A Comparison with Astronomy
Comparisons are always approximate and occasionally odious, but there are cases where it is difficult to define and place
a subject properly without reference to something similar (or somewhat similar), and music is certainly a case in point.The
choice of astronomy was made because both astronomy and music have very similar structures, and historically both sciences
developed from a common source (Pythagoras), both were led astray, and both have sought to find their way back to truth.
The original truth
Although a considerable knowledge of astronomy is evident from examination of Egyptian and Central American pyramids, for
the purposes of this presentation, we will start our comparison somewhat later with the fact that the all-important beginnings
of music and astronomy were well known to Pythagoras (-581 to -497) and to his surroundings. As a matter of fact, it is quite
difficult to separate the person from the school here because Pythagoras left us no writings directly. However we are quite
certain of the fact that he was aware that (a) the earth revolved around the sun and that its revolution on itself gave the
appearance of the sun revolving around it,
and (b) that the fifth was the interval of simplest proportion to produce a new note (the octave merely displacing the same
note to another range). This fundamental position of the fifth for Pythagoras is so firmly ingrained into our collective memory
that the form of tuning which uses only this interval bears his name (Pythagorean Tuning).
In astronomy, the culprit was certainly Ptolemy (Claudius Ptolemaeus 90-168) whose geocentric theory of astronomy placed the
earth at the center of the universe with all the heavenly bodies circumnavigating it. This theory dominated academic and
popular thinking for a millennium and a half.
In music, the culprits are not as easy to spot but two of them deserve particular notice.
1. Guido d'Arezzo (1000-1050) a Benedictine monk who provoked a revolution by inventing a new method of musical notation
based on the first syllables of the lines from the Hymn to Saint John the Baptist. This precision of nomenclature was considered
an affront and a menace to the existing habit of memorizing by rote.
2 Gioseffo Zarlino (1517-1590) priest and organist, established the mathematical proportions between the degrees of the
scale. Although his theoretical propositions were refuted by Vincenzo Galilei (father of Galileo), Zarlino (and to a certain
extent Guido) succeeded in establishing the principle that the proximity of notes (a horizontal manifestation, as in the scale)
was more fundamental than the simplicity of the mathematical relationship of the fifth (a vertical manifestation, as in chords).
Music (especially harmony) was being led astray from the original Pythagorean concepts.
Finding the way back
The battle to re-establish the Pythagorean heliocentric model (later endorsed by Aristarchos of Samos, -310 to -230) is a
well documented saga. The patient, persistent observations by Nicolaj Kopernik (1473-1543) to replace the sun in its rightful,
central position, the trial of Galileo Galilei (1564-1642), the additions and precisions of Johannes Kepler (1571-1630), of
Isaac Newton (1642-1727), and more recently of Albert Einstein (1900-1955), have gradually accumulated an incontrovertible
body of scientifically respectable astronomy. It is interesting to note that the path was not easy, neither rapid nor peaceful.
The geocentric model was evidently a very egocentric one, humanity priding itself on inhabiting the central body of the universe.
To maintain this glorified and preferential position, the "powerful" burnt Giordano Bruno (1548-1600) at the stake and, for
the 100 years following the death of Galileo, 80% of "technical" papers on astronomy did not even mention the Pythagorean-
Kopernican theory, and Bach probably still thought that the earth was the center of the universe. Astronomy painfully and
slowly worked its way out of its erroneous past.
Unfortunately, despite a few valiant efforts, music theory has not yet succeeded in establishing the truth.
In his "Traité de l'harmonie" (1722), Jean-Philippe Rameau (1683-1764) proposed the daring (for the time) concept that
harmony was more basic than melody. His first example of the dominant/tonic cadence is written in 5 voices (the 4 voice-leading
lines, plus the fundamental bass) and he had the audacity to suggest that the subdominant (counter) chord would posses a sixth
as fourth note. His work had no appreciable lasting influence and music theory remained proximity-oriented.
In his "Traité d'Harmonie" (1907), François-Auguste Gevaert (1828-1908), after the usual painful presentation of harmony
in triads, established light and order with progressions of tetrads by fifths, considering the seventh a true chordal tone,
with its own clear and definite function. Unfortunately, he did not go back over the first section to differentiate the different
categories of triads, real and deceptive, as incomplete tetrads. Very few academic theoreticians have even heard of Gevaert.
In his "Handbuch der Harmonielehre" (Simplified Harmony, 1887), Hugo Riemann (1849-1919) presented in great detail the whole process of harmonic symmetrical inversion, the logical
development of Rameau's symmetry between the dominant/tonic and sub-dominant/tonic progressions. However, Riemann still constructed
his chords on a single note, the root (instead of in a 2-note frame), and, in the process of inversion, had the misfortune
of calling the A minor chord the chord of E minor. The academic fraternity pounced on this weakness and threw out the precious
baby with the relatively clean bath-water. Riemann is better known than Gevaert, but his influence was minimal and harmony
remained unidirectional, with "seventh" chords only.
It was not until the mid XXth century, in the 40s, 50s, and 60s, that a first generation of researchers presented a truly
coherent and comprehensive view of harmony which is still largely unknown. Their concepts included the progressions of tetrads
by fifths (from Gevaert) and the harmonic symmetry (from Riemann) to which they added the possibility of a chord possessing
2 functions, one with respect to the preceding chord, and another with respect to the following chord (what MusicNovatory
now calls metamorphosis 4). They were also the first to perceive all the levels of rhythm. Needless to add that the resistance to these new concepts
I think it is the true purpose of [music] historical research
to uncover the basic laws common to all ages,
which govern all perception and forms of artistic expression.
In the fall of 1967, a second generation of researchers organized weekly meetings to consider the further unfolding of
the existing work. The unanimous decision was to restructure these analytical insights into a generative, synthetic model,
capable of producing all musical phenomena, without realizing, at the time, that generation would be the underlying scientific
principle of MusicNovatory. This generative model would offer unlimited new possibilities in rhythm, harmony, and melody.
Since 2000, a third generation of researchers has already added important insights, including the Langer Hinge, the Jordan Triangle, and Pete's Paradox.
Illusion and Reality
One Last Comparison With Astronomy
To reach a reasonable degree of truth and to start establishing order,
one must perceive illusions for what they are and not confuse them with reality.
In astronomy, the following illusions are commonly perceived for what they are -
1. The illusion of sunrise and sunset, in which the sun seems to move around the earth,
is interpreted as the result of the rotation of the earth upon itself.
2. The illusion of the sun and the moon having the same size, evident in a lunar eclipse,
is interpreted with the knowledge of the distance to them
(almost 500 times more for the sun, with its diameter 500 times that of the moon).
3. The illusion of the planets looking like stars (to the uninitiated eye)
is interpreted with the knowledge that the planets are much smaller, much closer,
and merely reflectors of the sun, rather than producers of their own light.
In music (harmony, for all practical purposes), the following illusions continue to be confused with reality -
1. The illusion of triads being considered bona fide complete chords
when in reality they are incomplete tetrads.
2. The illusion of diminished sevenths also being considered bona fide chords
when in reality they are basically and fundamentally diatonic tetrads
which have been transformed by chromaticism or non-chordal tones, possibly both.
3. The illusion of ninths, elevenths, and thirteenths being considered integral parts of a chord,
when in reality they are non-chordal tones of the root, the third, and the fifth, respectively.
Correct analysis will enable us to reduce all chords to their essence,
revealing them to be, invariably and inevitably, diatonic tetrads.
Well aware that it is heartbreaking to lose one's illusions,
minimal honesty prevents this site from promising a rose garden.
Back to Galileo
In 1633 Galileo was confined to house arrest, not for believing in the heliocentric theory of astronomy, not even for writing
about it and attempting to draw others into the fold of believers (even his persecuters, especially the Jesuits, were believers
themselves), but for stating that the heliocentric model was definitive and inevitable, that the heavenly bodies could not
possibly move in any other way. He was wide open to the one-two-punch : 1. "Are you telling us, signor Galileo Galilei, that
God had no choice when He created the universe ? ; 2. "And who are you, signor Galileo Galilei, to tell God how to create
his universe ? ". This was the unacceptable part, and pope Urbano VIII had been warning him for some time before the trial.
But Galileo was adamant on this point, especially with the evidence that could be clearly seen through his telescope, and
willing to suffer the consequences. He seems to have been the first scientist in history to have manifested this confidence
in what he considered a definitive model. Einstein was to follow his example three centuries later.
It would be reasonable to state that the science of music
is now at the point that astronomy had reached at the time of Galileo.
The knowledge is there but it has yet to be accepted.
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