<i>Kōan</i>-like ambiguities in John Cage's<i>Electronic Music for Piano</i>: a novel application of formal concept analysis
Bibliographic record
Abstract
In this article I present a novel application of Formal Concept Analysis (FCA) to the problem of interpreting and analysing the non-standard graphical music score Electronic Music for Piano (1965) by American composer John Cage. The avant-garde nature of Cage's score, presented on a single page as a series of anecdotal texts written in natural language, resists traditional approaches of music theory analysis. I utilise FCA for its suitability for delving into the work's taxonomy as well as its ability to visualise and analyse semiotic patterns and relationships within the natural language text fragments of the work. In this regard, FCA is also used as a means in which to frame what many writers have previously identified as kōan-like qualities in many of Cage's works. A kōan is generally understood as a type of unsolvable Zen Buddhist riddle filled with contradictions and ambiguities. I subsequently theorise Electronic Music for Piano as a type of musical kōan, and by applying FCA, demonstrate how various derived formal concepts, object extensions, and subset groupings of the work support this theory.
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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 | 0.005 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.005 | 0.029 |
| Scholarly communication | 0.007 | 0.008 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".