The Relationship Between Bore Resonance Frequencies and Playing Frequencies in Trumpets

Abstract

The aim of this work is to study experimentally the relationship between the resonance frequencies of the trumpet, extracted from its input impedance, and the playing frequencies of notes, as played by musicians. Three different trumpets have been used for the experiment, obtained by changing only the leadpipe of the same instrument. After ameasurement of the input impedance of these trumpets, four musicians were asked to play the first five regimes of the instrument, for four different fingerings. This wasd one for three dynamic levels and repeated three times. Statistical methods were implemented to assess the variability in the playing frequencies, and to study quantitatively their relationships with the bore resonance frequencies. Alimited influence of the musician on the instrument overall intonation is observed, as well as aweak influence of the dynamic levels on the pitch of the notes. The results showthat for most of the regimes, variations of the resonance frequencylead to same order variations of the playing frequencyo ft he corresponding note. We noticed also that the sum function, derived from the input impedance, does not give ab etter prediction of the playing frequencyt han the input impedance itself.

Effect of Vocal Tract Resonances on the Sound Spectrum of the Saxophone

“…The valves of the instruments are also very different. The lip has a much larger mass and, in lip-valve instruments, it is thought that its natural frequency lies close to the playing frequency [13,27], which is about 80 Hz for the didjeridu: well below the frequency of peaks in Z mouth . It is therefore plausible that the presence of a large acoustic impedance at frequencies well above that of the lip motion might have relatively little effect on the motion of the lip itself.…”

The Interactions Between Wind Instruments and their Players

“…The first peak lies belowt he first member of the harmonic series, the latter being indicated by av ertical arrowi ne ach plot of Figure 6. Thus the Bb trumpet with no valves depressed (Figure 6) readily plays near the second peak (Bb3), the third (F4),t he fourth (Bb4), the fifth (D5) and, for ag ood player,af ew more [50]. An ote can be sounded near the first maximum (G2) buti ts higher harmonics do not fall near impedance peaks, so the note is dark and weak.…”

“…This is due to the fact that nonlinearity causes combination of air-column modes and, if the inharmonicity is not too great, then the final result is ap eriodic, and thus harmonic, oscillation at af requencyt hat maximises the weighted contributions of all the modes (e.g. [50]). If the inharmonicity of the resonances is too great, as may be achievedb yn on-standard fingerings, then the vibra-tion may separate into twoo rm ore components, giving achord-likesound referred to as a"multiphonic".…”

Experimental Demonstration of the Modification of the Resonances of a Simplified Self-Sustained Wind Instrument Through Modal Active Control

“…In this last case, the control could not modify the modes separately. damping)a nd the instrument intonation and playability remains as ubject of investigation [20,21]. Modal active control provides at ool to study this relationship experimentally.I ta lso enables the role of each resonance in maintaining the self-sustained oscillations in playing conditions to be explored.…”