Selected Bibliography
Listed are the books, articles, and lectures consulted in the preparation of this book.
Ash Ashton, Anthony. Harmonograph: A Visual Guide to the Mathematics of Music. New York: Walker & Company, 2003.
Bar Barbera, C. André. “The Persistence of Pythagorean Mathematics in Ancient Musical Thought.” PhD diss., University of North Carolina at Chapel Hill, 1980.
Bark Barker, Andrew, ed. Greek Musical Writings: II: Harmonic and Acoustic Theory. Cambridge, UK: Cambridge University Press, 1989.
Benner Benner, Samuel. Benner’s Prophecies of Future Ups and Downs in Prices. 3rd ed. Cincinnati: Robert Clarke & Co., 1884.
Bru Brunés, Tons. The Secrets of Ancient Geometry-and Its Use. Translated by Charles M. Napier. Copenhagen: Rhodos, 1967.
Bur Burkert, Walter. Lore and Science in Ancient Pythagoreanism. Translated by E.L. Minar, Jr. Cambridge, MA: Harvard University Press, 1972.
Capt Capt, E. Raymond. A Study in Pyramidology, Muskogee, OK: Artisan Publishers, 1986.
Case Case, Paul Foster. The True and Invisible Rosicrucian Order. York Beach, ME: Samuel Weiser, 1989.
Chal Chalmers, John H., Jr. Divisions of the Tetrachord. Lebanon, NH: Frog Peak Music, 1993.
Cog Cogan, Robert. New Images of Musical Sound. Cambridge, MA: Harvard University Press, 1984.
Col Colman, Samuel. Nature’s Harmonic Unity: A Treatise on Its Relation to Proportional Form. Edited by C. Arthur Coan. New York: G.P. Putnam’s Sons, 1912.
Cond Condat, Jean-Bernard, ed. Golden Section and Music. New York: Peter Lang, 1988.
Cooke Cooke, Roger. The History of Mathematics. New York: John Wiley & Sons, 1997.
Cooper John M. Cooper, ed. Plato: Complete Works, by Plato. Indianapolis: Hackett Publishing Company, 1997.
Dew Dewey, Edward R. Cycles: The Mysterious Forces That Trigger Events. New York: Hawthorn Books, 1971.
Doc Doczi, Gyorgy. The Power of Limits: Proportional Harmonics in Nature, Art, and Architecture. Boston: Shambhala, 1994.
Dor Dorfman, Allen Arthur. “A Theory of Form and Proportion in Music.” PhD diss., University of California, Los Angeles, 1986.
Dunlap Dunlap, Richard A. The Golden Ratio and Fibonacci Numbers. Singapore: World Scientific, 1997.
El-Daly El-Daly, Okasha. Egyptology: The Missing Millennium: Ancient Egypt in Medieval Arabic Writings. London: UCL Press, 2005.
Far Farmer, H.G. The Sources of Arabian Music. Leiden, Netherlands: E.J. Brill, 1965.
Fau Fauvel, John, Raymond Flood, and Robin Wilson, eds. Music and Mathematics: From Pythagoras to Fractals. New York: Oxford University Press, 2003.
Fie Field, Michael, and Martin Golubitsky. Symmetry in Chaos: A Search for Pattern in Mathematics, Art and Nature. Oxford: Oxford University Press, 1992.
Frey Frey, Ronald Jan. “Attractiveness of the Golden Section in the Aesthetics of Sound Perception.” MA thesis, University of Toronto, 1994.
Gad97 Gadalla, Moustafa. Egyptian Cosmology: The Absolute Harmony. Erie, PA: Bastet Publishing, 1997.
Gad99 ———. Historical Deception: The Untold Story of Ancient Egypt, Greensboro, NC: Tehuti Research Foundation, 1999.
Garl95 Garland, Trudi Hammel, and Charity Vaughan Kahn. Math and Music: Harmonious Connections. Palo Alto, CA: Dale Seymour Publications, 1995.
Gaz Gazale, Midhat J. Gnomon: From Pharaohs to Fractals. Princeton, NJ: Princeton University Press, 1999.
Gies Gies, Joseph and Frances. Leonard of Pisa and the New Mathematics of the Middle Ages. New York: Crowell, 1969; Gaines ville, GA: New Classics Library, 1983.
Gillings Gillings, Richard J. Mathematics in the Time of the Pharaohs. Cambridge, MA: MIT Press, 1972; Mineola, NY: Dover Publications, 1982.
Godw Godwin, Joscelyn, ed. The Harmony of the Spheres: A Source-book of the Pythagorean Tradition in Music. Rochester, VT: Inner Traditions International, 1993.
Hall Hall, Manly P. The Secret Teachings of All Ages: An Encyclopedic Outline of Masonic, Hermetic, Qabbalistic, and Rosicrucian Symbolical Philosophy. New York: Penguin, 2003.
Hamb26 Hambidge, Jay. The Elements of Dynamic Symmetry. Originally published, n.p.; New York: Brentano’s, 1926; New Haven, CT: Yale University Press, 1948; New York, Dover Publications, 1967.
Hamb32 ———. Practical Applications of Dynamic Symmetry. New Haven, Yale University Press, 1932.
Hark Harkin, D. “On the Mathematical Works of François Edouard Anatole Lucas.” Enseignement mathématique 3 (1957): 276-288.
Hea Heath, Richard. Sacred Number and the Origins of Civilization. Rochester, VT: Inner Traditions, 2007.
Heath Heath, Sir Thomas L. Introduction and commentary to The Thirteen Books of Euclid’s Elements, by Euclid. 2nd ed. New York: Dover Publications, 1956.
Helm Helmholtz, Herrmann von. On the Sensations of Tone as a Physiological Basis for the Theory of Music. New York: Dover Publications, 1954.
Herz Herz-Fischler, Roger. A Mathematical History of the Golden Number. Originally published as A Mathematical History of Division in Extreme and Mean Ratio. Waterloo, Canada: Wilfrid
Laurier University Press, 1987. Reprint, Mineola, NY: Dover Publications, 1998.
Hof Hofstadter, Douglas. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Basic Books, 1979.
Kap Kaplan, Aryeh (Rabbi). Sefer Yetzirah: The Book of Creation: In Theory and Practice. 2nd rev. ed. Newburyport, MA: Red Wheel/Weiser, 1997.
Kays Kayser, Hans. Textbook of Harmonics, Vols. I and II. (Published originally as Lehrbuch Der Harmonik. Zurich: Occident- Verlag, 1950.) Edited by Joscelyn Godwin. Translated from the German by Ariel Godwin. Idyllwild, CA: Sacred Science Institute, 2006.
Kep Kepes, Gyorgy, ed. Module, Proportion, Symmetry, Rhythm. New York: George Braziller, 1966.
Klei Klein, Jacob. Greek Mathematical Thought and the Origin of Algebra. Cambridge, MA: MIT Press, 1968.
Kli Kline, Morris. Mathematical Thought from Ancient to Modern Times. 3 vols. New York: Oxford University Press, 1972.
Kra Kramer, Jonathan. “The Fibonacci Series in Twentieth- Century Music.” Journal of Music Theory 17, no. 1 (spring 1973): 110-148.
Lach Lachmann, R., and El-Hefni, M., translators. Risala fi hubr ta’lif al-alhan (Über die Komposition der Melodien), by al-Kindi. Leipzig, Germany: Fr. Kistner & C.F.W. Siegel, 1931.
Lar Larson, Paul. “The Golden Section in the Earliest Notated Western Music.” Fibonacci Quarterly 16, no. 6 (December 1978): 513-515.
Law Lawlor, Robert, Sacred Geometry: Philosophy and Practice. London: Thames & Hudson, 1982.
Leh Lehner, Mark. The Complete Pyramids: Solving the Ancient Mysteries. London: Thames & Hudson, 1997.
Lev Levin, Flora. Translation and a commentary for The Manual of Harmonics of Nicomachus the Pythagorean, by Nicomachus of Gerasa. Grand Rapids, MI: Phanes Press, 1994.
Lew Lewis, B., ed. Islam and the Arab World. New York: Alfred A. Knopf, 1976.
Liv Livio, Mario. The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number. New York: Broadway Books, 2002.
MAC Macran, H.S., ed. and trans. The Harmonics of Aristoxenus. Hildesheim; New York: Georg Olms Verlag, 1974.
Mad99 Madden, Charles. Fractals in Music: Introductory Mathematics for Musical Analysis. Salt Lake City, UT: High Art Press, 1999.
Mad05 ———. Fib and Phi in Music: The Golden Proportion in Musical Form. Salt Lake City, UT: High Art Press, 2005.
Mich Michell, John F. The Dimensions of Paradise: The Proportions and Symbolic Numbers of Ancient Cosmology. Kempton, IL: Adventures Unlimited Press, 2001.
New Newman, Rochelle, and Martha Boles. Universal Patterns: The Golden Relationship: Art, Math & Nature, Rev. ed. Bradford, MA: Pythagorean Press, 1992.
Neug Neugebauer, O. The Exact Sciences in Antiquity. Originally published, n.p.; Providence, RI: Brown University Press, 1957. Reprint, New York: Dover Publications, 1969.
Parm Parmanand, Singh. “Acharya Hemachandra and the (So Called) Fibona
cci Numbers.” Mathematical Education 20, no. 1 (1986): 28-30.
Pin Pingree, David. “The Mesopotamian Origin of Early Indian Mathematical Astronomy,” Journal for the History of Astronomy 4, no. 1 (1973): 1-12.
Rhind Rhind Mathematical Papyrus. British Museum. Also see vol. 1. Oberlin, OH: Mathematical Association of America.
Robin Robinson, Professor Daniel N. “The Great Ideas of Philosophy” lectures. Audio CD or DVD. Lectures from this Oxford University professor can be obtained from The Teaching Company, www.teach12.com.
Schoe Schoenberg, Arnold. Theory of Harmony. Translated by Roy E. Carter. Berkeley: University of California Press, 1983.
Stan Stanley, Thomas. Pythagoras: His Life and Teachings. (This is a photographic facsimile of the ninth section of the 1687 edition of Stanley’s History of Philosophy.) Los Angeles, CA: The Philosophical Research Society, 1970.
Stroh Strohmeier, John, and Peter Westbrook. Divine Harmony: The Life and Teachings of Pythagoras. Berkeley, CA: Berkeley Hills Books, 1999.
Taylor Taylor, Thomas. The Theoretic Arithmetic of the Pythagoreans. Originally printed in London, 1816. Reprint. CA: Phoenix Press, 1934; York Beach, ME: Samuel Weiser, 1972.
Tom Tompkins, Peter. Secrets of the Great Pyramid. New York: Harper & Row, 1971.
Vaj Vajda, Steven. Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications. Chichester, England: Ellis Horwood, 1989.
Vor Vorob’ev, N.N. Fibonacci Numbers. (Published originally in Russian as Chisla Fibonachchi. Moscow-Leningrad: Gostekhteoretizdat, 1951.) Translated by Halina Moss. New York: Blaisdell Publishing, 1961.
Index
angles, Fibonacci
Australian SP/ASX 200 Index 3-day chart
EUR/USD 2-month charts
angles, Gann
Archytas
Aristotle
Aristoxenus
arithmetic proportion
astrology/astonomy
difference between the two
Earth
Jupiter
Mars
Mercury
Moon
Pluto
Saturn
Sun
Venus
Australian All Ordinaries Index
monthly chart
Australian SP/ASX 200 Index
3-day charts
weekly charts
Barron’s
Benner, Samuel
Benner’s Prophecies of Future Ups and Downs in Prices (Benner)
Breakthroughs in Technical Analysis (Brown)
Caterpillar Inc. (CAT) weekly charts
CBOT wheat futures 1-week chart
Centex Corporation (CTX)
2-week chart
3-day charts
6-month chart
weekly charts
channels
Ch’ien, Ssu-ma (Sima Qian)
Colosseum, Roman
COMEX Gold 2-month chart
Composite Index
Australian SP/ASX 200 Index 3-day chart
Australian SP/ASX 200 Index weekly chart
COMEX Gold 2-month chart
Japanese Government Bond (10-year) 2-month chart
confluence zones
Australian SP/ASX 200 Index 3-day charts
Australian SP/ASX 200 Index weekly charts
CBOT wheat futures 1-week chart
Centex 3-day charts
Centex 3-week chart
Centex 6-month chart
COMEX Gold 2-month chart
defined
EUR/USD 2-month charts
Ford Motor Company (F) weekly chart
frog skeleton
harmonic analysis and
Hong Kong WEB 2-week chart
Japanese Government Bond (10-year) 2-month charts
market character between
oscillators, when to use
S&P 500 charts
U.S. 30-year Treasury bond 5-week chart
continuous proportions
defined
contraction, market. See expansion and contraction, market
crash of 1929
cycle analysis. See time cycles
Daly, Okasha el-
diatonic scale
DiNapoli, Joe
discontinuous proportions, defined
Divine Proportion, The (Divina Proportione) (Pacioli)
Dow Jones Industrial Average
Dow Jones 1897 Rails and Industrials chart
DuPuy, William Atherton
Earth, astrology/astronomy and
Egyptology: The Missing Millennium (Daly)
Elements of Harmony, The (Aristoxenus)
Elliott Wave Principle
Australian SP/ASX 200 Index weekly chart
Caterpillar weekly chart
Centex 3-day chart
COMEX Gold 2-month chart
EUR/USD 2-month chart
fifth wave
first wave
fourth wave
Japanese Government Bond (10-year) 2-month charts
orthodox top
second wave
third wave
zigzag correction
errors, common trading
Euclid
Eurodollar-month
EUR/USD 2-month charts
expansion and contraction, market
Caterpillar weekly charts
Centex 3-day charts
Centex weekly charts
introduction to
symmetry and
expansion price targets
CBOT wheat futures 1-week chart
Centex 3-day chart
Centex 6-month chart
COMEX Gold 2-month chart
EUR/USD 2-month charts
introduction to
Japanese Government Bond (10-year) 2-month charts
U.S. 30-year Treasury bond 5-week chart
Farabi, al-
Fibonacci, Gulielmo
Fibonacci, Leonardo
Liber Abaci (Book of the Abacus)
Fibonacci number series, defined
Ford Motor Company (F) weekly chart
Freemasons
frog skeleton
galaxy, spiral
Gann, John
Gann, W. D.
Natural Laws of Vibration
Gann analysis
angles
Gann Wheel Square of Nine
gaps
CBOT wheat futures 1-week chart
Centex 3-day charts
importance of
geometric proportion
gold bullion
COMEX Gold 2-month chart
Golden Ratio
defined
golden rectangle (Tablet of Shamash)
golden spiral
introduction to
Great Depression
harmonic analysis
Centex 2-week chart
confluence zones and
intervals
proportion
rhythmic wave diagram
S&P 500 charts
series
Ulam spiral
Hong Kong WEB 2-week chart
intervals, harmonic
Japanese Government Bonds (JGBs)
2-month charts of 10-year bond
Jupiter, astrology/astronomy and
Khufu, Great Pyramid of
Kindi, al-
Leonardo da Vinci
Liber Abaci (Book of the Abacus) (Fibonacci)
Lucas, Édouard Anatole
Manual of Harmonics (Nichomachus)
Market Technicians Association
Mars, astrology/astronomy and
mean
arithmetic
defined
geometric
harmonic
Menkaure, Pyramid of
Mercury, astrology/astronomy and
Metaphysica (Aristotle)
momentum oscillators. See oscillators
Money (DuPuy)
Moon, astrology/astronomy and
Nasdaq
<
br /> 2000-2001 crash
Nasdaq Composite Index chart
Natural Laws of Vibration (Gann)
nautilus shell spiral
geometry in
importance of
introduction to
Nichomachus
NYSE
oil, crude
oscillators
See also Composite Index; Relative Strength Index
Australian SP/ASX 200 Index 3-day chart
Australian SP/ASX 200 Index weekly chart
Centex 3-day chart
confluence zones and when to use
limitations of
Pacioli, Luca
parabolic rallies
pentagon
pentagram
Phaedo (Plato)
Phi (1.618)
historical development of
importance of
introduction to
proportional divider, using a
phi (0.618)
historical development of
importance of
introduction to
proportional divider, using a
Philolaus
Plato
Phaedo
Republic
Timaeus
Pluto, astrology/astronomy and
Porphyry
Prechter, Robert
price projections, support, and resistance. See support, resistance, and price projections
proportion
arithmetic
defined
geometric
harmonic
proportional analysis
proportional divider, using a
Ptolemy
Pyramid
of Khufu (Great Pyramid)
of Menkaure
pyramid triangle
Pythagorean(s)
diatonic scale
harmonic series
Pythagoras
quadrivium
Rassam, Hormuzd
ratio, defined
rectangle, golden (Tablet Shamash)
Relative Strength Index (RSI)
Australian SP/ASX 200 Index 3-day chart
Australian SP/ASX 200 Index weekly chart
Republic (Plato)
resistance
See also confluence zones
Australian SP/ASX 200 Index 3-day chart
Fibonacci Analysis Page 14