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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
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Astronomy
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,
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Music
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).
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Led astray
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Astronomy
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.
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Music
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.
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Finding the way back
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Astronomy
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.
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Music
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 callsmetamorphosis 4). They were also the first to perceive all the levels of rhythm. Needless to add
that the resistance to these new concepts was violent.
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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.
Hugo Riemann
Scientific Generation
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 theLanger Hinge, theJordan Triangle, andPete's Paradox.
Illusion and Reality
One Last Comparison With Astronomy
To reach a reasonable degree of truth and to start establishing order,
one must perceiveillusionsfor 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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