Popular music often features a high amount of stable harmonic patterns, which facilitates the establishment of stylistic idioms and recognizability, and the changing frequencies of such patterns are closely linked to style and genre: new patterns arise while others die out. Here, we employ a content-based transmission model from cultural evolution research and compare three 20th-century popular music genres from diferent geographical and cultural contexts. Prior work on the evolution of harmony often only considers a small vocabulary of chords with a binary distance metric (same or diferent). Here, we introduce music-theoretically sensible notions of harmonic distance between chords, that allows us to arrive at more fine-grained results regarding relative influences of diferent kinds of harmonic relations on diachronic changes. Inferring the substitution probabilities for diferent chord classes, our results indicate an increasing usage of chord categories, whereas chord extensions remain relatively stable. Our study provides a principled methodology for cross-cultural research on the evolution of harmony.
Empirical research on patterns in popular music research can draw on a number of data
sources for analysis. Some genres have produced songbooks that contain essential melodic
and harmonic information to be used in performance. Commonly, these songbooks contain
melodies annotated with chord symbols that experts have transcribed from recordings of the
original pieces of music, for which authoritative versions usually do not exist: popular music is
recorded rather than written down. However, the annotated chords in songbooks have
sometimes gained a status of authority, the most famous example probably being the volumes of the
Real Book for the case of jazz [
Another source for harmonic analysis of popular music are methods from music information
retrieval (MIR) applied to audio recordings of music, either through manual transcription or
algorithmic inference3[
With the rise of corpus studies in musicology in the last decades, harmonic analysis in
popular music has become a frequent use case. Examples include the study of chord idioms in
the Beatles andReal Book jazz standards [
While the aforementioned studies have laid the ground for large-scale stylistic analysis of
several styles in popular music, they remain largely descriptive. There are still relatively few
studies on popular music dealing explicitly with models of diachronic information
transmission. The growing field of cultural evolution50[
In the present study, we explicitly address the research question of how harmonic patterns
in popular music change over time, and how their diachronic transmission can be modeled
formally. We build on a recent model for selection and mutation probabilities in Japanese pop
music [
To study the fluctuating transmission probabilities of harmonies in diferent popular music genres, we assemble several datasets by drawing on existing scholarship in music corpus studies. Specifically, we analyze datasets of chord symbols from three diferent cultural contexts: Japanese Pop songs, US-Pop songs, and Brazilian Choro pieces. Summary statistics are shown in Table1, and Figure1 displays the absolute numbers of pieces per year for the three corpora.
Year
Japanese pop songs This dataset was collected by the author of44[] and is comprised of
Japanese popular songs composed in years from 1927 to 2019. In this period, the musical style
changed drastically under a strong influence from Western popular culture. The songs were
taken from the top ranked songs in the yearly charts in Japan and also from a collection of
songbooks published in Japan. The chord progressions were extracted from published scores.
US-Pop songs We analyze US popular music by drawing on thBeillboard Hot 100 charts
between 1958 and 1991 [
Assembling data from diferent sources usually means that they do not adhere to the same
encoding standards, a big challenge in many comparative studie1s6[]. In our case, we were
confronted with various encodings for harmony, each of which containing diferent selections
of harmonic features. Another issue is that the labels were generated in very diferent processes
with diverging–sometimes genre-dependent–conventions that may or may not be explicitly
stated. For instance, aG:13 chord in jazz is usually assumed to be a short-hand notation for
G:(7,9,11,13), that is, all thirds below the stacking implied. These labels can be found in lead
sheets that are used in jazz performance. On the other hand, labels in the pop corpora are
analytical in the sense that someone (a person or a machine) listened to the songs and estimated
the best-fitting chord symbol for a given segment of music. Moreover, the labels in the corpora
used areanalytical (describing what was played in a certain recording), but those are not fixed
as some genres involve improvisation and performance variation. Another difÏculty relates to
the functional interpretation. In pop music, sometimes it is not clear what the global or local
key is,2 hence chords can not be interpreted in function to the tonic, rendering the harmony
ambiguous [
For these reasons, finding an appropriate data representation for chords is challenging. In
music information retrieval (MIR) research, one of the most commonly used standards for
chords is the syntax proposed by Christopher Hart2e1[
Note that this syntax represents chords in anabsolute manner that does not assign any functional roles to the harmonies, which avoids the problem of functional ambiguity. While we do not assume functional roles in encoding the chords, using a common syntax ensures that chord sequences are comparable. We follow the common practice to transpose all pieces in a corpus to the same key (C major) in order to ensure that relative chord distances are comparable, while still maintaining a functionless interpretation. Naturally, the keys of popular music pieces can be as ambiguous as are the functional roles of chords, but these ambiguities often concern the primacy of mediants, e.g. whether a piece is in C major or A minor.
As we have seen, musical chords are complex objects that do not imply a canonical distance
measure. In fact, music theorists have proposed a variety of diferent distance metrics between
harmonies, each of which emphasizes a particular aspect of chords. Among the proposed
metrics, one can distinguish between theoretical or mathematica1l3[
The simplest distance metric is to assess whether two chords are identical or diferent (binary). This, however, obfuscates more subtle diferences, e.g. the fact that, in tonal harmony, one would generally considerGa chord to be more similar toGa7 or aC chord than to aE♭ chord.
For chord parsing we useThe Harte Library,3 a convenient framework to work with chord
for chords in a symbolic representation. For cho r1ds= ( 1, 1) and 2 = ( 2, 2):
labels in Harte notation1[
The coarsest distance compares whether two chor ds1 and 2 are of the same type, i.e. whether they share all features except their roots. (1) (2) (3) (4) (5) (6) type( 1, 2) = { 0 1 if 1 = 2 if 1 ≠ 2 LoF( 1, 2) = |( 2) − ( 1)|, Jaccard ( 1, 2) = | 1 ∩ 2| . | 1 ∪ 2|
Focusing on chord roots, we measure their distance as the diference
of their positions on theline of fiths
(LoF) [
To measure the distance between two chords represented as
pitchclass sets, we employ theJaccard distance [
We denote the (infinite) vocabulary of chord symbols in Harte syntax withΩ. For each piece in each of the corpora, we extract -grams (chord sequences of lengt h ), were repetitions are denote the collection of 4-grams of all pieces released in y ebary consists of multiples of four bars. Thus, we only examine chord sequences of le n=gth4 , and retained. Many chordal patterns correlate with the formal structure of songs that frequently where chord 4-grams are given by () = ( 1(), 2 (), 3 (), 4 ()) , () ∈ Ω,
for some year-specific index of distinct 4-grams. The set of 4-grams in earlier years is defined as < = ⋃=1 . We assume that 4-grams w ∈ are generated randomly by mutating an existing reference chord sequence from a past songw,′ ∈ < . First, a reference chord sequence w′ is sampled from < according to itsselection probability, ( w ′ | < ). The actual chord sequence w is then generated by a pure replication or by replacing one or several elements of w according to thesubstitution probabilities (w | w′) = ∏ ( | ′). is not necessarily symmetric because, in genera l, ( | ′ ) ≠ ( ′ | .
) Note that, here, substitution probabilities for chords within one 4-gram are considered independent. While it is possible to employ more elaborate probabilistic music sequence models, these would introduce further parameters and would thus necessitate a larger amount of data for reliable inference. The substitution probabilities between all chords in a corpus can be expressed as a ×
transition matrix, where is the number of chord types in the corpus, that
In the selection process, we suppose that a reference 4-gram is selected by first randomly choosing a past song and then choosing a 4-gram in that song. Since the selection probability of a 4-gram is then proportional to its frequency in the past dat a , (w; < ) is proportional to the relative frequency#w of a chord 4-gramw in year . In order to make the selection process more realistic, we introduce a bias that afects the selection probabilities. Specifically, we assume that more recent songs exert a stronger influence on present songs than songs −(−) further in the past, corresponding to raecency bias, which we model by a weighting factor for a 4-gram observed in year, where is the parameter controlling the strength of the recency bias. The selection probability is thus given by (7) (8) (9)
Finally, the full specification of our generative model is given by the following equation:
The model parameters and (w | w′)are inferred using the expectation-maximization (EM)
algorithm 3[] with grid search and likelihood optimization, where the reference chord 4-grams
w′ are considered to be latent variables for each observed chord 4-grwamins the datasets used.
After estimating the mutation probabilities, we analyze the temporal evolution of substitution
probabilities from the posterior probabilities of the referential 4-grams for each year. For some
years, there are only a small number of songs, or even no songs, in our datasets, and we apply
additional smoothing techniques to reliably estimate the substitution probabilities for each year.
Specifically, we use the Kalman smoothing method [
We analyze the three corpora under three perspectives: (1) evolution of the chord vocabulary, (2) historical changes in the substitution probabilities, and (3) relations with the chord distances defined above. As the chord vocabularies have diferent encodings and sizes, it is difÏcult to compare them directly in a quantitative manner. For this reason, we focus on the 25 most frequent chords or substitutions, analyze each corpus separately, and interpret the results qualitatively against the background of music theory.
We first analyze the changing frequencies of occurrence of chords symbols.
For J-Pop (Figure2(a)), one can observe a trend towards a more uniform distribution of harmonies used. Whereas a few chords dominate the earlier phases (notably diatonic triads and applied dominants), chord frequency entropy increases rendering the harmonic vocabulary in use more diverse. The strongest changes occur roughly between the 1970’s and the mid-90’s. It is difÏcult to assert whether this trend is due to a change in the harmonic language or due to changes in data, as this phase lies between the two peaks visible in Figur1e. However, after this phase, the entropy of the chord vocabulary is distinctively higher than in the earlier years.
In US-Pop (Figure3(a)), the chord vocabulary remains relatively stable throughout, although here, too, one can observe a slight increase in entropy towards the end of the timeline (chord frequencies become even more uniform). Choro (Figu4r(ea)), in contrast, shows a more mixed behavior, with some local fluctuation (as opposed to US-Pop), but no clear trend (as opposed to J-Pop).
1.0 0.8 liity0.6 b a b o rP0.4 0.2
FM9 Gsus4 CM7 Bm7(b5) Bb Fm A D Em7 FM7 C7 B7 Am7 D7 A7 Dm7 E Em G F Dm G7 E7 C Am 1.0 0.8 liity0.6 b a b o rP0.4 0.2
G->Gsus4 Am7->FM7 Dm7->FM7 FM7->Dm7 G->Em7 FM7->F F->FM7 Em->Em7 Em7->C G->Dm7 G->E Am7->Am Dm7->F Dm7->Dm Em->G F->Dm7 G->G7 E7->Em E7->E C->Am C->Em F->Dm Am->F Dm->F G7->G (a) Chord frequencies.
(b) Substitution probabilities.
The evolution of substitution probabilities is shown in Figur2e(bs), 3(b), and 4(b), respectively. The changes observed in the relative frequencies of harmonies also afects their substitutions,
Finally, we relate the substitution probabilities to the three chord distances defined above. For each of the three corpora, we correlate the mutation probability curves, and qualitatively interpret the resulting hierarchical clustering.
The results are clearest for the case of J-Pop (Figu5r)e. Here, two distinct clusters emerge, revealing two types of chord mutation dynamics. Their meaning, however, is less clear, as the clusters do directly correspond toUS-Pop again maintains a relatively stable scenario. one of the three chord distances introduced above.
For US-Pop (Figure6), the clustering is less pronounced, although here, too, two clusters appear. In contrast to J-Pop, their meaning is better interpretable: the smaller cluster contains mostly (but not exclusively) mutations between chords that are relative to one another (e.g., G:min and Bb:maj), (applied) dominants being replaced by their tonics (e.gA.:maj and D:maj), or, interestingly, stepwise downward mutations (e.gD.,:min and C:maj). The second cluster contains more subdominant-to-tonic patterns than the fist (e.g.G,:maj and D:maj), but also a number of mutations between relative chords. Moreover, a number of stepwuipsweard replacements can be found (e.g.,G:maj and A:min).
In the case of Choro (Figure7), there are three large clusters, and the picture is more mixed. The first cluster in the upper left constists of chord inversions (e.g.,D:min/b3 and D:min). In the second (middle) cluster, we see chord inversions as well, but also dominant replacements and chromatic alterationsD(:min and D:7), while the third cluster in the bottom right exclusively contains chord mutations that maintain the same root (leading to a minimal line-of-fiths distance).
In this study, we have employed a statistical evolutionary model to understand stylistic changes in chord usage in popular music from diferent cultural contexts. Utilizing a common representation for harmonic units in all corpora, we have observed historical changes in chord frequencies as well as the evolution of substitution probabilities in chord 4-grams.
Our results indicate stylistic diferences in how patterns change over time, but their relation to chord distances is less pronounced than anticipated. Further research needs to investigate to what extend this needs to be attributed to the diferent data sources, and to what extend these are musical factors. Moreover, future work needs to expand in several directions, specifically testing whether our findings can be replicated in diferent repertoires, and looking into how cross-cultural influences can be incorporated in the analyses.
This research was partially funded by the Junior Professorship for Digital Music Philology and Music Theory at Julius-Maximilians-Universität Würzburg, Germany. 1.0 0.5 1.0 0.5 1.0 0.5