Cosmic Harmony in Symbolism and Natural Science
By Rudolf Haase
Translated by Ariel Godwin
On the World-View of J.M. Hauer
Lecture at the Vienna Academy of Music and the Visual Arts
in the Josef Matthias Hauer Circle, Nov. 22, 1979
The Philosophy of Josef Matthias Hauer
Josef
Matthias Hauer's music, especially his twelve-tone compositions, hardly
presents a problem for human hearing; but their entire meaning can only
be grasped with the help of additional clarification. The music,
namely, is a component, even in a certain sense a result, of the
composer's very individual philosophy, which is not easily accessible,
especially since its understanding is still hindered by some of Hauer's
idiosyncrasies. Thus, we will attempt in the following to provide an
access to this world view of Hauer's, which may illuminate his
philosophical viewpoint and facilitate further study of his related
writings. Since it is impossible to give an exhaustive overview of his
world of thought, we will begin with a few characteristic quotations,
from which a suitable interpretation will develop.
“The eternal unchanging absolute music is the great writing and
language of the universe, the harmony of the spheres, the cosmic order,
the art of all arts, the science of all sciences, the culture, ...
religion as a connection to eternity, the highest, holiest, most
spiritual, valuable, intelligent thing in the world: truth.”
“If there were nothing else in the world but the twelve well-tempered
tones, we would still have to believe in a wise creator who had built
the world on a great plan. And if there is something that lets us at
least suspect this plan, it is the melody of these twelve tones.”
“The hearing human is therefore at the outset the spiritual, as opposed
to the simply speaking, seeing, comprehending. Hearing, perception
(reason) is the spiritual act of man, hearing the immutable,
untouchable, ungraspable, unchanging, eternal-melody. He who hears can
also perceive, interpret, think, speak, comprehend, conceive.”
From these three passages, it can be seen that Hauer believed in a
cosmic order, a harmony in the sense of the ancient harmony of the
spheres whose laws correspond to our earthly music. But how these laws
should be specifically obtained is a second set of problems, which we
will introduce with some further quotations.
“There are habits of hearing that are rooted in the natural ratios of
the overtone series-in the dullness of matter. They can only be
overcome by the spirit, i.e. by musical intuition (the non-sensory ...
hearing of the interval, which from its highest purity gives forth the
atonal melody as its own greatest creation). The spirit, in a certain
sense, forms the matter, the physical ear. Only those who set the
intervals free, in and of themselves, from their natural functions, who
can comprehend them as the seeds of melody, only they truly hear. The
ears of those who hear only sensorily, naturally, mechanically, are
dead.”
“Through equal tempering of tones and intervals, everything grossly
sensual (leading-tones, differences in the sounds of the individual
tones, etc.) is eliminated as much as possible ... the intuitive human,
the musician, suppresses the 'world,' space- naturally only
illusionary-he feels himself in the cosmos and lives in the temporal,
in the progression, in organic growth.”
“The interpretation, the rhythmic arrangement of the pure melody, of
the atonal-because only this is free of all sensory things-is therefore
a markedly spiritual act, the only one that exists in the scientific
and artistic life of man.”
From these further passages we see that Hauer understood the laws of
music as something very specific, namely tempered tuning. This, as we
know, involves a detuning of the interval proportions given by nature,
where by “nature” Hauer means the overtone series, whereas today we know
of another much more important natural component: the psychological
constitution of human hearing. However, our purpose here is not a
critical statement on Hauer's ideas, but as intensive an understanding
as possible of his viewpoint. And in this sense it is appropriate to
assume that Hauer was right in seeing tempering as something spiritual
of material nature; because tempered tuning (by which he means equal
tempering) is in fact an invention of the human mind, which thereby
uses mathematics, and these mathematical values appear as laws of
nature. This is therefore a pointed separation of mind and matter,
connected with the idea that only so-called atonal music, based on
tempered tuning, is in a position to reproduce the aforementioned
cosmic order, the harmony of the spheres.
This exposition of Hauer's ideas leads us logically to ask two questions:
1. Where do these ideas come from?
2. What truth lies in this philosophy?
The Mythos of the Sound-Cosmos
Josef
Matthias Hauer's ideas about a connection between universal order and
music are in fact ancient, and Hauer was well aware of this, even if he
could not know of the wealth of research on this subject existing
today. For an outline of the most important components of this
sound-worldview, we refer above all to the works of Marius Schneider,
in which much more material is accumulated than we can apply here.
In the advanced civilizations of antiquity, and also in modern
primitive societies, the idea is widespread that the world arose from
or is made from sounds. Of course this idea is not illustrated in
scientific form, but in myths and/or with the help of symbols, which
must be decoded. Through this, we can distinguish three types of
symbolism:
1. Mythological stories with possibly distinguishable forms of representation, especially from India;
2. Numeric symbolism, which is partly handed down in great systematic combinations, especially from China;
3. Harmonic symbolism as a particular type of numeric symbolism, applied almost exclusively by the Greeks.
We will give examples from each of these three domains, so that the
reader will at least have an approximate idea of what is being debated.
For the characterization of the sound myths, we will quote a sentence
from Marius Schneider's radio broadcast script, which outlines various
simple notions:
“The ancient Indian tradition tells of a sound which rose from the
perfect silence of nothingness and gradually formed the world of our
perceptions. In the Vedanta philosophy, which comments on the ancient
Indian Rig-Veda, it is written that the gods and all the rest of the
world are contained in the Word, or the rhythm of the Veda-Word, and
that the Creator God, while he was forming the world, remembered this
rhythm and used it as a guide for creation. The Aitareya Upanishad
encloses the primordial sound in an egg, from which the world emerged.
As Atman created (incubated) the world, his mouth opened like an egg
and speech, fire, and the whole world came out of him. In Javanese
cosmology, the creator himself is first created by a hearing entity,
which announces itself with bell tones. In the Brihadaranyaka
Upanishad, the creator of the world is hungry Death; he creates the
world by singing a song of praise and heating himself that way. Thus
emerged water, fire, and the song of speech.”
This text contains a few clear indications of the link between world
creation and sound; yet still other connections are hidden behind
single words, since these words are symbols and must be interpreted
differently. For example, the word “water” always means a pure sound,
whereas “fire” should be understood as rhythm. The old legends are
mostly far more complicated; we must therefore eschew detailed
description here and refer to relevant publications.
We will apply ourselves somewhat more closely to the second
possibility, relating cosmos and music to one another-numeric
symbolism. It played a large role above all in China, and we will use
this culture as our example. First, however, it must be emphasized that
the basis of this thought is analogical relationships, which were seen
in China between all imaginable domains and were illustrated in the
application of numbers, whereby an extensive system of logical
correspondences emerged. This way of thinking appears even in the most
ancient Chinese philosophical writings, e.g. the Hung-fan, from whose statements the following table was compiled.
1 |
Winter |
Water |
North |
f |
2 |
Summer |
Fire |
South |
c |
3 |
Spring |
Wood |
East |
g |
4 |
Fall |
Metal |
West |
d |
5 |
Year |
Earth |
Center |
a |
6 |
Winter |
Water |
North |
e |
7 |
Summer |
Fire |
South |
b |
8 |
Spring |
Wood |
East |
f# |
9 |
Fall |
Metal |
West |
c# |
To be more exact, we constructed the table incorporating of later stipulations from the Yüeh-ling,
so that each concepts has two numbers assigned to it, the differences
of which are always 5. As can easily be seen, the seasons, elements,
and directions stand in a significant interrelation of analogies; e.g.
winter is cold like the North and the rainy (water), summer is hot
(fire) like the South.
Typical for ancient China, furthermore, is the use of magic squares,
and one of the most important of these is that of the numbers 1 to 9,
with the 5 in the middle:
The sums of all the parallel and perpendicular rows, as well as the
diagonals, are 15. Now the four pairs of numbers surrounding the 5 are
opened, so to speak, forming a cross, which is the core of the
following illustration:
North - Winter
6
11 1
4 6 8
1
West - Fall 9 9 4 5 3 8 3 East - Spring
2
2 7 10
7 5
12
South - Summer
If one compares the number values of the bars of the cross with the
above table of analogies, it becomes apparent that 1 and 6 mean North
and Winter, 3 and 8 East and Spring, 2 and 7 South and Summer, and 4
and 9 West and Fall; a meaningful illustration has thus emerged, which
symbolically contains some of the important aspects of the cosmos. This
is also a kind of outline of the Ming-Tang, the Chinese calendar house
from the later Sung dynasty, whose 9 spaces correspond to the numbers.
There were, furthermore, 12 “stations of grace” (perhaps also windows)
in the calendar house, which the Emperor included when he gave his
instructions-corresponding to the 12 months. These stations were
likewise symbolized by numbers, and they form a circle in our
illustration; the arrangement of these numbers has a connection to that
of the bars of the cross; yet this is no longer strictly feasible,
since there are 12 numbers.
In the Yüeh-ling, the tones of the Chinese tone system, which we have
already set out in our table of analogies, are added to the
aforementioned correspondences, at least up to the 9th
tone, while the entire tone system has 12 so-called Lü (corresponding
to the tones or intervals in our 12-step chromatic scale), which were
indicated through a complicated proportion system that will not be
discussed here. The assignment of the tones to the numbers
and their completion to the number twelve allows one to see, through
comparison with the table of analogies, that a sequence emerges,
corresponding to those of the outer number circle in the Ming-Tang,
which can be illustrated thus:

If one follows the inscribed twelve-pointed star, beginning with 1, the
sequence of the table of analogies emerges as the circle of fifths; if
one proceeds in the other direction, clockwise from 1 (past 8, 3, 10,
etc.) around the circle, then the familiar chromatic scale emerges.
The result of this observation is a system built of numbers, in which
seasons, directions, elements, and tones are unified into a symbolic
layer, forming an analogy to cosmic principles. For our viewpoint, the
tones are naturally the most important, their succession being
identical with the stations or windows of the calendar house, so that
they have a direct relationship to the individual months. From this it
follows that in Chinese ritual music, their scales (selected pentatonic
scales) must each be transposed by month to a different keynote! The
music therefore has a symbolic connection to cosmic principles.
The third type of symbolic representation of sound-cosmic connections
is harmonic symbolism. It differs from the pure number symbolism of the
previous example in that only those numbers that are the acoustic basis
of music can be used for application. These are the so-called interval
proportions, as they have been used since ancient times in the most
varied cultures. In our own cultural domain, they were discovered by
the Pythagoreans through experiments with the monochord. Pythagoras,
however, played a key role above all with regard to the sound-cosmic
ideas we have outlined. It was obviously he who, one might say,
rationalized those mythical narratives in combination with the
emergence of the scientific mode of thought in ancient Greece, and with
the help of the aforementioned study of proportion, brought them into a
mathematic and scientific form. Unfortunately, this can only be
gathered in fragmentary form from the Pythagorean legacy; yet with
Plato, who was indubitably influenced by Pythagoras, we find very clear
references to what has since been handed down as “the harmony of the
spheres” or “universal harmony.” And these texts of Plato are
characteristic evidence for harmonic symbolism.
Most important of all is a statement in his Timaeus dialog
describing the creation of the so-called Soul of the World. Here, Plato
tells us that the world as a whole has a soul-just like all living
beings-and describes the almost architectural creation of this
structure by the Demiurge, Plato's lower god. The process is described
in detail, but in such a way that it makes no sense to the reader. The
passage is, in fact, a secret text, only understandable by readers who
approach it with certain prior knowledge. This fact already points to
the Pythagoreans, whose sect was indeed a kind of mystery religion with
a very strict policy of secrecy. But the essential knowledge for the
solution of the text is connected with the Pythagoreans; because it
relates to the interval proportions, whose mathematical
understanding-in no way simple-is assumed here, even though only the
subtlest references to it can be found.
The result of the decoding of the text is a scale, namely the Dorian,
the central scale of the Greek tone system, in the form of precisely
calculated proportions. This is the oldest of the Greek modes in the
most ancient diatonic scale, the invention of which is attributed to
Pythagoras and which also had the highest rank in the ethical
discipline of the Greeks. Plato therefore presents the soul of the
world as the basis of the Greek tone system, and with this symbol he
doubtless wished to express that musical laws have an important
function in the cosmos. The interpretation of this text can be somewhat
simplified and thus made more accessible;
but the passage also conceals more complications, which lead to
variations of the solution, so that even today new proposals appear
relating in part to the accompanying text, which is similarly puzzling.
Besides the Timaeus
scale, there are a few further examples of harmonic symbolism that we
cannot discuss here. About a hundred years ago, Albert von Thimus
applied himself exhaustively to this domain and wrote a two-volume work
on it, entitled The Harmonic Symbolism of the Ancients.
In this work he begins with the assumption that harmonic symbolism was
the core of ancient wisdom, and provides extensive and dense material
on this topic. Hans Kayser built his ideas upon those of Thimus, and
devoted space in his “Kayserian harmonics” to speculative symbolism
going much farther than Thimus. Today we know that Thimus proceeded
very speculatively,
and therefore we must make many exceptions to his theses; but once this
is done, the true core of harmonic symbolism remains undisturbed.
Thus we conclude the outline of the three forms of sound symbolism, and
can return to Josef Matthias Hauer. The reader will have already
noticed the similarities existing to Hauer's quoted statements. In
fact, he was very familiar with the second and third forms of sound
symbolism. Interestingly, Hermann Bahr made him aware of the work of
Albert von Thimus;
but at this time (1918), Hauer already knew Chinese symbolism, as can
be seen from the correspondence, and from this perspective he
repudiated Thimus, as we shall see.
We have now dealt with the question of the origin of Hauer's ideas
about a musical order of the cosmos, and must turn to the second
question: the truth of the content of these ideas.
Fundamental Harmonic Research
The
answer to this question should be anticipated: it has been proven that
true factual content lies at the basis of the sound symbolism
described, because the foundations of music are also provable as
general laws of nature. Therefore, a close connection to harmonic
symbolism exists; because this is a matter of the interval proportions,
which constitute the material of harmonic symbolism and are also
present in nature. Thus a circle, so to speak, is completed. If
Pythagoras, as can be reconstructed from later sources, presented the
idea that identical laws existed in nature (the planetary spheres), in
people, and in music, but carefully kept this wisdom secret and only
passed it on in symbolic code, then today we are in a position to prove
this connection scientifically.
The first and most important proof was made in the Baroque period by
Johannes Kepler, the famous astronomer and mathematician, who we now
know had the lifelong goal of proving the Pythagorean teachings of
universal harmony, handed down only in legendary form. He finally found
this proof, and published it in his Harmonices mundi libri V,
the five books of universal harmony, in 1619. The main conclusion is
shown in the following table, in which he compares the angular
velocities of the planets, measured relative to the sun, at the
farthest point from the sun in their orbits (aphelion) and the nearest
point (perihelion), and determines that simple proportions emerge
corresponding to those of musical intervals. For reasons of simplicity,
we have replaced Kepler's measured values with the letters A through M
in this table.
Saturn |
Aphelion A |
A : B = 4 : 5 (major third) |
c |
e |
|
|
|
|
|
Perihelion B |
A : D = 1 : 3 (duodecimal) |
c |
|
g |
|
|
|
|
|
C : D = 5 : 6 (minor third) |
|
e |
g |
|
|
|
Jupiter |
Aphelion C |
B : C = 1 : 2 (octave) |
c |
|
|
|
|
c′ |
|
Perihelion D |
C : F = 1 : 8 (3 octaves) |
c |
|
|
|
|
c′ |
|
|
E : F = 2 : 3 (fifth) |
c |
|
g |
|
|
|
Mars |
Aphelion E |
D : E = 5 : 24 (minor 3rd + 2 oct.) |
|
e |
g |
|
|
|
|
Perihelion F |
E : H = 5 : 12 (minor 3rd + octave) |
|
e |
g |
|
|
|
Earth |
Aphelion G |
G : H =15 : 16 (diatonic semitone) |
|
|
|
|
b |
c′ |
|
Perihelion H |
F : G = 2 : 3 (fifth) |
c |
|
g |
|
|
|
|
|
G : K = 3 : 5 (major sixth) |
|
e |
g |
|
|
|
Venus |
Aphelion I |
I : K =24 : 25 (chromatic semitone) |
|
|
g |
g# |
|
|
|
Perihelion K |
H : I = 5 : 8 (minor sixth) |
|
e |
|
|
|
c′ |
|
|
I : M = 1 : 4 (2 octaves) |
c |
|
|
|
|
c′ |
Mercury |
Aphelion L |
L : M = 5 : 12 (minor 3rd + octave) |
|
e |
g |
|
|
|
|
Perihelion M |
K : L = 3 : 5 (major sixth) |
|
e |
g |
|
|
|
It should also be noted that the values given by Kepler have remained
constant up to the present, despite ongoing changes in the orbits;
because these are angle measurements that are hardly affected by these
changes.
Of course, the intervals do not really make sounds, since these are
ideal proportions, but they can be transposed into the domain of
hearing and be made audible there. The same goes for all other natural
harmonic laws.
At the beginning of the 20th
century, the crystallographer Victor Goldschmidt also found
proportional laws that he recognized as harmonic in the structure of
crystals,
and later Hans Kayser successfully expanded this fundament of nature in
his “Kayserian harmonics.” Modern-day “fundamental harmonic research,”
established by the Author in Vienna in 1965, stems from this tradition.
Since then, numerous further harmonic laws have been proven by
inductive methods, building upon empirically confirmed facts, in
astronomy, crystallography, chemistry, physics, botany, zoology, and
anthropology.
There are similar interval proportions in significant places everywhere
in nature, so that a great analogical interrelation emerges between the
most varied domains and sciences.
But an analogy also exists, as has been mentioned many times, between
these natural laws and the foundations of music; because intervals also
appear there, and these have been based on simple number ratios since
ancient times. Here an argument often heard today presents
difficulties: that these mathematical foundations are mere convention,
and are based above all on acclimatization. If this were so, then the
relationship between nature and music would simply be coincidental, or
entirely arbitrary. However, this is not the case; because fundamental
harmonic research can also provide the proof that there is a natural
psychophysiological predisposition of human hearing, on the basis of
which the simple proportions are favored and have therefore emerged as
fundaments from the laws of nature. This predisposition of hearing will
now be discussed more thoroughly.
Our investigations into the physiological predisposition of hearing are
based on experiments and their interpretation by Heinrich Husmann.
He points out that, based on the non-linearity of the human ear,
supplementary tones emerge whose vibrations cause interferences. These
are the subjective overtones, which have the same laws of structure as
the objective, and-with at least two simultaneous tones-combination
tones (also of higher orders). From Husmann's specifications, we have
prepared the following table, from which it can be seen that the
interferences are different for each interval, since in each case a
different number of combination tones is identical with overtones. On
the basis of the differing identities, a series of intervals emerges.
Combination tones identical with overtones:
Number |
Percent |
Interval |
Proportion |
72 |
100 |
Octave |
1 : 2 |
42 |
58 |
Fifth |
2 : 3 |
28 |
39 |
Fourth |
3 : 4 |
24 |
33 |
Major sixth |
3 : 5 |
18 |
25 |
Major third |
4 : 5 |
14 |
19 |
Minor third |
5 : 6 |
10 |
14 |
Minor sixth |
5 : 8 |
8 |
11 |
Minor seventh |
5 : 9 |
2 |
3 |
Major second |
8 : 9 |
2 |
3 |
Major seventh |
8 : 15 |
0 |
0 |
Minor second |
15 : 16 |
0 |
0 |
Tritone |
32 : 45 |
This series also shows the degree of purity of the respective
intervals, since the combination tones falling in the gaps in the
overtone series can be viewed as dullings of the natural sound. The
third column now shows that the sequence yielded corresponds very
precisely to the differentiation of consonances and dissonances, known
for centuries, and that each interval has a specific degree of sonance,
which is expressed in percentages (2nd column).
The differentiation of consonances and dissonances is thus based on a
predisposition given as a law of nature by the physiology of the ear.
This “mechanism” of overtones and combination tones, however, only
works with the specified exactitude when the intervals are formed from
proportions of whole numbers (4th
column), since otherwise an identity of frequencies cannot be obtained.
But this means that these same proportions are perfect, because only
they lead to the optimal clarity of perception. This is the true reason
why simple number ratios were favored in the construction of intervals
in ancient times, especially among the Greeks. This
predisposition-determined explanation of the interval proportions is
most important for our subject, since our aim is to establish the
analogy between natural harmonic laws and musical fundamentals on a
scientifically confirmed basis. But further important musical
foundations can also be derived from the predisposition of hearing,
which we will indicate only briefly: the 12-step chromatic scale, the
diatonic scale, the favoring of the major and of other central scales
in tone systems. The complex reasoning can be found in other places.
It must be mentioned, however, that for some conditions of this musical predisposition
of hearing, a psychical predisposition works along with the explained
physiological one. The 12 familiar interval perceptions are obviously
anchored psychically; they are inborn sensory qualities, just like
colors, for example. The investigation of this psychical
predisposition, however, yields another important result. Namely, the
fact emerges that on this psychical plane, none of the kind of
exactitude is assessed as with the physiological disposition, indeed
quite the contrary: the interval perceptions have margins allowing for
deviations of up to 40% of the distance between two semitones to be
assigned the correct perception (these distances are the logarithms of
the proportions, since as is known we hear logarithmically). This
“adjusted hearing” of deviations is also an important fundament of
music, and is of great significance for our topic.
Those detunings of pure-tonal intervals consciously induced by people,
such as the tempering of instruments requires, also belong in these
domains of adjusted hearing; and here we are reminded immediately of
Josef Matthias Hauer, for whom tempering is the most important
fundament of music. The mathematical values of tempered tuning are not
natural laws, as we have already said, but the possibility of tempering
in principle is anchored in nature, in as much as adjusted hearing
assures that deviations from pure-tonal tuning are corrected and do not
bother us.
The mention of adjusted hearing has another result for our debate.
Namely, we can assume that the ancient Chinese (as well as the Greeks)
were aware of this quality of the sense of hearing. In the diagram of
the 12 Lü in the form of a twelve-pointed star, the twelve tones have
exactly equal distances, and this equality cannot be attained with
pure-tonal proportions (or their logarithms)! Only the logarithms of
equally vibrating tempered intervals have the same distance in the
psychical hearing space, and the Chinese diagram can be perceived as a
hearing space bent into a circle.
But here we must warn of a related fallacy. The existence of the
equidistant representation by the Chinese must in no way lead to the
conclusion that they knew of the mathematical or practical method of
the tempering of instruments! Their mathematics would not have made
this possible at all. It was sufficient to know that deviations from
the proportions (which the Chinese did know of, and applied) were
tolerated by hearing in order to allow the fascinating circular diagram
of the tone system to enter the plane of symbolism. (The Chinese
actually were the first to calculate equal tempering mathematically,
but that was some 2,000 years later: Chu Tsai-yü discovered it in 1584,
a year before it was discovered in Europe by Simon Stevin.)
Hauer's Spiritual Position
Our
investigations into sound symbolism and the harmonic laws of nature
have provided the requisite foundations for a presentation of Hauer's
philosophy, and we can now give an assessment of his viewpoint.
1. Hauer is completely right in principle when he describes music as “...the harmony of the spheres, the cosmic order...”;
because an interrelation of intervals with a multitude of harmonic
natural laws can be factually proven. Admittedly, these analogies rest
upon simple proportions of whole numbers, so that only those intervals
correspond to the conditions named that also emerge from proportions of
whole numbers-and Hauer dismisses this. For the clarification of his
viewpoint, we will let him speak for himself again, through his
comments on Thimus's Harmonic Symbolism of the Ancients in a letter to Hermann Bahr from April 11, 1918:
“In the latter work, what Thimus says matters less than the directions
of thought and perception of musical humanity stipulated there. The
good Baron von Thimus leans more to the side of the mathematician; he
has no hearing-oriented person within him to overcome. All
mathematicians have long combated tempering, that can be seen plainly
from Thimus's book; and all practical musicians have heard a finer play
of colors in tempering than in the pure intervals with the rational
numbers.”
Hauer therefore sees only the mathematical side of the interval
proportions and obviously undervalues their significance as a law of
nature, of which Thimus admittedly also made little mention, since at
that time he could only refer to Kepler, albeit very frequently.
2.
If a connection of Hauer to harmonic research is impossible, given how
much its modern results contradict his ideas, then it will work all the
better with symbolism. Since Hauer continually places the spiritual in
the foreground and pits himself against the material rooting of music
in the overtone series, he ends up on the same plane as symbolism, this
being also a product of the human spirit. At best, a connection with
Chinese number symbolism is possible, since it is on an astonishingly
high spiritual level and is also fully cosmically oriented. Hauer's
entirely logical conclusion is that this type of sound symbolism
corresponds at best to those musical foundations that are also created
entirely spiritually, and such is the case for tempering, the
mathematical principles of which are the product of human thought. This
unification is highly logical-only on this plane is the true “musical”
order of the cosmos not perceived, but only its symbolic image.
3.
The two viewpoints are, in fact, not so incompatible, as Hauer often
pointed out polemically. And had our modern-day knowledge been at his
disposal, his opinion would probably have been less extreme.
Disregarding the fact that sound symbolism and natural harmonic
research are only two different sides of the same issue, a unification
of the two mathematical foundations of music is easily possible, namely
through adjusted hearing, the spiritually-mathematically produced
detuning that tempering tolerates, in the following manner:
a)
the tempered atonal music assumed by Hauer could just as well be played
on pure-tonally tuned instruments, without other fundamental
perceptions emerging, and
b)
the natural harmonic laws, formed from proportions of whole numbers, if
played on tempered instruments, would also yield the same sensory
qualities.
Josef
Matthias Hauer cannot know the modern results of the harmonic research
that his philosophical ideas confirmed in principle, albeit in a
different form from what he assumed. His life's work will thus be
incorporated into the great framework of our knowledge of an
all-embracing musical universal order; how that can happen, we have
indicated in our studies. But precisely because he knew nothing of the
real existence or truth of a harmonic plane of creation, all the more
credit is due to Hauer for his own belief in a great spiritual
connection in which music plays a leading role. To this idea he
dedicated his life, with great personal sacrifice.
b) “Die Grundlagen der Kultsprache in der vedischen Kosmologie,” in: Sprache und Sprachverständnis, 1972
c) “Das Schöpfungswort in der vedischen Kosmologie,” in: Musicae scientiae collectanea, Festschrift für K.G. Fellerer, Köln 1973
a) G. Jahoda: “Die Tonleiter des Timaios - Bild und Abbild”;
b) W. Schulze: “Logos - Mesotes - Analogia. Zur Quaternität von Mathematik, Musik, Kosmologie und Staatslehre bei Platon”