Scala References
Tuning Theory
The following selective list of references to the tuning literature covers
material relevant to Scala:
- Balzano, Gerald J. "The group theoretic description of 12-fold and microtonal
pitch systems", Computer Music Journal vol. 4 no. 4, 1980, pp. 66-84.
- Barlow, Clarence. "Two Essays On Theory", Computer Music Journal vol.
11 no. 1, 1987, pp. 44-60.
- Barlow, Clarence. Bus journey to Parametron, Feedback Papers 21-23,
Feedback-Studio-Verlag, Köln, 1980.
- Blackwood, Easley. "Modes and Chord Progressions in Equal Tunings",
Perspectives of New Music vol. 29 no. 2, summer 1991, pp. 166-201.
- Bohlen, Heinz. "13 Tonstufen in der Duodezime", Acustica vol. 39 no.
2, S. Hirzel Verlag, Stuttgart, 1978, pp. 76-86.
- Brun, Viggo. "Euclidean algorithms and music theory", L'enseignement
mathématique revue internationale tome X, fasc. 1-2, 1964, pp. 125-137.
- Burt, Warren. "Adventures in Scale Generation Along a Wilsonian Path, part 1",
1/1 vol. 9 no. 3, summer 1996.
- Burt, Warren. "Adventures in Scale Generation Along a Wilsonian Path, part 2",
1/1 vol. 10 no. 1, winter 1998, pp. 4-10.
- Busch, Hermann R. Leonhard Eulers Beitrag zur Musiktheorie, Kölner
Beiträge zur Musikforschung 58, Gustav Bosse Verlag, Regensburg, 1970.
- Canright, David. "Superparticular Pentatonics", 1/1 vol. 9 no. 1,
1995, p. 10.
- Carey, Norman and David Clampitt. "Aspects of Well-Formed Scales", Music
Theory Spectrum vol. 11 no. 2, fall 1989, pp. 187-206.
- Carey, Norman and David Clampitt. "Self Similar Pitch
Structures, Their Duals, and Rhythmic Analogs", Perspectives of New
Music vol. 34 no. 2, summer 1996, pp. 62-87.
- Chalmers, John H. Jr. Divisions of the Tetrachord, Frog Peak Music,
Hanover NH, 1993. 234 pages.
- Day, C. R. The music and musical instruments of Southern India and the
Deccan, 1891. Reprint, Low Price Publications, Delhi, 1990, 181 pages.
- Fokker, A. D. Rekenkundige bespiegeling der muziek, Noorduijn,
Gorinchem, 1945. 228 pages.
- Fokker, A. D. "Les mathématiques et la musique. Trois conférences",
Archives du Musée Teyler vol. 10, Martinus Nijhoff, Den Haag, 1947.
- Fokker, A.D. "Unison
vectors and periodicity blocks in the three-dimensional (3-5-7-) harmonic
lattice of notes", Proceedings of the KNAW, Series B, vol. 72,
Amsterdam, 1969, pp. 153-168.
- Helmholtz, Hermann L. F. von. Die Lehre von den Tonempfindungen als
physiologische Grundlage für die Theorie der Musik, 6th edition, Friedrig
Vieweg & Sohn, Braunschweig, 1913. 668 pages. Olms, Hildesheim, 1983.
On the Sensations of Tone as a Psychological basis for the Theory of
Music, 2nd English edition translated by Alexander John Ellis, based on
the 4th German edition of 1877 with extensive notes, foreword and afterword:
1885. Reprint by Dover Publications, 1954.
- Partch, Harry. Genesis of a Music: An Account of a Creative Work, its
Roots and its Fulfillment, 2nd enl. edition, Da Capo Press, New York,
1974. 517 pages. Reprint, 1979.
- Rapoport, Paul. "Notes Toward Quasi-Triskaidekaphilia",
Xenharmonikôn vol. 13, spring 1991, pp. 45-53.
- Rapoport, Paul. "The Structural Relationships of Fifths and Thirds in Equal
Temperaments", Journal of Music Theory vol. 37 no. 2, pp. 351-389,
fall 1993.
- Rapoport, Paul. "The Notation of Equal Temperaments",
Xenharmonikôn vol. 16, 1995, pp. 61-84.
- Rasch, Rudolf (ed.) Corpus Microtonale, vol. 1: Adriaan Daniël Fokker
- Selected Compositions, with introduction by Rudolf Rasch, Diapason
Press, Utrecht, 1987. 217 pages.
- Rothenberg, David. "A Model for Pattern Perception with Musical Applications.
Part I: Pitch Structures as Order-Preserving Maps", Mathematical Systems
Theory vol. 11, pp. 199-234, 1978.
- Sábat, Eduardo. Principios de la Gama Dinámica, Arca,
Montevideo, 1994. 238 pages.
- Sauveur, Joseph. Collected writings on musical acoustics (Paris
1700-1713), R.A. Rasch (ed.), Diapason Press, Utrecht, 1984.
- Wille, Rudolf. "Mathematik und Musiktheorie", in Musik und Zahl,
Verlag für systematische Musikwissenschaft, Bonn-Bad Godesberg, 1976, pp. 233-264.
- Wilson, Ervin. "D'alessandro, Like a Hurricane", Xenharmonikôn
vol. 12, spring 1989, pp. 1-39.
Algorithms
Some algorithms used in Scala can be found in the following references:
- Khinchin, A. Ya. Continued fractions. 1935. Translated from Russian.
University of Chicago Press, 1964. Dover Publications, New York, 1997, 95
pages.
- Reingold, Edward M., Jurg Nievergelt and Narsingh Deo. Combinatorial
Algorithms. Theory and Practice, Prentice Hall, Englewood Cliffs NJ,
1977, 433 pages.
Modes
Many of the modes in the list of modes come
from the following sources:
- Chalmers, John H. Jr. Divisions of the Tetrachord, Frog Peak Music,
Hanover NH, 1993. 234 pages.
- Fritsch, Ingrid. Analysen von Solo-Honkyoku der Tozan-Schule, Studien
zur traditionellen Musik Japans, Band 4, Bärenreiter Verlag, Kassel, 1979,
241 pages.
- Helmholtz, Hermann L.F. von. On the Sensations of Tone as a
Psychological basis for the Theory of Music, 2nd English edition
translated by Alexander John Ellis, 1885.
- Pesch, Ludwig. Raga Dhana. An alpha-numerical directory of ragas, 2nd
edition, Natana Kairali, Kerala, 1993, 226 pages.
- Rasch, Rudolf (ed.) Corpus Microtonale, vol. 1: Adriaan Daniël Fokker
- Selected Compositions, with introduction by Rudolf Rasch, Diapason
Press, Utrecht, 1987. 217 pages.
- Swets, Wouter. Traditionele Turkse kunstmuziek, KRO, Hilversum, 1983,
179 pages.
- Wiersma-te Nijenhuis, Emmy. Dattilam. A compendium of ancient Indian
music, E.J. Brill, Leiden, 1970, 477 pages.
- Zonis, Ella. Classical Persian Music: An Introduction. Harvard
University Press, Cambridge MA, 1973.