Musical scales optimize pitch spacing: a global analysis of traditional vocal music
Bibliographic record
Abstract
The dominant model of musical scales in academic theories is derived from instrument tunings. However, the study of vocal scales – most especially in indigenous cultures – has been all but ignored. The voice is almost certainly the original musical instrument, and so an analysis of vocal scales provides a more naturalistic means of understanding the evolution of music. In particular, we explore the idea that the structure of musical scales is a reflection of the vocal imprecision inherent in the way that people sing, regardless of culture. To investigate this issue globally, we carried out a large-scale computational analysis of 418 ethnographic field recordings of vocal songs from indigenous/traditional cultures, spanning the 10 principal musical-style regions of the world, analyzing the number of pitch-classes, the number of interval-classes, the pitch-class distribution, the scale intervals, and scale typology. The results revealed that vocal scales have reliably larger intervallic spacings between pitch-classes than do theory-based and instrumental scales in Western culture. In addition, the mean interval-size of the scales was significantly correlated with people’s imprecision in singing pitches across the world regions. These results lend support to a physiological model in which musical scales optimize pitch spacing in order to accommodate the imprecision inherent in vocal production and thereby maintain distinguishability between pitch-classes during musical communication.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".