金管楽器の吹奏時における実効入力インピーダンスの導出と音高設計への適用

摘要

従来，金管楽器の音響管としての共振特性の解析については多くの報告がある．Benadeの文献では3件の音響インピーダンスの計測手法が紹介されている．また，計測実験と数値解析を比較した報告もある．最近ではGibiatらによるTMTC法やIWKによるBIAS法などの音響インピーダンス解析の報告がある．これらはいずれも実際の吹奏モデルの解析ではなく，共鳴実験モデルにより計測と数値解析を行って，音響管の共振周波数特性解析のために音響インピーダンス解析が有用であることを示しているものである%It is specially analyzed about the problem of the pitch of stationary sound in the acoustic analytic subjects of brass instruments. It is modeled as a combination of the conical horn elements for the trumpet. First, the end of mouthpiece is set as the closed end, the resonance frequency is calculated as a characteristic value of the modeled trumpet by the technique of Cavity Resonance. Next, when it is played, the effective input impedance at the end of mouthpiece and those relative angles are calculated. Based on these characteristics, quantitative examined considerations are added to the playing methods, and a blowing pattern is set up. Furthermore, it is calculated the virtual additional length for the end of mouthpiece. It is examined correspondence with the playing methods of brass players. This playing method is taken into consideration, the CAD system for the pitch design of trumpet is built, and a suitable example to the pitch design is shown, with the utility of the system. The validity of a blowing pattern is shown.