Musical Mathematics

ON THE ART AND SCIENCE OF ACOUSTIC INSTRUMENTS

BIBLIOGRAPHY

Chapters 1–9

Askenfelt, A., Editor (1990). Five Lectures on The Acoustics of the Piano. Royal Swedish Academy of Music No. 64, Stockholm, Sweden.

Askill, J. (1979). Physics of Musical Sound. D. Van Nostrand Company, New York.

Baines, A. (1967). Woodwind Instruments and Their History. Dover Publications, Inc., New York, 1991.

Barbera, A., Translator (1991). The Euclidean Division of the Canon: Greek and Latin Sources. University of Nebraska Press, Lincoln, Nebraska.

Barker, A., Translator (1989). Greek Musical Writings. Two Volumes. Cambridge University Press, Cambridge, Massachusetts.

Bell, A.J., and Firth, I.M. (1986). The physical properties of gut musical instrument strings. Acustica 60, No. 1, pp. 87–89.

Benade, A.H., and French, J.W. (1965). Analysis of the flute head joint. Journal of the Acoustical Society of America37, No. 4, pp. 679–691.

Benade, A.H. (1967). Measured end corrections for woodwind toneholes. Journal of the Acoustical Society of America41, No. 6, p. 1609.

Benade, A.H. (1976). Fundamentals of Musical Acoustics. Dover Publications, Inc., New York, 1990.

Berliner, P.F. (1978). The Soul of Mbira. University of California Press, Berkeley, California, 1981.

Blevins, R.D. (1979). Formulas for Natural Frequency and Mode Shape, Reprint. Krieger Publishing Company, Malabar, Florida, 1993.

Boehm, T. (1847). On the Construction of Flutes, Über den Flötenbau. Frits Knuf Buren, Amsterdam, Netherlands, 1982.

Boehm, T. (1871). The Flute and Flute-Playing. Dover Publications, Inc., New York, 1964.

Boyer, H.E., and Gall, T.L., Editors (1984). Metals Handbook, Desk Edition. American Society for Metals, Metals Park, Ohio, 1989.

Bray, A., Barbato, G., and Levi, R. (1990). Theory and Practice of Force Measurement. Academic Press, San Diego, California.

Burkert, W. (1962). Lore and Science in Ancient Pythagoreanism. Translated by E.L. Minar, Jr. Harvard University Press, Cambridge, Massachusetts, 1972.

Cadillac Plastic Buyer’s Guide. Cadillac Plastic and Chemical Company, Troy, Michigan, 1986.

Campbell, M., and Greated, C. (1987). The Musician’s Guide to Acoustics. Schirmer Books, New York, 1988.

Capstick, J.W. (1913). Sound. Cambridge University Press, London, England, 1932.

Chapman, R.E., Translator (1957). Harmonie universelle: The Books on Instruments, by Marin Mersenne. Martinus Nijhoff, The Hague, Netherlands.

Cohen, H.F. (1984). Quantifying Music. D. Reidel Publishing Company, Dordrecht, Netherlands.

Coltman, J.W. (1979). Acoustical analysis of the Boehm flute. Journal of the Acoustical Society of America 65, No. 2, pp. 499–506.

Cremer, L., Heckl, M., and Ungar, E.E. (1973). Structure-Borne Sound, 2nd ed. Springer-Verlag, Berlin and New York, 1988.

Cremer, L. (1981). The Physics of the Violin, 2nd ed. The MIT Press, Cambridge, Massachusetts, 1984.

Crew, H., and De Salvio, A., Translators (1914). Dialogues Concerning Two New Sciences, by Galileo Galilei. Dover Publications, Inc., New York.

D’Addario Brochure (2007). Catalog Supplement/String Tension Specifications. Online publication, pp. 1–14. J. D’Addario Company, Inc., Farmingdale, New York.

Den Hartog, J.P. (1934). Mechanical Vibrations. Dover Publications, Inc., New York, 1985.

Den Hartog, J.P. (1948). Mechanics. Dover Publications, Inc., New York, 1984.

D’Erlanger, R., Bakkouch, ‘A.‘A., and Al-Sanusi, M., Translators (Vol. 1, 1930; Vol. 2, 1935; Vol. 3, 1938; Vol. 4, 1939; Vol. 5, 1949; Vol. 6, 1959). La Musique Arabe. Librairie Orientaliste Paul Geuthner, Paris, France.

Diels, H. (1903). Die Fragmente der Vorsokratiker, Griechisch und Deutsch. Three Volumes. Weidmannsche Verlagsbuchhandlung, Berlin, Germany, 1951.

D’Ooge, M.L., Translator (1926). Nicomachus of Gerasa: Introduction to Arithmetic. The Macmillan Company, New York.

Dunlop, J.I. (1981). Testing of poles by using acoustic pulse method. Wood Science and Technology 15, pp. 301–310.

Du Pont Bulletin: “Tynex 612 Nylon Filament.” Du Pont Company, Wilmington, Delaware.

Düring, I., Translator (1934). Ptolemaios und Porphyrios über die Musik. Georg Olms Verlag, Hildesheim, Germany, 1987.

Einarson, B., Translator (1967). On Music, by Plutarch. In Plutarch’s Moralia, Volume 14. Harvard University Press, Cambridge, Massachusetts.

Elmore, W.C., and Heald, M.A. (1969). Physics of Waves. Dover Publications, Inc. New York, 1985.

Fenner, K., On the Calculation of the Tension of Wound Strings, 2nd ed. Verlag Das Musikinstrument, Frankfurt, Germany, 1976.

Fishbane, P.M., Gasiorowicz, S., and Thornton, S.T. (1993). Physics for Scientists and Engineers. Prentice-Hall, Englewood Cliffs, New Jersey.

Fletcher, H., Blackham, E.D., and Stratton, R.S. (1962). Quality of piano tones. Journal of the Acoustical Society of America 34, No. 6, pp. 749–761.

Fletcher, H. (1964). Normal vibration frequencies of a stiff piano string. Journal of the Acoustical Society of America36, No. 1, pp. 203–209.

Fletcher, N.H., and Rossing, T.D. (1991). The Physics of Musical Instruments, 2nd ed. Springer-Verlag, Berlin and New York, 1998.

Fogiel, M., Editor (1980). The Strength of Materials Mechanics of Solids Problem Solver. Research and Education Association, Piscataway, New Jersey, 1990.

Goodway, M., and Odell, J.S. (1987). The Historical Harpsichord, Volume Two: The Metallurgy of 17th– and 18th–Century Music Wire. Pendragon Press, Stuyvesant, New York.

Gray, D.E., Editor (1957). American Institute of Physics Handbook, 3rd ed. McGraw-Hill Book Company, New York, 1972.

Halliday, D., and Resnick, R. (1970). Fundamentals of Physics, 2nd ed. John Wiley Sons, New York, 1981.

Hamilton, E., and Cairns, H., Editors (1963). The Collected Dialogues of Plato. Random House, Inc., New York, 1966.

Helmholtz, H.L.F., and Ellis A.J., Translator (1885). On the Sensations of Tone. Dover Publications, Inc., New York, 1954.

Hoadley, R.B. (1980). Understanding Wood. The Taunton Press, Newtown, Connecticut, 1981.

Hubbard, F. (1965). Three Centuries of Harpsichord Making, 4th ed. Harvard University Press, Cambridge, Massachusetts, 1972.

Ingard, U. (1953). On the theory and design of acoustic resonators. Journal of the Acoustical Society of America 25, No. 6, pp. 1037–1061.

Ingard, K.U. (1988). Fundamentals of Waves and Oscillations. Cambridge University Press, Cambridge, Massachusetts, 1990.

Jan, Karl von, Editor (1895). Musici Scriptores Graeci. Lipsiae, in aedibus B.G. Teubneri.

Jerrard, H.G., and McNeill, D.B. (1963). Dictionary of Scientific Units, 6th ed. Chapman and Hall, London, England, 1992.

Jones, A.T. (1941). End corrections of organ pipes. Journal of the Acoustical Society of America 12, pp. 387–394.

Kinsler, L.E., and Frey, A.R. (1950). Fundamentals of Acoustics, 2nd ed. John Wiley Sons, Inc., New York, 1962.

Klein, H.A. (1974). The Science of Measurement. Dover Publications, Inc., New York, 1988.

Land, F. (1960). The Language of Mathematics. Doubleday Company, Inc., Garden City, New York.

Lemon, H.B., and Ference, M., Jr. (1943). Analytical Experimental Physics. The University of Chicago Press, Chicago, Illinois.

Levin, F.R., Translator (1994). The Manual of Harmonics, of Nicomachus the Pythagorean. Phanes Press, Grand Rapids, Michigan.

Liddell, H.G., and Scott, R. (1843). A Greek-English Lexicon. The Clarendon Press, Oxford, England, 1992.

Lide, D.R., Editor (1918). CRC Handbook of Chemistry and Physics, 73rd ed. CRC Press, Boca Raton, Florida, 1992.

Lindeburg, M.R. (1988). Engineering Unit Conversions, 2nd ed. Professional Publications, Inc., Belmont, California, 1990.

Lindeburg, M.R. (1990). Engineer-in-Training Reference Manual, 8th ed. Professional Publications, Inc., Belmont, California, 1992.

Lindley, M. (1987). “Stimmung und Temperatur.” In Geschichte der Musiktheorie, Volume 6, F. Zaminer, Editor. Wissenschaftliche Buchgesellschaft, Darmstadt, Germany.

McLeish, J. (1991). Number. Bloomsbury Publishing Limited, London, England.

Moore, J.L. (1971). Acoustics of Bar Percussion Instruments. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Morse, P.M., and Ingard, K.U. (1968). Theoretical Acoustics. Princeton University Press, Princeton, New Jersey, 1986.

Nash, W.A. (1957). Strength of Materials, 3rd. ed. Schaum’s Outline Series, McGraw-Hill, Inc., New York, 1994.

Nederveen, C.J. (1969). Acoustical Aspects of Woodwind Instruments. Frits Knuf, Amsterdam, Netherlands.

Nederveen, C.J. (1973). Blown, passive and calculated resonance frequencies of the flute. Acustica 28, pp. 12–23.

Newton, R.E.I. (1990). Wave Physics. Edward Arnold, a division of Hodder Stoughton, London, England.

Norton, M.P. (1989). Fundamentals of Noise and Vibration Analysis for Engineers. Cambridge University Press, Cambridge, Massachusetts.

Oberg, E., Jones, F.D., Horton, H.L., and Ryffel, H.H. (1914). Machinery’s Handbook, 24th ed. Industrial Press Inc., New York, 1992.

Olson, H.F. (1952). Music, Physics and Engineering, 2nd ed. Dover Publications, Inc., New York, 1967.

Pierce, A.D. (1981). Acoustics. Acoustical Society of America, Woodbury, New York. 1991.

Pierce, J.R. (1983). The Science of Musical Sound. Scientific American Books, W.H. Freeman and Company, New York.

Pikler, A.G. (1966). Logarithmic frequency systems. Journal of the Acoustical Society of America 39, No. 6, pp. 1102–1110.

Rao, S.S. (1986). Mechanical Vibrations, 2nd ed. Addison-Wesley Publishing Company, Reading, Massachusetts, 1990.

Richardson, E.G. (1929). The Acoustics of Orchestral Instruments and of the Organ. Edward Arnold Co., London, England.

Rossing, T.D. (1989). The Science of Sound, 2nd ed. Addison-Wesley Publishing Co., Inc., Reading, Massachusetts, 1990.

Sadie, S., Editor (1984). The New Grove Dictionary of Musical Instruments. Macmillan Press Limited, London, England.

Schlesinger, K. (1939). The Greek Aulos. Methuen Co. Ltd., London, England.

Schuck, O.H., and Young, R.W. (1943). Observations on the vibrations of piano strings. Journal of the Acoustical Society of America 15, No. 1, pp. 1–11.

Sears, F.W., Zemansky, M.W., and Young, H.D., University Physics, 7th ed. Addison-Wesley Publishing Company, Reading, Massachusetts, 1988.

Skudrzyk, E. (1968). Simple and Complex Vibratory Systems. Pennsylvania State University Press, University Park, Pennsylvania, 1981.

Smith, D.E. (1925). History of Mathematics. Two Volumes. Dover Publications, Inc., New York, 1958.

Standards Handbook, Part 2 — Alloy Data, Wrought Copper and Copper Alloy Mill Products, Eighth Edition, Copper Development Association, Inc., Greenwich, Connecticut, 1985.

Stauss, H.E., Martin, F.E., and Billington, D.S. (1951). A piezoelectric method for determining Young’s modulus and its temperature dependence. Journal of the Acoustical Society of America 23, No. 6, pp. 695–696.

Steinkopf, O. (1983). Zur Akustik der Blasinstrumente. Moeck Verlag, Celle, Germany.

Stiller, A. (1985). Handbook of Instrumentation. University of California Press, Berkeley, California.

Suzuki, H. (1986). Vibration and sound radiation of a piano soundboard. Journal of the Acoustical Society of America80, No. 6, pp. 1573–1582.

Thompson, S.P. (1910). Calculus Made Easy, 3rd. ed. St. Martin’s Press, New York, 1984.

Timoshenko, S., and Woinowsky-Krieger, S. (1940). Theory of Plates and Shells, 2nd ed., McGraw-Hill Book Company, New York, 1959.

Timoshenko, S.P. (1953). History of Strength of Materials. Dover Publications, Inc., New York, 1983.

Towne, D.H. (1967). Wave Phenomena. Dover Publications, Inc., New York, 1988.

Tropfke, J. (1921). Geschichte der Elementar-Mathematik. Seven Volumes. Vereinigung Wissenschaftlicher Verleger, Walter de Gruyter Co., Berlin and Leipzig, Germany.

U.S. Business and Defense Services Administration (1956). Materials Survey: Aluminum. Department of Commerce, Washington, D.C.

Weaver, W., Jr., Timoshenko, S.P., and Young, D.H., Vibration Problems in Engineering, 5th ed. John Wiley and Sons, New York, 1990.

White, W.B. (1917). Piano Tuning and Allied Arts, 5th ed. Tuners Supply Company, Boston, Massachusetts, 1972.

Wogram, K. (1981). Akustische Untersuchungen an Klavieren. Teil I: Schwingungseigenschaften des Resonanzbodens. Das Musikinstrument 24, pp. 694–702, 776–782, 872–879. English translation: Acoustical research on pianos. Part I: Vibrational characteristics of the soundboard. In Musical Acoustics: Selected Reprints, T.D. Rossing, Editor, pp. 85–98. American Association of Physics Teachers, College Park, Maryland, 1988.

Wolfenden, S. (1916). A Treatise on the Art of Pianoforte Construction. The British Piano Museum Charitable Trust, Brentford, Middlesex, England, 1975.

Wood, A.B. (1930). A Textbook of Sound. The Macmillan Company, New York, 1937.

Wood, A. (1940). Acoustics. Dover Publications, Inc., New York, 1966.

Young, R.W. (1952). Inharmonicity of plain wire piano strings. Journal of the Acoustical Society of America 24, No. 3, pp. 267–272.

Zanoncelli, L., Translator (1990). La Manualistica Musicale Greca. Angelo Guerini e Associati, Milan, Italy.

Zebrowski, Jr., E. (1979). Fundamentals of Physical Measurement. Duxbury Press, Belmont, California.

Chapter 10

Adkins, C.D. (1963). The Theory and Practice of the Monochord. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Al-Faruqi, L.I. (1974). The Nature of the Musical Art of Islamic Culture: A Theoretical and Empirical Study of Arabian Music. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Asselin, P. (1985). Musique et Tempérament. Éditions Costallat, Paris, France.

Barbera, C.A. (1977). Arithmetic and geometric divisions of the tetrachord. Journal of Music Theory 21, No. 2, pp. 294–323.

Barbera, A., Translator (1991). The Euclidean Division of the Canon: Greek and Latin Sources. University of Nebraska Press, Lincoln, Nebraska.

Barbour, J.M. (1933). The persistence of the Pythagorean tuning system. Scripta Mathematica, Vol. 1, pp. 286–304.

Barbour, J.M. (1951). Tuning and Temperament. Da Capo Press, New York, 1972.

Barker, A., Translator (1989). Greek Musical Writings. Two Volumes. Cambridge University Press, Cambridge, England.

Barnes, J. (1979). Bach’s keyboard temperament. Early Music 7, No. 2, pp. 236–249.

Beck, C., Translator (1868). Flores musice omnis cantus Gregoriani, by Hugo Spechtshart [von Reutlingen]. Bibliothek des Litterarischen Vereins, Stuttgart, Germany.

Bower, C.M., Translator (1989). Fundamentals of Music, by A.M.S. Boethius. Yale University Press, New Haven, Connecticut.

Briscoe, R.L., Translator (1975). Rameau’s “Démonstration du principe de l’harmonie” and “Nouvelles reflections de M. Rameau sur sa démonstration du principe de l’harmonie:” An Annotated Translation of Two Treatises by Jean-Philippe Rameau. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Brun, V. (1964). Euclidean algorithms and musical theory. L’Enseignement Mathématique X, pp. 125–137.

Burkert, W. (1962). Lore and Science in Ancient Pythagoreanism. Translated by E.L. Minar, Jr. Harvard University Press, Cambridge, Massachusetts, 1972.

Chalmers, J.H., Jr. (1993). Divisions of the Tetrachord. Frog Peak Music, Hanover, New Hampshire.

Chandler, B.G., Translator (1975). Rameau’s “Nouveau système de musique théorique:” An Annotated Translation With Commentary. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Chapman, R.E., Translator (1957). Harmonie universelle: The Books on Instruments, by Marin Mersenne. Martinus Nijhoff, The Hague, Netherlands.

Coelho, V., Editor (1992). Music and Science in the Age of Galileo. Kluwer Academic Publishers, Dordrecht, Netherlands.

Cohen, H.F. (1984). Quantifying Music. D. Reidel Publishing Company, Dordrecht, Netherlands.

Compact Edition of the Oxford English Dictionary. Oxford University Press, Oxford, England, 1974.

Crew, H., and De Salvio, A., Translators (1914). Dialogues Concerning Two New Sciences, by Galileo Galilei. Dover Publications, Inc., New York.

Crocker, R.L. (1963). Pythagorean mathematics and music. The Journal of Aesthetics and Art Criticism XXII, No. 2, Part I: pp. 189–198, and No. 3, Part II: pp. 325–335.

Crocker, R.L. (1966). “Aristoxenus and Greek Mathematics.” In Aspects of Medieval and Renaissance Music: A Birthday Offering to Gustave Reese, J. LaRue, Editor. Pendragon Press, New York.

Crone, E., Editor; Fokker, A.D., Music Editor; Dikshoorn, C., Translator (1966). The Principal Works of Simon Stevin. Five Volumes. C.V. Swets Zeitlinger, Amsterdam.

Crookes, D.Z., Translator (1986). Syntagma musicum II: De organographia, Parts I and II, by Michael Praetorius. The Clarendon Press, Oxford, England.

Daniels, A.M. (1962). The De musica libri VII of Francisco de Salinas. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

De Haan, D.B., Publisher (1884). Vande Spiegeling der Singconst, by Simon Stevin. Amsterdam.

D’Erlanger, R., Bakkouch, ‘A.‘A., and Al-Sanusi, M., Translators (Vol. 1, 1930; Vol. 2, 1935; Vol. 3, 1938; Vol. 4, 1939; Vol. 5, 1949; Vol. 6, 1959). La Musique Arabe, Librairie Orientaliste Paul Geuthner, Paris, France.

Diels, H. (1903). Die Fragmente der Vorsokratiker, Griechisch und Deutsch. Three Volumes. Weidmannsche Verlagsbuchhandlung, Berlin, Germany, 1951.

D’Ooge, M.L., Translator (1926). Nicomachus of Gerasa: Introduction to Arithmetic. The Macmillan Company, New York.

Dupont, W. (1935). Geschichte der musikalischen Temperatur. C.H. Beck’sche Buchdruckerei, Nördlingen, Germany.

Düring, I., Editor (1930). Die Harmonielehre des Klaudios Ptolemaios. Original Greek text of Ptolemy’s Harmonics. Wettergren Kerbers Förlag, Göteborg, Sweden.

Düring, I., Translator (1934). Ptolemaios und Porphyrios über die Musik. Georg Olms Verlag, Hildesheim, Germany, 1987.

Farmer, H.G. (1965). The Sources of Arabian Music. E.J. Brill, Leiden, Netherlands.

Farmer, H.G., Translator (1965). Al-Farabi’s Arabic-Latin Writings on Music. Hinrichsen Edition Ltd., New York.

Fend, M., Translator (1989). Theorie des Tonsystems: Das erste und zweite Buch der Istitutioni harmoniche (1573), von Gioseffo Zarlino. Peter Lang, Frankfurt am Main, Germany.

Fernandez de la Cuesta, I., Translator (1983). Siete libros sobre la musica, by Francisco Salinas. Editorial Alpuerto, Madrid, Spain.

Flegg, G., Hay, C., and Moss, B., Translators (1985). Nicolas Chuquet, Renaissance Mathematician. D. Reidel Publishing Company, Dordrecht, Holland.

Forster, C. (2015). The Partch Hoax Doctrines. Online article, pp. 1–24. The Chrysalis Foundation, San Francisco, California.

Gossett, P., Translator (1971). Traité de l’harmonie [Treatise on Harmony], by Jean-Philippe Rameau. Dover Publications, Inc., New York.

Green, B.L. (1969). The Harmonic Series From Mersenne to Rameau: An Historical Study of Circumstances Leading to Its Recognition and Application to Music. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Guthrie, K.S., Translator (1987). The Pythagorean Sourcebook and Library. Phanes Press, Grand Rapids, Michigan.

Hamilton, E., and Cairns, H., Editors (1966). The Collected Dialogues of Plato. Random House, Inc., New York.

Hawkins, J. (1853). A General History of the Science and Practice of Music. Dover Publications, Inc., New York, 1963.

Hayes, D., Translator (1968). Rameau’s Theory of Harmonic Generation; An Annotated Translation and Commentary of “Génération harmonique” by Jean-Philippe Rameau. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Heath, T.L., Translator (1908). Euclid’s Elements. Dover Publications, Inc., New York, 1956.

Heath, T. (1921). A History of Greek Mathematics. Dover Publications, Inc., New York, 1981.

Hitti, P.K. (1937). History of the Arabs. Macmillan and Co. Ltd., London, England, 1956.

Hubbard, F. (1965). Three Centuries of Harpsichord Making, 4th ed. Harvard University Press, Cambridge, Massachusetts, 1972.

Hyde, F.B. (1954). The Position of Marin Mersenne in the History of Music. Two Volumes. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Ibn Sina (Avicenna): Auicene perhypatetici philosophi: ac medicorum facile primi opera in luce redacta… This Latin translation was published in 1508. Facsimile Edition: Minerva, Frankfurt am Main, Germany, 1961.

Jacobi, E.R., Editor (1968). Jean-Philippe Rameau (1683–1764): Complete Theoretical Writings. American Institute of Musicology, [Rome, Italy].

James, G., and James, R.C. (1976). Mathematics Dictionary, 4th ed. Van Nostrand Reinhold, New York.

Jorgensen, O. (1977). Tuning the Historical Temperaments by Ear. The Northern Michigan University Press, Marquette, Michigan.

Jorgenson, D.A. (1957). A History of Theories of the Minor Triad. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Jorgenson, D.A. (1963). A résumé of harmonic dualism. Music and Letters XLIV, No. 1, pp. 31–42.

Kastner, M.S., Editor (1958). De musica libri VII, by Francisco Salinas. Facsimile Edition. Bärenreiter-Verlag, Kassel, Germany.

Kelleher, J.E. (1993). Zarlino’s “Dimostrationi harmoniche” and Demonstrative Methodologies in the Sixteenth Century. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Lawlor, R. and D., Translators (1978). Mathematics Useful for Understanding Plato, by Theon of Smyrna. Wizards Bookshelf, San Diego, California, 1979.

Levin, F.R., Translator (1994). The Manual of Harmonics, of Nicomachus the Pythagorean. Phanes Press, Grand Rapids, Michigan.

Lindley, M. (1984). Lutes, Viols and Temperaments. Cambridge University Press, Cambridge, England.

Litchfield, M. (1988). Aristoxenus and empiricism: A reevaluation based on his theories. Journal of Music Theory 32, No. 1, pp. 51–73.

Mackenzie, D.C., Translator (1950). Harmonic Introduction, by Cleonides. In Source Readings in Music History, O. Strunk, Editor. W. W. Norton Company, Inc., New York.

Macran, H.S., Translator (1902). The Harmonics of Aristoxenus. Georg Olms Verlag, Hildesheim, Germany, 1990.

Marcuse, S. (1964). Musical Instruments: A Comprehensive Dictionary. W. W. Norton Company, Inc., New York, 1975.

Maxham, R.E., Translator (1976). The Contributions of Joseph Sauveur to Acoustics. Two Volumes. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Mersenne, M. (1636–37). Harmonie universelle contenant la théorie et la pratique de la musique. Three Volumes. Facsimile Edition. Éditions Du Centre National De La Recherche Scientifique, Paris, France, 1963.

Meyer, M.F. (1929). The Musician’s Arithmetic. Oliver Ditson Company, Boston, Massachusetts.

Miller, C.A., Translator (1993). Musica practica, by Bartolomeo Ramis de Pareia. Hänssler-Verlag, Neuhausen-Stuttgart, Germany.

Niven, I. (1961). Numbers: Rational and Irrational. Random House, New York.

Palisca, C.V. (1961). “Scientific Empiricism in Musical Thought.” In Seventeenth Century Science and the Arts, H.H. Rhys, Editor. Princeton University Press, Princeton, New Jersey.

Palisca, C.V. (1985). Humanism in Italian Renaissance Musical Thought. Yale University Press, New Haven, Connecticut.

Palisca, C.V., Translator (2003). Dialogue on Ancient and Modern Music, by Vincenzo Galilei. Yale University Press, New Haven, Connecticut.

Partch, H. (1949). Genesis of a Music, 2nd ed. Da Capo Press, New York, 1974.

Rameau, J.P. (1722). Traité de l’harmonie reduite à ses principes naturels. Facsimile Edition. Biblioteca Nacional de Madrid, Spain, 1984.

Rasch, R., Editor (1983). Musicalische Temperatur, by Andreas Werckmeister. The Diapason Press, Utrecht, Netherlands.

Rasch, R., Editor (1984). Collected Writings on Musical Acoustics, by Joseph Sauveur. The Diapason Press, Utrecht, Netherlands.

Rasch, R., Editor (1986). Le cycle harmonique (1691), Novus cyclus harmonicus (1724), by Christiaan Huygens. The Diapason Press, Utrecht, Netherlands.

Reichenbach, H. (1951). The Rise of Scientific Philosophy. The University of California Press, Berkeley and Los Angeles, California, 1958.

Roberts, F. (1692). A discourse concerning the musical notes of the trumpet, and the trumpet-marine, and of the defects of the same. Philosophical Transactions of the Royal Society of London XVII, pp. 559–563.

Rossing, T.D. (1989). The Science of Sound, 2nd ed. Addison-Wesley Publishing Co., Inc., Reading, Massachusetts, 1990.

Sadie, S., Editor (1980). The New Grove Dictionary of Music and Musicians. Macmillan Publishers Limited, London, England, 1995.

Shirlaw, M. (1917). The Theory of Harmony. Da Capo Press Reprint Edition. Da Capo Press, New York, 1969.

Solomon, J., Translator (2000). Ptolemy Harmonics. Brill, Leiden, Netherlands.

Soukhanov, A.H., Executive Editor (1992). The American Heritage Dictionary of the English Language, 3rd ed. Houghton Mifflin Company, Boston, Massachusetts.

Stephan, B. (1991). Geometry: Plane and Practical. Harcourt Brace Jovanovich, Publishers, San Diego, California.

Truesdell, C. (1960). The Rational Mechanics of Flexible or Elastic Bodies: 1638–1788. Orell Füssli, Zürich, Switzerland.

Wallis, J. (1677). Dr. Wallis’ letter to the publisher, concerning a new musical discovery. Philosophical Transactions of the Royal Society of London XII, pp. 839–842.

West, M.L. (1992). Ancient Greek Music. The Clarendon Press, Oxford, England, 1994.

White, W.B. (1917). Piano Tuning and Allied Arts, 5th ed. Tuners Supply Company, Boston, Massachusetts, 1972.

Wienpahl, R.W. (1959). Zarlino, the Senario, and tonality. Journal of the American Musicological Society XII, No. 1, pp. 27–41.

Williams, R.F., Translator (1972). Marin Mersenne: An Edited Translation of the Fourth Treatise of the “Harmonie universelle.” Three Volumes. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Williamson, C. (1938). The frequency ratios of the tempered scale. Journal of the Acoustical Society of America 10, pp. 135–136.

Winnington-Ingram, R.P. (1932). Aristoxenus and the intervals of Greek music. The Classical Quarterly XXVI, Nos. 3–4, pp. 195–208.

Winnington-Ingram, R.P. (1936). Mode in Ancient Greek Music. Cambridge University Press, London, England.

Winnington-Ingram, R.P. (1954). “Greek Music (Ancient).” In Grove’s Dictionary of Music and Musicians, Volume 3, 5th ed., E. Blom, Editor. St. Martin’s Press, Inc., New York, 1970.

Zarlino, R.M.G. (1571). Dimostrationi harmoniche. Facsimile Edition, The Gregg Press Incorporated, Ridgewood, New Jersey, 1966.

Zarlino, R.M.G. (1573). Istitutioni harmoniche. Facsimile Edition, The Gregg Press Limited, Farnborough, Hants., England, 1966.

Chapters 11

Chinese Music

Apel, W., Editor (1944). Harvard Dictionary of Music, 2nd ed. Harvard University Press, Cambridge, Massachusetts, 1972.

Gulik, R.H., Translator (1941). Poetical Essay on the Lute, by Hsi K’ang. In Gulik’s Hsi K’ang and His Poetical Essay on the Lute, Sophia University, Tokyo, Japan.

Kaufmann, W. (1967). Musical Notations of the Orient. Indiana University Press, Bloomington, Indiana.

Kaufmann, W. (1976). Musical References in the Chinese Classics. Detroit Monographs in Musicology, Detroit, Michigan.

Kuttner, F.A. (1965). A musicological interpretation of the twelve lüs in China’s traditional tone system. Journal of the Society for Ethnomusicology IX, No. 1, pp. 22–38.

Lieberman, F., Translator (1977). The Mei-an Ch’in-p’u, by Hsü Li-sun. In Lieberman’s The Chinese Long Zither Ch’in: A Study Based on the Mei-an Ch’in-p’u. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Lieberman, F., Translator (1983). The Mei-an Ch’in-p’u, by Hsü Li-sun. In Lieberman’s A Chinese Zither Tutor. University of Washington Press, Seattle, Washington.

Lui, T. (1968). A short guide to ch’in. Selected Reports I, No. 2, pp. 180–201. Publication of the Institute of Ethnomusicology of the University of California at Los Angeles.

Needham, J. (1962). Science and Civilization in China, Volume 4, Part I. Cambridge University Press, Cambridge, England.

Reinhard, K. (1956). Chinesische Musik, 2nd ed. Im Erich Röth-Verlag, Kassel, Germany.

Robinson, K. (1980). A Critical Study of Chu Tsai-yü’s Contribution to the Theory of Equal Temperament in Chinese Music. Franz Steiner Verlag GmbH, Wiesbaden, Germany.

Sachs, C. (1940). The History of Musical Instruments. W. W. Norton Company, Inc., New York.

Sadie, S., Editor (1980). The New Grove Dictionary of Music and Musicians. Macmillan Publishers Limited, London, England, 1995.

Wang, K. (1956). Chung-kuo yin yueh shih. Taipei, Formosa: Chung hua shu chu.

Wang, L., and Needham, J. (1955). Horner’s Method in Chinese Mathematics: Its origins in the root-extraction procedures of the Han Dynasty. T’oung Pao Archives XLIII, No. 5, pp. 345–401. Leiden, Netherlands.

Indonesian Music

Apel, W., Editor (1944). Harvard Dictionary of Music, 2nd ed. Harvard University Press, Cambridge, Massachusetts, 1972.

Blom, E., Editor (1954). Grove’s Dictionary of Music and Musicians, 5th ed. St. Martin’s Press, Inc., New York, 1970.

Hood, M. (1954). The Nuclear Theme as a Determinant of Patet in Javanese Music. Da Capo Press, Inc., New York, 1977.

Hood, M. (1966). Sléndro and pélog redefined. Selected Reports I, No. 1, pp. 28–48. Publication of the Institute of Ethnomusicology of the University of California at Los Angeles.

Lentz, D.A. (1965). The Gamelan Music of Java and Bali. University of Nebraska Press, Lincoln, Nebraska.

Martopangrawit, R.L. (1972). Catatan-Catatan Pengetahuan Karawitan [Notes on Knowledge of Gamelan Music], translated by M.F. Hatch. In Karawitan, Volume 1, J. Becker and A.H. Feinstein, Editors. Center for South and Southeast Asian Studies, The University of Michigan, 1984.

McDermott, V., and Sumarsam (1975). Central Javanese music: The patet of laras sléndro and the gendèr barung. Journal of the Society for Ethnomusicology XIX, No. 2, pp. 233–244.

McPhee, C. (1966). Music in Bali: A Study in Form and Instrumental Organization in Balinese Orchestral Music. Yale University Press, New Haven, Connecticut.

Ornstein, R.S. (1971). Gamelan Gong Kebjar: The Development of a Balinese Musical Tradition. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Poerbapangrawit, R.M.K. (1955). Gendhing Jawa [Javanese Gamelan Music], translated by J. Becker. In Karawitan, Volume 1, J. Becker and A.H. Feinstein, Editors. Center for South and Southeast Asian Studies, The University of Michigan, 1984.

Rai, I, W. (1996). Balinese Gamelan Semar Pagulingan Saih Pitu: The Modal System. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Randel, D.M., Editor (1986). The New Harvard Dictionary of Music, 6th ed. The Belknap Press of Harvard University Press, Cambridge, Massachusetts, 1993.

Sadie, S., Editor (1984). The New Grove Dictionary of Musical Instruments. Macmillan Press Limited, London, England.

Schaareman, D., Editor (1992). Balinese Music in Context: A Sixty-fifth Birthday Tribute to Hans Oesch. Amadeus Verlag, Winterthur, Switzerland.

Sindoesawarno, K. (1955). Ilmu Karawitan [Knowledge About Gamelan Music], translated by M.F. Hatch. In Karawitan, Volume 2, J. Becker and A.H. Feinstein, Editors. Center for South and Southeast Asian Studies, The University of Michigan, 1987.

Sumarsam (1975). Gendèr barung, its technique and function in the context of Javanese gamelan. Indonesia 20, pp. 161–172.

Sumarsam (1992). Gamelan: Cultural Interaction and Musical Development in Central Java. The University of Chicago Press, Chicago, Illinois, 1995.

Surjodiningrat, W., Sudarjana, P.J., and Susanto, A. (1972). Tone Measurements of Outstanding Javanese Gamelans in Jogjakarta and Surakarta, 2nd ed. Gadjah Mada University Press, Jogjakarta, Indonesia.

Tenzer, M. (2000). Gamelan Gong Kebyar: The Art of Twentieth-Century Balinese Music. The University of Chicago Press, Chicago, Illinois.

Toth, A.F. (1975). The Gamelan Luang of Tangkas, Bali. Selected Reports II, No. 2, pp. 65–79. Publication of the Institute of Ethnomusicology of the University of California at Los Angeles.

Toth, A.F. (1993). “Selera Yang Selaras: Pepatutan Gong Ditinjau Dari Segi Akustika dan Estetika.” Mudra: Jurnal Seni Budaya, pp. 92–117. Edisi Khusus.

Indian Music

Aiyar, M.S.R., Translator (1932). Svaramelakalanidhi, by Ramamatya. The Annamalai University, India.

Ayyar, C.S. (1939). The Grammar of South Indian (Karnatic) Music. Smt. Vidya Shankar, Madras, India, 1976.

Bhandarkar, R.S.P.R. (1912). Contribution to the study of ancient Hindu music. The Indian Antiquary XLI, pp. 157–164, pp. 185–195, pp. 254–265.

Bhandarkar, R.S.P.R. (1913–1914). Kudimiyamalai inscription on music. Epigraphia Indica XII, No. 28, pp. 226–237.

Bhatkhande, V.N. (1930). A Comparative Study of Some of the Leading Music Systems of the 15th, 16th, 17th, and 18th Centuries. Indian Musicological Society, Baroda, India, 1972.

Bhise, U.R., Translator (1986). Naradiya Siksa, by Narada. Bhandarkar Institute Press, Poona, India.

Coomaraswamy, A.K. (1930). The parts of a vina. Journal of the American Oriental Society 50, No. 3, pp. 244–253.

Gangoly, O.C. (1935). Ragas and Raginis. Nalanda Publications, Bombay, India, 1948.

Ghosh, M., Translator (Vol. 1, Ch. 1–27, 1950; Vol. 2, Ch. 28–36, 1961). The Natyasastra, by Bharata. Bibliotheca Indica, The Asiatic Society, Calcutta, India.

Iyer, T.L.V. (1940). The scheme of 72 melas in Carnatic Music. The Journal of the Music Academy XI, Parts I–IV, pp. 80–86, Madras, India.

Jairazbhoy, N.A. (1971). The Rags of North Indian Music. Wesleyan University Press, Middletown, Connecticut.

Jairazbhoy, N.A. (1975). An interpretation of the 22 srutis. Asian Music VI, Nos. 1–2, pp. 38–59.

Junius, M.M. (1974). The Sitar. Heinrichshofen’s Verlag, Wilhelmshaven, Germany.

Kaufmann, W. (1968). The Ragas of North India. Indiana University Press, Bloomington, Indiana.

Kaufmann, W. (1976). The Ragas of South India. Indiana University Press, Bloomington, Indiana.

Krishnaswamy, A. (1981). Melakarta and Janya Raga Chart. Sakthi Priya Publication, Madras, India.

Lath, M., Translator (1978). A Study of Dattilam: A Treatise on the Sacred Music of Ancient India. Impex India, New Delhi, India.

Marcotty, T. (1974). Djovari: Giving Life to the Sitar. This essay on how to make a parabolic sitar bridge is in The Sitar, by Manfred M. Junius. Heinrichshofen’s Verlag, Wilhelmshaven, Germany.

Nijenhuis, E.W., Translator (1970). Dattilam: A Compendium of Ancient Indian Music. E. J. Brill, Leiden, Netherlands.

Powers, H.S. (1958). The Background of the South Indian Raga-System. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Ramachandran, K.V. (1938). The melakarta — a critique. The Journal of the Music Academy IX, Parts I–IV, pp. 31–33, Madras, India.

Ramachandran, K.V. (1950). Carnatic ragas from a new angle — Sankarabharana. The Journal of the Music Academy XXI, Parts I–IV, pp. 88–99, Madras, India.

Ramachandran, K.V. (1950). Carnatic ragas and the textual tradition. The Journal of the Music Academy XXI, Parts I–IV, pp. 99–106, Madras, India.

Ramachandran, K.V. (1950). Apurva ragas of Tyagaraja’s songs. The Journal of the Music Academy XXI, Parts I–IV, pp. 107–109, Madras, India.

Ramachandran, N.S. (1938). The Ragas of Karnatic Music. University of Madras, Madras, India.

Rao, T.V.S. (1945 and 1946). The ragas of the Sangita Saramrita. The Journal of the Music Academy XVI, Parts I–IV, pp. 45–64, and XVII, Parts I–IV, pp. 104–134, Madras, India.

Rowell, L. (1981). Early Indian musical speculation and the theory of melody. Journal of Music Theory 25.2, pp. 217–244.

Roy, H.L. (1937). Problems of Hindustani Music. Bharati Bhavan, Calcutta, India.

Sachs, C. (1940). The History of Musical Instruments. W. W. Norton Company, Inc., New York.

Sadie, S., Editor (1980). The New Grove Dictionary of Music and Musicians. Macmillan Publishers Limited, London, England, 1995.

Sadie, S., Editor (1984). The New Grove Dictionary of Musical Instruments. Macmillan Press Limited, London, England.

Sambamoorthy, P. (1960). History of Indian Music. The Indian Music Publishing House, Madras, India.

Sambamoorthy, P. (Vol. 1, A–F, 1952; Vol. 2, G–K, 1959; Vol. 3, L–N, 1971). A Dictionary of South Indian Music and Musicians. The Indian Music Publishing House, Madras, India.

Sastri, S.S. (1931). Venkatamakhi and his twelve notes. The Journal of the Music Academy II, No. 1, pp. 22–23, Madras, India.

Sathyanarayana, R., Editor (1957). Kudimiyamalai Inscription on Music. Sri Varalakshmi Academies of Fine Arts, Parimala Press, Mysore, India.

Shankar, R. (1968). My Music, My Life. Simon and Schuster, New York, New York.

Sharma, P.L., Editor and Translator (Vol. 1, Ch. 1, 1992; Vol. 2, Ch. 2–6, 1994). Brhaddesi of Sri Matanga Muni. Indira Gandhi National Centre for the Arts in association with Motilal Banarsidass Publishers, Delhi, India.

Shringy, R.K., and Sharma, P.L., Translators (Vol. 1, Ch. 1, 1978; Vol. 2, Ch. 2–4, 1989). Sangitaratnakara, by Sarngadeva. Volume 1, Motilal Banarsidass, Delhi, India; Volume 2, Munshiram Manoharlal, New Delhi, India.

Sorrell, N., and Narayan, R. (1980). Indian Music in Performance. New York University Press, New York, New York. This book comes boxed with an excellent cassette tape recording.

Widdess, R. (1995). The Ragas of Early Indian Music. The Clarendon Press, Oxford, England.

Arabian, Persian, and Turkish Music

Al-Faruqi, L.I. (1981). An Annotated Glossary of Arabic Musical Terms. Greenwood Press, Westport, Connecticut.

Avenary, H., Translator (1974). The Hebrew version of Abu l-Salt’s treatise on music. Yuval III, pp. 7–82.

Barker, A., Translator (1989). Greek Musical Writings. Two Volumes. Cambridge University Press, Cambridge, England.

Cowl, C., Translator (1966). Al-Kindi’s essay on the composition of melodies. The Consort, No. 23, pp. 129–159.

Crookes, D.Z., Translator (1986). Syntagma musicum II: De organographia, Parts I and II, by Michael Praetorius. The Clarendon Press, Oxford, England. The first edition of this work was published in 1618.

Dieterici, F., Translator (1858–1890; 16 Volumes). Die Philosophie der Araber im IX. und X. Jahrhundert n. Chr. aus der Theologie des Aristoteles, den Abhandlungen Alfarabis und den Schriften der Lautern Brüder. The quoted passage on music is in Volume 6, entitled: Die Propaedeutik der Araber im zehnten Jahrhundert. E.S. Mittler und Sohn, Berlin, Germany, 1865.

El-Hefny, M., Translator (1931). Ibn Sina’s Musiklehre [Ibn Sina’s teaching on music]. Ph.D. dissertation printed by Otto Hellwig, Berlin, Germany.

Farhat, H. (1965). The Dastgah Concept in Persian Music. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Farhat, H. (1990). The Dastgah Concept in Persian Music. Cambridge University Press, Cambridge, England.

Farmer, H.G. (1925). Clues for the Arabian influence on European musical theory. The Journal of the Royal Asiatic Society, First Quarter, pp. 61–80.

Farmer, H.G. (1928). Ibn Khurdadhbih on musical instruments. The Journal of the Royal Asiatic Society, Third Quarter, pp. 509–518.

Farmer, H.G. (1929). A History of Arabian Music. Luzac Oriental, London, England, 1994.

Farmer, H.G. (1953–1954). The song captions in the Kitab al-aghani al-kabir. Transactions of the Glasgow University Oriental Society XV, pp. 1–10.

Farmer, H.G. (1954). “‘Ud.” In Grove’s Dictionary of Music and Musicians, Volume 8, 5th ed., E. Blom, Editor. St. Martin’s Press, Inc., New York, 1970.

Farmer, H.G. (1957). “The Music of Islam.” In New Oxford History of Music, Volume 1: Ancient and Oriental Music, E. Wellesz, Editor. Oxford University Press, London, England, 1960.

Farmer, H.G. (1965). The Sources of Arabian Music. E.J. Brill, Leiden, Netherlands.

Farmer, H.G., Translator (1965). Al-Farabi’s Arabic-Latin Writings on Music. Hinrichsen Edition Ltd., New York.

Farmer, H.G. (1965). The old Arabian melodic modes. Journal of the Royal Asiatic Society, Parts 3 4, pp. 99–102.

Farmer, H.G. (1978). Studies in Oriental Musical Instruments, First and Second Series. Longwood Press Ltd., Tortola, British Virgin Islands.

Hitti, P.K. (1937). History of the Arabs. Macmillan and Co. Ltd., London, England, 1956.

Lachmann, R. and El-Hefni, M., Translators (1931). Risala fi hubr ta’lif al-alhan [Über die Komposition der Melodien], by Al-Kindi. Fr. Kistner C.F.W. Siegel, Leipzig, Germany.

Lewis, B., Editor (1976). Islam and the Arab World. Alfred A. Knopf, New York.

Maas, M. and Snyder, J.M. (1989). Stringed Instruments of Ancient Greece. Yale University Press, New Haven, Connecticut.

Marcus, S.L. (1989). Arab Music Theory in the Modern Period. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Marcus, S.L. (1992). Modulation in Arab music: Documenting oral concepts, performance rules and strategies. Ethnomusicology 36, No. 2, pp. 171–195.

Muallem, D. (2010). The Maqam Book: A Doorway to Arab Scales and Modes. OR-TAV Music Publications, Kfar Sava, Israel.

Racy, A.J. (1977). Musical Change and Commercial Recording in Egypt, 1904–1932. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Racy, A.J. (1978). “Music.” In The Genius of Arab Civilization, 2nd ed., J.R. Hayes, Editor. MIT Press, Cambridge, Massachusetts, 1983.

Ribera, J. (1929). Music in Ancient Arabia and Spain. Translated and abridged from the Spanish by Eleanor Hague and Marion Leffingwell. Stanford University Press, Stanford University, Californa.

Ronzevalle, P.L., Translator (1913). Un Traité de Musique Arabe Moderne, by Mikha’ il Mashaqah. Mélanges de la Faculté Orientale VI, pp. 1–120. Université Saint-Joseph, Beirut, Lebanon.

Sachs, C. (1940). The History of Musical Instruments. W. W. Norton Company, Inc., New York.

Sadie, S., Editor (1984). The New Grove Dictionary of Musical Instruments. Macmillan Press Limited, London, England.

Shiloah, A. (1972). The simsimiyya: A stringed instrument of the Red Sea area. Asian Music IV, No. 1, pp. 15–26.

Shiloah, A., Translator (1978). The Epistle on Music of the Ikhwan Al-Safa. Tel-Aviv University, Tel-Aviv, Israel.

Shiloah, A. (1979). The Theory of Music in Arabic Writings (c. 900–1900). G. Henle Verlag, München, Germany.

Shiloah, A. (1981). The Arabic concept of mode. Journal of the American Musicological Society XXXIV, No. 1, pp. 19–42.

Signell, K.L. (1973). The Turkish ‘Makam’ System in Contemporary Theory and Practice. Ph.D. dissertation printed and distributed by University Microfilms, Inc., Ann Arbor, Michigan.

Signell, K.L. (1986). Makam: Modal Practice in Turkish Art Music. Da Capo Press, New York, New York.

Smith, E., Translator (1847). A Treatise on Arab Music, by Mikha’ il Mashaqah. Journal of the American Oriental Society I, No. 3, pp. 173–217. Boston, Massachusett.

Touma, H.H. (1996). The Music of the Arabs. Amadeus Press, Portland, Oregon.

Wright, O. (1966). Ibn al-Munajjim and the early Arabian modes. The Galpin Society Journal XIX, pp. 27–48.

Chapter 12

Writings on Cris Forster

• Editors. “Cris Forster.” In Für Augen und Ohren, Magazine of the Berlin Music Festival. January–February, 1980, pp. 16–17. Dr. Ulrich Eckhardt, Publisher. Berlin, Germany.

• Mahlke, S. “Barde mit zwei Saitenspielen.” Der Tagesspiegel. January 25, 1980. Berlin, Germany.

• Garr, D. “The Endless Scale.” Omni. March, 1981, p. 48. New York, New York.

• McDonald, R. “Cris Forster: Making Music.” San Diego Magazine. September, 1982, pp. 136–139, 198, 228. San Diego, California.

• Fleischer, D. “Sounds of Infinity.” Connoisseur. August, 1983, pp. 102, 105. New York, New York.

• Levine, J. “Expanded Musical Palette Is Inventor’s Note-able Goal.” The Tribune. September 6, 1983. San Diego, California.

• Brewster, T. “A Medley of New Instruments: A Wheel Like the Wind.” Life Magazine. November, 1983, p. 142. New York, New York.

• Editors. “Klingen wie der Wind.” Stern. January, 1984, pp. 146–148. Hamburg, Germany.

• Davies, H. (1984). “Microtonal Instruments,” pp. 656–657. In The New Grove Dictionary of Musical Instruments, Volume 2, S. Sadie, Editor. Macmillan Press Limited, London, England.

• Drye, S.L. (1984). The History and Development of the Musical Glasses, pp. 46–49. Master’s thesis, North Texas State University.

• Arnautoff, V. “Hill Musician Composes, Builds Own Instruments.” The Potrero View. November, 1985, p. 5. San Francisco, California.

• Editors. “This Californian and His Bearings Are Making Beautiful Music Together.” Precisionist: A Publication of the Torrington Company. Summer, 1987, pp. 14–15. Torrington, Connecticut.

• Bowen, C. “Making Music from Scratch.” Métier. Fall, 1987, p. 7. San Francisco, California.

• Snider, J. “Chrysalis: A Transformation in Music.” Magical Blend. April, 1989, pp. 98–102. San Francisco, California.

• Hopkin, B. “Review.” Experimental Musical Instruments V, No. 6. April, 1990, p. 4. Nicasio, California.

• Editors. “Forster, Cris.” PITCH for the International Microtonalist I, No. 4, Spring 1990, p. 142. Johnny Reinhard, Editor. New York, New York.

• Canright, D. “Performance: Concert in Celebration of the Chrysalis New Music Studio — Instruments and Music by Cris Forster.” 1/1, the Journal of the Just Intonation Network 11, No. 4. Spring, 2004, pp. 19–20. San Francisco, California.

• Kaliss, J. “Cris Forster’s ‘Just’ Musical Menagerie.” San Francisco Classical Voice. July 23, 2013. San Francisco, California. (See San Francisco Classical Voice Article.)

• Spaulding, B. “How Math Is Helping One Man Push the Boundaries of Acoustic Music.” PTC Product Lifecycle Report. January 4, 2016. Needham, Massachusetts. (See PTC Mathcad Article.)

• Forster, H. “Support the Evolution of Acoustic Music.” Kickstarter Project. November 29, 2016–January 15, 2017. Brooklyn, New York. (See Kickstarter Article.)

Videos on Cris Forster

• Gaikowski, R., Videographer and Editor (1988). Musical Wood, Steel, and Glass: A video featuring Cris Forster, composer, musician, inventor. A One Way Films/ Videos Production, San Francisco, California.

• Noyes, E., Videographer and Editor; Forster, H., Producer and Writer (2006). A Voyage in Music: A retrospective of Cris Forster’s work over the past thirty years. An Alligator Planet Production, San Francisco, California.

• Thomas, R., Videographer and Editor; Forster, H., Writer (2016). Support the Evolution of Acoustic Music. A Sponsored Films Production, San Francisco, California.

• Video performances of solo and ensemble compositions by Cris Forster at the Chrysalis New Music Studio. (See https://www.youtube.com/user/CrisForster/feed.)