THE JOURNAL OF THE ACOUSTICAL SOCIETY OF JAPAN

Show abstractHide abstract

Using a mechanical blowing apparatus, flute playing was simulated, and acoustical properties of generated tone were investigated. Five sorts of parameters were chosen for description of harmonic structure, and their variations with nine sorts of drive conditions, which were found in a previous work of the author (reported in the last issue of J. A. S. J. ), were measured on a typical instrument (H. Hammig). (Tab. 1). The parameters of harmonic structure (Fig. 1) were 1. The number of harmonics (N): The number of harmonics, of which relative levels are not less than -35dB as compared with the level of the fundamental. 2. Average level of harmonics (M_kdB): M_k=1/(k_1)��^^k__2L_i, where L_i is the relative level in dB of the i-th harmonics. In the low, middle and high registers, k=7, 5 and 3 respectively. 3. Attenuating degree of harmonics level with its order (ZdB/oct): This parameter is expressed by N and M as the following equation. Z=(M+35)log2/(log(N+2)-1/(k_1)log(k!)). 4. Level difference between even and odd harmonics (L_e-L_0): For low register tones, L_e-L_0=1/3(L_2+L_4+L_6)-1/3(L_3+L_5+L_7). For middle and high register tones, L_e-L_0=L_2-L_3. 5. Formant: The term is used in the same meaning as used in phonetic acoustics. The results obtained are as follows: In the low register, M_7 is proportional to the air beam velocity u. Its increasing rate as well as its value at equal velocity are in proportion to the pitch of the tone (Fig. 3, Equation 5. 3). In the middle or the high register, M_5 or M_3 depends on the pitch only (Fig. 4, Equation 5. 4). A fixed correlation was found between N and M_k regardless of drive conditions (Fig. 2, Equation 5. 1 and 5. 2). Therefore the attenuating degree Z is also constant in each of three registers, (15-16dB/oct in the low register, 13dB/oct and 8dB/oct in the middle and high register respectively). L_e-L_0 varies critically with air beam bias e in all three registers (Fig. 6). Anti-formant is observed in low register tones, when u is large(u≧9m/sec) and e is near the soundable limit (about -2. 0mm or 0mm) (Fig. 7). The probable ranges of M_k and L_e-L_0 in the actual flute playing were discussed, based on the above data and those derived in the previous work, and the resultant models of harmonic structure were shown (Fig. 8 and 9).

View full abstract

Download PDF (828K)

A theoretical approach is made to the influence of air flow on the propagation characteristics of sound in a tube with an open end. Standing wave patterns in a tube are presented. The result indicates the standing wave ratio decreases with the increasing velocity of air flow, while the distance between nodal points is reduced by the factor 1-M^2, where M is the Mach number of air flow.

View full abstract

Register with J-STAGE for free!