PROPORTION AND SYMMETRY AS MUTUAL ANTAGONISTS IN TUNING: SOME QUARTER-TONE RESOURCES
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract Quarter-tones have the dubious honour of being the microtonal default in Western art music, yet they have been of little recent interest to those most involved with extended intonation. Other microtonal equal divisions have appealed as pragmatic approximations of consonant just-intonation intervals, something that quarter-tones do not offer. This article proposes that quarter-tones can be valued in a different way, for their ability to generate symmetrical harmonic resources that divide the fourth and fifth as the tritone does the octave. These resources are offered as examples of a broader aesthetic of symmetry, which is contrasted with an aesthetic of proportion. These antagonistic principles are explored through the case of the ever problematic tritone, illustrating how proportion and symmetry are best understood using the symbolic resources of just intonation and equal temperament respectively. Drawing on the work of Robert Hasegawa, Georg Friedrich Haas and Ivan Wyschnegradsky, the article argues for a hybrid approach that embraces both just intonation and equal temperament.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| 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 it