Physical modeling of the piano: An investigation into the effect of string stiffness on the hammer string interaction.
Bibliographic record
Abstract
The stiff string wave equation has four solutions, two of which are fast-decaying waves introduced by the string stiffness. In the case of digital waveguide modeling of piano strings these are normally neglected. Some recent reports have suggested that all four traveling waves should be considered, at least at the neighborhood of interaction points (i.e., the hammer and the boundaries). This paper investigates the effect of omitting string stiffness in the context of sound synthesis of the piano by physical modeling. A stiff, lossy string with a spatially distributed hammer force excitation is implemented using both a finite-difference time-domain scheme and a digital waveguide model. The two models are designed so as to have the exact same features but for the two stiffness-related solutions. Numerical experiments are employed to study the contact force and string velocity signals for different initial hammer velocity values. The results generally confirm that the two fast-decaying waves have only a marginal effect on the overall string motion. However, small audible differences result for bass strings struck with high initial hammer velocities.
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How this classification was reachedexpand
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 | 0.001 | 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 | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".