A Re-Analyzed Australian Western Desert Song: Frequency Performance and Interval Structure

Will, Udo; Ellis, Catherine J.

doi:10.2307/852059

Cited by 11 publications

(10 citation statements)

References 9 publications

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“…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.…”

Section: Introductionsupporting

confidence: 71%

“…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.…”

Section: Resultsmentioning

confidence: 60%

“…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).…”

Section: Resultsmentioning

confidence: 70%

“…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.…”

Section: Methodsmentioning

confidence: 99%

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Two types of octave relationships in central Australian vocal music?

Will

1997

Musicology Australia

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Five performance sections from four different CentralAustralian songlines with a melodic range larger than an octave have been analysed. Although octave ratios exist, they are limited to one octave interval in each songline: only the finalis has an 'octave' counterpart, other intervals in the upper melodic range are shown to be linear shifts of intervals in the lower range. There is evidence that the octave ratio is not treated as an octave in the common musical sense (octave identity) but much more as a specific ratio (as part of the characterization of the songlines). This helps considerably in understanding of how a musical system based on intricate patterns of linear (frequency difference) intervals can, at the same time, contain ratio intervals as essential elements without contradictions: this music does not seem to know a generalized principle of octave identity.

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Section: Introductionsupporting

confidence: 71%

Section: Resultsmentioning

confidence: 60%

Section: Resultsmentioning

confidence: 70%

Section: Methodsmentioning

confidence: 99%

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Two types of octave relationships in central Australian vocal music?

Will

1997

Musicology Australia

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“…Also worthy of note are the pitches used by Aboriginal Australians from the western desert area, which do not exhibit periodicity, but which do seem to contain repetitions of frequency differences rather than ratios (Will and Ellis 1996).…”

Section: Other Non-periodic Structuresmentioning

confidence: 99%

Linking Sonic Aesthetics with Mathematical Theories

Milne

2018

Oxford Handbooks Online

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Pure mathematics provides principles, procedures, and ways of thinking that can be fruitful starting points for music composition, performance, and algorithmic generation. In this chapter, a number of mathematical methods are suggested as useful ways to define and transform underlying musical structures such as meters and scales, and to realize these structures as finished pieces of music. The mathematical methods include the discrete Fourier transform, geometry, algebraic word theory, and tiling, and how these relate to musical features such as periodicity (or lack of periodicity), well-formedness, microtonality, canons, rhythmic hierarchies, and polyrhythms. The chapter closes with a detailed examination of a musical piece derived from the described processes.

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The difficulty of learning microtonal tunings rapidly: The influence of pitch intervals and structural familiarity.

Leung¹,

Dean²

2018

Psychomusicology: Music, Mind, and Brain

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The current study investigates the learning of microtonal tuning systems, which have a different pitch interval structure than the Western tonal system (12-tone equal temperament). To examine the influence of structural similarity, we included systems that differed from the 12-tone equal temperament system in different degrees in terms of temperament, pitch ratio, and pitch differences. After a brief exposure phase in which participants became acquainted with the previously unfamiliar systems, we assessed aspects of their learning. We measured pitch memory performance and the knowledge of pitch membership using a pitch deviant detection task and a goodness-of-fit perception task. In the pitch deviant detection task, participants were required to detect pitch shifts in a second playing of a given melody, whereas in the goodness-of-fit task, they made judgments about whether the last tone (probe) fits or does not fit with the context of the just presented melody. A total of 30 musically untrained individuals were tested in each experiment, and results showed that learning was limited; hence the task was difficult in such a short period. Pitch deviant detection was better in the microtonal system that is well-formed with two step sizes than that in the other systems in the test. Goodness-of-fit perception was similar between 12-tone equal temperament and the other microtonal systems, and participants who were fundamentally better at pitch discrimination and contour perception were better at rejecting incongruent probes (nonmember of the system) in the goodness-of-fit task. This study has implications for music perception of pitch ratio-and pitch difference-based tuning systems.

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A Re-Analyzed Australian Western Desert Song: Frequency Performance and Interval Structure

Cited by 11 publications

References 9 publications

Two types of octave relationships in central Australian vocal music?

Two types of octave relationships in central Australian vocal music?

Linking Sonic Aesthetics with Mathematical Theories

The difficulty of learning microtonal tunings rapidly: The influence of pitch intervals and structural familiarity.

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