Study 01 · The Anatomy of Influence
Influence in jazz is usually told as a lineage of names. Here we take a measured genealogy of trumpet players and ask a harder question: what actually predicts an influence tie, playing with the same people, or sounding the same? Scroll to follow the argument.
The trumpeter and teacher John McNeil drew a genealogy of 52 players, a chart of who influenced whom. The musicologist Paul Berliner then checked it against years of interviews with the musicians themselves. We treat this expert judgment as our starting point.
Unlike collaboration, influence is asymmetric: a mentor shapes a disciple. Every arrow here runs from influencer to influenced.
Influence is concentrated. A handful of players, namely Miles Davis, Clifford Brown, and Freddie Hubbard, account for most of the arrows, while many others receive influence without passing it on. These hubs are highlighted.
Colour marks birth year, from King Oliver in the 1880s to players born in the 1970s. Influence tends to flow between adjacent generations; jazz musicians look to their near-elders, not to the distant past.
Take any two trumpet players. On their own they tell us nothing about influence. What matters is the company they keep on record.
From the discographies we pull everyone each player recorded with. Some of those collaborators are shared: the same bassists, drummers, and pianists appear on both players' sessions. Links between collaborators are removed for demonstration.
We reduce that shared crowd to a single number: the share of one player's collaborators that the other also played with. More shared sidemen, a heavier tie. The measure is directed and it asks how much of your circle sits inside mine.
Do this for all pairs and the field becomes a matrix. Darker cells are players who move in the same social world. This is one of the two things we will test against influence.
For every player we gather 30-second random previews of their recordings, approximately 16,000 tracks. Each one becomes a mel-spectrogram: time along one axis, pitch along the other, brightness for energy. The mel scale spaces those pitches the way human hearing does. This image, not the raw waveform, is what our embedding model reads. On the right is the spectrogram of King Oliver's Chattanooga Stomp from 1923.
Each spectrogram passes through VGGish, a convolutional network pre-trained on a large audio corpus. It returns a 128-number embedding for every track, a compact fingerprint of its timbre and phrasing. Reduced to a plane, each point here is a single recording.
Averaging a player's tracks gives one representative point per artist, and the cosine similarity between those points is our measure of sonic closeness. Lay the genealogy on top and a pattern appears: influenced players sit at a moderate distance from those who shaped them, close enough to share a language yet far enough to have a voice of their own.
First, the genealogy again, every documented influence tie drawn with equal weight. This is the pattern the other two measures will be laid against.
Now the same layout, but each tie's thickness is the collaboration overlap between the two players. Heavier lines mark influence pairs who also moved among the same musicians. A cutoff is introduced for easier plot interpretability.
Finally, thickness is acoustic similarity. Some influence ties are carried by sound, others by social overlap, and they are not the same ties. That mismatch is the whole point: collaboration and sound are distinct routes into influence, not proxies for one another. A cutoff is introduced for easier plot interpretability.
Every session happened somewhere, so we locate each one in space. Named-entity recognition pulls place names from the session records, the Google Places service turns them into coordinates, and we check each result by hand. Grouped into eight regional clusters, the map shows where jazz was recorded. Three centres dominate: the Eastern United States, the Western United States, and Central Europe, with Japan a notable secondary hub. We use the overlap between two players' locations over time as a control, so that sharing a city does not by itself pass for influence.
Each player carries a birth year, from King Oliver in 1885 to players born in the 1970s. Louis Armstrong, pictured here with his family, was born in 1901 and learned directly from Oliver, his mentor a generation ahead. That shape holds across the field: influence tends to pass from older players to younger ones, and between near generations rather than across distant eras. Generation is a scaffold the ties are built on, so we account for it before reading anything into sound or collaboration.
Standing in the field matters too. We measure success by how many releases a player accumulated, counting albums issued in a five-year window around each session and setting aside posthumous compilations. Releases track what record companies chose to put out in response to demand, so they register public and critical appetite rather than mere studio activity. Miles Davis, pictured here, sits near the top on this measure, and the most released players (Davis, Gillespie, Brown, Hubbard) are also the ones the genealogy marks as most influential.
An exponential random graph model treats the whole influence network as the outcome. It asks a simple question: out of every network we could have drawn on these players, what makes the one we actually see more likely? Compared here are the real network, purely random networks, and networks from a bare model that fixes only the number of ties. The random and bare versions match the count of connections but miss the shape, which is why we need terms that capture real structure.
We build the model up piece by piece. Alongside the core tendencies of the network, such as a few players attracting most of the ties, we add the two measures at the heart of the study: overlap in collaborators and similarity in sound. We also control for players' year of birth, where they played, and how successful they were. The goodness-of-fit panels show that the fitted models reproduce the real network's structure across degree, shared partners, and distance.
Both playing with the same people and sounding alike make influence more likely. Yet past a point the pattern reverses: players who share almost the same collaborators and also sound almost the same are seen as imitators rather than influences. Influence lives in the balance between honouring a tradition and departing from it. The full account, with the models and the numbers behind this trade-off, is in the paper.
Side B · Track 4
Our article shows that influence ties are jointly structured by overlapping collaboration networks, audio similarity, network endogenous effects, and sociodemographic attributes.
We find that audio similarity yields a strong, positive, and statistically significant estimate in both the basic and full models, suggesting that influence ties tend to form between musicians who sound similar. Our analysis shows that overlap in collaboration partners is highly predictive of an ascribed influence tie between two trumpet players, and remains predictive after including the term capturing audio similarity. This result illustrates that social and stylistic similarity are not mere proxies for one another when studying influence; rather, both contribute to the structure of ascribed influence, even when considered simultaneously.
Top audio similarity, defined as the binary indicator of high audio similarity, has a negative and marginally significant coefficient, supporting the notion that excessive sonic similarity reduces the probability of ascribing an influence relationship. Unlike audio similarity, being among the top 10% of collaboration-overlap dyads is not negatively associated with influence. Hence, the absence of influence ties between artists with excessive audio similarity cannot be attributed to a shared mentor, but rather points to a genuine role of sonic similarity.
We find that the interaction term is negative and significant. This suggests that musicians who both sound similar and share a similar set of collaborators are less likely to be seen as influences of one another. We assume that this closeness lacks the necessary differentiation to ascribe influence, since musicians are seen as belonging to the same scene rather than as occupying distinct positions in the genealogy.
The negative activity term for birth year indicates that older players are more likely to exert influence, whereas younger players are more likely to be influenced, as evidenced by the positive popularity term for birth year. The negative coefficient indicates that players of different ages are less likely to share an influence tie. We interpret this to be a sign that jazz musicians do not reach far back in time for inspiration, but look to their relative contemporaries for influence.
Our findings suggest that the structure of cultural influence can be characterized by a balance between closeness and distance in social and stylistic space. We find that both shared collaborators and high similarity in musicians' recordings are positively associated with ascribing influence, but that a simultaneous social and stylistic overlap decreases the likelihood of influence. Likewise, excessive similarity in sound decreases the probability of ascribing an influence tie.
By studying influence ties, we add to previous accounts that examine the structure of collaboration networks to understand the organization of cultural fields.
Our study opens a path to understanding field
change from a network-theoretical perspective by examining how artists build
on the past while proposing novel cultural content and establishing their
positions within the current instantiation of a field.
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