Hz

( ) 2006 1

3 3 3 4 10 Hz

1 1 1.1.................................... 1 1.2.................................... 1 2 2 2.1.................................... 2 2.2.................................... 3 2.3.................................. 4 2.3.1............................... 4 2.3.2............................. 5 2.3.3............................... 9 3 11 3.1.................................. 11 3.2........................... 14 3.3.................................... 14 4 17 4.1............................... 17 4.2......................... 17 4.2.1................................... 17 4.2.2................................ 24 4.2.3.................... 24 4.3............... 29 4.3.1............................... 29 4.3.2.................................. 32 5 FM 35 6 37 6.1.................................... 37 6.2................................. 38 i

39 40 ii

2.1.................................... 2 2.2............................ 3 2.3.............................. 4 2.4....................... 8 2.5................................. 9 2.6............................... 9 2.7............................... 9 3.1............................... 12 3.2........................... 12 3.3................................. 13 4.1................................... 19 4.2 1.................. 20 4.3 2.................. 20 4.4 3.................. 21 4.5 4.................. 21 4.6 5.................. 22 4.7 6.................. 22 4.8 7.................. 23 4.9 2................. 23 4.10 E 4............................... 25 4.11 F 4............................... 25 4.12 A 4.............................. 26 4.13 A 4............................... 26 4.14 B 4.............................. 27 4.15 B 4............................... 27 4.16 C 5............................... 28 4.17 D 5.............................. 28 4.18 D 5............................... 29 4.19 (A) p1-m2..... 30 4.20 (A) p1-m2 (2).... 30 iii

4.21 (B) p1-m2..... 31 4.22 (C) p1-m2..... 31 4.23 (D) p1-m2..... 32 4.24 (1) p1-m5...... 33 4.25 (2) p1-m5...... 33 4.26 (3) p1-m5...... 34 5.1.............................. 36 5.2...................... 36 iv

1 1.1 [2 4] FFT [1] 1.2 2 3?? 5 6 1

2 2.1 2.1 [5] required tone air Player flow buzzing Lip Instrument tone reflected wave 2.1: 2

(a) (b) 2.2: (a): (b): 2.2 [5] 2.2(a) 2.2(b) [6] 1 ) [2 4] 3

a -x0 x 2.3: 2.3 2.3.1 [5] [7, 8] 2.3 x a a = b(x + x 0 ) γ (2.1) γ b x 0 4

f n f n c 4(l + x 0 ) { (2n 1) + β } γ(γ + 1) (2.2) [9] c l β γ < 0.8 0.6 γ > 0.8 0.7 γ = 1 f n nc 2(l + x 0 ) γ γ 0.7 [10] [10,11] (0.7,2,3,4,...) f 0 [5] (2.3) 2.3.2 2 3 5 7 2 3 n 2 n/12 [12] 1 2 2 3 7 2 3 2 4 5

5 3 6 2 3 7 n b n (n = 1,2,3) b n = 2 n 12 1 (2.4) b 1 0.060 (2.5) b 2 0.123 (2.6) b 3 0.189 (2.7) 5 4 ˆb 4 b 1 + b 3 0.249 < ˆb 4 0.260 (2.8) 6 7 b 2 + b 3 0.312 < ˆb 5 0.335 (2.9) b 1 + b 2 + b 3 0.371 < ˆb 6 0.414 (2.10) b 3 3 2 b 1 0.060 (2.11) b 2 0.123 (2.12) b 3 = ˆb 4 b 1 0.201 (2.13) (2.14) 4 : b 1 + b 2 0.182 (2.15) 5 : b 1 + b 3 = ˆb 4 0.260 (2.16) 6 : b 2 + b 3 0.323 (2.17) 7 : b 1 + b 2 + b 3 0.382 (2.18) 6

2.1: 1 0 position 1 2 3 4 4 5 6 7 piston 1 0 0 1 1 0 0 1 1 piston 2 0 1 0 1 0 1 0 1 piston 3 0 0 0 0 1 1 1 1 7 b 3 7 1 / : 2 2 / : 3 / : 3 on/off 2.1 4 4 p1-m2 2.4 2.5 r R Keefe Benade [13] B = r/r Z 0 = ρc/πr 2 δz ( ) 1 δz 2I 2 = 1 (2.19) Z 0 πb π ( ) 2 1 + Bcosθ I = cosθ ln dθ (2.20) 0 1 Bcosθ 7

2.4: p m p1-m2 1 2 8

( 2.5: 2.6: 2.3.3 2.6 [5] 2.7 V C = V ρc 2 (2.21)!" #$ % & '! 2.7: 0 9

ρ c l c S c R Z IN L = ρl c S c (2.22) Z IN = R + Z p + jωl 1 ω 2 LC + jωc(r + Z p ) (2.23) Z p ω 0 = 1 LC (2.24) Z p ω 0 Z p (2.23) 10

3 3.1 [5, 14] 3.1 3.2 3.3 3.3 [15] 3 [1] 11

3.1: 3.2: 12

wave hanning window FFT log10 20log 10 IFFT power spectrum cepstrum Peak Picking peak profile FFT cepstrum window spectrum envelope 3.3: 13

3.2 p m f pm [Hz] f pm = ma 4 2 p+22 12 (3.1) A 4 A 4 = 440 Hz f pm 10 3.3 F s = 48 khz 2 12 f f = F s 11.7Hz (3.2) 212 [1] N f A P 0 x(i) = Ae 2π j(p 0+i f /F s ) = Ae 2π j(p 0+i f /N) (i = 0,1,2,...,N 1) (3.3) ( f = N f F s ) (3.4) f ( ) 2πi w(i) = 1 cos N G(k) G(k) = (3.5) N 1{ w(i)x(i)e 2π jik/n} (3.6) i=0 cos(t) = (e jt + e jt )/2 w(i) = Ae 2π jp 0 N 1{ e 2π j( f k)/n 1 i=0 2 e2π j( f k+1)/n 1 } 2 e2π j( f k 1)/N (3.7) 14

a 1 N 1 a i = an 1 i=0 a 1 (3.8) e jt 1 = 2 j sin 1 2 e jt/2 (3.9) G(k) = Ae 2π jp 0 sin π( f k 1) N cos π( f k) N sin π( f k) N sin 2 π N sin π( f k+1) N G(k) k k max k max 1 2 f k max + 1 2 sinπ( f k))e π j( f k) 3.10 G(k max 1) G(k max ) r r = G(k max 1) G(k max ) cos π( f k max +1) = cos π( f k max ) N sin π( f k max 1) N N sin π( f k max +2) N (3.10) (3.11) (3.12) N θ 1 (3.13) cosθ 1 (3.14) sinθ θ (3.15) 3.12 π( f k max 1 N r π( f k max +2 N = f k max 1 f k max + 2 f = k max + 1 2r ( 1 + r f = k max + 1 2r ) Fs 1 + r N (3.16) (3.17) (3.18) 15

s = G(k max 1) G(k max ) (3.19) f = k max 1 2s 1 + s ( f = k max 1 2s ) Fs 1 + s N (3.20) (3.21) 3.18 3.21 r s G(k max ±1) f 3.10 A = G(kmax ) N π( f k max) sinπ( f k max ) ( f k max 1)( f k max + 1) (3.22) 16

4 4.1 4.1 0.9 m cm 48 khz DAT 4.1 (A) (1) (A1) 12 1 2 6 (A1) 2 6 4.1: (a) (b) A YTR-8335UGR 1 17D(inner gold) B V. Bach 180ML 2 1A C YTR-8335HS 3 Schilke 8A4 D YTR-800GS 4.2 4.2.1 4.2 4.8 1 7 2 6 17

A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3 4.2: A1 A2 A3 B1 B1 C1 C1 C1 C1 C1 D1 D1 18

Player Trumpet 0.9m Mic DAT 4.1: 1 1 khz 0.6 khz 2 19

4.2: 1 4.3: 2 20

4.4: 3 4.5: 4 21

4.6: 5 4.7: 6 22

4.8: 7 4.9: 2 23

4.2.2 4.9 2 3 1 3 4 7 1 3 2.1 3 4 7 3 4 3 3 3 3 3 4 1 1 1 2 4 (A1) 4.2.3 2.4 4.10 4.18 E 4 F 4 A 4 D 5 24

4.10: p2-m3 p7-m4(e 4 ) 4.11: p1-m3 p6-m4(f 4 ) 25

4.12: p3-m4 p7-m5(a 4 ) 4.13: p2-m4 p6-m5(a 4 ) 26

4.14: p1-m4 p5-m5(b 4 ) 4.15: p4-m5 p7-m6(b 4 ) 27

4.16: p3-m5 p6-m6(c 5 ) 4.17: p2-m5 p5-m6(d 5 ) 28

4.18: p1-m5 p4-m6(d 5 ) 4.3 4.3.1 3 p1-m2 4.19 (A) p1-m2 (A1) (A1) 4.20 4.23 (1) (C) 4 3 4 3 (C) (D) 29

4.19: (A) p1-m2 4.20: (A) p1-m2 30

4.21: (B) p1-m2 4.22: (C) p1-m2 31

4.23: (D) p1-m2 4.3.2 4.24 4.26 p1-m5 (1) (2) (3) 4 2 3 10 (3) (3) 32

4.24: (1) p1-m5 4.25: (2) p1-m5 33

4.26: (3) p1-m5 34

5 FM (A1) p1-m6 5.1 FFT (A1) p1-m6 5.2 100 ms 1/0.1 = 10 Hz 7Hz [16] 35

5.1: (A1) p1-m6 5.2: (A1) p1-m6 36

6 6.1 3 3 3 4 10 Hz 37

6.2 38

17 3 3 OB 39

[1],. FFT., J70-A, 5 pp. 798 805, 1987. [2],,,.. 16, pp. 133 134, 2004. [3] Kaneko, Y., Mizuhara, S., Mizutani, K., and Nagai, K. Artificial Lips for Automatic Trombone Blower. Proceedings of The First Asian Pacific Conference on Biomechanics Sponsored by The Japan Society of Mechanical Engineering, T-13-015, pp. 23 24, 2004. [4],,,.., MA2004-27, pp. 55 56, 2004. [5] Fletcher, N.H., and Rossing, T.D. The Physics of Musical Instruments. Springer-Verlag New York, 1998. [6] Yoshikawa, S. Acoustical Behavior of Brass Player s Lips. Journal of Acoustic Society of America, 97, pp. 1929 1939, 1995. [7] Benade, A.H. On Woodwind Instrument Bores. Journal of Acoustic Society of America, 31, pp. 137 146, 1959. [8] Benade, A.H., and Jansson, E.V. On Plane and Spherical Waves in Horns with Nonuniform Flare. Acustica, 31, pp. 80 98, 1974. [9] Benade, A.H. Fundamentals of Musical Acoustics. Oxford University Press, New York, 1976. [10] Young, F.J. The Natural Frequencies of Musical Horns. Acustica, 10, pp. 91 97, 1960. [11] Pyle, R.W. Effective Length of Horns. Acustica, 57, pp. 1309 1317, 1975. [12] Smithers, D., Wogram, K., and Bowsher, J. Playing the Baroque Trumpet. Scientific American, 254(4), pp. 108 115, 1986. [13] Keefe, D.H., and Benade, A.H. Wave Propagetion in strongly curved ducts. Journal of Acoustic Society of America, 74, pp. 320 332, 1983. 40

[14].., 1978. [15],.., 2005. [16]. FM AM. 21-3 pp. 109-116 1985. 41