The First International Conference on Music Perception and Cognition
نویسنده
چکیده
In the traditional representation, musical pitch is a helix – a single valued function existing in three space, much like a stretched coil spring (see Ueda & Ohgushi, 1987 for a review). The pitch helix has a circular dimension, referred to as "tone chroma", and a vertical dimension referred to as "toneheight", and pitch rises one octave per revolution of the circular dimension. This representation of pitch is supported by the perception of pure tones; in this case the only continuous path from a note to its octave is along the helix through all of the intervening tone-chroma values. For any given chroma value, say C, tone-height is a discrete variable, namely the set of octaves CO, Cl, C2 ... C8. In the case of multi-harmonic tones, it is possible to move continuously from a note towards its octave without changing chroma. For example, consider the complex sound composed of all harmonics of 100 Hz starting in cosine phase (i.e. a pulse train), and the perceptual change that occurs when the odd harmonics are attenuated as a group. As the attenuation increases from 0 to 10 dB tone-height rises smoothly from the original octave (100 Hz) to the final octave (200 Hz) and there is no change in tone-chroma during this transition. This indicates that the domain of pitch for musical notes is more like the surface of the space enclosed by the pitch helix rather than a helical wire. There are at least three ways of modifying a pulse train and producing sets of waves that all have the same tone-chroma but which sound "higher" or "lower" than the starting pulse train. This paper presents an experiment in which listeners judged the tone height of a large collection of these sounds. The experiments show that waves with the same period can produce tone-height judgments that consistently differ by more than an octave.
منابع مشابه
Toussaint Proof
1 This is an extended version of a paper that appeared in the Proceedings of the 12th International Conference on Music Perception and Cognition (ICMPC), and 8th Triennial Conference of the European Society for the Cognitive Sciences of Music (ESCOM), in Thessaloniki, Greece, on July 2328, 2012, pp. 1001–1008, under the title: “The pairwise variability index as a tool in musical rhythm analysis.”
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