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Comparative Acoustical and Psychoacoustical Analyses of Gamelan Instrument Tones

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Comparative Acoustical and Psychoacoustical Analyses of Gamelan Instrument Tones J. Acoust. Soc. Jpn.(E) 14, 6 (1993) Comparative acoustical and psychoacoustical analyses of gamelan instrument tones Edward C.Carterette,*,** Roger A.Kendall,** and Sue Carole DeVale** * Departments of Psychology, Brain Research Institute, and **Music Perception, Cognition and Acoustics Laboratory, Department of Ethnomusicology and Systematic Musicology, University of California, Los Angeles [UCLA], 405 Hilgard Avenue, Los Angeles, California 90024, USA (Received 1 March 1993) The comparative acoustical and psychoacoustical elements of the Javanese gamelan were studied with a focus on tuning, vibrational characteristics and associated per ceptual effects. In addition to relating acoustical, perceptual, and musical frameworks- to each other, we seek to clarify some common misconceptions about tuning modes, scales, and the assignment of pitch to metallophones which have inharmonic spectra. We found that the inharmonic modes of the spectra of the bars of the gamelan instru ments saron demung, saron barung, and saron peking are described well by the standard- physical theory of rectangular bars. The makers have tuned the bars by shaping so that harmonic partials also appear. The frequencies of the scale of the seven measured bars of each instrument (Low 6, Middle 1, 2, 3, 5, 6, High 1) are fit perfectly by an ex ponential function. Results of perceptual experiments show that, although many octave- mismatches occur, both Indonesian and Western subjects generally matched a pitch chroma. In judging small-cents deviations from equi-pentatonic tuning, we found one professional Indonesian musician of four who could reliably discern them. We argue that the paradox of three different pathets (modes) for equi-pentatonic tunings can be explained by differing distributions of chroma based on Markof chains of order 0, 1, 2 or higher and other imposed formulaic and hierarchical structures, which we call chromals. Key words:Musical acoustics, Pitch, Gamelan, Tuning systems, Psychoacoustics PACS number:43.75.Bc, 43.75.Cd, Kk linked. 1. INTRODUCTION For us, there is a continuing concern about all There has been considerable controversy in the musicological research in its tendency to focus on interpretation of data, variously obtained, regarding single frames of reference in isolation. For example, both the gamelan metallophone tuning and spectral music theorists working in the notational frame of and timbral characteristics (e.g. Hood, 1954; Kunst, reference impute perceptual meaning to their anal 1973; Beurmann and Schneider, 1989; Surjodinin yses, when in fact they have not explicitly or - em grat, Sudarjana and Susanto, 1972). These- acous pirically linked the notational to the perceptual- tical and psychoacoustical facets of organological- frame of reference. This failing is often found in and musicological research have spawned additional the work of cognitive musicologists, and is an im controversies regarding the classification of pathets portant weakness in contemporary trends in cogni- or modes. Many of these problems evaporate when tive science. Recently a paradigm has been outlined- the various frames of reference are appropriately for psychomusicological studies wherein converging 383 J. Acoust. Soc. Jpn.(E) 14, 6 (1993) methods link various frames of reference (Kendall those of the gamelan, and to what extent the pitch and Carterette, 1990; Carterette and Kendall, 1993); is ambiguous. for example, the ability of the performer to com Such inharmonic spectra do have periodic pat municate musical expression to the listener was- in terns, and cognitive rules apparently exist to make- vestigated, which involved relationships among the- sense out of such patterns. Several models have perceptual, acoustical, and notational frames of been proposed, including numerous attempts to reference. acount for perceptual resolution of missing funda The present study is designed to investigate the mentals (Schouten, 1940; Goldstein, -1973; comparative psychomusicology of elements of the Wightman, 1973; Terhardt, 1974; Patterson, 1989). Javanese gamelan. Our initial explorations focus The fact is, people do hear bell pitches, even on the tuning, vibrational characteristics, and as though bell spectra may not contain energy at the sociated perceptual effects. We seek here also -to frequency to which pitch is assigned. Bell foundries clarify some common misconceptions. routinely strive to tune bells by traditional artisan The acoustical characteristics of the glockenspiel rules, even casting the intended pitch into the metal and related rectangular bar instruments which are itself, as in the case of the two-pitched bronze chime free at both ends have been described well and bells of the Shang-Zhou dynasty manufactured modeled by Rossing (Rossing, 1990; Fletcher and about 500 BC (Ma Chengyuan, 1981). The tedious Rossing, 1991). Although such bars have spectra process of tuning bells after casting by filing and with partials which are not integer multiples of the shaping nearly has been eliminated by successful fundamental, in contrast to most aerophones and computer modeling in recent experimental studies chordophones, the pitch class often can be assigned (Shoofs, van Asperen, Maas, and Lehr, 1987; reliably. There nevertheless appears to be a mis Houtsma and Tholen, 1987; Lehr, 1987). conception in musicology that inharmonic spectra,- Rao, Carterette and Wu (1987) show that both especially those produced by metallophones or bells, Chinese and Americans readily make pitch matches cannot be assigned a pitch easily (Beurmann and to the sound of a subset of the Zhou bells. Further Schneider, 1989; Schneider and Stoltz, 1988; more, both Westerners and non-Westerners- per Schneider, 1991). [At the other pole, some musi ceived the same pitch to a given bell. It is easy- to cologists apparently believe that all music emanates- induce from their study three simple rules for the from the harmonic series (e.g. Hindemith, 1937).] assignment of pitch to Chinese bell spectra Rule 1: For example, Schneider and Stoltz (1988) cite the case The frequency associated with the pitch is equal to of ancient Chinese bronze bells (see discussion be the frequency of the lowest partial if it also has low), in which none of the observed partials (N=4)- maximal amplitude. Rule 2:If the partial having fit into a single harmonic series. They exhibit highest amplitude is not lowest in frequency, the signal analysis of gamelan tones (saron and bonang) frequency associated with the pitch is associated stating that their unstable vibration patterns make it with a sub-partial (f/2) of that partial. Rule 3 impossible to assign pitch to these instruments: If neither Rule 1 nor Rule 2 applies, then the fre … the fact remains that most bell sounds (as well quency of the partial associated with the pitch is -the as those obtained from many gongs and other ratio of the mean of the low frequency local maxima metallophones) show several non-harmonic com to the mean of the two strongest high-frequency ponents or spectra [sic] which tend to confuse - the local maxima. Of course, additional experimenta perception of 'pitch'(Schneider and Stoltz, 1988, tion and connection to hearing models - needs to be p.273). done, but these rules cover all thirteen of the Zhou Earlier in the same article they remark that bells, and clearly exemplify auditory contrast and In any case, there is a more or less marked grouping mechanisms. ambiguity•cfor "Western" bell sounds as well As we will see in the present study, the gamelan as for stimuli having similar spectral character bars have inharmonic components, the upper ones istics (e.g.instruments of the Javanese- and of which die out extremely quickly, leaving a strong, Balinese gamelan)•c(p.267). salient first partial. This is also true of the Western Of course, it is an experimental question to deter glockenspiel (Rossing, 1990). We turn now to the mine to what extent the spectra of bells are similar - to gamelan, in which metal bars are the principal 384 E. C. CARTERETTE et al.: GAMELAN INSTRUMENT TONES generators. namics, and duration of the work. The function of the saron barung metallophone in 2. THE GAMELAN the classical gamelan orchestra is to play the nuclear Gamelan is the term for a specific type of classical melody in its unembellished form, thereby function- orchestra in Java and Bali. Generally, it consists ing in manner analogous to a cantus firmus. The of seven to seventy-five percussion instruments, metal bars of the saron barung are positioned over a mainly individual gongs, gong chimes and metal- trough resonator (Fig. 1), and usually rest on woven lophones [xylophones with metal keys]. The sound- rattan squares through nails at the nodes of the first ing parts are usually bronze. mode of vibration, which minimizes damping, There are two tuning systems in Javanese gamelan, allowing the struck bar to ring. It is this important one of five tones, called slendro, the other of seven melodic instrument that we studied. tones, called pelog. The pelog system has seven unequally-spaced intervals and slendro have five 3. ACOUSTICAL ANALYSES OF SARON BARUNG ' WILAH' (BARS) (relatively) equally-spaced intervals. Each of the pelog and slendro tunings yields three modes. In the 3.1 Characteristics of the Bar pelog system, the three modes contain five subsets In order to assess our contention that the gamelan of the original seven; the remaining two tones are wilah (bars) are well-modeled by standard acoustical used for embellishment. theory dealing with rectangular bars, we measured Only the slendro system is involved in the present the wilah or bar of the first scale tone saron barung paper. Each of the three slendro modes or pathets slendro of the UCLA Javanese gamelan Kyai contains the same five tones. One way a pathet Mendung [The Venerable Dark Cloud] (Hood and (= "to constrain") differs from another is in the Susilo, 1967) (Figs. 2(a); 2(b)). Thickness measure- prominence accorded to certain of the five tones, in ments were made to the nearest 0.0001 inch with a other words by a (statistical) limiting of the choices Mitutoyo micrometer.
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