Flute acoustics: measurement, modelling and design - School of ...

More documents

Recommendations

Info

104 CHAPTER 7. THE EMBOUCHURE HOLE AND PLAYER CORRECTIONS The impedance of the played flute is then Z played flute = Z face + Z flute , (7.1) where Z flute is the input impedance of the flute with a temperature gradient and CO 2 and H 2 O partial pressures in air equal to those in a played flute, as seen through an orifice with radius somewhat smaller than the input radius of the embouchure hole. The exact size of the orifice to use is difficult to determine, since the excitation of a played flute is not at all like the excitation used in Chapter 5, where the flute was excited with plane waves from the end of a 7.8 mm diameter impedance head. To get an idea of the extent to which the embouchure hole is covered by the player’s lower lip, a flutist was asked to ‘mime’ several notes over the range of the flute. Miming should give representative results, since flutists are trained to regularly set their embouchure before playing, so that the initial transient of a note is strong and in tune. (The face impedance was measured simultaneously, but the results are erratic and do not show the expected variation with frequency.) Photographs of the embouchure for these notes are shown in Figure 7.1. It is clear from these photographs that the lower lip covers approximately 25% of the embouchure hole, and the upper lip protrudes somewhat further than the lower lip. The jet length appears to shorten slightly for higher notes. The jet length was estimated from the photographs to be 7.3 mm for C4 and 6.7 mm for F7—a decrease of 8%. For a more detailed study of the lip configuration of flute players see Fletcher (1975). As was seen in §5.3.3, reducing the input radius of the embouchure hole lowers the frequency of impedance minima. Given the difficulty in determining the exact size of the input radius, a radius of 3.9 mm was used. This corresponds to the size of the impedance head used in Chapter 5, which in an earlier study was chosen to simulate the amount of the embouchure hole which remained uncovered by the player’s lip (Wolfe et al. 2001a). 7.2 MODERN FLUTE TUNING We choose to determine Z face empirically based on tuning data. Three experienced flutists were asked to play each standard fingering on the same flute that was used for impedance measurements (Botros et al. 2006). The stopper and tuning slide of the flute were set at the same position as for measurements (i.e. 17.5 and 4 mm respectively). The flutists were asked to avoid correcting the pitch for notes that were out of tune; rather the goal was to achieve the best tone. As discussed in §2.2.12, the frequency of any note on the flute varies with the amplitude of excitation. For this reason the players were asked to play each note mezzo forte. The resulting pitch correction is then only strictly valid when the flute is played at this level; but a single pitch correction for each note is needed for flute design purposes, and the correction derived at mezzo forte is in my view most appropriate. The test notes were ordered so as to minimise the effect of pitch memory: the intervals between successive notes were large and mostly not simple consonances. Each note was repeated four times and the pitch was measured on a tuning meter with a resolution of 5 cents. The results are shown in Figure 7.2. It is immediately obvious from Figure 7.2 that this modern flute in this configuration does not have perfect tuning, at least, not for these players. There is a general trend towards sharper
7.2. MODERN FLUTE TUNING 105 C4 F4 B4 F5 B5 F6 A6 D7 F7 Figure 7.1: Photographs of the embouchure for mimed notes. 60 FL1 FL2 FL3 50 40 Tuning (cents) 30 20 10 0 -10 -20 C4 C#4 D4 D#4 E4 F4 F#4 G4 G#4 A4 A#4 B4 C5 C#5 D5 D#5 E5 F5 F#5 G5 G#5 A5 A#5 B5 C6 C#6 D6 D#6 E6 F6 F#6 G6 G#6 A6 A#6 B6 C7 C#7 D7 D#7 Note Figure 7.2: Tuning for three flutists over the range of the instrument. To reduce clutter, error bars have been omitted from this graph; the average range of tuning for four attempts at the same note was around 10 cents, with a maximum of 25 cents.
Page 1 and 2:
Flute acoustics: measurement, model
Page 3:
To Renée iii
Page 6 and 7:
vi I am grateful to my parents, Ros
Page 8 and 9:
viii
Page 10 and 11:
x 4.4 Conclusions and further direc
Page 12 and 13:
2 CHAPTER 1. INTRODUCTION and the p
Page 14 and 15:
4 CHAPTER 1. INTRODUCTION Figure 1.
Page 16 and 17:
6 CHAPTER 1. INTRODUCTION 1.5 ACOUS
Page 18 and 19:
8 CHAPTER 1. INTRODUCTION ‘in-tun
Page 20 and 21:
10 CHAPTER 1. INTRODUCTION
Page 22 and 23:
12 CHAPTER 2. THEORY AND LITERATURE
Page 24 and 25:
Page 26 and 27:
k = ω c and pressure given by p(x,
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
32 CHAPTER 3. MEASURING ACOUSTIC IM
Page 44 and 45:
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65: 54 CHAPTER 4. FINGER HOLE IMPEDANCE
Page 80 and 81: 70 CHAPTER 5. IMPEDANCE SPECTRA OF
Page 108 and 109: 98 CHAPTER 6. MATERIAL AND SURFACE
Page 116 and 117: 106 CHAPTER 7. THE EMBOUCHURE HOLE
Page 122 and 123: 112 CHAPTER 8. SOFTWARE IMPLEMENTAT
Page 138 and 139: 128 CHAPTER 9. APPLICATIONS AND FUR
Page 152 and 153: 142 APPENDIX A. IMPEDANCE SPECTRA C
Page 154 and 155: 144 APPENDIX A. IMPEDANCE SPECTRA F
Page 156 and 157: 146 APPENDIX A. IMPEDANCE SPECTRA A
Page 158 and 159: 148 APPENDIX A. IMPEDANCE SPECTRA C
Page 160 and 161: 150 APPENDIX A. IMPEDANCE SPECTRA D
Page 162 and 163: 152 APPENDIX A. IMPEDANCE SPECTRA F
Page 164 and 165:
154 APPENDIX A. IMPEDANCE SPECTRA A
Page 166 and 167:
156 APPENDIX A. IMPEDANCE SPECTRA D
Page 168 and 169:
158 APPENDIX A. IMPEDANCE SPECTRA F
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
164 APPENDIX A. IMPEDANCE SPECTRA C
Page 176 and 177:
166 APPENDIX A. IMPEDANCE SPECTRA E
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
Page 186 and 187:
Page 188 and 189:
Page 190 and 191:
Page 192 and 193:
Page 194 and 195:
Page 196 and 197:
Page 198 and 199:
Page 200 and 201:
Page 202 and 203:
Page 204 and 205:
194 APPENDIX A. IMPEDANCE SPECTRA
Page 206 and 207:
196 APPENDIX B. PROGRAM LISTINGS /*
Page 208 and 209:
198 APPENDIX B. PROGRAM LISTINGS f:
Page 210 and 211:
200 APPENDIX B. PROGRAM LISTINGS Ca
Page 212 and 213:
202 APPENDIX B. PROGRAM LISTINGS 1.
Page 214 and 215:
204 APPENDIX B. PROGRAM LISTINGS Z_
Page 216 and 217:
Page 218 and 219:
208 APPENDIX B. PROGRAM LISTINGS co
Page 220 and 221:
210 APPENDIX B. PROGRAM LISTINGS */
Page 222 and 223:
212 APPENDIX B. PROGRAM LISTINGS nu
Page 224 and 225:
214 APPENDIX B. PROGRAM LISTINGS pr
Page 226 and 227:
216 APPENDIX B. PROGRAM LISTINGS +
Page 228 and 229:
218 APPENDIX B. PROGRAM LISTINGS el
Page 230 and 231:
220 APPENDIX B. PROGRAM LISTINGS }
Page 232 and 233:
Page 234 and 235:
224 APPENDIX B. PROGRAM LISTINGS
Page 236 and 237:
226 APPENDIX B. PROGRAM LISTINGS 7
Page 238 and 239:
Page 240 and 241:
230 APPENDIX B. PROGRAM LISTINGS 11
Page 242 and 243:
Page 244 and 245:
234 APPENDIX B. PROGRAM LISTINGS
Page 246 and 247:
236 APPENDIX B. PROGRAM LISTINGS Re
Page 248 and 249:
238 APPENDIX B. PROGRAM LISTINGS Re
Page 250 and 251:
Page 252 and 253:
Page 254 and 255:
Page 256 and 257:
Page 258 and 259:
Page 260 and 261:
Page 262 and 263:
Page 264 and 265:
Page 266 and 267:
256 APPENDIX B. PROGRAM LISTINGS Mi
Page 268 and 269:
Page 270 and 271:
Page 272 and 273:
262 APPENDIX B. PROGRAM LISTINGS ma
Page 274 and 275:
264 APPENDIX B. PROGRAM LISTINGS if
Page 276 and 277:
266 APPENDIX B. PROGRAM LISTINGS x
Page 278 and 279:
268 APPENDIX B. PROGRAM LISTINGS Li
Page 280 and 281:
Page 282 and 283:
Page 284 and 285:
Page 286 and 287:
Page 288 and 289:
Page 290 and 291:
Page 292 and 293:
Page 294 and 295:
284 APPENDIX B. PROGRAM LISTINGS in
Page 296 and 297:
286 APPENDIX B. PROGRAM LISTINGS do
Page 298 and 299:
Page 300 and 301:
Page 302 and 303:
292 APPENDIX B. PROGRAM LISTINGS re
Page 304 and 305:
294 APPENDIX B. PROGRAM LISTINGS fp
Page 306 and 307:
Page 308 and 309:
Page 310 and 311:
300 APPENDIX B. PROGRAM LISTINGS #e
Page 312 and 313:
302 APPENDIX B. PROGRAM LISTINGS p2
Page 314 and 315:
304 APPENDIX B. PROGRAM LISTINGS po
Page 316 and 317:
Page 318 and 319:
Page 320 and 321:
310 APPENDIX B. PROGRAM LISTINGS re
Page 322 and 323:
Page 324 and 325:
314 APPENDIX B. PROGRAM LISTINGS Un
Page 326 and 327:
Page 328 and 329:
Page 330 and 331:
320 APPENDIX B. PROGRAM LISTINGS em
Page 332 and 333:
Page 334 and 335:
324 APPENDIX B. PROGRAM LISTINGS s
Page 336 and 337:
326 APPENDIX B. PROGRAM LISTINGS le
Page 338 and 339:
328 APPENDIX B. PROGRAM LISTINGS in
Page 340 and 341:
Page 342 and 343:
Page 344 and 345:
Page 346 and 347:
Page 348 and 349:
338 APPENDIX C. QUANTIFYING MUSIC s
Page 350 and 351:
340 REFERENCES Botros, A., Smith, J
Page 352 and 353:
342 REFERENCES Kob, M. & Neuschaefe
show all

Flute acoustics: measurement, modelling and design - School of ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?