A schematic of the regimes on the (P,F) plane. Above the extinction curve P ext(F) and below the threshold P osc(F), there is no periodic sound. Between the two lies an area in which the intended note is produced. A second smaller area is often present in which various high-frequency regimes such as squeaks are produced.
(Color online) Schematic sketch (not to scale) of the clarinet mouthpiece inside the artificial mouth indicating the positions used for the application of lip force.
Measured frequency f and sound level L as a function of mouth pressure P for each value of the lip force F (shown in newtons). The reed has hardness 2, and the teeth are at the middle position (see Fig. 2 ). The fingering is that for the note (written) G4. On this plane, a crescendo or decrescendo at constant pitch would be a horizontal line and so would require varying F. For the forces of 0.25 and 0.5 N, the clarinet sound is not extinguished below the pressure of 6.7 kPa (the highest that can be achieved with the current system). The error bars that indicate the variability in frequency or sound level in the entire recorded sound sample (approximately 1.5 s) are shown in gray for all points. These are usually too small to be clearly visible. However, three points show atypically large error bars: The low P limit of the F = 0.25 and 1.0 N curve and the high P limit of the 1.5 N curve. This is the result of hysteresis, instability, and sometimes turbulent noise at the perimeter of the playing regime.
(a) (top) is a frequency contour plot of the note G4 played with a reed of hardness 2 and the lip force applied at the middle position. Measurement points are shown as dots. The shaded area in (a) and the bounding lines in (b) (bottom) indicate the region where the instrument plays a note. The black lines in (a) are contours of equal frequency with values in hertz. Contours of the sound level are indicated by the gray scale. (b) shows hysteresis in two consecutive experiments conducted under conditions similar to those in (a). The black lines show the playing regime for one trial played in the same conditions as (a), and the gray lines show the playing regime measured in a later experiment, using the same reed and lip force position. In both cases, solid lines demark the range over which a periodic sound was produced, while dotted lines indicate the boundary of the regions where the instrument played a frequency far from the expected (a higher regime). Outside of these two areas, no pitched sound was produced.
Results of the experiment shown in Figs. 3 and 4 , but this time plotting the spectral centroid rather than pitch as a function of pressure (a) and with contours of equal spectral centroid (b) on the pressure/force plane. The strong correlation between spectral centroid and sound level (gray scale) is evident.
Frequency contour plot for the note G4 played with a reed of hardness 2 and the lip in two different positions: (a) shows the results for the “long bite” position (point of lip force application moved further from the tip) and (b) those for the “short bite” position. The pressure axis and sound level scale are the same in both figures but because of the very different ranges of force applied, the force axis of Fig. 4(a) has been changed. For comparison, the limits of the “normal bite” [Fig. 4(a) ] are shown as a dashed light gray line on both figures. Measurement points are shown as dots.
Frequency contour plot for the note G4 played with a reed of hardness 3.5 and the lip in the “middle” position. For comparison, the limits for a reed of hardness 2 [from Fig. 4(a) ] are shown by a dashed gray line. Measurement points are shown as dots.
Frequency contour plots for the notes G3 (top) and G5 (bottom) played with a reed of hardness 2 and the lip force applied in the “middle” position. To compare these with Fig. 4 , which shows the note G4 for similar conditions, the outline of the playing regime from Fig. 4(a) is shown as a light gray line. Measurement points are shown as dots.
Article metrics loading...
Full text loading...