Three-dimensional tuning of idiophone bar modes via finite element analysis
Bibliographic record
Abstract
The timbre of marimba and other idiophone bars can sometimes be polluted by untuned torsional modes, leading to substandard instruments or rejected materials. Makers have complained of problems with these untuned modes over a specific range of notes. Marimba, vibraphone, and similar idiophone bars are tuned by carving one side of the bar to bring up to three flexural modes into harmonic relationships. Torsional and other mode types are commonly left untuned. The relative frequency of these untuned modes with respect to the fundamental mode will vary along the keyboard. This paper investigates tuning both torsional and flexural modes simultaneously. This tuning is achieved using sophisticated carved geometries, and without employing concentrated masses or additional materials. Bars are modeled using three-dimensional finite elements. Geometry is defined by a large number of input parameters. Algorithms are implemented to identify bar modes automatically, eliminating the need for human intervention. Tuning is performed via a Newton-Raphson approach using the Moore-Penrose generalized matrix inverse to solve systems of tuning equations. This method is found to be effective at finding satisfactory bar geometries in proximity to initial conditions. Numerous example marimba and vibraphone bar models are provided, representing both typical and atypical modal tuning ratios.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 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".