The Piano

  • Neville H. Fletcher
  • Thomas D. Rossing
Part of the Springer Study Edition book series (SSE)


The piano has become the most versatile and popular of all musical instruments. It has a playing range of more than seven octaves (A0 to C8), and a wide dynamic range as well. It is widely used as a solo instrument, but it is also used to accompany other solo instruments and especially singing.


Decay Time Sound Radiation Spectrum Envelope Electrical Transmission Line Piano Action 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Askenfelt, A., and Jansson, E. (1985). Piano touch, hammer action and string motion. Proc. SMAC 83. Royal Swedish Academy of Music, Stockholm.Google Scholar
  2. Askenfelt, A., and Jansson, E. (1987). From touch to string vibrations-The initial course of piano tone. Paper CC3, 113th Meeting, Acoust. Soc. Am., Indianapolis.Google Scholar
  3. Burns, E.M., and Ward, W.D. (1982). Intervals, scales, and tuning. In “The Psychology of Music” ( D. Deutsch, ed.). Academic Press, San Diego, California.Google Scholar
  4. Byrd, D., and Yavelow, C. (1986). The Kurzweil 250 digital synthesizer. Computer Music. J. 10(1), 64–86.CrossRefGoogle Scholar
  5. Carp, C. (1986). The inharmonicity of strung keyboard instruments. Acustica 60, 295–299.Google Scholar
  6. Conklin, H. (1970). Longitudinal mode tuning of stringed instruments. U.S. patent No. 3,523, 480.Google Scholar
  7. Conklin, H. (1987). Augmented bass hammer striking distance for pianos. U.S. patent No. 4,674, 386.Google Scholar
  8. Dijksterhuis, P.R. (1965). De piano. Nederlandse Akoest. Genootschap 7, 50–65.Google Scholar
  9. Fletcher, H., Blackham, E.D., and Stratton, R. (1962). Quality of piano tones. J. Acoust. Soc. Am. 34, 749–761.ADSCrossRefGoogle Scholar
  10. Hall, D.E. (1986). Piano string excitation in the case of small hammer mass. J. Acoust. Soc. Am. 79, 141–147.ADSCrossRefGoogle Scholar
  11. Hall, D.E. (1987). Piano string excitation II: General solution for a hard narrow hammer; III: General solution for a soft narrow hammer. J. Acoust. Soc. Am. 81, 535–555.ADSCrossRefGoogle Scholar
  12. von Helmholtz, H.L.F. (1877). “On the Sensations of Tone,” 4th ed. Translated by A.J. Ellis, Dover, New York, 1954.Google Scholar
  13. Henderson, M.T. (1936). Rhythmic organization in artistic piano performance. In “Objective Analysis of Musical Performance” (C.E. Seashore, ed.), Iowa Studies in Piano Perf. 4, 281–305. Univ. Press, Iowa City, Iowa.Google Scholar
  14. Houtsma, A.J.M., Rossing, T.D., and Wagenaars, W.M. (1987). “Auditory Demonstrations,” Demonstration # 16. Inst. Percept. Res., Eindhoven, The Netherlands.Google Scholar
  15. Kent, E.L. (1982). Influence of irregular patterns in the inharmonicity of piano-tone partials upon tuning practice. Das Musikinstrument 31, 1008–1013.Google Scholar
  16. Kindel, J. (1989). Modal analysis and finite element analysis of a piano soundboard. M.S. thesis, University of Cincinnati.Google Scholar
  17. Kindel, J., and Wang, I. (1987). Modal analysis and finite element analysis of a piano soundboard, Proc. 5th International Modal Analysis Conf. (IMAC), pp. 1545–1549.Google Scholar
  18. Kock, W. (1937). The vibrating string considered as an electrical transmission line. J. Acoust. Soc. Am. 8, 227–233.ADSCrossRefGoogle Scholar
  19. Lieber, E. (1979). The influence of the soundboard on piano sound. Das Musikinstrument 28, 304–316 [original German version in Das Musikinstrument 9, 858 (1966)].Google Scholar
  20. Lieber, E. (1982). On the tuning stability of pianos. Das Musikinstrument 31, 602–604.Google Scholar
  21. Lieber, E. (1985). On the possibilities of influencing piano touch. Das Musikinstrument 34, 58–63.Google Scholar
  22. Martin, D.W. (1946). Decay rates of piano tones. J. Acoust. Soc. Am. 19, 535–547.ADSCrossRefGoogle Scholar
  23. Martin, D.W., and Ward, W.D. (1961). Subjective evaluation of musical scale temperament in pianos. J. Acoust. Soc. Am. 33, 582–585.ADSCrossRefGoogle Scholar
  24. Meyer, J. (1978). “Acoustics and the Performance of Music.” Verlag das Musikinstrument, Frankfurt am Main.Google Scholar
  25. Meyer, J. and Melka, A. (1983). Messung and Darstellung des Ausklingverhaltens von Klavieren. Das Musikinstrument 32, 1049–1064.Google Scholar
  26. Nakamura, I. (1982). Simulation of string vibrations on the piano-a struck string. Proceedings of Co-op Workshop on Stringed Muscial Instruments. (A. Segel, ed.). Wollongong, Australia.Google Scholar
  27. Nakamura, I. (1983). The vibrational character of the piano soundboard. Proc. 11th ICA, Paris, 385–388.Google Scholar
  28. Pfeiffer, W. (1948). “Vom Hammer.” Verlag Das Musikinstrument, Frankfurt am Main. English translation by J. Engelhardt, 1978.Google Scholar
  29. Podlesak, M., and Lee, A. R. (1987). Longitudinal vibrations in piano strings. Paper CC5, 113th Meeting, Acoust. Soc. Am., Indianapolis. See also J. Acoust. Soc. Am. 83, 305–317 (1988).Google Scholar
  30. Reblitz, A. (1976). “Piano Servicing, Tuning, and Rebuilding”. Vestal Press, Vestal, New York.Google Scholar
  31. Rossing, T.D. (1982). “The Science of Sound,” Addison-Wesley, Reading, Massachusetts. Chapter 14.Google Scholar
  32. Sanderson, A. (1983). “Piano Technology Topics: # 5 Piano Scaling Formulas.” Inventronics, Chelmsford, Massachusetts.Google Scholar
  33. Schuck, O.H., and Young, R.W. (1943). Observations of the vibrations of piano strings. J. Acoust. Soc. Am. 15, 1–11.ADSCrossRefGoogle Scholar
  34. Suzuki, H. (1986). Vibration and sound radiation of a piano soundboard. J. Acoust. Soc. Am. 80, 1573–1582.ADSCrossRefGoogle Scholar
  35. Terhardt, E., and Zick, M. (1975). Evaluation of the tempered tone scale in normal, stretched, and contracted intonation. Acustica 32, 268–274.Google Scholar
  36. Vernon, L.N. (1936). Synchronization of chords in artistic piano music. In “Objective Analysis of Musical Performance” (C.E. Seashore, ed.) pp. 306–345. Univ. Press, Iowa City, Iowa.Google Scholar
  37. Weinreich, G. (1977). Coupled piano strings. J. Acoust. Soc. Am. 62, 1474–1484. (Reprinted in “Musical Acoustics: Selected Reprints.” T.D. Rossing, ed., American Association of Physics Teachers, College Park, Maryland.)Google Scholar
  38. White, W.B. (1906). “Theory and Practice of Piano Construction.” Edward Lyman Bill, New York. Reprinted by Dover, 1975.Google Scholar
  39. Wogram, K. (1981). Acoustical research on pianos, part I: Vibrational characteristics of the soundboard. Das Musikinstrument 24, 694–702, 776–782, 872–880 [original German version in Das Musikinstrument 23, 380–404 (1980)].Google Scholar
  40. Wogram, K. (1988), The strings and the soundboard. In “Piano Acoustics”, Royal Academy of Music, Stockholm.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • Neville H. Fletcher
    • 1
  • Thomas D. Rossing
    • 2
  1. 1.CSIRO Australia, Research School of Physical SciencesAustralian National UniversityCanberraAustralia
  2. 2.Department of PhysicsNorthern Illinois UniversityDe KalbUSA

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