Vagaries of Harmony: Global Major-Third Relations in the Instrumental Music of Brahms
Bibliographic record
Abstract
Internal key relationships in Brahms’s music are an important yet often overlooked area in which he adapted classical forms to a new harmonic language. Using analytical resources developed by Richard Cohn and other so-called “neo-Riemannian” theorists, Brahms’s harmonic ingenuity can be better analyzed in the context of nineteenth-century chromaticism, rather than in a context that is entirely beholden to the principles of diatonic tonality. Nineteenth-century harmonic features that are relevant to Brahms’s music include modulation by major third, augmented triads as structural objects, and hexatonic cycles. This paper will incorporate these harmonic features into a discussion of three compositional trends. First, local modulations by major thirds are used as central contents of sonata-form theme groups. Second, Brahms employs a Schubertian treatment of second subjects in major-third related keys, resolving both the key and the key relations in the recapitulation, but his practice deviates slightly from Schubert’s. Third, he replaces typical dominant or subdominant key relationships with major thirds in the most global contexts. While Brahms was only one of many composers using major-third related harmonies in the nineteenth century, the interplay between diatonic and chromatic structures in his classical forms contribute several interesting innovations to Romantic compositional practice.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.002 | 0.008 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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 source (direct Gemma or distilled Codex), 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".