Evidence for linear transposition in Australian western desert vocal music

Two types of octave relationships in central Australian vocal music?

“…Confirming a previous hypothesis of Ellis (1992), some recent studies (Will and Ellis 1994;Will and Ellis 1996;Will 1994;Will 1995) have given several lines of evidence that a linear organization of frequencies is one important aspect of Central Australian Aboriginal music: interval arrangements of the tonal space (i.e. the distribution of recurring frequencies in song performances) show linear structures, sequences of frequency differences are shifted linearly in transpositions, and a clearly defined, short sequence of frequency differences associated with the finalis 'tone' has been identified as a common feature of different songlines.…”

“…The variability of intonation in each of the songlines (established by the same methods as in Will andEllis 1994, andWill andEllis 1996) is comparable to that identified in those previous analyses although they were performed by different singers. Maximum variability of intonation is -+ 1 Hz for the items from the Urumbulal, JM3, and Printi songline and slightly larger (+ 1.5 Hz) for the Bandicoot and the Urumbula2 performance.…”

“…More than through the approximation of physical octaves, the notion of octave identity is characterized by functional and hierarchical equivalents. As has been demonstrated elsewhere (Will and Ellis 1994, Will and Ellis 1996,Will 1994, crests in frequency-of-occurrence graphs like figs. 1-6 correspond to main 'pitch'-areas of the melodic lines and have certain hierarchical features (main peak(s) and 'side' peaks) with certain invariant Gestalt characteristics (the linear structure of peak distances within crests and the general shape of the crests is maintained in transpositions).…”

“…The analysing software is based on period determination of the complex sound wave using zero crossings as reference points for period and corresponding frequency calculations. The error due to the limited resolution of the sampling rate has been minimized by interpolating the zero crossing assuming a linear slope of the waveform between the closest bin points (see Will and Ellis 1994). The original period measurements were averaged over 3 cycles and the inverse values (frequency/Hz) stored for later processing.…”

“…Since the methods applied here have been described in detail elsewhere (Will 1994;Will and Ellis 1994;Will and ELlis 1996), only a summary is provided here: The original recordings or DAT copies of them were sampled into a computer via a 16 bit A/D converter. All signals were unfiltered and the sampling rate was 19.2 kHz.…”