具有近乎完美和谐度的小号：设计与声学效果。

J Acoust Soc Am. 2011 Jan;129(1):404-14. doi: 10.1121/1.3518769.

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.

本文提出了一种用于确定具有近乎完美谐和性、无间断性且输入阻抗峰值在演奏范围内平衡的喇叭气柱形状的数学设计方法。所采用的仿真模型假设线性波传播，并使用圆柱单元离散化和平行波近似。使用具有估计相对测量误差为 ±3 音分的测试装置进行声学测量。给出了所提出的设计（Macaluso 小号）和相同的小号气柱的测量结果比较，其中喇叭被形状未知的商用通用小号喇叭（通用小号）代替。对于声学共振模式 2-13（233-1515 Hz），Macaluso 小号的测量均方根（rms）谐和偏差为 5 音分，而通用小号的偏差为 18 音分。然而，考虑到估计的测量不确定性，每个偏差都有些夸大。对于相同的共振范围，Macaluso 小号的测量和计算共振频率之间的 rms 偏差为 3 音分，从而验证了所提出的仿真模型和方程。