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Sacred Geometry Overview

  • Sacred Geometry: Philosophy & Practice—Robert Lawlor. (London: Thames & Hudson, 1982; 1989)—A workbook with illustrations and step-by-step instructions for drawing (with compass and straight edge) the golden mean (phi) and the root harmonies of all life forms. With this book one quickly discovers that the only way to begin to grasp and digest the deep principles and philosophy of sacred geometry is by constructing these drawings. 202 pp. pb.

  • A Beginner's Guide to Constructing the Universe: the Mathematical Archetypes of Nature, Art and Science: A Voyage from One to Ten—Michael Schneider. (New York: Harper, 1994) 351 pp. pb.

  • How The World Is Made: The Story Of Creation According To Sacred Geometry—John Michell and Allan Brown—(Rochester, VT: Inner Traditions, 2009)—Galileo described the universe as a large book written in the language of mathematics, which can only be read by those with knowledge of its characters – triangles, circles, and other geometrical figures. The laws of geometry are not human inventions. They are found ready-made in nature and hold a truth that is the same in all times and all places and is older than the world itself. Michell explains how ancient societies that grasped the timeless principles of sacred geometry were able to create flourishing societies. He explains how Brown's colored illustrations reveal the secret code within these geometrical figures and how they express the spiritual meanings in the key numbers from one through twelve. He shows how to construct the basic polygons and reveals their symbolisms, meetings, matings, breeding of other shapes, and their functions within the universal order. He weaves together numbers and shapes into an all-inclusive cosmic image that Socrates said, "anyone can find and establish within themselves."

  • Infinite Measure: Learning to Design in Geometric Harmony with Art, Architecture, and Nature—Rachel Fletcher—(GTF Publishers, 2013)—Both a creative workbook and an authoritative reference guide for teachers, students, and practitioners of architecture, interior design, landscape architecture, painting, sculpture, the graphic arts, crafts, theater and stage design, and even musical instrument makers. Taking pages from books on Nature, art, and architecture, and decades of her own professional practice, Fletcher provides visual and environmental designers with step-by-step methods to create harmonious spaces and places using a compass and straight edge. Also includes studies of traditional proportional schemes; commentaries on geometric symbols and useful theorems; definitions; and etymologies of essential mathematical terms. A highlight of the book are Fletcher's original studies that analyze harmonious proportions in world-famous art, architecture, landscape design, and other compositions. These include the South Rose Window at Notre Dame Cathédral in Paris, Andrea Palladio's Villa Emo and Teatro Olimpico, a Stradivari violin, Thomas Jefferson's Poplar Forest residence, Beatrix Farrand's garden courtyard for the Oriental Institute at the University of Chicago, the illuminated Lindisfarne Gospels, a Louis Sullivan stencil for the Chicago Stock Exchange, and Eero Saarinen's North Christian Church in Richmond, Indiana. 400 pg., pb.

  • Elements of Dynamic Symmetry—Jay Hambridge (New York: Dover. 1926, 1967)—Seminal work on the root rectangles and golden ratio, based on analysis of growth patterns in Nature and the human body, and on proportions found in Greek art. 133 pp, pb.

  • The Divine Proportion: A Study in Mathematical Beauty — H. E. Huntley (New York: Dover, 1970)—An exploration of the relationships between geometry, the golden ratio, aesthetics and human consciousness. Based on an analysis of art that is generally recognized as aesthetically pleasing, Huntley investigates whether there is a correspondence between beauty and a universal order in the forms of life, and whether artists manifest that order consciously or unconsciously. 186 pp. pb.

  • Harmony by Design: The Golden Mean as a Design Tool—Rachel Fletcher (Beverly Russell Enterprises, 1995)—This catalog for the traveling exhibition “Harmony by Design: The Golden Mean’ is an indispensable teaching tool for all design disciplines: industrial design; graphic design; interior design; architecture; landscape architecture; and textile design. The information includes five methods to draw the golden mean with a compass and straight edge: how to draw a golden mean rectangle; a golden mean spiral; a golden mean system of proportion beginning with a double square; a pentagon; and how to divide a line by the golden section. 29 pg.

  • Cut and Assemble 3-D Geometrical Shapes—A.G. Smith (New York: Dover, 1986)—an easy way to create models of the Platonic Solids, the five regular polyhedra, and learn about paper-fold geometry construction. 16 plates, pb.

  • Order in Space: A Design Sourcebook—Keith Critchlow (London: Thames & Hudson, 1987)—workbook on spatial geometry, the enclosure and division of space, the most economical ways to pack, stack and arrange solids in space by one of the greatest practitioners and teachers of sacred architecture and geometry. When you understand divine proportions in two dimensions and are ready to move into solid geometry, this is the best book for studying the five Platonic solids and semi-regular polyhedra. Illustrations, which can be used to make 3-D paper-fold models. 120 pp., pb.

Geometry of Life & Cosmos

  • The Power of Limits: Proportional Harmonies in Nature, Art and Architecture—Gyorgy Doczi. (Berkeley: Shambhala, 1981.) Through a multitude of proportional diagrams based on his measurement of hundreds of natural patterns and forms, Doczi reveals how the limits of growth create universal proportions in humans, other organisms and dynamic forces and how traditional architecture and music have recreated the underlying harmonic order. 150 pp. pb.

  • Patterns in Nature—Peter S. Stevens (Little, Brown & Co, Atlantic Monthly Press, Boston, 1974)—wonder-full, easily understood descriptions of the universal patterns in the physical world, and why Nature uses branching, radiating, close packing, spiraling, etc. to support life efficiently without waste of resources. This understanding should be the basis of all architecture and design. 256 pp., pb.

  • Sensitive Chaos: The Creation of Flowing Forms in Water and Air—Theodor Schwenk. London: Rudolf Steiner Press, 1965, 1996. The revolutionary work that replaces the mechanistic view of nature with a vision of the unity between organic forms and natural forces. (It also inspired the creation of flow-form sculptures and natural flood control and sewage treatment.) Reveals how the flights of birds, the forms and movements of fish and water plants, and the shape of the human heart, intestines, eye, ear, bones and muscles arise from the archetypal forms of fluid movement, i.e., spirals and vortices. Shows that the natural laws that create these patterns also govern the shaping of all forms that live in movng air and water. The awe-inspiring illustrations show the marvelously complex forces and forms within a stream's meanders, whirlpools and eddies. Gives a new and deeper way to understand human nature and why air and water are essential for life. Argues that solving air and water pollution depends on our rediscovery of the spiritual nature of those living elements "whose essence is to flow." Discusses how an open-minded observation of water's forms can transform our way of thinking about all forms of life and enable us to restore air and water's life-giving powers, by allowing it to flow in its natural way. 232 pp. pb.

  • Cymatics, Volume 2—Hans Jenny (Basilius Press, 1974)— seminal work on the inherent geometry of form, revealed when liquids are set into consistent vibration. Illustrated with mandala-like photographs of vibrating paraffin, turpentine, etc., showing their distinct symmetry patterns. 185 pp, hb.

  • On Growth and Form—D'Arcy Thompson. Cambridge: Cambridge University Press,1917/New York: Dover, 1942, 1992. The seminal work on the mathematical, geometrical patterns in the way things grow and the shapes they take. All the familiar illustrations and analyses of the shape of bees' cells, raindrops, a splash of milk, soap bubbles, animal horns, tusks and bones, plant buds, leaves and seeds, seashells, and single cells come from this book. Complete edition 1116 pp.; abridged ed. 346 pp. pb.

  • The Geometry of Art and Life—Matila Ghyka. New York: Dover, 1946, 1977. Classic source for golden ratio within nature. 174 pp. pb.

  • The Curves of Life: Being an Account of Spiral Formations and their Application to Growth in Nature, to Science and to Art—Theodore Cook. New York: Dover, 1914, 1978. A classic work on how the golden proportion (phi) relates to spirals and helices in nature. Suggests that the golden mean spiral may be the essence of "life's first principle" – growth, and may embody the essence of beauty. Illustrates spirals discussed in On Growth and Form, plus climbing vines, ferns, pine cones, water, human heart, DNA, the atomic table, cosmic nebulae, classical architecture and art, etc. Includes how to make a logarithmic spiral with paper. 512 pp. pb.

  • Harmonium Mundi—Johannes Keppler—the principle that geometry provided the model for Creation and was implanted into Humanity together with God's own likeness.

  • Water: The Element of Life—Theodor & Wolfram Schwenk. (Hudson, NY: Anthroposophic Press, 1989)—scientific study of the life-giving forces of water and the use of "drop pictures" to determine whether a water source is healthy or lifeless. 268 pp., pb.

  • Chaos, Rhythm and Flow in Nature—William Forward and Andrew Wolpert, ed. (Edinburgh: Floris Books, 1993)—collection of essays on applications of sensitive chaos and complexity theory. Includes research findings about flow form design by John Wilkes. 93 pp., pb.

Geometry and Consciousness

  • Spirituality in Islamic Art—S. H. Nasr—the geometry and colors in Islamic art are not arbitrary; they evolved from direct experience of the solar system, the elements, etc. Through geometry we can move from multiplicity back to Unity. The mosque dome is a symbol of the heart turned back toward heaven.

  • Symbol is Archetype—Martin—geometry of earthly realm (4 fold symmetry), heavenly realm (16 fold), etc.

  • Sentics: The Touch of the Emotions—Manfred Clynes (Prism/Unity Press, revised 1989)—reveals how emotions are communicated in daily life, music and the arts through biology. Clyne's research has uncovered genetically programmed nervous system patterns for basic emotions like joy, anger, grief and love. He has developed, from these studies, easily learned emotional exercises and art of touch, called Sentic Cycles, which can remove emotional blocks, improve communication and lead to a profound sense of well-being. 234 pp, pb.

Sacred Architecture & Sacred Space Overview

  • Sacred Architecture—A.T. Mann (Rockport, Me: Element, 1993)— Start with this book if you want to re-discover the sacred elements in architecture! It reminds us that all architecture, not just religious buildings, was once created as sacred space. Mann masterfully brings together all the essential elements, principles and most important examples of a timeless tradition of creating human-made domains for reflection of the sacred. With the broadest, most culturally diverse survey of buildings from the Neolithic age to the present, he describes and profusely illustrates a language of the sacred, which has been employed to connect humanity to the cosmos. This symbolic language depicts cosmic principles that guide the site selection, orientation, floor plan and proportions of these edifices. Mann explains how the ancients used their sophisticated knowledge of sacred geometry, cosmological mandalas, astronomical cycles, earth energies and the transformation of consciousness to embody their culture's beliefs about heaven, earth and the purpose of life. These mystical aspects of sacred architecture, which are woefully missing in other texts, are here presented with left-brained clarity, right-brained beauty and soulful awe. 192 pp. pb.

  • Sacred Space (Parabola v.3, #1)—ed. D. M. Dooling (1978)—a collection of essays exploring the sacred as a force which connects us to another level, and sacred space as the container filled with this power. Includes Robert Lawlor's famous essay on the use of pure undecorated proportion to create spaces to contain the vibrations of prayer in "Cistercian Mystic Architecture." Other essays trace common cosmological themes found in Hindu and Jewish temples, Machu Picchu, the Nazca markings, Silbury Hill, Gavr'inis passage mound, and the skill of reading the spiritual qualities of place developed in Chinese geomancy. 136 p., pb.

  • Sacred Art in East and West—Titus Burckhardt (Perennial Books, 1967)—Christian, Hindu and Oriental temple traditions. Source to understand the Hindi Vastupurush mandala for laying out a house, temple or city.

  • The Temple: Meeting Place of Heaven and Earth—Lundquist. (London: Thames & Hudson)

  • The Sense of Unity: The Sufi Tradition in Persian Architecture—Nadar Ardalan & Laleh Bakhtiar (Chicago: Univ. of Chicago Press, 1973, 1979)—masterful exposition of one of the most spiritually based, living, intact traditions of architecture. Reveals how the fundamental principle of Sufism, unity in multiplicity, generates an architecture and urban form which strives to embody nothing more than multiple faces of the One. "Every aspect of reality (is seen as) a reflection of a transcendent source which is given symbolic expression through all of man's activities," especially works of art. The book's layout and presentation itself demonstrates this Persian integrity of thought and form. Every sentence is laden with golden meaning and a unity of message. Herein is a way to heal the arbitrary schism of spirit/matter, space/time, sacred/profane which modern man has invented. Covers concepts of space, time, orientation, shape, number, geometry, surface pat-terns, color harmonies, the elements of matter, and their realization in architectural form. 151 pp., pb.

  • Egyptian Miracle—R. A. Schwaller de Lubicz (Inner Tradition, 1985)—includes esoteric teachings from de Lubicz masterwork, Le Temple de L'Homme , about how to orient oneself in the "intelligence of the heart" in order to penetrate the mysteries of Egyptian and Pythagorian sacred science, which is embodied in the initiatory temple of Luxor. Discusses sacred measure, proportion, number, geometry, color, sound, and esoteric structure of solar system, in more comprehensible language than in the original text. 254 pp., pb.

  • The Hindu Temple—Stella Kramrisch (India: 1946, 1986)—the definitive work on the Hindu temple as an embodiment of Reintegration through its total integration of building form, architectural rituals and cosmological myths. Gives details on geomantic site analysis, the mandala regulating temple plan, the cultivation of sacred knowledge required of an architect, and the meaning of form, measure, proportion, symbolic images. 2 vol., 267 pp., hb.

  • The Hindu Temple: An Introduction to Its Meaning and Forms—George Michell. (Univ. of Chicago Press, 1977, 1988) —The temple as a link between the gods and humans, a representation of the Hindu worldview and a focus of culture. Encompasses tiny iconic shrines worn around the neck, sexually explicit sculpture, simple shrines under trees and near ponds, rock-cut temples, Angkor Vat, etc. and the process of construction and maintenance. One of the clearest explanations of the pantheon of Indian dieties. 192 pp. pb.

  • Psycho-cosmic Symbolism of the Buddhist Stupa—Lama Anagarika Govinda. (Berkeley: Dharma Press, 1976, 1989)—Explanation of the forms, proportion, symbolism, origin and purpose of the stupa as an embodiment of and channel for enlightened knowledge. Explains how the stupa evolved into a universal symbol that reveals the secrets of the harmony and perfection of the natural laws of the universe, and the key to awakening higher consciousness, e.g. in its relationship to the chakras and the Buddhist stages of meditation. 120 pp. pb.

  • The Mysteries of King's College Chapel—Nigel Pennick. (Aquarian Press, 1982)—Explores the Masonic and geomantic mysteries involved in the location and forms of the chapel built in Cambridge by the English King Henry VI. 128 pp., pb.

  • Sacred Geometry: Symbolism and Purpose in Religious Structures—Nigel Pennick (Harper/Turnstone, 1982)—eloquently explains why the principles underlying sacred geometry are universal and non-sectarian; how their application to religious buildings serves to express the oneness of the universe and creates spaces imbued with magic powers and profound psychological meaning. Pennick reveals the key to all structure–from molecules to humans to galaxies–as he traces the history of the sacred architecture of megalithic, Classical, Medieval, Renaissance, Baroque and Art Nouveau temples in Egyptian, Mesopotamian, Hebrew, Greek, Islamic and European cultures. 160 pp., pb.

  • Manasara Shilpa Shastra – sacred approach to architecture from India. Processes to orient temples so they embody the archetypal Absolutes of Creation. Vedic layout of plots in Ch. VII.

  • Harmonic Astrology—John Addey (Am Federation of Astrologers)—way to base house design on Japanese medicine principle of chi moving thru body in 24 hour cycle.

  • The Hall Of Light—Soothill—analysis of Temple of Heaven in Beijing: occurrence of number nine and magic squares.

  • House in Asia—assignment of functions within dwellings, comparable to ba gua. Look at Madagasi house, Japanese house examples.

Geometry in Art & Architecture

  • Homage to Pythagoras: Rediscovering Sacred Science: Form, Number, Geometry, Architecture, Light, Color, Music, Poetry—Keith Critchlow, Robert Lawlor, Christopher Bamford, et. al. (Lindisfarne Press, 1994)—Excellent introduction and glimpse into the depths of metaphysics, cosmology and philosophy available in the Platonic and Egyptian traditions of sacred geometry and architecture. Includes discussions of the nature of the sacred; key points of paradigm shift necessary for creating culture which is whole; the nature and meaning of proportion, number, consciousness, the Creation from Plato's Timaeus; concepts of resonance, perception, the geometrical symbolization of time and transformation, the cosmic number nineteen (relationship of solar and lunar time, etc.) from de Lubicz's Temple of Man; and ancient temple architecture as symbolic record of sacred science, a way to structure archetypal concepts of space and (cyclic, non-quantified) time. 302 pp. pb.

  • The Frozen Fountain: Being Essays on Architecture and the Art of Design in Space—Claude Bragdon. (New York: Ayers Co Pubs/New York: Knopf. 1932)—One of the best books ever written on the use of divine proportions and the philosophical principles of sacred geometry in the creation of space and ornamentation. Contains the clearest explanations and drawings of the properties and formation of the root harmonies/rectangles, log spirals, magic squares and magic lines. Every paragraph is laden with gems of understanding of a spiritual approach to art and architecture, so that each work: expresses the generic and abstract, typical and archetypal, is true to life (universal patterns), the materials used, and tells the story of creation. He speaks eloquently to the necessity for architects to practice their trade with ethical integrity, only creating buildings that embody their philosophical convictions and the first principles upon which architecture was originally founded, i.e. no compromise for profitability. 125 pp. hb.

  • The Temple in Man: Sacred Architecture and the Perfect Man—R. A. Schwaller de Lubicz (1949, 1977)—reveals that the Egyptian Temple at Luxor's plan, multiple axes, geometry and hieroglyphic symbolism represent a sophisticated map of man's physical and spiritual anatomy. Its function is to reawaken humanity's awareness of its spiritual essence and the inward realization of the temple in man, i.e., the ultimate evolution of consciousness. This book stimulated a complete reappraisal of Egyptian civilization. 132 pp., pb.

  • Temple of Man—R. A. Schwaller de Lubicz. (Inner Tradition)—de Lubicz's masterpiece, finally translated into English. (2 vols. in slipcase) 400 illus., hb.

  • The Dimensions of Paradise: The Proportions & Symbolic Numbers of Ancient Cosmology—John Michell (Harper & Row, 1988)—a wealth of information for creating buildings in tune with the cosmos. Revision and expansion of his classic, City of Revelation. Numbers in the sacred science of ancient civilizations were regarded as symbols of the universe and keys to its structure and form. Explains how a canon, or numerical code of universal proportions, was applied to maintain high principles in art, music, statecraft and all cultural institutions over thousands of years. Demonstrates how the same canon underlies sacred structures in many cultures and eras, e.g., Stonehenge, Glastonbury Abbey, Plato's ideal city and the vision of the New Jerusalem in the Revelation of John. Discusses units of measure related to the earth's dimensions, and gematria, the origin of alphabets and sacred names from the sounds found most effective in evoking the various aspects of the vital principle in nature. 216 pp.,hb.

  • Order in Space: A Design Sourcebook—Keith Critchlow (1987)—workbook on spatial geometry, the enclosure and division of space, the most economical ways to pack, stack and arrange solids in space by one of the greatest practitioners and teachers of sacred architecture and geometry. When you understand divine proportions in two dimensions and are ready to move into solid geometry, this is the best book for studying the five Platonic solids and semi-regular polyhedra. Illustrations, which can be used to make 3-D paper-fold models. 120 pp., pb.

  • Five Books of Architecture - Sebastiano Serlio. (Dover)—Renaissance classic on room volumes, architectural proportions.

  • Projective Ornament—Claude Bragdon (1915, 1992)—79 pp, pb.

Islamic Sacred Art

  • Cosmological Doctrines of Islam—H. S. Nasr—includes all the best references from Sufism. The unfolding of Creation through the cycle of magic squares from 3 by 3 to 9 by 9. All matter can be explained with the section of the square of 9, which includes 1, 3, 5, and 8.

  • Islamic Patterns: An Analytical and Cosmological Approach—Keith Critchlow (London: Thames & Hudson, 1976; 1989)—shows how the purpose of geometrical Islamic art is to reveal to the aware observer the inherent cosmological laws affecting all Creation, thereby leading one from the mundane manifest world to the underlying reality. Through construction and contemplation of Islamic patterns, one can drop Illusion and unite with the One. With 150 drawings, the correlations between Islamic geometry, Pythagorean mathematics, magic squares and numerical patterns created by the earth-centered view of the planets' orbits is demonstrated as a manifestation of the unity of archetypal cosmic patterns. Erases the Western misunderstanding of Islamic art as mere decoration, and develops a realization of its use as generator of space-filling patterns which keep all components of a building, from single tile to wall to entirety, in proportional harmony. 192 pp., pb.

  • Geometric Concepts in Islamic Art—Issam El-Said & Ayse Parman. (London: World of Islam Festival Publ Co., Ltd., 1976)—Clear progression of construction steps for Islamic mosaic patterns, showing the diverse possibilities of artistic expression for 2, 3 and 5-fold symmetries. Drawings demonstrate how to divide the circle and generate regulating lines, reveal a variety of shapes, and determine the repeat unit to expand the pattern through space. With unique graphics, he shows these steps as sections of the overall grid. Starts with basic constructions of polygons, and the root harmony proportional systems. Supportive chapters discuss calligraphy, poetry, music, rung designs, and the generating geometry for Egyptian, Greek and Islamic temples.

  • Islamic Designs: A Genius for Geometry—Daud Sutton (New York, Wooden Books, Walker & Co, 2007)— Unravels the mysteries behind some of the most exquisite geometric design patterns ever conceived by humanity. Discusses their origins, the Divine messages encoded within them, and how to draw them.

  • Spirituality in Islamic Art—S. H. Nasr—the geometry and colors in Islamic art are not arbitrary; they evolved from direct experience of the solar system, the elements, etc. Through geometry we can move from multiplicity back to Unity. The mosque dome is a symbol of the heart turned back toward heaven.

  • The Decorative Art of Arabia—Presse D’Avennes and Jules Bourgoin (London, Studio Editions, 1989)—exquisite large-format collection of color lithographs from the 1870’s, illustrating the diversity of geometrical Islamic art, from mosaic tiles, murals and paintings to carpets, fabrics and ceramics. Provides one of the most comprehensive sources of authentic Islamic patterns and color schemes as an invaluable source of inspiration for serious students and decorative artists.

  • Islamic Designs in Color—Nikolai Simakoff (New York, Dover, 1883, 1993)—diverse examples of geometrical designs and color schemes as a source for inspiration for artists creating mosaic patterns, murals, carpets and paintings based on Islamic patterns.

Gothic Cathedrals

  • Chartres and the Birth of the Cathedral—Titus Burckhardt. (Bloomington, IN: World Wisdom Books)—a cosmological, metaphysical approach to understanding the full significance of the masterpiece of the Medieval period.

  • Rose Windows—Painton Cowen (1979, 1990)—unveils the cosmological, theological themes and the meaning of the geometrical relationships incorporated in the rose windows of the cathedrals of Western Europe. Interprets their function as mandalas which serve as healing images of divine order and unity in a chaotic world. The 59 color photo-graphs are so exquisite that it appears that light is radiating out of the page. 144 pp., pb.

  • Chartres: The Masons Who Built A Legend—John James (Routledge & Kegan Paul, 1982) 200 pp., pb.—from the Australian architect who spent seven years measuring Chartres Cathedral in great detail, and revealing many of its geometrical secrets.

  • Gothic Cathedral—Otton von Simpson—best source on Gothic Cathedrals.

  • Chartres Maze: A Model of the Universe?—Keith Critchlow, Jane Carroll, Llewylyn Vaughan Lee (London, Research into Lost Knowledge Organization, 1975)—original study of the geometric relationships linking the pavement labyrinth with the rest of the cathedral. Suggests that the relationships of the length of the interior, height of the towers, position of western rose window, and circumference, position and hidden generating geometry of the labyrinth are related to a cosmological schema of reconciliation between solar and lunar forces and cycles. The progress of the traveler through this mandala re-enacts the process of incarnation from World Soul to physical body. [Available through www.kairos-foundation.com]

  • The Mysteries of Chartres Cathedral—Louis Charpentier (1972)—controversial book. Many scholars critique it as being inaccurate and out of date, based on later research that debunked some of the information and theories presented here. 192 pp, pb.

Cosmological Mandalas - Overview

  • Mandala—José and Miriam Argüelles (Berkeley, Shambhala, 1972)—the first and still the best cross-cultural study on all aspects of cosmological mandalas, covering the purpose, form, components, symbolism, ritual use and artistic process of mandalas.

  • Yantra: The Tantric Symbol of Cosmic Unity—Madhu Khanna, forward by Ajit Mookerjee (London, Thames & Hudson, 1979)—this pioneering study reveals the dynamics of the Tantric spiritual journey to the primordial center using yantras as a way to perceive the unity of self and cosmos. By explaining the grammar, syntax and vocabulary of the symbolic language of yantras; the complex geometries of their construction; and the correspondence between colors, geometrical forms, and cosmological and psychological concepts; and the associated mantras, rituals and meditation techniques, Khanna opens up the practice of yantra to westerners. Detailed break-down of the intricate parts and symbols of the Sri Yantra and others illuminates their metaphysical significance. Also introduces the subject of the three-dimensional expression of yantras as temple architecture.

  • The Mandala: Sacred Circle in Tibetan Buddhism—Martin Brauen (Boston, Shambhala, 1997)—the most complete and deepest exposition of Tibetan Buddhist mandalas available. Literally opens the world of the mandalas to the seeker, by showing in multi-dimensional ways how these wheels make a connection between the individual and the cosmos. Depicts mandalas as three-dimensional palaces, reveals the underlying generating sacred geometry, and shows the correlations to the human body and chakras. Discusses the numerous ritual aspects of mandalas, from their creation to meditative uses. Describes how to become the mandala through visualization, mantra and mudra, and to meditate on the Buddha at the center of the wheel.

  • Sacred Art in East and West: Its Principles and Methods—Titus Burckhardt (Bedfont, Middlesex, UK, Perennial Books, 1967)—describes the genesis and foundation of Christian, Hindu, Buddhist, Chinese and Islamic sacred art and temple traditions. Source to understand the Hindi Vastu-Purusha mandala for laying out a house, temple or city.

  • Mandala: The Architecture of Enlightenment—Denise Patry Leidy & Robert Thurman (New York, Asia Society Publishers and Tibet House, 1997)—compiled for a touring exhibit, with commentary on the mandalas displayed, which explains in brief what deities are depicted, what states of consciousness they represent, and the potential benefits from meditating on the mandala, as well as notes on the historical and artistic styles. Authoritative essays give great insight into the use of mandalas to guide the process of enlightenment, the Buddhist worldview of perfected states or “Pure Lands,” and a detailed explication of what is represented in each of the concentric rings of the Kalachakra/Wheel of Time mandala.

  • Manasara Shilpa Shastra – the manual for the sacred approach to architecture from India. Processes to orient and lay out temples so they embody the archetypal Absolutes of Creation. Chapter seven for the Vedic application of the mandala for village planning.

Native American Medicine Wheels

  • Navajo and Tibetan Sacred Wisdom: The Circle of the Spirit—Peter Gold (Rochester, VT, Inner Traditions, 1994)— comparison of Navajo and Tibetan cosmologies, particularly as illustrated in medicine wheels, sandpaintings, cosmological mandalas and landscape-based mythologies, which reveals a worldview in which their cosmology is embodied in the sacred geography of the region which they inhabit. Draws parallels between their similar creation myths, cosmology, geomancy, psychology, and healing and initiatory rituals. One of the best sources to understand the sacred geography of central Tibet, the Mt. Kailas region, and the Four Corners or Colorado Plateau. Suggests ways for westerners to revolutionize our relationship with the land, and thus ourselves.

  • Seven Arrows—Hyemeyohsts Storm (New York, Ballantine, 1972)—still the best introduction to the Plains Indian medicine wheel as a meditative, healing, cosmological device. Valuable resource for utilizing Native American knowledge about the significance of your orientation to the four directions, and the development of those archetypes within your psyche.

  • Sandpaintings of the Navajo Shooting Chant—Franc J. Newcomb and Gladys A. Reichard (New York, Dover, 1975)—an authoritative accurate account of one of the most important Navajo (Diné) healing ceremonies, which involves the creation and use of sandpaintings. Explains the myth of the Divine Twins on which the ritual is based, the symbols used, the rules of composition, and the artistic process.

Musical Harmonics

  • The Power of Limits, p. 8-13 and Lawlor's Sacred Geometry, Chapter VIII—recommended for brief concise introductions to musical proportions and the natural overtone sequence (octave, fifth, fourth, third, etc.) before reading the following books.—see first two sections.

  • Harmonograph: A Visual Guide to the Mathematics of Music—Anthony Ashton (New York: Walker & Co. Wooden Books, 2003) —introduction to the evolution of harmonic theory from Pythagoras onward and the beautiful patterns within music. Each page briefly discusses the essence of the principles of harmonics, overtones, resonance, tuning systems, Chladni patterns, and the monochord and harmonograph as instruments to explore musical harmonics 58 pp. hb.

  • The Manual of Harmonics of Nicomachus the Pythagorean—Flora Levin, transl. (Grand Rapids, MI: Phanes)—the best introduction to the study of the monochord and tuning theory in the Pythagorean tradition. The monochord demonstrates visually, audibly and mathematically the relationship between spatial and sound harmonics. An additional commentary explains the philosophical meaning of harmony. pb.

  • World is Sound: Nada Brahma: Music and the Landscape of Consciousness—Joachim-Ernst Berendt

  • Harmonies of Heaven And Earth: The Mystical Dimensions of Music—Joscelyn Godwin (1987)—fullest account of music's effects on matter and behavior, and theories of celestial harmony from Pythagoras, Kepler to Rudolf Steiner. Expands upon ancient ideas of harmonics as the underlying substance of the universe. Discusses ritual music-making as ways to touch our unconscious roots and participate in cosmic rhythm. Explains connections between the physiology of the human ear and the internal proportions of our musical systems. 208 pp., pb.

  • Cosmic Music: Musical Keys to the Interpretation of Reality—Joscelyn Godwin, ed. (1989)—collection of essays pointing to the mystical approach to music as the most accurate mirror of reality and an initiatory path into the mysteries of human and cosmos. Explores the ancient notion that the universe is created out of sound, harmonic vibrations or music and therefore is music. Connects the evolution of human consciousness and changing abilities to hear certain overtones with the development of tonal systems. Draws on Indian mythology and texts, Kepler's proof of the Pythagorean vision of the geometrical relationships between the planets' orbits, providing translated extracts from his "World Harmony" and "Cosmic Mystery." 255 pp., pb.

  • The Harmony of the Spheres: A Sourcebook of the Pythagorean Tradition in Music—Jocelyn Godwin, ed. (Inner Traditions) 495 pp., pb.

  • Through Music to the Self: How to Appreciate and Experience Music Anew—Peter Michael Hamel—the spiritual functions of music, healing effects, proportioning spaces to create specific resonance. 228 pp., pb.

  • Music and Sound in the Healing Arts—John Beaulieu—The author and music therapist discusses his years of experimentation and observations in using music as a means for healing. Includes both theory and practical guides for understanding how music affects us physically, emotionally, mentally and spiritually.

  • Mystery of the Seven Vowels—Godwin—The first book written in English that discusses how language vowels are harmonic phenomena based in the law of number and ultimately based in cosmological structure. A fascinating discussion of the names of God. Includes both theory and practical guides for discovering personal "tones", and the vowels' power to "uplift, center and heal."

  • A Little Book of Coincidences—John Martineau. (Presteigne, Wales: Wooden Books, 1995; New York: Walker Publishing, 2002)— reveals the exquisite geometrical patterns created by the orbits, sizes and distances of the planets. The illustrations are mind-boggling; they show just how ordered is our solar system. This new cosmological study, aided by computerized models, confirms that the ancient notion of the music of the spheres does indeed exist in the choreography of the planets dancing around the earth. Drawings depict the astounding relationships between various pairs of planets, in which the ratio between their diameters and/or orbits conform to the nesting geometries of polygrams (e.g., a five pointed star within a pentagon, that nests a smaller circle). 58 pp/ hb. Harmony of the Spheres—Ofmil C Haynes (Presteigne, Wales: Wooden Books, 1997)—reiteration of A Little Book of Coincidences, with some additional drawings and relationships, created when original book went out of print for a while.

  • Retrograde planet maps - Stem/Stern? Calendar for each year- Rudolf Steiner Institute, Goetheanum + Chin Shu - Chinese Classic 635 CE.

Pythagorean Mysteries

  • Divine Harmony: The Life and Teachings of Pythagoras—John Strohmeier & Peter Westerbrook. (Berkeley: Berkeley Hills Books. 1999)—the most concise telling of the complete story of Pythagoras, restoring his pivotal role in the convergence and redistribution of wisdom from most of the cultures of the ancient western world. Get to know him, not just as a mathematician and scientist, but as a radical social reformer, founder of a utopian community, mystic, and martyr. His teachings reveal the unity of science and spirituality, which existed at the roots of Western thought, before the Reductionist revolution.

  • The Pythagorean Sourcebook and Library—compiled and translated by Kenneth Sylvan Guthrie—a complete compendium of the written sources about Pythagoras and his teachings. (1987) 361 pp, pb.

  • The Theology of Arithmetic: On the Mystical, Mathematical and Cosmological Symbolism of the First Ten Numbers—Iamblichus, translated by Robin Waterfield, foreward by Keith Critchlow—introduction to Pythagoras’ primary teaching symbol, the tetraktys. (1988) 130 pp, pb.

  • A Study of Numbers: A Guide to the Constant Creation of the Universe—R..A.Schwaller de Lubicz (1986)—74 pp, pb.

  • Philolaus: The Croton—(1994)—fragments from the first person to write down the Pythagorean Mysteries, which is what Plato studied.

  • Plato’s Universe—Vlastos—correct translation of Timaeus’s choreography of the gods with Greek words given.

Most of these books are out of print, some rare, so if you want your own copy, search on the internet for rare and used books. The internet has made it much easier to find these oddities. My favorite web search sites are: http://www.alibris.com/ http://www.abebooks.com/ http://addall.com/ Amazon is a good place to start to sample price ranges, so you know if you are getting a reasonable deal elsewhere.

Notes on Chant in Christian sacred choral traditions

Plainchant – parallel melody lines (from 4C)

  • Gregorian (codifed 590)

  • Cistercian, e.g., for Feast of St Bernard

  • Ambrosian

  • Benedictine

  • Slavonic

  • Russian Orthodox

Organum – simple melody line, second group singing it slowly as drone, creating changing harmonics 10-13C Cathedral School of Notre Dame de Paris:

  • Perotin – 1183 – Invented 4-part chant by adding two additional voices to plainchant

  • Leonin - 1175

  • Phillipe le Chancelier

Polyphony – harmonies, non-parallel melodies (flourishes from 14C on) Motets have more harmonic invention than masses Pre-Bach early music notables:

  • Guillaume

  • De Machaut

  • Guillaume

  • Dufay

  • Johannes

  • Ockeghem

  • Josquin des Prez

  • Thomas Tallis

  • Palestrina

  • Orlando di Lasso

  • Tomas Luis Victoria

  • Gregorio

  • Allegri - Miserere

  • William Byrd

  • Giovanni

  • Gabrieli

  • Monteverdi

  • Charpentier

Performers of note:

  • Hilliard Ensemble

  • Ensemble Organum of Paris, Maurice Peres (organum & early masses)

  • Tallis Scholars

  • Early Music Consort of London

  • Chanticleer

Sources:

  • Musical Offering Store, 2430 Bancroft Way, Berkeley, CA

  • Musical Heritage Society – produces authentic recordings

Stabat Mater sacred choral music

Among the most emotionally moving sacred choral music I have found are those written for the Stabat Mater, a Medieval poem which imagines the feelings of Mary watching her son being crucified. It seems from the samples I’ve heard that whenever a composer writes for this text, they create their most exquisitely beautiful music, which touches the heart chakra like no other composition.

It would be an enlightening project to study this body of work from different time periods, to hear if there are common elements between them, if the composers are using similar intervals, modes, etc.

Here is a sampling, the first one opens my heart the most:

  • Marc Antoine Charpentier

  • Gorecki – Symphony of 3 Sorrowful Songs (#3) – energetically rather than literally a Stabat Mater

  • Aavo Paart

  • Pergolesi

  • Orlando de Lassus

  • Josquin des Prez

  • Palestrina

  • Dominico Scarlatti

  • Josef Hadyn

Lute – mystical music of the heart

  • Silvius Leopold Weiss – 18C

  • Kapsberger – 17C

  • Denis Gaultier “le Jeune” – 17C court of Louis 13th

  • Enaman Gaultier

  • Antoine Gallot – 17C court of Louis 13th

  • Robert de Bizet – 17C –favorite of Louis 14th

  • Robert Johnson – 17C – son of Elizabeth I’s lutenist

Best performers:

  • Hopkinson Smith (Brit)

  • Paul Odette (Am)

French 17C Music from the Heart

  • Ste. Colombe, and his student, Marin Marais

  • Recordings: For the movie “Tous les Matins du Monde” – Jordi Savall and the Concert des Nation