A Spectral Pitch Class Model of the Probe Tone Data and Scalic Tonality

Abstract

IN THIS PAPER, WE INTRODUCE A SMALL FAMILY OFnovel bottom-up (sensory) models of the Krumhansl and Kessler (1982) probe tone data. The models are based on the spectral pitch class similarities between all twelve pitch classes and the tonic degree and tonic triad. Cross-validation tests of a wide selection of models show ours to have amongst the highest fits to the data. We then extend one of our models to predict the tonics of a variety of different scales such as the harmonic minor, melodic minor, and harmonic major. The model produces sensible predictions for these scales. Furthermore, we also predict the tonics of a small selection of microtonal scales-scales that do not form part of any musical culture. These latter predictions may be tested when suitable empirical data have been collected.

Empirically testingTonnetz, voice-leading, and spectral models of perceived triadic distance

“…For the spectral pitch-class model, the optimized smoothing width falls within the expected range (3-13 cents), as does the roll-o↵, which corresponds approximately to the loudnesses of the partials in the string sounds used (similar optimized values were also obtained in the related models detailed in Sharp 2015 andSharp 2016). As shown in Figure 7, the optimized spectral pitch-class distance model can calculate values for any interval size, including microtonal.…”

“…This is because combining such distances across di↵erent musical levels may allow us to build more complex models that elucidate the complex and apparently asymmetrical perception of harmonic relationships in tonal (and microtonal) music. An example of such a methodology is given in Milne, Laney, and Sharp (2015) with their model of the tonicness of chords in a variety of conventional and microtonal scales.…”

“…Other recent research has demonstrated that spectral models can successfully predict the perceived fit of chromatic probe tones to an established key (Krumhansl's (1982) tonal hierarchies) (Milne, Laney, and Sharp 2015) and the perceived a nity of microtonal melodies (Milne, Laney, and Sharp 2016). The spectral model tends to make chords with more common tones and more tones a perfect fifth/perfect fourth apart (between any voices) closer than those with fewer such intervals.…”

Dissociating sensory and cognitive theories of harmony perception through computational modeling

“…It avoids much of the complexity of Leman's (2000) model: it has no explicit modeling of the peripheral auditory system and does not model the time-course of echoic memory. Nonetheless, the model has demonstrated best-in-class results in modeling certain important results from the psychological literature (Milne & Holland, 2016;Milne, Laney, & Sharp, 2015). Milne et al's (2011) model estimates the perceptual dissimilarity of pairs of pitch or pitch-class sets.…”

Tone Profiles of Isolated Musical Chords: Psychoacoustic Versus Cognitive Models

“…A theory of harmony based on the perception of harmonic patterns among the partials of complex sounds is promising, considering the biological importance of voiced speech sounds (Bowling & Purves, 2015;Bowling, Purves, & Gill, 2017). It is also possible to predict interesting structural aspects of tonality using a pitch-commonality model that considers only spectral pitch and ignores harmonic pitch patterns and virtual pitch (Milne, Laney, & Sharp, 2015). Parncutt (1989) adapted the pitch model of Terhardt et al (1982) for music-theoretical purposes, assigning all input frequencies and output pitches to 12 equally spaced categories per octave across the range of hearing (120 categories altogether).…”