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Figure 4: /PD of one frequency of a blown (top) and overblown (bottom) note at a distance of Im (black), 1.5m (dark gray) and 3m (light gray).

Figure 4 /PD of one frequency of a blown (top) and overblown (bottom) note at a distance of Im (black), 1.5m (dark gray) and 3m (light gray).

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is the position vector containing distance r from the origin Yo and azimuth angle y. P;(w,ro) = Ps (w,y) Ps (w, 10) is the yet unknown source spectrum, a solution to the homogeneous Helmholtz equation. Solutions to the first differential equation of Eq. (1) are the radiation characteristic ['(w,@) of the musical instruments in the horizontal plane. These are implicitly measured for 128 angles by the microphone array. Solutions to the second differential equation are complex transfer functions. One solution is the free field Green’s function It is feasible to consider a musical instrument a point source if its volume is small compared to the radiated wave length. This is of course a simplification which is physically untrue. Naturally, musical instruments radiate sounds from different parts of the body and the enclosed air. The radiated sounds interfere and create different amplitudes and phases at the different locations in space. Thus, there is no exclusive source point. Therefore, the head of the musician is taken as source point for the investigation, as commonly done, e.g. in [2]. This simplification means that all sound is considered as originating fom one common source point, namely the center of the microphone array, at which a complex point source radiates sound. In the frequency domain, this situation is described by the two- dimensional inhomogeneous Helmholtz equation which can be formulated as a set of ordinary differential equations in spherical coordinates:
is the position vector containing distance r from the origin Yo and azimuth angle y. P;(w,ro) = Ps (w,y) Ps (w, 10) is the yet unknown source spectrum, a solution to the homogeneous Helmholtz equation. Solutions to the first differential equation of Eq. (1) are the radiation characteristic ['(w,@) of the musical instruments in the horizontal plane. These are implicitly measured for 128 angles by the microphone array. Solutions to the second differential equation are complex transfer functions. One solution is the free field Green’s function It is feasible to consider a musical instrument a point source if its volume is small compared to the radiated wave length. This is of course a simplification which is physically untrue. Naturally, musical instruments radiate sounds from different parts of the body and the enclosed air. The radiated sounds interfere and create different amplitudes and phases at the different locations in space. Thus, there is no exclusive source point. Therefore, the head of the musician is taken as source point for the investigation, as commonly done, e.g. in [2]. This simplification means that all sound is considered as originating fom one common source point, namely the center of the microphone array, at which a complex point source radiates sound. In the frequency domain, this situation is described by the two- dimensional inhomogeneous Helmholtz equation which can be formulated as a set of ordinary differential equations in spherical coordinates:
Figure 3: ILD of one frequency of a blown (top) and overblown (bottom) note at a distance of 1m (black), 1.5m (dark gray) and 3m (light gray).
Figure 3: ILD of one frequency of a blown (top) and overblown (bottom) note at a distance of 1m (black), 1.5m (dark gray) and 3m (light gray).
Table 2: Results from the listening test with 14 subjects. Cases in which perceived size and distance differ by more than 2 are gray.
Table 2: Results from the listening test with 14 subjects. Cases in which perceived size and distance differ by more than 2 are gray.
Figure 5: BQI of blown (top) and overblown (bottom) note at a distance of 1m (black), 1.5m (dark gray) and 3m (light eray). calculated quantities behave as expected: They decrease with increasing distance. This confirms the applicability of the method—at least for instruments as small and simple as the shakuhachi—and shows that ILD, R ILD, o ILD, IPD, R BOI, o IPD, BQI and o BQI seem to be appropriate measures to describe the effect that the perceived source extent decreases with distance. Only in case of the overblown note R IPD does not decrease with distance. Furthermore, the overblown note creates typically higher interaural differences than the blown note, except R IPD. Certainly, one reason for the higher interaural differences in case of the overblown note is that it has a higher overall loudness and contains more energy in higher frequencies which tend to have a more complicated radiation characteristic. Still, results of the listening test do not show that the overblown shakuhachi note appear bigger than the normal blown note or that it increases with increasing distance. This indicates that the magnitude of interaural differences alone is not crucial for the perception of source extent. A ratio of JLD and absolute level or a weighting of
Figure 5: BQI of blown (top) and overblown (bottom) note at a distance of 1m (black), 1.5m (dark gray) and 3m (light eray). calculated quantities behave as expected: They decrease with increasing distance. This confirms the applicability of the method—at least for instruments as small and simple as the shakuhachi—and shows that ILD, R ILD, o ILD, IPD, R BOI, o IPD, BQI and o BQI seem to be appropriate measures to describe the effect that the perceived source extent decreases with distance. Only in case of the overblown note R IPD does not decrease with distance. Furthermore, the overblown note creates typically higher interaural differences than the blown note, except R IPD. Certainly, one reason for the higher interaural differences in case of the overblown note is that it has a higher overall loudness and contains more energy in higher frequencies which tend to have a more complicated radiation characteristic. Still, results of the listening test do not show that the overblown shakuhachi note appear bigger than the normal blown note or that it increases with increasing distance. This indicates that the magnitude of interaural differences alone is not crucial for the perception of source extent. A ratio of JLD and absolute level or a weighting of
Related topics:
EthnomusicologyMusical acousticsSystematic MusicologyMicrophone Arrays
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