# 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.