Overtones and the Music of the Spheres: Legacy of Pythagoras

Introduction

Pythagoras was wrong. The planets in our solar system do not revolve around Earth, nor are they carried in their orbits by crystal spheres. However, his theory of “music of the spheres” holds truths that continue to be uncovered with modern scientific advances. This paper explores the inextricable links between music, science, and faith that are contained within the music of the spheres. Whether or not we believe in the spiritual aspects of the theory is irrelevant; the practical application of these principles affects us every day.

The Music of the Spheres from Antiquity to the Age of Discovery

“The music of the spheres is an ancient concept that the universe is arranged in a logical and orderly manner, consistent with the principles of musical harmony.”[1] The theory involves the planets in our solar system rapidly revolving around Earth, each contained in their own crystal sphere. “Such rapid motion was believed to produce sound, as is commonly experienced when large objects move quickly.”[2] One can envision the scraping of planetary bodies against crystal cages creating all manner of noises. For Greek theorist Pythagoras, who lived from approximately 580 to 500 B.C.E., those sounds formed the structure of music. Mercury, Venus, Mars, Jupiter, Saturn, the sun, and the moon were all visible to ancient scholars who lived before the invention of the telescope. “These seven bodies…were sometimes matched with the seven tones in a musical scale or mode. The eighth sphere was the ‘fixed stars’…The stars thus completed the octave in the planet scale.”[3]

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“Although some writers in antiquity seemed to treat the celestial music as actual sounds, most took ‘harmony’ to refer to a logical congruence of elements in the heavens.”[4] The Medieval philosopher Boethius expounded on the idea of music of the spheres in his treatise De Institutione musica, written in the early sixth century. He describes three categories of music, including musica mundana, musica humana, and musica instrumentalis. Musica mundana describes “the numerical relations controlling the movement of the planets, the changing of the seasons, and the combination of elements.”[5] Musica humana “harmonizes and unifies the body and soul and their parts.”[6] Musica instrumentalis, the only category audible to the human ear, includes instrumental and vocal music.

Johannes Kepler, a sixteenth-century German astronomer and mathematician, believed Pythagorean ‘harmony’ to be “in thought, not in sound.”[7] He is known for his three laws of planetary motion and for championing Pythagoras’ theory of ‘celestial music.’[8] His view of ‘heavenly harmony’ posited that “each planet ‘sings’ not a single tone but a range of notes depending on its speed at a particular point in its orbit [around the sun].”[9] The ‘pitch’ of each planet was based on its angular velocity from the sun; as quoted in Rogers, “Venus, having the most nearly circular orbit, remains almost on unison (1:1). Mercury, closest to the sun and with the most eccentric (least circular) orbit, has the widest range (a ratio of 12:5) and the highest ‘voice.’”[10] “Pythagorean ideas about cosmic harmony continued to be elaborated by Neoplatonists from Carolingian times until the end of the Renaissance. These ideas strongly influenced astronomers and astrologers, physicians, architects, humanist scholars and poets.”[11] Isaac Newton, quoted in Rogers, “describes the similarity of the gravitational force to the effect of tension on the strings of a musical instrument: The Sun by his own force acts upon the planets in that harmonic ratio of distances by which the force of tension acts upon strings of different lengths, that is reciprocally in the duplicate ratio of the distances.”[12] He was channeling Pythagoras with this statement, as “Pythagoras showed that a string two feet long would vibrate with a certain tone, and that a string half as long would yield a tone an octave higher.”[13] Thus, the ratio of an octave is 2:1, a perfect fourth is 4:3, a perfect fifth is 3:2, and so on.

The Music of the Spheres in Science Today

With the advent of modern technology, new discoveries are made daily in the fields of science, math, and music. While we know that our planets do not ‘sing,’ we do know that they emit sound far beyond our own hearing abilities. “The new science of helioseismology reveals that the sun itself vibrates with acoustic pressure waves.”[14] Our own planet reverberates with sound as well: “The Schumann Resonances denote a phenomenon that occurs in the Earth’s ionospheric cavity as a result of continual lightning discharges striking the Earth. This ongoing agitation causes the Earth to ring as if it were a giant bell, resulting in a set of quasi-standing waves that measure between approximately 8 Hz and 45 Hz.”[15] Composer David First writes of his fascinating project involving the Schumann Resonances in The Leonardo Music Journal. He was able to network with Davis Sentman of the geophysics department at the University of Alaska, Fairbanks. Sentman records the Schumann Resonances in the area for data to be used in determining global weather patterns; he was able to write a program to send the live data feed to First in Manhattan. Using audio synthesis software, First was able to “transform the real-time data feed into various species of sonic material”[16] with which to compose new music. He writes of the project, named Operation:Kracpot:

My primary method for audification of the Schumann Resonances was to multiply data that was coming in…by a factor of 16, thereby placing the relatively low set of original frequencies into a reasonable musical range- a four-octave transposition. This result was, indeed, a quite beautiful-sounding set of harmonic relationships unlike anything I had previously heard- a transparent, bell-like chordal hum.[17]

First continues his article by explaining that the first bell-like tones that he heard were not represented accurately; he had to account for the “harmonic resonances of a spherical cavity resonator.”[18] In other words, the Earth itself had to be contained in the equation “instead of doing the traditional overtone math.”[19] It was as if someone had left the overtone series out in the rain, and it had warped…There was an emerging pattern revealing all the linear overtone series relationships embedded within the spherical one. They simply were not following a simple line- they were following an ever-widening curve…It begins ‘out of tune’ and rises to a theoretical perfect resolution- albeit one significantly above our range of hearing. But what a beautiful construction to wax poetic about- our imperfect earthly existence reaching perfection somewhere in the heavens.[20] Pythagoras would have been beyond proud.

Overtones and the Music of the Spheres

Overtones are an important part of resonance and must be included in discussion involving music of the spheres. “Every musical note is a composite sound consisting of a fundamental tone, which is usually the pitch we perceive, combined with a number of additional pure tones above it called harmonics or overtones.”[21]

Pythagoras discovered the overtone series, which forms the building blocks of consonant intervals and influences Western music to the present era. The order of the intervals in the overtone series starts with an octave, then a perfect fifth, a perfect fourth, a major third, and the intervals continue to shrink smaller and smaller until all twelve tones of the scale have been heard. This is the reason a perfect fifth and a perfect fourth are considered the most consonant intervals. [22]

The music of the spheres has long inspired belief in a cosmic creator/composer, as evidenced in this statement made by Kepler, quoted in Rogers’ cross-curricular article in the Music Educators Journal: “I feel carried away and possessed by an unutterable rapture over the divine spectacle of the heavenly harmony.”[23] Indeed, Western music has been profoundly influenced and preserved because of the institution of the church. In light of early church beliefs pertaining to the beauty of creation, the linking of consonant, beautiful sounds to the act of worshipping God was inevitable. Delving further into this connection exposes the matter of overtones. “When people hear overtone singing for the first time, the universal reaction is one of amazement. With its otherworldly quality, it is easy to see how the sound of overtone singing is often associated with sacred utterance.”[24]

“The term ‘overtone singing’ refers to techniques that allow a singer to isolate one (or more) of the natural harmonic partials in the overtone series of a sung fundamental pitch, thus making audible two discrete pitches simultaneously.”[25]

It is a vocal technique used by some musicians to strengthen their awareness of overtones, thus enhancing their ability to use these overtones to create a more resonant singing voice. However, Stuart Hinds, a practicing overtone singer, writes that many people use overtone singing for “physical and mental well-being and…as spiritual expression. It should be understood…that for many overtone singers, these holistic and spiritual aspects are the primary reasons for overtone singing.”[26]

The music of the spheres has come full circle, from a means of describing the handiwork of God to a tool with which to praise God for his handiwork.

There are those who use the mystical power of overtones to reach further into human consciousness and even into the human physical form. “Gong sounds affect the human soul and penetrate to deep levels in the subconscious.”[27] Gongs do not have definite pitch; they are aurally identified not by their lowest fundamental, but by their consonant and dissonant overtones. “The overtone series of the various gongs were found to provide satisfactory explanation to the effect of the gongs on patients subjected to music therapy with gongs.”[28] When a gong is played that has strong overtones combining to sound the interval of a diminished sixth, for instance, “people report a pleasant feeling of warmth and security, as if being totally immersed in the sound…In music [the diminished sixth] is considered as a lyrical and consoling interval, and gives a pleasant nostalgic feeling.”[29] The article in the

Journal of New Music Research also recounts an instance of a patient who is cured of chronic pain after listening to repeated playings of Schoenberg’s “Poѐme en Mi” on percussion instruments. The most prominent overtones in the composition consisted of E4, E5, Bflat5, E6, G6, Bflat6, essentially an E diminished chord. “Such personal sensitivity, up to self-identification of a person with an individual note, as if being tuned by it, was reported by Blass in her long experience in work with severely mentally retarded patients.”[30]

Further Applications of the Theory of Music of the Spheres

The theory of music of the spheres has guided music composition and education for thousands of years. Can the intricacies involved therein continue to direct musicians and music educators in 2019?

Fifty years ago, New York’s Union Theological Seminary provided doctoral degrees in church music…today that program is essentially defunct. Just last year…Northwestern University eliminated its degree programs in organ, thus terminating its historic training in the church’s musical art…In many communities, public school music education is a casualty of a pinched budget…Community orchestras are disbanding, and classical music radio broadcasts are being dropped. Perhaps the greatest tragedy is that most younger people today fail to learn to sing- either at the ball game or in church.[31]

Many would agree that the nature of music and of music education is changing. But should we abandon our rich heritage in this age of political correctness just to avoid music’s long history with the church? Donald Paul Hustad, prominent church music historian, does not think so: “I believe that God expects all persons to be ‘ecologists of culture.’”[32] In his article in the Choral Journal, he calls on musicians to preserve our rich history by continuing to contribute to music in church: the driving force behind, and the very reason for, Western music. Many composers (like Beethoven, Schubert, Mendelssohn, and Brahms) contributed masterworks that we still use for worship. That phenomenon demonstrates what theologians call ‘common grace’ – that even unbelieving artists may use God’s creative gifts so well that God takes delight in their works, whether they are offered to God as worship or as competition in creativity.[33]

Pythagoras was wrong. Yet his theory shaped and influenced music, art, architecture, philosophy, science, and religion far beyond his lifetime. Because of the music of the spheres, we experience the mystical, healing, worshipful gift that is Western music today. We must work to keep the spirit of Pythagoras’ theory alive by continuing to create, learn, and collaborate in the fields of science, math, and music.

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2. Rogers.
3. Rogers.
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5. Barbara Russano Hanning and J. Peter. Burkholder. Concise History of Western Music. New York: Norton et Company (2014): 22.
6. Hanning, 22.
7. Johannes Kepler. Harmonice Mundi. Translated by E.J. Aiton, A.M. Duncan, and J.V. Field. Phildelphia: American Philosophical Society (1997): 446.
8. Rogers.
9. Rogers.
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11. James Haar, 'Music of the spheres.' Grove Music Online. 2001
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13. “The Music of the Spheres.” Wilson Quarterly 30, no. 4 (September 2006): 82.
14. Rogers.
15. David First. “The Music of the Sphere…”Leonardo Music Journal 13, no. 1 (December 2003): 32.
16. First, 33.
17. First, 34.
18. First, 34.
19. First, 34.
20. First, 35.
21. Stuart Hinds. “Argument for the Investigation and Use of Overtone Singing.” Journal of Singing 62, no. 1 (September 2005): 33.
22. Richard Cole and Ed Schwartz, eds. “Overtone.” OnMusic Dictionary - Term, June 6, 2016.
23. Rogers.
24. Hinds, 36.
25. Hinds, 33.
26. Hinds, 33.
27. E. Rapoport, S. Shatz, and N. Blass. “Overtone Spectra of Gongs Used in Music Therapy.” JOURNAL OF NEW MUSIC RESEARCH (2008).
28. Rapoport.
29. Rapoport.
30. Rapoport.
31. Donald Paul Hustad. “CREATION, CULTURE, and the ‘MUSIC OF THE SPHERES.’” The Choral Journal 47, no. 9 (2007): 28.
32. Hustad, 29.
33. Hustad, 26.