Resonance modes of a flute with one open tone hole

Abstract

A minimal model explaining intonation anomaly, or pitch sharpening, which can sometimes be found in baroque flutes, recorders, shakuhachis etc. played with cross-fingering, is presented. In this model, two bores above and below an open tone hole are coupled through the hole. This coupled system has two resonance frequencies ! AE , which are respectively higher and lower than those of the upper and lower bores ! U and ! L excited independently. TheThe normal effect of cross-fingering, i.e., pitch flattening, corresponds to excitation of the ! À -mode, which occurs when ! L ' ! U and the admittance peak of the ! À -mode is higher than or as high as that of the ! þ -mode. Excitation of the ! þ -mode yields intonation anomaly. This occurs when ! L / ! U and the peak of the ! þ -mode becomes sufficiently high. With an extended model having three degrees of freedom, pitch bending of the recorder played with cross-fingering in the second register has been reasonably explained.

Effect of the dimension of a tone hole on the fundamental frequency of flutes

“…The transmission matrix of a tone hole T hole can be represented by the shunt impedance Z s and the series impedance Z a as follows [5]:…”

Harmonic series experiments: end-correction factor of the Indonesian Angklung

“…The end correction exists at any opening of the resonance tube such as open-end * Author to whom any correspondence should be addressed. [2,3], mouth region [4], tone hole [4][5][6][7], and fipple section [1].…”

“…The end correction of a resonance tube can be determined from the product of the end correction factor and its diameter [2][3][4]8]. Most previous studies assumed that the values of the end correction factor are 0.33 for one-closed-end tubes [2,3,8], and 0.60 for both open-end tubes [4]. However, the end correction factor depends on the dimension of the open end [9].…”

Harmonic series experiments: length correction of the Malaysia pan flute

“…Previous studies determined the values of length correction of a resonance tube from the values of length correction coefficient and its diameter [4][5][6]. The length correction of a musical wind instrument occurs at any opening of the instrument such as its open end [1,2,7], mouth region [8] and tone hole [8][9][10][11]. Therefore, it is one of the critical factors that should be considered in designing musical wind instruments such as the Boomwhacker [1], oboe [10], recorder [11], flute [8,12], organ pipe [13] and pan flute [14].…”