Heaps’ law and vocabulary richness in the history of classical music harmony

Abstract

Music is a fundamental human construct, and harmony provides the building blocks of musical language. Using the Kunstderfuge corpus of classical music, we analyze the historical evolution of the richness of harmonic vocabulary of 76 classical composers, covering almost 6 centuries. Such corpus comprises about 9500 pieces, resulting in more than 5 million tokens of music codewords. The fulfilment of Heaps’ law for the relation between the size of the harmonic vocabulary of a composer (in codeword types) and the total length of his works (in codeword tokens), with an exponent around 0.35, allows us to define a relative measure of vocabulary richness that has a transparent interpretation. When coupled with the considered corpus, this measure allows us to quantify harmony richness across centuries, unveiling a clear increasing linear trend. In this way, we are able to rank the composers in terms of richness of vocabulary, in the same way as for other related metrics, such as entropy. We find that the latter is particularly highly correlated with our measure of richness. Our approach is not specific for music and can be applied to other systems built by tokens of different types, as for instance natural language.

Cultural evolution and music

“…For example, research on traditional and folk music have revealed that scales around the world have a tendency to converge towards similar patterns (McBride and Tlusty, 2019;Brown and Jordania, 2013;Kuroyanagi et al, 2019), musical variation is correlated with social complexity (Lomax, 1968;Wood et al, 2021) and sometimes population history (Brown et al, 2014; but see Matsumae et al, 2021), and that certain styles of music are reliably associated with particular behavioral contexts across cultures (Mehr et al, 2019) according to their acoustic features (Mehr et al, 2018;Hilton et al, 2021). Studies of classical music have found that melodic intervals are associated with particular historical periods (Rodriguez Zivic et al, 2013;Weiß et al, 2019;Harasim et al, 2021), and that tonal complexity and harmonic richness have increased over time ( Weiß et al, 2019;Serra-Peralta et al 2021). Studies of contemporary and popular music have tracked changes in a variety of music characteristics such as diversity, loudness, and the emotional valence of lyrics (Mauch et al, 2015;Serrà et al, 2012;Napier and Shamir, 2018;Brand et al, 2019), and have used detailed information on population structure and the distribution of cultural variants to try to understand the processes underlying such changes (Youngblood, 2019b;Klimek et al, 2019;Youngblood et al, 2021;Rosati et al, 2021).…”

“…European "common practice" music since the 17th century is particularly richly documented (Taruskin, 2005). The Kunst der Fuge database, for example, has ~19,500 full MIDI transcriptions that have been used to investigate 4 everything from changes in harmonic richness (Serra-Peralta et al 2021) to statistical regularities in temporal structure ( González-Espinoza et al, 2020). Other databases, like the Classical Music Navigator and ArkivMusic , provide detailed 5 6…”

“…The major and minor modes also appear to have changed over time, and are thought to have been preceded by multiple ancestors (Albrecht & Huron, 2014). Over larger time scales, both transcription and audio data have been used to conclude that factors like tonal complexity and harmonic richness have increased over the history of Western classical music ( Weiß et al, 2019;Serra-Peralta et al 2021), possibly driven by a novelty bias for more rare musical events (Nakamura and Kaneko, 2019). Even individual composers appear to have greater maximum pitch uctuations later on in the historical record (Liu et al, 2013).…”

Cultural Evolution and Music

“…The major and minor modes also appear to have changed over time, and are thought to have been preceded by multiple ancestors (Albrecht and Huron, 2014). Over larger time scales, both transcription and audio data have been used to conclude that factors like tonal complexity have increased over the history of Western classical music ( Weiß et al, 2019;Serra-Peralta et al, 2021), possibly driven by a novelty bias for more rare musical events (Nakamura and Kaneko, 2019). Even individual composers appear to have greater maximum pitch uctuations later on in the historical record (Liu et al, 2013).…”

Proposed Marketing Strategy For PT. Harmony Land Group in Facing off Uncertainty Period

“…In quartal one, 2020, Harmony Land only sold 1 unit house. It is the lowest from five years of Harmony Land history (Serra-Peralta, Serrà, & Corral, 2021). However, with a solid and learner team.…”