microstructures, which in aggregate created dense sound masses (Bernard, 1994). Of micropolyphony, Ligeti said: “The polyphonic structure does not come through, you cannot hear it; it remains hidden in a microscopic, underwater world, to us inaudible.” (Bernard, 1994 ) Xenakis used stochastic processes to craft dense granular textures . (Xenakis, 1992).
A foundational work in auditory cognition involving the cohesion of auditory events into larger structures is Miller and Heise’s “Trill Experiment” (1950). Miller and Heise showed that a series of alternating tones is heard as one melody when the difference in frequency is small, and as two separate entities when the frequency difference passes some threshold (Heise & Miller, 1950). The most developed work involving the coherence of auditory information, for which Miller and Heise’s experiment is arguably the impetus, comes from the lab of Albert Bregman at McGill University. Bregman introduced the concept of auditory scene analysis, which describes how we parse an auditory surface by organizing it into auditory streams. This is achieved by two processes: sequential integration and simultaneous integration (Bregman, 1990). Bregman shows that the two most important variables at work in sequential stream fusion/integration and segregation are frequency and tempo (Bregman, 1979): higher tempo and higher frequency separation result in the segregation of musical objects into separate streams. He has investigated the effects of many variables on stream fusion and stream segregation, including timbre and dynamic level, and the effects of streaming on our perception of rhythm, melody and harmony (Bregman, 1979). For Bregman, texture is the result of a “perceptual decomposition” which occurs when tempo, frequency separation, or both are increased past a certain threshold. As you increase tempo and/or frequency, a musical object is segregated into more and more streams; eventually this hyper-segregation leads to more global cohesion. Bregman has not studied in much depth the kind of complex textures used by the postwar avant-garde, or the feeling of stasis that I have described. He has, however, suggested that the particles comprising the visual “textons” described by Beta Julesz (which will be discussed below) may be analogous to acoustic grains (Bregman, 1990).
John MacKay (1982, 1984) takes a more direct interest in the textural composition of the 1950s and 1960s. MacKay shows how, for complex musical objects, frequency bandwidth and event density, as expressed on a vertical frequency axis and a horizontal time axis, are the two most important factors determining cohesion into static textural percepts (MacKay, 1984). MacKay notes that extreme density, extreme sparseness, or unpredictability may contribute to the formation of the static texture percept (MacKay, 1982). MacKay discusses musical texture in the context of figure/ground percepts in visual perception, noting that the dense textures of the postwar avant-garde eschew “figure” and emphasize “ground” (MacKay, 1982). He synthesizes ideas from Gestalt psychology and Bregman’s auditory streaming, noting that stream structure, the Gestalt principle of continuity, and brute perceptual constraints all contribute to the formation of the texture percept. He distinguishes between two poles of a continuum on which complex fields of musical events lie: “either stratified, involving streaming relations, or, at the other extreme, totally fused, in which case there is an unresolvable complexity of overlapping streaming relations” (MacKay, 1982). Finally, MacKay invokes the work of neuroscientist Bela Julesz on the perception of visual texture, in which he has shown that we can discriminate pre-attentively between textural images using “1st order statistics,” which are concerned with average densities.  In the context of Julesz’s work, MacKay suggests that granular density  is the determining factor in the formation of the textural percept; borrowing from Xenakis, (Xenakis, sodifoij and MacKay, 1982), MacKay suggests that quantitative density could be viewed in terms of a frequency/time slice (i.e., 30 Hz – 10,000 Hz over .5 second) and the number of micro-structural grains within the slice; density, could also involve a third dimension, with dynamic differentiation between slices (MacKay, 1982). MacKay, however, does not directly address the issue of the feeling of stasis vs. activity – he assumes that the cohesion of a musical object into a textural percept necessarily involves the feeling of stasis.
Nystrom (2011) uses Julesz as his starting point in his discussion of musical texture. He discusses auditory “textons,” which are organization schemes for complex fields of granular activity (Nystrom, 2011). Nystrom’s work is interesting for the novel way in which he conceptualizes texture; this way of approaching the building of texture may help us understand different organizational schemes that result in the macroscopic texture percept. Nystrom notes:
“textural immersion can happen along a continuum, especially when music presents an ambiguous ecology of spatial percepts… the intention here is not to imply the existence of a unidirectional causal path from the bottom up, but rather to map out elemental space as a facet of texture, in mutual interdependency with macroscopic percepts. This involves the introduction a new category of spectromorphological phenomena – textons – which exist only by virtue of texture, and, conversely, the aggregates of which can be the spatial substance of texture, when there is enough internal resolution.” (Nystrom, 2011)
Nystrom reiterates the idea that “internal resolution” or density is the most important factor in the formation of the textural percept. He distinguishes between various “texton propagation modes” (fixed, intermittent, switching, gradual, oscillating, etc.), which are novel ways of describing phenomena closely related to auditory streams; various distributions of these propagation schemes in spatial texture; and the various emergent textural states, i.e., projective, entitative, coagulated, fluid, vaporous, and gaseous (Nystrom, 2011).
Brute constraints on auditory perception have been outlined by London (2012). According to London, we cannot hear the separation between two tones if their IOI is 2 ms or less; we cannot hear the order if the IOI is 20 ms or less; and we cannot hear them as part of a metric hierarchy if the IOI is 100 ms or less (London, 2012). These constraints are pertinent for the issue of fast tones “blurring” together into a texture or drone.
Barrington, L., Chan, A.B. & Lanckriet, G. (2010). Modeling music as a dynamic texture. —–IEEE Transactions on Audio, Speech and Language Processing, 18(3), 602-612. —–http://cosmal.ucsd.edu/~gert/papers/TASLP-DTM-10.pdf.
Bernard, J.W. (1994). Voice leading as a spatial function in the music of Ligeti.
—–Music Analysis 13(2/3), 227-253. http://www.jstor.org/stable/854260.
Bregman, A.S. (1990). Auditory Scene Analysis: The Perceptual Organization of Sound. —–Cambridge, MA: The MIT Press.
Cohen, D. & Dubnov, S. (1997). Gestalt phenomena in musical texture. In Marc Leman —– (Ed.), Music, Gestalt and Computing: Studies in Cognitive and Systematic —————–Musicology (pp. 386-406). Berlin: Springer-Verlag.
London, J. (2012). Hearing in Time: Psychological Aspects of Musical Meter. New York: — Oxford University Press.
MacKay, J. (1982). Some comments on the visual/spatial analogy in studies of the — — — perception of music texture. Ex tempore: A Journal of Compositional and Theoretical— Research in Music 2(1). http://www.ex-tempore.org/texture/texture.htm.
MacKay, J. (1984). On the perception of density and stratification in granular sonic — —— textures: An exploratory study. Interface, 13, pp.171-186. — — ————————– http://www.tandfonline.com/doi/abs/10.1080/09298218408570451.
Madsen, S.T. & Widmer, G. (2006). Music complexity measures predicting the listening — experience. Proceedings of the 9th International Conference on Music Perception & — Cognition (ICMPC9)
McAdams, S. & Bregman, A.S. (1979). Hearing musical streams. Computer Music ——— –Journal 3(4), pp. 26-43+60. http://www.jstor.org/stable/4617866 .
Miller, G.A. & Heise, G.A. (1950). The trill threshold. Journal of the Acoustical Society —–of America 22(5), pp. 637-638. ——— ———– ———– ———– ———– – http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JASMAN000022000005000637000001&idtype=cvips&doi=10.1121/1.1906663&prog=normal.
Nystrom, E. (2011). Textons and the propagation of space in acousmatic music. ——— – Organised Sound 16(1), pp. 14-26. doi: 10.1017/S1355771810000397
Strizich, R. Texture in post-world war II music. ex tempore: A Journal of Compositional—— and Theoretical Research in Music 2(1). http://www.ex-tempore.org/texture/texture.htm.
Xenakis, I. (1992). Formalized Music. Hillsdale, NY: Pendragon.