References

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1. H. L. F. Helmholtz, On the sensations of tone as a physiological basis for the theory of music (1887), (New York: Dover Publications, Inc., 1954), pp. 186-196.

2. R. Plomp and W. J. M. Levelt, “Tonal consonance and critical bandwidth”, Journal of the Acoustical Society of America 38 (1965), pp. 548-560.

3. W. J. Dowling and D. L. Harwood, Music Cognition, (Orlando, Academic Press, Inc., 1986), p. 50.

4. W. J. Dowling and D. L. Harwood, Ibid, p. 83.

5. J. R. Pierce, “Attaining consonance in arbitrary scales”, Journal of the Acoustical Society of America 40 (1968), p. 249.

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6. A. Kameoka and M. Kuriyagawa, “Consonance theory Part II. Consonance of complex tones and its calculation method”, Journal of the Acoustical Society of America 45 (1968), pp. 1460-1469.

7. F. H. Slaymaker, “Chords from tones having stretched partials”, Journal of the Acoustical Society of America 47 (1968), pp. 1469-1571.

8. J. M. Geary, “Consonance and dissonance of pairs of inharmonic sounds”, Journal of the Acoustical Society of America 67, pp. 1785-1789.

9. M. V. Mathews and J. R. Pierce, “Harmony and nonharmonic partials”, Journal of the Acoustical Society of America 68 (1980), pp. 1252-1257.

10. W. A. Sethares, “Local consonance and the relationship between timbre and scale”, Journal of the Acoustical Society of America 94, (3), Pt. 1 (1993), p. 1218.

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11. H. L. F. Helmholtz, Ibid., p. 171.

12. A. H. Benade, Fundamentals of musical acoustics, (New York: Oxford University Press, 1976), p. 62.

13. P. Walker, ed. Chambers Science and Technology Dictionary (Edinburgh: W & R Chambers Limited, 1991), p. 363

14. A. H. Benade, Ibid., p. 315.

15. H. L. F. Helmholtz, Ibid., p. 323.

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16. J. R. Pierce, The science of musical sound, (Scientific American Books, 1992), p. 98.

17. J. R. Pierce, Ibid., p. 202.

18. J. R. Pierce, Ibid., p. 203.

19. F. H. Slaymaker, “Chords from tones having stretched partials”, Journal of the Acoustical Society of America 47 (1968), p. 1469.

20. A. H. Benade, Ibid., p. 412.

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21. H. Holmes, ed., Spohr's Violin School, (London, Boosey and Co., c. 1907), p. 8.

22. Ibid., p. 102.

23. H. Schenker, Free Composition, (New York, Longman Inc., 1979).

24. Ibid, p. xxii.

25. Ibid. p. 10.

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26. Ibid., p. 12.

27. S. Sadie (ed.), The New Grove Dictionary of Music, (London, Macmillan Press Ltd, 1980), “Harmonic seventh”.

28. Ibid., “Beethoven”.

29. O. Jonas, Introduction to the Theory of Heinrich Schenker, (New York, Longman Inc., 1982), p. 15.

30. Ibid., p. 16.

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31. Ibid., p. 16.

32. Helmholtz, Ibid., p. 171.

33. E. B. Goldstein, Sensation and Perception, (Pacific Grove, Brooks/Cole Publishing Company, 1996), pp. 36, 123-124, 140, 167, 257-258, 290, 297, 301, 451.

34. C. Schwarz et al, eds., The Chambers Dictionary, (Chambers Harrap Publishers Ltd, Edinburgh, 1994).

35. H. Schenker, Ibid., p. xxiii.

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Section 9