Modelling the similarity of pitch collections with expectation tensors

Milne, Andrew J.; Sethares, William A.; Laney, Robin; Sharp, David B.

doi:10.1080/17459737.2011.573678

Cited by 26 publications

(40 citation statements)

References 14 publications

(34 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The techniques used are based on those introduced by Milne et al (2011). The MATLAB routines that embody these routines can be downloaded from http://www.dynamictonality.com/probe_tone_ files/.…”

Section: Appendix C Formal Specification Of the Spectral Pitch Class mentioning

confidence: 99%

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

Milne

Laney²,

Sharp

2015

Music Perception

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Appendix C Formal Specification Of the Spectral Pitch Class mentioning

confidence: 99%

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

Milne

Laney²,

Sharp

2015

Music Perception

Self Cite

View full text Add to dashboard Cite

show abstract

“…There are essentially two research lines for computational models of tonal attraction data. The first, psychoacoustic bottom-up models are inspired by Hermann von Helmholtz' (1877) attempts on spectral representations and the overtone series (Milne et al 2011, Stolzenburg 2015. The second, cognitive top-down models go back to Lerdahl and Jackendoff's (1983) generative theory of tonal music, using either hierarchically structured representations of tonal space (Lerdahl 1988, 1996, Krumhansl and Kessler 1982, Krumhansl and Cuddy 2010 or statistical correlations in large music corpora that are modeled by probabilistic approaches, such as Gaussian Markov chains (Temperley 2007(Temperley , 2008.…”

Section: Introductionmentioning

confidence: 99%

Quantum approaches to music cognition

Graben

Blutner

2019

Journal of Mathematical Psychology

View full text Add to dashboard Cite

Quantum cognition emerged as an important discipline of mathematical psychology during the last two decades. Using abstract analogies between mental phenomena and the formal framework of physical quantum theory, quantum cognition demonstrated its ability to resolve several puzzles from cognitive psychology. Until now, quantum cognition essentially exploited ideas from projective (Hilbert space) geometry, such as quantum probability or quantum similarity. However, many powerful tools provided by physical quantum theory, e.g., symmetry groups have not been utilized in the field of quantum cognition research sofar. Inspired by seminal work by Guerino Mazzola on the symmetries of tonal music, our study aims at elucidating and reconciling static and dynamic tonal attraction phenomena in music psychology within the quantum cognition framework. Based on the fundamental principles of octave equivalence, fifth similarity and transposition symmetry of tonal music that are reflected by the structure of the circle of fifths, we develop different wave function descriptions over this underlying tonal space. We present quantum models for static and dynamic tonal attraction and compare them with traditional computational models in musicology. Our approach replicates and also improves predictions based on symbolic models of music perception. Highlights.• Quantum models for tonal attraction are compared with symbolic models in musicology• Symbolic models of tonal attraction are parsimoniously derived from fundamental symmetries of music cognition• Tones appear as Gestalts, i.e. wave fields over the circle of fifths

show abstract

“…In this way, they were able to reconstruct historical temperaments such as Werckmeister III, Young's temperament (see, e.g, Benson [1]) and equal temperament quite closely. Recently, Milne et al [20] developed a similarity metric for pitch collections based on the novel concept of expectation tensors.…”

Section: Introductionmentioning

confidence: 99%

Constructing an optimal circulating temperament based on a set of musical requirements

Farup

2014

Journal of Mathematics and Music

View full text Add to dashboard Cite

A novel parametric circulating temperament is presented using a constructive approach. The temperament is optimal with respect to a heuristically chosen set of musical requirements. It is parametric in the sense that the tempering of the narrowest (i.e., closest to pure) major third can be freely chosen. Equal temperament arises as a limiting case. The temperament is optimal in the sense that the tempering of the widest major third and the narrowest fifth are minimised given the size of the least tempered major third. Also, under this constraint, the tempering of the major thirds closest to the least tempered third along the circle of fifths are minimised. The remaining degree of freedom is used to minimise the number of unique intervals. The resulting temperament exhibits various symmetries, and has, in general, two differently sized fifths and five differently sized major thirds. The temperament has no historic relevance as such, but can find good uses within all keyboard music from early baroque till today due to the selection of optimisation criteria that closely follow historical requirements for good temperaments. With some exercise it can be tuned by ear.

show abstract

Modelling the similarity of pitch collections with expectation tensors

Cited by 26 publications

References 14 publications

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

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

Quantum approaches to music cognition

Constructing an optimal circulating temperament based on a set of musical requirements

Contact Info

Product

Resources

About