Role of the Resonator Geometry on the Pressure Spectrum of Reed Conical Instruments

Abstract

Spectra of musical instruments exhibit formants or 2 anti-formants which are important characteristics of 3 the sounds produced. In the present paper, it is shown 4 that anti-formants exist in the spectrum of the mouth-5 piece pressure of saxophones. Their frequencies are 6 not far but slightly higher than the natural frequen-7 cies of the truncated part of the cone. To determine 8 these frequencies, a first step is the numerical deter-9 mination of the playing frequency by using a simple 10 oscillation model. An analytical analysis exhibits the 11 role of the inharmonicity due to the cone truncation 12 and the mouthpiece. A second step is the study of 13 the input impedance values at the harmonics of the 14 playing frequency. As a result, the consideration of 15 the playing frequency for each note explains why the 16 anti-formants are wider than those resulting from a 17 Helmholtz motion observed for a bowed string. Fi-18 nally numerical results for the mouthpiece spectrum 19 are compared to experiments for three saxophones 20 (soprano, alto and baritone). It is shown that when 21 scaled by the length of the missing cone, the anti-22 formant frequencies in the mouthpiece are very similar 23 for the three instruments. The frequencies given by 24 the model are close to the natural frequencies of the 25 missing cone length, but slightly higher. Finally, the 26 numerical computation shows that anti-formants and 27 formants might be found in the radiated pressure. 28 85 spectively. 86 It is still the only model that yields analytical ex-87 pressions for the sound produced, and therefore it is 88 used as a reference for the present study. In a pa-89 per written by some of the present authors, it was 90 shown that a simple numerical model can largely im-91 prove the model of the Helmholtz motion [16]. We call 92 it the "Reed-Truncated-Cone" model (RTC model). 93 The difference between the two models lies in the res-94 onator model. Example of waveshapes obtained with 95 the two models are shown in Fig. 2. Using the RTC 96 model for the present investigation on the spectrum, 97 the paper aims at further understanding of the exis-98 tence of formants or anti-formants in the mouthpiece 99 pressure spectrum, and, to some extent, of the exter-100 nal pressure. The computation is done ab initio in the 101 time domain. 102 The study is limited to the first register, which re-103 sembles the Helmholtz motion (periodic regime, one 104 positive pressure and one negative pressure episodes). 105 The RTC model is based upon the observation that 106 in practice the mouthpiece volume is approximately 107 equal to that of the missing cone [17], entailing a weak 108 0, which depend on the note; ii) the solutions of 231 sin(kx 1) = 0, which do not depend on the note. Fig. 232 3 shows an example of input impedance curve. For 233 this figure, realistic visco-thermal losses (for an aver-234 age cone radius) have been taken into account in Eq.

Towards 3D printed saxophone mouthpiece personalization: Acoustical analysis of design variations

“…The artificial blowing machine allows to adjust the blowing pressure and lip position and provides repeatable conditions for the comparison of the mouthpieces. The used artificial blowing machine is based on the control of the air pressure in a 170 cm 3 plexiglass box representing the oral cavity of a player, as shown in Fig- ure 5a. This is achieved by the control of a proportional valve (SMC; type PVQ33-5G-23) at the air entrance to the cavity.…”

“…The saxophone sound is produced by the oscillation of a single reed as the air flows through the internal cavity of the mouthpiece [1]. The volume and the internal geometry of the mouthpiece have been shown to affect the input impedance of the instrument and hence the resulting sound [2,3]. Moreover, small design changes on the mouthpiece may significantly affect the oscillations of the reed and cause playability, intonation or timbre differences [3][4][5].…”

“…The volume and the internal geometry of the mouthpiece have been shown to affect the input impedance of the instrument and hence the resulting sound [2,3]. Moreover, small design changes on the mouthpiece may significantly affect the oscillations of the reed and cause playability, intonation or timbre differences [3][4][5]. For instance, wider tip openings result in higher thresholds of oscillation [6,7], requiring higher blowing pressure to start a tone.…”

The bassoon tonehole lattice: Links between the open and closed holes and the radiated sound spectrum

“…no attempt is made to include other factors, such as the influence of the reed dynamics 9,10 or conicity. 11 First, the radiated spectrum of the bassoon is discussed in Sec. II, where the presence of formants and weak frequency bands is demonstrated for the first register of the bassoon.…”

Expressive goals for performing musicians: The case of clarinetists

“…We decided to limit our sample of participants to clarinetists to reduce the number of unknown variables and because the instrument itself is well understood (Almeida et al, 2013(Almeida et al, , 2017Bak & Dolmer, 1987;Chen et al, 2009;Dalmont et al, 2005;Dickens et al, 2007;Kergomard et al, 2000;Li et al, 2016aLi et al, , 2016bLulich et al, 2017). Simple physical models can be used to explain the way it works and several teams of researchers (e.g., Dalmont & Frappe, 2007;Guillemain, 2007;Li et al, 2016b;Pàmies-Vilà et al, 2018, 2020 have measured the parameters modified by performers when playing the clarinet, such as blowing pressure and bite force (playing parameters).…”