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The Harmonic Lyre book cover

The Harmonic Lyre
Sacred Sound of Universal Unity

Conceived, Designed and Written
by Stephen Ian McIntosh

1997 Now & Zen, Inc.
P.O. Box 110
Boulder, Colorado


Like all Now & Zen products, the Harmonic Lyre is more than a decorative object. This booklet explains how it functions as spiritual technology by playing an active part in your personal growth.


The Harmonic Lyre is a chime set tuned to the Pythagorean Fifth--a sound universally recognized for its beauty. The Harmonic Lyre's ancient tuning produces a tone that is not only beautiful, but also subtly energizing and healing. The ancient Greek master Pythagoras discovered that the naturally occurring musical intervals could be used to entrain the vibrations of the human body for better health. The Harmonic Lyre can be used for meditation or prayer, or to begin and end meetings. The Lyre's tones can be sounded to celebrate a breakthrough or signal an epiphany. And the Lyre can also be used to tune your environment with the vibrations of harmony, and to create sacred space for ritual. This book explains the Harmonic Lyre's many uses as well as the physics of harmony and the ancient Greek tradition of musical healing and sacred sound.


I. Introduction--Pythagoras and the Ancient Significance of Harmony

II. Therapeutic Tones

III. The Musical Fifth

IV. Suggested Uses

V. About Now & Zen and the Spiritual Renaissance Art Movement

I. Introduction--Pythagoras and the Ancient Significance of Harmony

The Harmonic Lyre is intended to be an artistic part of your spiritual lifestyle. The Lyre is part of a larger art movement that emphasizes sacred geometry and the practice of living in the presence of Deity. This art movement focuses on the spiritual significance of beauty and receives inspiration from the masterpieces of history. To fully appreciate and use your Lyre it is helpful to understand the ancient traditions from which it comes.

The Harmonic Lyre takes its inspiration from the ancient Greek master Pythagoras who lived in the 6th century B.C. Pythagoras is one of history's most mystical geniuses. Although he is best known for his theorem in geometry, Pythagoras was primarily a religious teacher, and his understanding of the universe retains much vitality for our day. Pythagoras embodied the ancient Greeks' zest for understanding and their passion for the "physics of spirit."

Pythagoras was part of the ancient cult of Orpheus, the Greek God of music and science. And the tradition of Orpheus has continued to be a potent source of artistic inspiration down through the ages. Legend recounts how Orpheus was given a lyre by Apollo and was taught to play by the muses. By playing his lyre, Orpheus produced harmonies that joined all of nature together in peace and joy. In Greek mythology, Orpheus, through his music, acts as the mediator between humanity and the gods--fitting together that which is separate. And this is the definition of harmony: an agreement between disagreeing elements.

Inspired by this Orphic tradition of music and science, Pythagoras was led to conduct perhaps the world's first physics experiment. By playing strings of different lengths, Pythagoras discovered that sound vibrations naturally occur in a sequence of whole tones or notes that repeat in a pattern of seven. Like the seven naturally occurring colors of the rainbow, the octave of seven tones we recognize as do re mi fa so la ti* reveals the sevenfold structure that orders all vibrations in the universe. These tones can be identified by their specific vibrational frequencies which are measured in cycles per second.

*The word octave means eight. In this pattern of seven intervals, the eighth note repeats the first note, only at twice the vibrational frequency.

[Pythagoras Illustration Omitted]

In the course of his experiments with sound, Pythagoras discovered that certain tones sound very good together, while other combinations of tones are rather displeasing. One combination of tones that always sounds good together is known as the Fifth. The Fifth is a harmonic sound produced when two tones are in a specific relationship to each other. That is, when one tone is vibrating one-and-a-half times as fast as the other. For example, if you sound a middle "C" on the piano, and then sound the "G" five notes ahead on the scale, it will sound satisfying and harmonious.

The two chimes on your Harmonic Lyre are tuned to produce the musical Fifth. Since its discovery by Pythagoras, the Fifth has come to be universally recognized for its beauty; it forms the structural basis of musical compositions in almost every cultural tradition. And as this booklet explains, the Fifth is an archetypal expression of harmony that demonstrates the "fitting together" of microcosm and macrocosm in an inseparable whole. That is, the Fifth is a beautiful sound because it demonstrates how the universe works.

II. Therapeutic Tones

In addition to their Fifth relationship, the chimes on your Harmonic Lyre are tuned according to the ancient method developed by Pythagoras. The large chime corresponds to an "E" note and the small chime to a "B" note. However, these notes vibrate at different frequencies than their equivalent notes on a modern piano. As explained in the next section, modern tuning makes each note slightly flat or sharp so a whole range of instruments can play together. But modern tuning compromises the enchanting and therapeutic quality--the purity--of the naturally occurring tones discovered by Pythagoras. As a result of their natural tuning, the tones of your Harmonic Lyre correspond to the vibrations of nature--the motion of the planets and the frequencies of life. This is the secret of their therapeutic effect.

The ancients took harmony very seriously. Healing music was practiced in ancient Egypt, China, Africa, and especially in the Pythagorean mystery schools. Number patterns and harmony were central to Pythagoras' metaphysical philosophy. The Pythagoreans studied the harmonies of music as a key to understanding the harmony of the cosmos. The primary focus of the Pythagorean schools was the use of music and vibration in the healing arts. Their symbol was the pentagonal star--representing health and harmony.

[Star from cover Illustration Omitted]

The ancients recognized in the seven-note scale the macrocosmic design of creation. The ancient lyre (the original ancestor of the guitar and all other stringed instruments) had seven strings. The lyre's seven-tone scale was considered an imperfect representation of the pure vibrational pattern that orders the universe. The playing of the lyre was thought to entrain the vibrations of body and mind so as to bring them into tune with the pure vibrations emanating from the Creator.

The music of the lyre was used to heal through its affect on one's emotions. Pythagoras was said to have subdued the murderous wrath of a drunken man and to have calmed a raging bear by playing appropriate tunes on his lyre. The ancients well knew the connection between emotions and the immune system--they used musical harmony as a way of bypassing the intellect and directly affecting one's emotional well-being.

III. The Musical Fifth

As described in the Introduction, certain combinations of tones naturally sound good together. These beautiful sounding combinations or "consonances" are known as the musical root harmonies. The primary musical root harmonies are the Octave (2:1, where the first tone vibrates twice as fast as the second), the Fifth (3:2, where the first tone vibrates 1.5 times faster than the second) and the Fourth (4:3, where the first tone vibrates 1.333 times faster than the second).

[Piano Keys Illustration Omitted]

These "objectively" beautiful combinations also appear in the harmonic overtones which reverberate within every musical sound. The sounding of any single tone inevitably causes that tone's corresponding overtones to be sounded simultaneously. For example, the sounding of an E note in any octave is accompanied by the subtle sounds of that octave's B (the fifth note ahead) as well as the E in the next octave above (the eighth note ahead). Overtones demonstrate that the musical root harmonies are an essential part of the mathematical structure of sound vibration--the elemental physics of the universe.

To produce the Fifth, the Harmonic Lyre's chimes have been tuned so that the longer chime vibrates at approximately 1336 cycles per second (the vibrational frequency achieved through Pythagorean tuning starting with "C" at 264 cycles per second). The shorter chime vibrates at approximately 2005 cycles per second, or 1.5 times as fast as the longer chime.

Tuning to the Vibrations of Nature

As mentioned in the previous section, the actual frequencies of the tones used by the ancients to heal and uplift the soul were different from the tones we hear in the music of today. Up until the late Renaissance musical instruments were tuned with the aid of a single-stringed instrument known as a monochord--the instrument originally used by Pythagoras in his discovery of the musical tones and their corresponding intervals. Musicians tuned their instruments with the monochord by following the phenomena known as the Circle of Fifths.

The circle of Fifths begins by the division of the monchord's string at two-thirds its length. The two-thirds portion of the string is the Fifth of the whole undivided string. The circle of Fifths is produced through the continuous division of the string into smaller two-thirds segments. Every two-thirds division begins a new scale wherein all the notes of the first scale will be sounded in the next scale (only in a higher octave) except one. The proper tuning for the notes in every octave can be found in this manner. However, the scale of tones produced by the monochord forms a spiral structure as it ascends the octaves such that the higher octaves do not perfectly "match up" with the lower octaves. This slight difference between ascending octaves in natural tuning is known as the "comma of Pythagoras."

[Spiral of Fifths Illustration Omitted]

When orchestras developed in the seventeenth century, musicians wanted to tune their instruments precisely with each other. Composers required, for example, that a flute and a cello be able to play the same melody in different octaves yet sound in accord. This led to the development of the so called "equal tempered scale." In equal tempered tuning, each note is made slightly flat or sharp so as to distribute the comma of Pythagoras among all the octaves. And while the equal tempered method of tuning is convenient for the writing of multi-instrument musical compositions, it robs the tones of their ability to entrain one's vibrations to the fundamental frequencies of the universe.

The tiny differences in the tones resulting from equal tempered tuning makes the odd-numbered pattern of seven evenly divisible. However, it is through the precise sonic reproduction of the indivisible pattern of seven that musical vibrations achieve their maximum therapeutic effect. That is, the tones used by the ancients for musical healing were effective because they communicated the essence of the archetypal pattern of creation--they were tuned to the music of the spheres.


The Chord of Triumph

Of all the musical root harmonies, the Fifth occupies a special place because it demonstrates self-similarity--that is, it subtly reveals the macrocosm within the microcosm. Self-similarity is an organizing principle of the universe that is dramatically demonstrated in holographic film and fractal mathematics. Wherever self-similar unity across scale appears, it makes a superconscious appeal to your sense of beauty--it hints at your connection with the infinite.

For an idea of how the Fifth embodies self-similarity, recall the single-stringed monochord example. When you divide the string at the two-thirds point and pluck each segment, the two parts sound the same as each other, only an octave apart. The two parts of the string reproduce the octave pattern that is their origin. But this two-thirds division gives rise to a third element that provides a unification between the original tone and its octave double--the Fifth unifies the octave's duality by harmoniously fitting back together the original division. No matter what the length of the monochord's string, the string that is two-thirds its length will have a certain feel to it--the sound conveys the meaning of agreement. And it is the Fifth's self-similarity that produces the phenomenon of the Circle of Fifths. That is, the continuous 2/3 division of the Fifth provides the method of Pythagorean tuning because the Fifth contains, by virtue of its self-similar structure, the whole spectrum of vibrations. It can thus be used to produce all the tones.

[Illustration of String Lengths Omitted]

The self-similarity of the Fifth also plays an important role in musical composition through its use in the technique known as modulation. The Fifth has been used as a building block of musical composition from ancient Greek music, through Gregorian chants, to the music of Palestrina, Bach, Mozart, Wagner, the big bands, Frank Sinatra, Elvis Presley, the Beatles, and U2.

With the exception of the atonal music of modern "classical" composers, the history of Western music since 1400 has largely been an exploration of the special characteristics of the relationship of the Fifth. Music evolved from compositions within a single scale to compositions which included notes from multiple scales. Composers found that music written primarily within the key of a given scale could incorporate notes from other scales most harmoniously if those notes were from the scale beginning a fifth ahead of the initial scale.

The musical forms of the sonata and the symphony are based on this first-note-to-its-fifth relationship. And many great composers have explored the relationship of the key, its Fifth, and the "Fifth of the Fifth." Mozart and Haydn fully explored the Fifth of the Fifth, and Beethoven explored the Fifth of the Fifth of the Fifth and beyond. The Fifth has come to be known as "the chord of triumph" for the inspirational way it moves everyone who hears it. It is not the tones themselves that produce the beauty, it is their special relationship.


The Fifth and the Golden Mean

The German mystic Goethe understood the relationship between sound and form when he declared that "geometry is frozen music." Scientists are increasingly recognizing that the fundamental nature of the material world is understandable only through its underlying patterns of wave forms. The wave forms of the fundamental musical root harmonies have a remarkable correspondence to the fundamental geometric patterns that order the form of objects in space. For example, in his book The Power of Limits, architect Gyorgy Doczi demonstrates the similarity between the Fifth and the golden mean.

[Golden mean graphic Illustration Omitted]

The golden mean, which is known by many names including the "Divine Proportion," is a special relationship among the unequal parts of any given whole. Just as the Fifth naturally sounds good through its expression of self-similar unity among unequal parts, the golden mean relationship naturally looks good for the same reasons. The golden mean is discovered throughout nature--from galaxies to subatomic particles--as a fundamental technique of evolution. And the human body is replete with golden mean proportions, so it is only natural that it is a relationship that humans find most beautiful. Like the musical Fifth, the golden mean can be found as an organizing principle in art movements throughout history.

[Wave form comparison Illustration Omitted]

The golden mean and the musical Fifth each partake of the heart of beauty. Through their harmonious unification of contrasts they model the unifying direction of the flow of the universe. Both of these relationships demonstrate the dynamic division wherein the resulting parts retain a fundamental unity with the original whole. They thus express the essence of beauty by portraying the drama of the unification of the vastness of the cosmic extremes of creature and Creator. It is through this understanding that we come to recognize the Fifth as truly a sacred sound of universal unity.

IV. Suggested Uses

Meditation and Prayer

The Harmonic Lyre has been created to look and sound like a sacred instrument; it is ideal for signaling the beginning or ending of a period of stillness or reverence. Sound the Fifth to mark the beginning or end of your meditation or prayer time. It will fill your space with harmonic vibrations and subtly tune and cleanse your environment.

Because the Lyre's chimes naturally resonate for an extended period, you can focus on the diminishing tone as it gradually fades out. Try using the chime for a sixty-second "mini-meditation" when the stress of the day takes its toll on you. Also as an exercise, try sitting in a quite room and, with your eyes closed, strike the two chimes in quick succession and listen to them fade out. At the moment that you can no longer hear the tone, strike the chimes again and listen to them fade out until you can no longer hear them. As you become quiet within yourself and repeat the process of "riding out the tone to its conclusion" you will find that you can hear the tone's vibration for longer and longer periods. If you practice this exercise long enough, you may eventually hear the tone of the Fifth join with its octave in a subtle but profound crescendo. This is the effect of the discrete sound of the Fifth reintegrating with the spectrum of vibrations which is its source.

Bells and gongs play an essential role in the sacred practices of almost every spiritual tradition. In this time of spiritual renaissance we are now entering, the Harmonic Lyre provides a new form of sacred sound for the new forms of spiritual tradition we are creating in our everyday lives. Use your Lyre creatively as a part of the rituals that connect you to your source.

Therapy and Healing

The ancients used the sound of the lyre for healing in conjunction with a larger therapeutic system that involved colors, aromas, herbs, minerals, and theology. As in all forms of healing, intention is paramount. To use the sound of the Pythagorean Fifth as an aid in healing, have the person seeking therapy hold an intention for healing in their mind. As the Fifth is sounded, ask the person to concentrate on the sound and visualize it carrying their intention into the vibrations of their cells. The sound acts as an amplifier of the healing intention.

Forms of musical therapy are used in hospitals throughout the world. There are over 2,000 practicing musical therapists in the United Sates alone. To learn more about music therapy, see the reading list at the end of this section or contact the National Association For Music Therapy, 1133 Fifteenth Street N.W., Suite 1000, Washington, D.C. 20005.

Social Uses

The Harmonic Lyre can serve as a distinctive signal for the beginning or end of a meeting or an address. The Lyre is an artistic way to get a group's attention without producing an unpleasant noise or yelling. The Fifth can also be sounded as a form of punctuation during a talk or presentation--the ancient art of story telling was always accompanied by the playing of intervals on a lyre.

The Harmonic Lyre can be used as a specific signal that is understood by a group, such as a call to dinner or the end of work. And the "chord of triumph" can be used to celebrate an epiphany or breakthrough. Try striking the chimes at your next gathering when someone says something profound or the group comes to an insight.

The Lyre can also be used as a teaching tool to share the truths about the structure of sonic vibrations and the harmonies of the universe. The Lyre's design incorporates sacred geometry in every aspect.

Operation of your Harmonic Lyre

Assemble your Harmonic Lyre by attaching its base with the two screws provided. The small hole in the back of the base is designed as a holder for the Lyre's striker when it is not in use. Because the Harmonic Lyre is a musical instrument, you may have to adjust it slightly to get the best sound. To maximize the quality and sustain of the chimes' tones, make sure the strings come in contact with each chime bar so that there is an equal amount of space on each side of the tie strings. Experiment by striking and listening to the chimes as you slightly and gently scoot the chime bars up and down on the strings.

The Fifth can best be heard by firmly striking each chime once with equal force and in quick succession. It was the tradition of the ancients to play their scales downward as if descending from heaven. This tradition suggests that you should strike the smaller chime first. However, you can obviously strike the two chimes in any manner that pleases you. The Harmonic Lyre is designed for indoor use only.

Further Reading

Schneider, Michael S. A Beginner's guide to Constructing the Universe. New York, NY: HarperCollins, 1994.
Doczi, Gyorgy The power of Limits: Proportional Harmonies in Nature, Art and Architecture. Boston, MA: Shambala, 1981.
Goldman, Jonathan Healing Sounds: The Power of Harmonics. Rockport, MA: Element, 1992.
Beaulieu, John Music and Sound in the Healing Arts. Barrytown, NY: Station Hill Press, 1989.
Blackwood, Easley The Structure of Recognizable Diatonic Tunings. Princeton, NJ: Princeton University Press, 1985.
Bamford, Christopher, Ed. Homage to Pythagoras: Rediscovering Sacred Science. Hudson, NY: Lindisfarne Press, 1994.
McIntosh, Stephen Ian. Divine Proportion: Creating Beauty as a Spiritual Practice. Boulder, CO: Now & Zen, 1997.

[Lyre Illustration Omitted]

V. About Now & Zen and the Spiritual Renaissance Art Movement

Now & Zen, Inc. is a manufacturing and publishing company formed in 1995 to create products that can best be described as "cultural artifacts of the spiritual renaissance." Headquartered in Boulder, Colorado, Now & Zen's mission is to make beautiful tools which are subtle parts of a spiritual lifestyle and that remind us we live in the presence of Deity. Every Now & Zen product has been created to be beautiful, useful, affordable, and to embody and express principles of universe harmony in every aspect of the design. Ultimately, we are trying to express a new art movement that is about beauty, truth and goodness. This art movement seeks to capture the feeling of magical synchronicity, fresh possibilities, and spiritual focus that is alive in our time. For a catalog of current Now & Zen products, please call (800) 779-6383 or (303) 774-6344, visit our website at, drop us an e-mail at, or write us at P.O. Box 110, Boulder, Colorado 80306-0110. Thanks for participating in the spiritual renaissance!