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Reference: David Meredith, (2007). Computing pitch names in tonal music: a comparative analysis of pitch spelling algorithms. DPhil. University of Oxford.Citable link to this page:


Computing pitch names in tonal music: a comparative analysis of pitch spelling algorithms

Abstract: A pitch spelling algorithm predicts the pitch names (e.g., C♯4, B♭5 etc.) of the notes in apassage of tonal music, when given the onset-time, MIDI note number and possibly the durationand voice of each note. A new algorithm, called ps13, was compared with the algorithms ofLonguet-Higgins, Cambouropoulos, Temperley and Chew and Chen by running various versionsof these algorithms on a ‘clean’, score-derived test corpus, C, containing 195972 notes, equallydivided between eight classical and baroque composers. The standard deviation of the accuraciesachieved by each algorithm over the eight composers was used to measure style dependence (SD).The best versions of the algorithms were tested for robustness to temporal deviations by runningthem on a ‘noisy’ version of the test corpus, denoted by C'.A version of ps13 called PS13s1 was the most accurate of the algorithms tested, achievingnote accuracies of 99.44% (SD = 0.45) on C and 99.41% (SD = 0.50) on C'. A real-time versionof PS13s1 also out-performed the other real-time algorithms tested, achieving note accuraciesof 99.19% (SD = 0.51) on C and 99.16% (SD = 0.53) on C'. PS13s1 was also as fast and easyto implement as any of the other algorithms.New, optimised versions of Chew and Chen’s algorithm were the least dependent on styleover C. The most accurate of these achieved note accuracies of 99.15% (SD = 0.42) on C and99.12% (SD = 0.47) on C'. It was proved that replacing the spiral array in Chew and Chen’salgorithm with the line of fifths never changes its output.A new, optimised version of Cambouropoulos’s algorithm made 8% fewer errors over C thanthe most accurate of the versions described by Cambouropoulos himself. This algorithm achievednote accuracies of 99.15% (SD = 0.47) on C and 99.07% (SD = 0.53) on C'. A new implementationof the most accurate of the versions described by Cambouropoulos achieved note accuraciesof 99.07% (SD = 0.46) on C and 99.13% (SD = 0.39) on C', making it the least dependent onstyle over C'. However, Cambouropoulos’s algorithms were among the slowest of those tested.When Temperley and Sleator’s harmony and meter programs were used for pitch spelling,they were more affected by temporal deviations and tempo changes than any of the other algorithms tested. When enharmonic changes were ignored and the music was at a natural tempo,these programs achieved note accuracies of 99.27% (SD = 1.30) on C and 97.43% (SD = 1.69)on C'. A new implementation, called TPROne, of just the first preference rule in Temperley’stheory achieved note accuracies of 99.06% (SD = 0.63) on C and 99.16% (SD = 0.52) on C'.TPROne’s performance was independent of tempo and less dependent on style than that of theharmony and meter programs.Of the several versions of Longuet-Higgins’s algorithm tested, the best was the originalone, implemented in his music.p program. This algorithm achieved note accuracies of 98.21%(SD = 1.79) on C and 98.25% (SD = 1.71) on C', but only when the data was processed a voiceat a time.None of the attempts to take voice-leading into account in the algorithms considered in thisstudy resulted in an increase in note accuracy and the most accurate algorithm, PS13s1, ignoresvoice-leading altogether. The line of fifths is used in most of the algorithms tested, includingPS13s1. However, the superior accuracy achieved by PS13s1 suggests that pitch spelling accuracycan be optimised by modelling the local key as a pitch class frequency distribution insteadof a point on the line of fifths, and by keeping pitch names close to the local tonic(s) on the line of fifths rather than close on the line of fifths to the pitch names of neighbouring notes.

Digital Origin:Born digital Type of Award:DPhil Level of Award:Doctoral Awarding Institution: University of Oxford


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 Bibliographic Details

Issue Date: 2007

Copyright Date: 2007 Identifiers

Urn: uuid:fa543bd6-cbdc-4206-a6f6-518f54c8c49a Item Description

Type: thesis;

Language: en Keywords: computer algorithms musical pitch tonality music theorySubjects: Music Applications and algorithms Computing Tiny URL: ora:6787


Author: Dr David Meredith - institutionUniversity of Oxford facultyHumanities Division - Music Faculty ox



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