2019
DOI: 10.1371/journal.pone.0217242
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Statistical characteristics of tonal harmony: A corpus study of Beethoven’s string quartets

Abstract: Tonal harmony is one of the central organization systems of Western music. This article characterizes the statistical foundations of tonal harmony based on the computational analysis of expert annotations in a large corpus. Using resampling methods, this study shows that 1) the rank-frequency distribution of chords resembles a power law, i.e. few chords govern a large proportion of the data; 2) chord transitions are referential and chord predictability is significantly affected by distinguished chord features;… Show more

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Cited by 29 publications
(21 citation statements)
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“…For the domain of harmony, the key criterion is root motion 7,15 . In common-practice tonality, there is a strong preference for root motion to be in descending fifths (this also applies to the Jazz idiom 16 ), followed by descending thirds and ascending seconds; root motions inverting these interval directions (ascending fifth, ascending third, and descending second) are less prominent [17][18][19] . This distribution sets common-practice tonality apart from Pop/ Rock tonality, which is characterised by almost a reversal of these frequencies 20 .…”
Section: Methodsmentioning
confidence: 99%
“…For the domain of harmony, the key criterion is root motion 7,15 . In common-practice tonality, there is a strong preference for root motion to be in descending fifths (this also applies to the Jazz idiom 16 ), followed by descending thirds and ascending seconds; root motions inverting these interval directions (ascending fifth, ascending third, and descending second) are less prominent [17][18][19] . This distribution sets common-practice tonality apart from Pop/ Rock tonality, which is characterised by almost a reversal of these frequencies 20 .…”
Section: Methodsmentioning
confidence: 99%
“…The study of (tonal) harmony thus occupies a prominent position in musicological research. Owing to the growing availability of machine-readable datasets of harmonic analyses (see Section 2), harmony can now be examined across different styles and periods using advanced computational and empirical methods (e.g., Quinn and Mavromatis, 2011;Broze and Shanahan, 2013;Temperley and de Clercq, 2013;Jacoby et al, 2015;Chen and Su, 2018;White and Quinn, 2018;Moss et al, 2019). The main contribution of this paper is the introduction and description of a new corpus of annotated scores under the FAIR principles of Open Science (Wilkinson et al, 2016).…”
Section: Introductionmentioning
confidence: 99%
“…With the advent of digital technology, musicology is being enriched with novel research methods. Digital archives and computational strategies enable musical corpus studies in a quantitative and systematic fashion [41,44,56,61,64,69,76]. Such studies have recently been performed based on a variety of different music representations including scanned sheet music images [61,74], symbolic scores [5,44,73], MIDI files [35,47,79], and audio recordings [1,41,64,75,76].…”
Section: Introductionmentioning
confidence: 99%
“…In the first case, music experts analyze and annotate the primary material (e.g., scores or recordings) based on their music theory knowledge [11,48] (piece analysis). Subsequently, computational and statistical methods are applied for systematically analyzing the annotations and drawing conclusions from these statistics [44] (corpus analysis). This approach entails full human control of the piece analysis but involves a decent amount of manual work, which becomes impractical in the case of large corpora.…”
Section: Introductionmentioning
confidence: 99%