Coherence and sameness in well-formed and pairwise well-formed scales

Journal of Mathematics and Music

Volumn 1, Issue 2, 2007, Pages 79-98

  Carey, Norman ^a  

^a CITY UNIVERSITY OF NEW YORK   (United States)

Author keywords

Coherence; Distribution modulo 1; Fibonacci sequence; Scale theory; Well formed scales

Indexed keywords

EID: 84975835292     PISSN: 17459737     EISSN: 17459745     Source Type: Journal    
DOI: 10.1080/17459730701376743     Document Type: Article

References (22)

1. Clough, J., and Myerson, G., 1985. Variety and multiplicity in diatonic systems. Journal of Music Theory, 29:249–270.
2. Clough, J., 1979. Aspects of diatonic sets. Journal of Music Theory, 23:45–61.
3. Clough, J., and Douthett, J., 1991. Maximally even sets. Journal of Music Theory, 35:93–173.
4. Clough, J., Engebretsen, N., and Kochavi, J., 1999. Scales, sets, and interval cycles:a taxonomy. Music Theory Spectrum, 21:74–104.
5. Rahn, J., 1981. Coordination of interval sizes in seven-tone collections. Journal of Music Theory, 35:33–60.
6. Carey, N., 2002. On coherence and sameness, and the evaluation of scale candidacy claims. Journal of Music Theory, 46:1–56.
7. Balzano, G., 1980. The group-theoretic description of 12-fold and microtonal pitch systems. Computer Music Journal, 4 (4):66–84.
8. Agmon, E., 1989. A mathematical model of the diatonic system. Journal of Music Theory, 33:125
9. Agmon, E., 1996. Coherent tone systems:A study in the theory of diatonicism. Journal of Music Theory, 40:39–59.
10. Rothenberg, D., 1978, A model for pattern perception with musical applications. Part I:Pitch structures as order preserving maps. Mathematical Systems Theory, 11, 199–234. Part II:The information content of pitch structures. Mathematical Systems Theory, 11, 353–372. Part III:The graph embedding of pitch structures Mathematical Systems Theory, 12, 73–101.
11. Halton, J.H., 1965. The distribution of the sequence (nζ) (n=0, 1, 2, …). Proceedings of the Cambridge Philosophical Society, 61:665–670.
12. Sós, V.T., 1958. On the distrubution mod 1 of the sequence nα. Annals of the University of Science, Budapest Eötvös, Sect. Math., I:127–134.
13. Carey, N., 1998, Distribution modulo 1 and musical scales. PhD dissertation, University of Rochester.
14. Dahlhaus, C., 1990, Studies on the Origin of Harmonic Tonality (translated by Robert Gjerdingen from the original:Untersuchungen über die Entstehung der Harmonischen Tonalität (Kassel:Bárenreiter, 1967, 1988)). (Princeton:Princeton University Press).
15. Carey, N., and Clampitt, D., 1989, Aspects of well-formed scales. Music Theory Spectrum, 11(2), 187–206.
16. Wooldridge, M., 1992, Rhythmic implications of diatonic theory:A study of Scott Joplin's Ragtime piano works. PhD dissertation, State University of New York at Buffalo.
17. Clough, J., and Myerson, G., 1986. Musical scales and the generalized circle of fifths. American Mathematical Monthly, 93:695–701.
18. Carey, N., and Clampitt, D., 1996. Self-similar pitch structures, their duals, and rhythmic analogues. Perspectives of new music, 34 (2):6287
19. Blackwood, E., 1985. The Structure of Recognizable Diatonic Tunings, Princeton:Princeton University Press.
20. Kornerup, T., 1930. Das Goldene Tonsystem als Fundament der theoretischen Akustik, Copenhagen:Aschehoug Forlag.
21. Yasser, J., 1975 [1932], A Theory of Evolving Tonality. American Library of Musicology (Reprint:New York:Da Capo Press).
22. Clampitt, D., 1997, Pairwise well-formed scales:Structural and transformational properties. PhD dissertation, State University of New York at Buffalo.