title: Trumpet with near-perfect harmonicity: design and acoustic results.
abstract: This paper presents a mathematical design methodology for determining the shape of a trumpet air column that has near-perfect harmonicity, whose components are discontinuity-free, and whose input impedance peak heights are balanced over the playing range. The simulation model employed assumes linear wave propagation and uses cylindrical element discretization with a plane wave approximation. Acoustic measurements are made using a test set-up with an estimated relative measurement error of ±3 cents. Comparisons of measured results are given for the presented design (Macaluso trumpet) and the same trumpet air column with the bell replaced by a commercially used generic trumpet bell of unknown shape (Generic trumpet). For acoustic resonance modes 2-13 (233-1515 Hz), the measured root-mean-square (rms) harmonicity deviation is 5 cents for the Macaluso trumpet, whereas it is 18 cents for the Generic trumpet. However, considering the estimated measurement uncertainty, each of those deviations is somewhat over-stated. For that same range of resonances, the rms deviation between measured and calculated resonance frequencies for the Macaluso trumpet is 3 cents, thus validating the presented simulation model and equations.
authors.affiliation: cmacaluso1@comcast.net
authors.forename: Charles A
authors.initials: CA
authors.lastname: Macaluso
authors.forename: Jean-Pierre
authors.initials: JP
authors.lastname: Dalmont
mesh_terms: D000162:Acoustics / Q000295:instrumentation*; D003198:Computer Simulation; D017076:Computer-Aided Design; D004867:Equipment Design; D016014:Linear Models; D008962:Models, Theoretical; D009146:Music; D009716:Numerical Analysis, Computer-Assisted; D015203:Reproducibility of Results; D012815:Signal Processing, Computer-Assisted; D013016:Sound; D013018:Sound Spectrography; D035501:Uncertainty; D014732:Vibration