Music composers have a long history of learning from other composers. In a new working paper (PDF link) with Karol Jan Borowiecki and Maria Marchenko, we explore this tradition in composer education. How does a composer’s quality influence the quality of the composers he or she teaches?
Our analysis draws on a comprehensive dataset of 17,433 composers over several centuries. We confirm the presence of quality transmission from teachers to students. Moreover, we find evidence of quality carrying through to subsequent generations of students: that is, not just teacher to student, but to student’s student, student’s student’s student and so on.
Quality, of course, can be many things. We define quality in terms of reputation and cultural impact. To provide a reasonably objective measure, we use biographies of composers in the musical encyclopaedia Grove Music Online. We infer quality from the length of a composer’s biography: the longer the biography, the more notable and influential the composer. As Grove is principally a reference work for music researchers, the biographies are focused on individuals’ musical careers. The word counts of biographies in Grove are thus a useful proxy for quality.
My very dear master
The central insight that inspires our analysis is that teacher quality matters for student performance. In contrast to schooling, where teachers have responsibility for classes of students at a time, the teacher–student relationship among composers is historically closer to a master–apprentice model. In this light, it makes sense to consider teacher quality in terms of a composer’s professional accomplishments. We hypothesise that the more acclaimed (higher quality) a composer is, the higher the observed quality of his or her students.
As an example of this, consider Franz Liszt: a prominent Hungarian composer during the nineteenth century. Liszt studied under the Austrian composer, Carl Czerny (himself a student of Beethoven). Czerny recognised a remarkable talent in Liszt, writing of his pupil that ‘never before had I had so eager, talented, or industrious a student’.
Just as Czerny was impressed by Liszt, Liszt was likewise grateful to Czerny. As Liszt’s career advanced, he wrote to Czerny to credit his ‘master’ for his success:
Franz Liszt (Vienna, 1828), writing to Carl Czerny
My very dear Master, (…) ‘Yes,’ I said to myself with a deep feeling of bitterness, ‘I am an ungrateful fellow; I have forgotten my benefactor, I have forgotten that good master to whom I owe both my talent and my success.’ (…) You have doubtless heard that I have been playing your admirable works here with the greatest success, and all the glory ought to be given to you. (…)
Image source: Thomas Goller / Wikimedia Commons
Liszt’s letter to Czerny hints at the idea of quality transmission, but is far from definitive proof of the concept. Czerny and Liszt constitute just one of the nearly 37,000 teacher–student pairs identified in our dataset. This provides a rich evidence base for examining whether other composers might have grounds to say they ‘owe both (their) talent and (their) success’ to their teachers?
Our data show a correlation between teacher quality and student quality (as measured by biography word counts). As students can have multiple teachers, we consider both the average word count of a student’s teachers as well as the maximum word count of a student’s highest quality teacher. Either way, our results show that a 1 per cent increase in the length of the average/maximum teacher’s biography is associated with an average 0.1 per cent increase in the length of a student’s biography — an effect that is statistically significant.
Correlation is not causation!
The above is not direct evidence of teachers influencing the performance of their students. Pairing between teachers and students is not necessarily random: good students might seek out accomplished teachers; good teachers might choose only the most promising students.
To address this, we compare actual teacher–student pairs with counterfactual pairs: that is, composers who could plausibly have connected (for example, they were alive at the same time), but did not. We use these counterfactual pairs to estimate the probability of two composers actually connecting given place of birth. A student might choose a teacher (and vice versa), but cannot choose where he or she is born. We then apply this probability of connection as a ‘discount factor’ to teacher quality, which allows us to construct a measure of estimated teacher quality.
Underpinning the validity of this estimated quality measure is that when teachers and students share similar backgrounds, there is greater transmissibility of quality. Put another way, students are better able to absorb the talents of their teachers when they come from the same place — for example, because they both speak the same language. In our estimated quality measure, geography (an exogenous factor, which no composer chooses) determines the probability of connecting. And the greater the probability of connecting, the greater the weight placed on the effect of a teacher’s quality on a student’s quality.
When considering all teacher–student pairs individually, we find that a 1 per cent increase in effective teacher quality results in a 0.25 per cent increase in student quality (when controlling for the individual teacher and the geographical similarities between teacher and student). Applying the average probability of connection (around 5 per cent), this means that a 1 per cent increase in the teacher’s word count on average leads to a 0.013 per cent increase in the student’s word count. To the extent that a given teacher and student share a place of birth, the probability of connection — and therefore the transmission effect — will be higher.
As our dataset covers teacher–student pairs from the fourteenth century onwards, we can also examine quality transmission across multiple generations of students. Our longest chain, starting with the French composer Jean Mouton, includes a minimum of 21 generations of composers. (That chain also includes Beethoven, Czerny and Liszt.)
We estimate the effect of teacher quality on up to ten generations of students. When controlling for individual teacher effects, we find a strong and significant correlation with the quality of students up to the eighth generation from the teacher. The effect is strongest for the first generation (the direct student) and diminishes. The results of our multigenerational analysis provide another perspective on quality transmission: though teachers and students may select each other (hence the two-stage approach discussed above), a teacher does not choose his or her third generation of student. Similarly, a student is unlikely to choose a teacher on the basis of his or her teacher’s teacher. The relationship between composers across non-adjacent generations is as good as random.
That the quality of teachers has an effect on student performance is not, of itself, a surprising result — in any event, the relationship is one we expected to find. More striking is the persistence of quality transmission. I confess, when we discussed looking at effects across multiple generations, I was sceptical that we would find much. Yet our results are clear: we find signs of composer quality from teachers passing through multiple generations of students. The contribution of an outstanding teacher goes beyond the direct relationship with his or her own students — those students, harvesting the gains from having a high quality teacher, will also pass some of that benefit on to their own students.
The question left largely unanswered by our analysis is why quality transmission occurs. Our data do not enable us to unpack the specific causal channels. In the context of education, an obvious candidate relates to skills: more accomplished teachers equip their students with a better range of competencies. But equally, it might be that having an acclaimed composer as teacher provides a strong springboard for a student’s career — for example, due to reputational effects or better access to professional networks.
I started working on this project as a research assistant over two years ago, and have learned a great deal during that time. Karol, Maria and I have had many rich and interesting discussions about our data and how to make use of it. It was a welcome surprise to be asked to co-author this paper, and I have been grateful for the opportunity to work with my colleagues on such a novel and interesting topic. That we now have a working paper to share is an exciting milestone.