[DSRP Evidence](https://dsrpevidence.org/)

# Why twelve notes? An economic model of scale size and evidence on chromatic pitch-class use in Western classical music, 1485–1963

Eamon McGinn, Sergey Alexeev, 2026, Journal of Cultural Economics — Economics

Patterns: [Distinctions](https://dsrpevidence.org/pattern/distinctions), [Relationships](https://dsrpevidence.org/pattern/relationships)

## In short

The finding shows that a categorical structure — a finite set of discrete pitch classes rather than a continuous pitch space — emerges from a trade-off relationship between the value gained from more categories and the cost of acquiring and building them.

## What they found (results)

Pitch-class entropy rose over historical time and within composers' careers; use of the twelve encoded semitone classes broadened before 1900 and then saturated, consistent with the model's prediction that rising learning costs eventually cap the optimal number of discrete pitch categories even as construction costs fall.

## What they set out to do (purpose)

To explain why musical systems organize pitch into finite discrete sets rather than a continuous pitch space, modeling scale-system size as an economic trade-off between harmonic value and instrument-construction/learning costs, and to test the model's predictions against historical composition data.

## Abstract

Why do musical systems organise pitch into finite sets rather than draw without limit on the pitch continuum? We model scale-system size as an economic choice that balances harmonic possibilities against instrument-construction and learning costs. An acoustic calibration indicates that total harmonic value grows faster than linearly but more slowly than the number of possible interval pairs. When learning costs eventually rise more steeply than harmonic value, the model yields a finite optimum even as physical construction costs approach zero. We evaluate the model's comparative patterns using 623 Western classical MIDI compositions by 48 composers spanning 1485–1963. Pitch-class entropy rises over historical time and within composers' careers; its association with national income is positive but fragile. Use of the twelve encoded semitone classes broadens before 1900 and then saturates, while dissonance continues to rise and usage evenness can keep changing within the fixed palette. Because MIDI represents pitch within twelve semitone classes, these results measure chromatic pitch use rather than historical scale-system size itself. Evidence from instrument history and electronic music complements the corpus analysis. Together, the model and evidence show how technological and cognitive costs can shape the evolution of musical form.

These researchers were not testing DSRP. The finding is theirs; the correspondence to DSRP is drawn by this site.

[Source](https://doi.org/10.1007/s10824-026-09607-y)