Vocal imprecision as a universal constraint on the structure of musical scales
Bibliographic record
Abstract
Abstract Theories of the origin of musical scales from the ancient Greeks to the present day have assumed that the intervals comprising scales are defined by specific mathematical ratios. Such theories are predicated on pre-tunable instruments, and yet the voice is almost certainly the original musical instrument. Therefore, the analysis of vocal scales offers a more naturalistic approach to understanding the origin of musical scales. In the present study, we conducted a large-scale computational analysis of vocal pitch-class properties and their implications for scale structure. We analyzed 417 field recordings of solo, unaccompanied songs from across 10 principal musical-style regions of the world. The results revealed a mean vocal pitch-class imprecision of approximately 1.5 semitones, and comparable results were obtained across all regions. These results suggest that vocal imprecision is universal and is mainly derived from the physiological limitations of the voice. Such vocal imprecision fundamentally constrains the formation of musical scale structure: it provides a lower limit on the spacing between adjacent scale tones, and thereby an upper limit on the number of scale tones that an octave can contain. We discuss these results in terms of an Interval Spacing model of the evolution of musical scales.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.023 | 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".