Comparisons between trumpet models using numerical continuation methods
Bibliographic record
Abstract
This thesis describes the use of numerical continuation methods to analyze the behavior of a modeled trumpet-player system, and to make comparisons between the instruments based on parameters that are relevant to players. The acoustic impedances of four B-flat trumpets were measured, and modal parameters were derived to describe each measured impedance. The modal impedance parameters were then incorporated into a physical model representing the player-trumpet system. Linear stability analysis (LSA) was used to refine the lip frequency parameter used, and then the system was studied using numerical continuation methods to determine how the mouthpiece pressure varies with the blowing pressure. Bifurcation diagrams of downstream mouthpiece pressure versus upstream blowing pressure were generated using the numerical continuation software Manlab, and it was found that all four trumpets displayed subcritical, or inverse, Hopf bifurcations at the note onset. This means that each instrument displayed hysteresis behavior, so that the minimum onset blowing pressure and dynamic were higher than the extinction blowing pressure and dynamic. The location of the Hopf bifurcation point, the mouthpiece pressure at an estimate of the players’ maximum blowing pressure, and location of the fold, where the oscillating solution becomes extinct as the blowing pressure is reduced, were determined for each instrument. The locations of these landmarks were used to make conjectures about the amount of blowing pressure needed to begin a note, the maximum and minimum dynamics of the instrument, the dynamic range, and the amplitude of the hysteresis for each instrument. A small-scale perceptual trial was conducted to determine whether players could perceive these differences, and whether their observations agreed with the conjectures made based on the results from numerical continuation
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".