The Science of Brass Instruments

Myers, Arnold; Campbell, Murray; Gilbert, Joël

doi:10.1007/978-3-030-55686-0

Cited by 23 publications

(41 citation statements)

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“…According to the so-called Bouasse-Benade prescription [58][59][60], near perfect inharmonicity between the resonances is cited as a condition for good playability of the instrument. This prescription is also discussed in recent studies [9,61]. On the saxophone, experimental studies using an artificial mouth have shown that varying inharmonicity greatly affects regime production [2,8].…”

Section: Effect Of the Resonator's Inharmonicity On Regime Productionmentioning

confidence: 89%

Multistability of saxophone oscillation regimes and its influence on sound production

et al. 2021

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The lowest fingerings of the saxophone can lead to several different regimes, depending on the musician’s control and the characteristics of the instrument. This is explored in this paper through a physical model of saxophone. The harmonic balance method shows that for many combinations of musician control parameters, several regimes are stable. Time-domain synthesis is used to show how different regimes can be selected through initial conditions and the initial evolution (rising time) of the blowing pressure, which is explained by studying the attraction basin of each stable regime. These considerations are then applied to study how the produced regimes are affected by properties of the resonator. The inharmonicity between the first two resonances is varied in order to find the value leading to the best suppression of unwanted overblowing. Overlooking multistability in this description can lead to biased conclusions. Results for all the lowest fingerings show that a slightly positive inharmonicity, close to that measured on a saxophone, leads to first register oscillations for the greatest range of control parameters. A perfect harmonicity (integer ratio between the first two resonances) decreases first register production, which adds nuance to one of Benade’s guidelines for understanding sound production. Thus, this study provides some a posteriori insight into empirical design choices relative to the saxophone.

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Section: Effect Of the Resonator's Inharmonicity On Regime Productionmentioning

confidence: 89%

Multistability of saxophone oscillation regimes and its influence on sound production

et al. 2021

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“…The magnitude of the input impedance exhibits a series of "strong" resonances (1-9), followed by "weak" resonances (10)(11)(12). Each of these resonances, except the first one, allows the musician to play a note with a pitch close to the resonance frequency (such a note is referred to as a "natural note") [26]. The 12th resonance peak corresponds to a F5 note.…”

Section: Approximation Of the Input Impedance Of A Bass Trombonementioning

confidence: 99%

Peak-picking identification technique for modal expansion of input impedance of brass instruments

Ablitzer

2021

Acta Acust.

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The paper presents a method to obtain the modal expansion of the measured input impedance of a brass instrument. The method operates as a peak-picking procedure, which makes it particularly intuitive for users who are not experts in modal analysis. To bypass the limitation of usual peak-picking approaches, which are valid only for well separated resonances, the present method is based on a semi-local optimization problem. It consists in adjusting the frequency and damping of one mode at a time while taking into account the presence of all other modes in the basis. The practical application of the method involves four elementary actions, which can be chained in different ways to progressively approximate a measured input impedance. This procedure is illustrated through the approximation of the input impedance of a bass trombone. The supervised nature of the method allows the user to favour modes that have a physical meaning, i.e. that can be associated with a resonance peak. A single spurious mode can however be deliberately introduced to approximate the input impedance curve beyond the last visible peak. The method applies directly to the frequency-domain data provided by an impedance sensor and does not require any preprocessing. Nevertheless, it is fairly robust to noisy data. Since the method allows a reconstruction of the input impedance using either complex modes or real modes, results obtained with each approximation are critically compared.

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“…Of particular interest is the influence of the musician's control parameters on the oscillation frequency (linked to the intonation), and the minimum mouth pressure required to achieve auto-oscillations (related to the ease of playing). Indeed, it is assumed here that the musician's feeling of ease of playing partly relies on the threshold blowing pressure: the higher the latter, the higher the physical effort the player has to make to play a note [1]. In practice, the musician can play several notes without depressing any valves in the case of a tuba, or moving the slide in the case of a trombone.…”

Section: Introductionmentioning

confidence: 99%

“…In practice, the musician can play several notes without depressing any valves in the case of a tuba, or moving the slide in the case of a trombone. These playing regimes are called the natural notes (B[1, B[2, F3, B[3, D4, F4,... in the case of a trombone or a euphonium for instance), and their frequencies are close to the resonance frequencies of the instrument as a whole, except for the lowest note playable (B [1).…”

Section: Introductionmentioning

confidence: 99%

“…We consider here a simple model: the player's lips are modeled through the "outward-striking valve" [1,3,4], a one degree-of-freedom system. Also, the nonlinear sound propagation in the instrument's bore which accounts for the "brassy sounds" [1] at high sound levels is neglected [5,6]. The airflow blown by the musician into the instrument is described by a nonlinear algebraic equation.…”

Section: Introductionmentioning

confidence: 99%

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Minimal blowing pressure allowing periodic oscillations in a model of bass brass instruments

et al. 2021

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In this study, an acoustic resonator – a bass brass instrument – with multiple resonances coupled to an exciter – the player’s lips – with one resonance is modelled by a multidimensional dynamical system, and studied using a continuation and bifurcation software. Bifurcation diagrams are explored with respect to the blowing pressure, in particular with focus on the minimal blowing pressure allowing stable periodic oscillations and the associated frequency. The behaviour of the instrument is first studied close to a (non oscillating) equilibrium using linear stability analysis. This allows to determine the conditions at which an equilibrium destabilises and as such where oscillating regimes can emerge (corresponding to a sound production). This approach is useful to characterise the ease of playing of a brass instrument, which is assumed here to be related – as a first approximation – to the linear threshold pressure. In particular, the lower the threshold pressure, the lower the physical effort the player has to make to play a note [The Science of Brass Instruments. Springer-Verlag, 2021]. Cases are highlighted where periodic solutions in the bifurcation diagrams are reached for blowing pressures below the value given by the linear stability analysis. Thus, bifurcation diagrams allow a more in-depth analysis. Particular attention is devoted to the first playing regime of bass brass instruments (the pedal note and the ghost note of a tuba in particular), whose behaviour qualitatively differs from a trombone to a euphonium for instance.

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The Science of Brass Instruments

Cited by 23 publications

References 0 publications

Multistability of saxophone oscillation regimes and its influence on sound production

Multistability of saxophone oscillation regimes and its influence on sound production

Peak-picking identification technique for modal expansion of input impedance of brass instruments

Minimal blowing pressure allowing periodic oscillations in a model of bass brass instruments

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