Bibliographic Notes

1. H. Bouasse. (1929). Instruments à vent, 2 vols. (Paris, Librairie Delagrave), vol. 1, pp. 5-29.

2. Bouasse. Instruments d vent, vol. 1, pp. 68-79; Hermann L. F. Helmholtz. (1885). Sensations of Tone, trans. A. J. Ellis (reprint, New York, Peter Smith, 1948), p. 390.

3. Helmholtz, Sensations of Tone, pp. 388-394.

4. Arthur H. Benade. (1960). Horns, Strings and Harmony (Garden City, NY, Doubleday), pp. 142-233. Corrected reprint, 1992 (New York, Dover Publications), with the same pagination.

5. A. H. Benade. (1973). "Physics of Brasses," Scientific American, July, pp. 24-35.

6. Edward Eisner. (1967). "The Complete Solutions of the "Webster" Horn Equation," J. Acoust. Soc. Am. 41, 1126-1146. This paper is an excellent source of technical and historical information on the general theory of horns as it concerns an acoustician.

7. Eric Halfpenny. (1962). "William Bull and the English Trumpet," Galpin Society Journal XV, 18; Eric Halfpenny. (1963). "Two Oxford Trumpets," Galpin Society Journal XVI, 49; Joseph Wheeler. (1965). "Further Notes on the Classic Trumpet," Galpin Society Journal XVIII, 14.

8. H. Bouasse. (1929). Tuyaux et résonateurs (Paris, Librairie Delagrave), pp. 383-384.

9. E. G. Richardson. (1929). The Acoustics of Orchestral Instruments (London, Arnold), p. 75.

10. E. L. Kent. (1961). U. S. Patent 2,987,950, filed April 1958, granted June 1961.

11. Frederick J. Young. (1960). "The Natural Frequencies of Musical Horns," Acustica 10, 91-97; "Impedance of Tapered Structures," J. Acoust. Soc. Am. 33, 1206-1210; Frederick J. Young. (1966). "Impedance of Tapered Structures," J. Acoust. Soc. Am. 39, 841-846.

12. W. T. Cardwell. (1970). U. S. Patent 3,507,181, filed Oct. 1967, granted April 1970.

13. Arthur H. Benade and Erik V. Jansson. (1973). "On Plane and Spherical Waves in Horns with Nonuniform Flare: 1. Theory of Radiation, Resonance Frequencies, and Mode Conversion; 11. Prediction and Measurements of Resonance Frequencies and Radiation Losses," Speech Transmission Laboratory Technical Report (March 15, 1973), Royal Institute of Technology (KTH), Stockholm.

14. Klaus Wogram. (1972). "Ein Beitrag zur Ermittlung der Stimmung von Blechblasinstrument." (Dr.-Ing. diss., Technischen Universitat Carolo-Wilhelmina zu Braunschweig).

15. A. H. Benade. (1966). "Relation of Air-Column Resonances to Sound Spectra Produced by Wind Instruments," J. Acoust. Soc. Am. 40, 247-249.

16. A. H. Benade and D. J. Gans. (1968). "Sound Production in Wind Instruments," Annals of the New York Academy of Science 155, 247-263.

17. Walter E. Worman. (1971). "Self-Sustained Nonlinear Oscillations in Clarinet-Like Systems," (Ph.D. diss., Case Western Reserve University, Cleveland, Ohio).

18. Robert W. Pyle, Jr. (1969). "Mathematical Model of the Brass Player's Embouchure," J. Acoust. Soc. Am. 45, 296. This is one of six papers presented as part of a symposium on brass instrument acoustics.

19. Josef Merhaut. (1969). "Method of Measuring the Acoustical Impedance," J. Acoust. Soc. Am. 45, 331.

20. John W. Coltman. (1968). "The Sounding Mechanism of the Flute," J. Acoust. Soc. Am 44, 983-992.

21. Philip Bate. (1966). The Trumpet and Trombone (London, Benn), pp. 121-122.

22. Werner Menke. (1934). History of the Trumpet of Bach and Handel (London, Reeves).

23. Victor Mahillon. (1874). Elements d'acoustique musicale et instrumentale (Brussels, Mahillon), p. 94.

24. Mahillon, Elements d'acoustique, p. 94.

Trumpet Acoustics
Acoustical Preliminaries
The "Water Trumpet"-- An Analog to What Happens inside a Trumpet
The Function of the Player's Lips
The Function of the Pipe and Bell--Inside the Air Column
The Cooperation Needed for Musical Results
The Baroque Trumpet
The 'Internal' Spectrum of the Modern Trumpet
The 'Internal' Spectrum of the Baroque Trumpet
Relation of Internal to External Tone Color Spectrum
The Menke Trumpet
The Problem of Clean Attack
Mahillon in Retrospect
Bibliographic Notes