Design and tone in the mechanoacoustic piano. Part III. Piano strings and scale design

Journal of the Acoustical Society of America

Volumn 100, Issue 3, 1996, Pages 1286-1300

  Conklin Jr , Harold A ^a  

^a NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTICS; ARTICLE; MUSIC; PRIORITY JOURNAL; SOUND TRANSMISSION;

EID: 9544233543     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.416017     Document Type: Article

References (42)

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2. M. Goodway and J. S. Odell, "The Metallurgy of 17th and 18th Century Music Wire," in The Historical Harpsichord (Pendragon, Stuyvesant, NY, 1987), Vol. 2.
3. H. C. Schonberg, The Great Pianists (Simon and Schuster, New York, 1963), p. 152.
4. P. M. Morse, Vibration and Sound (McGraw-Hill, New York, 1948), 2nd ed., Chap. III, pp. 91-96.
5. A. H. Benade, Fundamentals of Musical Acoustics (Oxford U.P., London, 1976), Chap. 17, pp. 333-338.
6. Reference 44, 1927 Supplement, Chap. XVIII, p. 208.
7. H. A. Conklin, Jr., "Tuning the longitudinal mode of piano strings," J. Acoust. Soc. Am. Suppl. 1 73, S84 (1983).
8. T. Yanagisawa, K. Nakamura, and I. Shirayanagi, "Longitudinal Vibration and Inharmonic Tone of Piano String - Vibration Analysis of Piano String and Sound Board by Finite Element Method (II)," J. Acoust. Soc. Jpn. 33, 412-416 (1977) (in Japanese, with English abstract).
9. M. Podelsak and A. R. Lee, "Longitudinal vibrations in piano strings," J. Acoust. Soc. Am. Suppl. 1 81 S61 (1987).
10. M. Podelsak, "Dispersion of waves in piano strings," J. Acoust. Soc. Am. 83, 305-317 (1988) (see pp. 313-316).
11. Lord Rayleigh (J. W. Strutt), The Theory of Sound (Dover, New York, 1945), Vol. I, p. 252 (a quotation re: longitudinal mode of piano strings from p. 154 of Donkin's Acoustics).
12. A. F. Knoblaugh, "A Discussion of Wolf Tones," excerpt from report for months of June and July, 1928, Sound Research Dept., Institute of Scientific Research, University of Cincinnati.
13. A. F. Knoblaugh, "The clang tone of the pianoforte," J. Acoust. Soc. Am. 16, 102 (1944).
14. H. A. Conklin, Jr., U.S. Patent No. 3,532,480, "Longitudinal Mode Tuning of Stringed Instruments" (11 August 1970).
15. H. A. Conklin, Jr., U.S. Patent No. 4,055,038, "Apparatus for Wrapping Strings for Musical Instruments (25 October 1977).
16. R. S. Shankland and J. W. Coltman, "The departure of the overtones of a vibrating wire from as true harmonic series," J. Acoust. Soc. Am. 10, 161-166 (1939).
17. Reference 110, Chap. IV, pp. 166-170.
18. O. H. Schuck and R. W. Young, "Observations on the vibrations of piano strings," J. Acoust. Soc. Am. 15, 1-11 (1943).
19. E. D. Blackham, "The Physics of the Piano," Sci. Am. 213 (6), 88-99 (Dec. 1965), p. 94.
20. A. Reinholdt, E. Jansson, and A. Askenfelt, "Analysis and synthesis of piano tone," J. Acoust. Soc. Am. Suppl. I 81, S61 (1987).
21. H. Fletcher, E. D. Blackham, and R. Stratton, "Quality of piano tones," J. Acoust. Soc. Am. 34, 749-761 (1962).
22. R. W. Young, "Inharmonicity of plain wire piano strings," J. Acoust. Soc. Am. 24, 267-273 (1952).
23. 4=309.99 Hz.
24. Reference 4, p. 61.
25. O. L. Railsback, "Scale temperament as applied to piano tuning," J. Acoust. Soc. Am. 9, 274A (1938).
26. Reference 124, pp. 8-11.
27. D. W. Martin and W. D. Ward, "Subjective evaluation of musical scale temperament in pianos," J. Acoust. Soc. Am. 33, 582-585 (1961) (shows stretch diagram).
28. Reference 111, Chap. 16, p. 318.
29. This can be verified experimentally (but only by placing the tone, tuning, and stability of the instrument at risk) by tuning the strings of each of several successively higher keys flat to the same fundamental frequency of an unchanged lower key.
30. R. Plomp, "Pitch of complex tones," J. Acoust. Soc. Am. 41, 1526-1533 (1967) (contains an excellent historical review relating to the perception of the pitch of complex tones, including extensive references).
31. A. J. M. Houtsma and J. L. Goldstein, "The central origin of the pitch of complex tones: Evidence from musical interval recognition," J. Acoust. Soc. Am. 51, 520-529 (1972). (They conclude that a fundamental is unnecessary in establishing the pitch of complex tones.)
32. A. E. Sanderson, "Piano stringing scale design," J. Acoust. Soc. Am. Suppl. 1 81, S60 (1987).
33. R. W. Young, "Inharmonicity of Piano Strings," Acoustica 4, 259-262 (1954).
34. C. Karp, "The inharmonicity of strung keyboard instruments," Acoustica 60(4), 295-299 (1986).
35. R. W. Young, "Inharmonicity of piano bass strings," J. Acoust. Soc. Am. 26, 144(A) (1954).
36. H. Fletcher, "Normal vibration frequencies of a stiff piano string," J. Acoust. Soc. Am. 36, 203-209 (1964), p. 208.
37. D. Roberts, "Calculating Technician Part X," Piano Technicians Journal (June), pp. 22-23 (1980).
38. D. Roberts, "Calculating Technician Part XI," Piano Technicians Journal (July), pp. 25-26 (1980).
39. A. E. Sanderson, "Piano Technology Topics - #5," Inventronics, Inc., 8 Acton Rd., Chelmsford, MA 01824.
40. A. E. Sanderson, "The Inharmonicity of Wound Piano Strings," lecture given at Piano Acoustics Conference, Steinway and Sons, New York, 20 May 1989.
41. I. Nakamura and S. Iwaoka, "On the inharmonicity of a piano string wrapped a single copper copper winding," Trans. Acoust. Soc. Jpn. Spring Meeting, 353-354 (1986) (in Japanese).
42. F. Miller, Jr., "A proposed loading of piano strings for improved tone," J. Acoust. Soc. Am. 21, 318-322 (1949).