Harmony of the Spheres: Cosmological Resonances & Rhythms
Stephen Martin
CGU School of Music
ABSTRACT
As a musical ideology born in antiquity, the harmony of the spheres
has subsequently entertained significant attention and philosophical
inquiry over the centuries. Scientists, musicians, and astronomers in
support of the notion have gone to great lengths to substantiate
various corollaries between the motions of the planets and
recognizable musical parameters, systems, and scales. In this paper,
we revisit some of the key philosophical aspects of the case, in
addition to the geometrical considerations explored by Johannes
Kepler and others. The rotational, iterative, and process-oriented
structures embedded within Gothic cathedral architecture provide
clues and metaphorical insight into a similar architecture embedded
within our solar system. As a result, the case can be made for a
geometrically-oriented, iterative harmony of the spheres, bounded by
rhythm/pulse/orbital period, and consonance/planetary conjunction.
Iterations of geometrical rhythm and consonance are established over
time by way of planetary conjunctions, determined by and responding
to, previous iterations. We have provided a musical example entitled
Spheres, illustrating the combination of rhythm (pulses represented
by percussion) and consonance (musical intervals represented by
tubular bells). Spheres includes musical content derived both
quantitatively (mathematically derived from orbital length of the
planets), and qualitatively (musical intervals based on arbitrary note
assignments according to each planet).
COMPOSITION RESULTS
QUANTITATIVE PARAMETERS
Quantitative parameters are utilized according to orbital length and the
resulting planetary conjunctions. These two parameters directly affect
the resulting iterative geometries, played out over long spans of time.
In addition, one audio recording is utilized in the piece, taken from the
spacecraft Cassini during its orbit of Saturn. (The recording was
captured by NASA as radio emissions from Saturn and converted into
the discernible audio spectrum.)
Understand “Rotational, Process-Driven Geometry” in Gothic
Cathedral Architecture, as elucidated by Robert Bork
OBJECTIVES
1) Revisit philosophical discussion of a “harmony of the spheres,” as
a means of outlining basic viewpoints of the ideology.
2) Investigate the possibilities for direct correlation between musical
scale and orbital length, angular velocity, or solar distance.
3) Seek to understand other connections that may or may not exist
between music and geometry in the cosmos.
4) Contend for a “harmony of the spheres,” as related to rhythm and
musical consonances in geometrical ways.
5) Ask the question: “What could this potentially sound like?”
Subsequently, create a musical piece to support.
METHODS
Investigate Geometrical-Musical Ratios
(as understood by Euclid and Kepler)
Compare with the work of Hartmut Warm.
QUALITATIVE PARAMETERS
Qualitative parameters are represented by musical resonances,
performed as intervals played by tubular bells. These are based on the
latest suggestions for ‘planetary notes’ by Hartmut Warm in
“Signature of the Celestial Spheres.”
CALCULATIONS
Mercury’s orbit comprises 88 Earth days, and is subsequently used as
the guiding pulse for the piece, with each complete cycle of Mercury
(M) equal to 1 quarter note in 4/4 time.
(At beginning: Quarter note = 60BPM. That is, 1 Mercurian year is
equal to one second.)
In Logic Pro X, each 16th note is divided into 240 ticks (divisions).
Therefore, four 16ths = 960 ticks.
Since Mercury’s orbit is equal to 88 Earth days, each planet’s orbit is
calculated accordingly.
Example: Venus
The orbit of Venus is equal to 224.7 Earth days. 224.7 ÷ 88 = 2.55.
960 (number of ticks in 1 quarter note) X 2.55 (in relation to Mercury,
or “M”) = 2448 ticks.
Venus = 2.55M.
In Logic Pro X, Venus was plotted as a percussion hit every 2448
ticks.
Piece begins @ Quarter = 60BPM. Increase of 30BPM every 8
measures for the first 64 measures. From m. 65 to the end, steady
increase to 990BPM.
SOFTWARE USED TO CREATE SPHERES
Logic Pro X
v. 10.1.1
Listen Here: https://soundcloud.com/stephen-martin/spheres
(Screenshot of Spheres, from Logic Pro X)
CONCLUSIONS
1) A rotational geometry is taking place within the solar system,
evidenced by patterns of layered complexity and designs that rotate
in measured ways after each full iteration.
2) As a result, the solar system is harmonious in terms of its structural
integrity, counterpoint, and tuning, maintained within a processdriven architecture.
3) We contend for a “harmony of the spheres,” understood as
geometrically-oriented, derivational in process, and internally
organized. Just as the harmonious relationships in Gothic cathedral
architecture are reliant on rotation and derivation, so too are the
harmonious relationships among the planets and their satellites.
REFERENCES
Selected Sources
Boethius, Calvin M. Bower, and Claude V. Palisca. Fundamentals of
Music. Music Theory Translation Series. New Haven: Yale University
Press, 1989.
Bork, Robert. The Geometry of Creation. Ashgate, 2011.
Dahlhaus, Carl. Studies on the Origin of Harmonic Tonality. Translated
by Robert O. Gjerdingen. Princeton University Press, 2014.
Daines, Gary. “NASA Audio Files.” Text. NASA, June 28, 2013.
http://www.nasa.gov/connect/sounds/index.html.
Godwin, Joscelyn. The Harmony of the Spheres: The Pythagorean
Tradition in Music. First edition. edition. Inner Traditions, 1992.
Kepler, Johannes, E. J. Aiton, A. M. Duncan, and Judith Veronica Field.
The Harmony of the World. Memoirs of the American Philosophical
Society ;v Volume 209. Philadelphia, Pa.: American Philosophical
Society, 1997.
Miller, Frederic P., Agnes F. Vandome, and McBrewster John.
Astronomia Nova. VDM Publishing, 2011.
“NASA Planetary Fact Sheet.” Accessed April 18, 2015.
http://nssdc.gsfc.nasa.gov/planetary/factsheet/.
Plato. The Works of Plato, Viz His Fifty-Five Dialogues and Twelve
Epistles: Translated from the Greek, Nine of the Dialogues by the Late
Floyer Sydenham, and the Remainder by Thomas Taylor ; with
Occasional Annotations on the Nine Dialogues Translated by
Sydenham and Copious Notes by the Latter Translator., 1804.
Pollio, Vitruvius. Translated by Morris Hicky Morgan. The Ten Books
on Architecture. Harvard University Press, 1914.
Schmidt, Thomas Michael. Musik und Kosmos als Schopfungswunder.
Frankfurt Main: Schmidt, 1974.
Shu, Frank H. The Physical Universe: An Introduction to Astronomy.
Mill Valley, Calif: University Science Books, 1982.
Warm, Hartmut. Signature of the Celestial Spheres: Discovering Order
in the Solar System. Translated by J. Collis. Forest Row: Rudolph
Steiner Pr, 2010.
CONTACT
Stephen Martin
stephen.martin@cgu.edu
RESEARCH POSTER PRESENTATION DESIGN © 2012
www.PosterPresentations.com