Consonance and prevalence of sonorities in Western polyphony: Roughness, harmonicity, familiarity, evenness, diatonicity

Abstract

We counted trichords in a database of vocal polyphony. In modern terminology, the most common in the thirteenth to sixteenth centuries were major (in semitones: 047), minor (037), suspended (027), unnamed (025, 035), and diminished (036). Prevalence profiles correlated with predictions of simple models of roughness and harmonicity; sometimes also with evenness (pitch-class spacing), but not diatonicity. From the thirteenth to the fifteenth century, 047 and 037 became more relatively prevalent, after which profiles stabilized. Our results imply that today the C/D of trichords depends mainly on familiarity, roughness, and harmonicity. C/D is best understood in an interdisciplinary, psychohistoric approach.

Simultaneous consonance in music perception and composition

“…Most previous work solely discusses beating and its psychological correlate, roughness (e.g. Cousineau et al, 2012;McDermott et al, 2010McDermott et al, , 2016Parncutt & Hair, 2011;Parncutt et al, 2018;Terhardt, 1984). However, we contend that the existing evidence does little to differentiate beating and masking theories, and that it would be premature to discard the latter in favor of the former.…”

“…It has correspondingly been proposed that periodicity/harmonicity determines consonance perception (Bidelman & Heinz, 2011;Boomsliter & Creel, 1961;Bowling & Purves, 2015;Bowling et al, 2018;Cousineau et al, 2012;Ebeling, 2008;Heffernan & Longtin, 2009;Lee, Skoe, Kraus, & Ashley, 2015;Lots & Stone, 2008;McDermott et al, 2010;Nordmark & Fahlén, 1988;Patterson, 1986;Spagnolo, Ushakov, & Dubkov, 2013;Stolzenburg, 2015;Terhardt, 1974;Ushakov, Dubkov, & Spagnolo, 2010). 4 The nature of this potential relationship depends in large part on the unresolved issue of whether listeners detect periodicity/harmonicity using autocorrelation or pattern-matching (de Cheveigné, 2005), as well as other subtleties of auditory processing such as masking (Parncutt, 1989;Parncutt & Strasburger, 1994), octave invariance (Harrison & Pearce, 2018;Parncutt, 1988;Parncutt, Reisinger, Fuchs, & Kaiser, 2018), and nonlinear signal transformation (Lee et al, 2015;Stolzenburg, 2017). It is also unclear precisely how consonance develops from the results of periodicity/harmonicity detection; competing theories suggest that consonance is determined by the inferred fundamental frequency (Boomsliter & Creel, 1961;Stolzenburg, 2015), the absolute degree of harmonic template fit at the fundamental frequency (Bowling et al, 2018;Gill & Purves, 2009;Parncutt, 1989;Parncutt & Strasburger, 1994), the degree of template fit at the fundamental frequency relative to that at other candidate fundamental frequencies (Parncutt, 1988;…”

“…4 The nature of this potential relationship depends in large part on the unresolved issue of whether listeners detect periodicity/harmonicity using autocorrelation or pattern-matching (de Cheveigné, 2005), as well as other subtleties of auditory processing such as masking (Parncutt, 1989;Parncutt & Strasburger, 1994), octave invariance (Harrison & Pearce, 2018;Parncutt, 1988;Parncutt, Reisinger, Fuchs, & Kaiser, 2018), and nonlinear signal transformation (Lee et al, 2015;Stolzenburg, 2017). It is also unclear precisely how consonance develops from the results of periodicity/harmonicity detection; competing theories suggest that consonance is determined by the inferred fundamental frequency (Boomsliter & Creel, 1961;Stolzenburg, 2015), the absolute degree of harmonic template fit at the fundamental frequency (Bowling et al, 2018;Gill & Purves, 2009;Parncutt, 1989;Parncutt & Strasburger, 1994), the degree of template fit at the fundamental frequency relative to that at other candidate fundamental frequencies (Parncutt, 1988;Parncutt et al, 2018), or the degree of template fit as aggregated over all candidate fundamental frequencies (Harrison & Pearce, 2018). This variety of hypotheses is reflected in a diversity of computational models of musical periodicity/harmonicity perception (Ebeling, 2008;Gill & Purves, 2009;Harrison & Pearce, 2018;Lartillot, Toiviainen, & Eerola, 2008;Parncutt, 1988Parncutt, , 1989Parncutt & Strasburger, 1994;Spagnolo et al, 2013;Stolzenburg, 2015).…”

Pitch-class prevalence in plainchant, scale-degree consonance, and the origin of the rising leading tone

“…A preference for consonant (or beautiful) sounds and careful procedures for the resolution of dissonances onto consonances is a characteristic of most Western music since antiquity (Cazden, 1945). In general, consonance/dissonance depends on a mixture of nature (acoustics) and nurture (familiarity), of which the latter changes historically; psychoacoustics involves both (Parncutt, Reisinger, Fuchs, & Kaiser, 2018). Given the long history of aesthetic theory and the importance of concepts such as 'euphony', 'beauty', and 'sweetness' in medieval aesthetics (Wegman, 1995), singers of chant may have been striving for both sonic beauty (consonance) and similarity with speech (the word of God).…”

“…It is possible that singers of chant were sensitive to these variations (perhaps more sensitive than we are today) and intuitively favoured more consonant tones (cf. Parncutt et al, 2018). This sensitivity may have influenced the relative frequency of occurrence (prevalence) of scale degrees.…”