Tuning idiophone bar torsional modes with three-dimensional cutaway geometries
Bibliographic record
Abstract
The bars of marimbas, vibraphones and similar idiophones are tuned by shaping their “cutaway” or “undercut” geometries. Makers commonly shape bar cutaways to tune three flexural modes of vibration. The first flexural mode is tuned to the fundamental frequency of the bar’s musical note. Two other flexural modes are tuned such that their frequencies become specific multiples of the fundamental. The remaining flexural modes and all other modes are left untuned. Makers have complained of untuned torsional modes polluting bar timbre over specific sections of the keyboard. In wooden marimba bars this problem has proven difficult to predict, filling reject bins with valuable tonewood. This work investigates tuning these torsional modes by varying bar cutaway geometry in three dimensions. No additional mass or heterogeneous materials are employed. Modal frequencies are determined via finite element analysis. Mode shapes are identified algorithmically, enabling analyses to explore the parameter space unsupervised. Geometries are tuned using a gradient-based search method. The approach, designed to efficiently solve underdetermined systems with multiple objectives, is readily applicable to other problems. A selection of tuned example models will be showcased, including rosewood and aluminum bars with common and uncommon tuning ratios.
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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 | 0.000 | 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) | 0.002 | 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".