Remarks on Plato's “Harmony of the Spheres”
By Rudolf Haase
Translated by Ariel Godwin
(Part of an introductory lecture)
The
concepts of the “harmony of the spheres,” “universal harmony,” and the
like, coming from literature-especially the Romantic-are familiar
enough to us, and their various interpretations can be followed up to
present times. Not so well known, however, is the origin of these ideas
and their true meaning; we shall discuss this subject briefly.
The term “harmony of the spheres” comes from Plato, who as we know was
influenced by the Pythagoreans, and who applies it in the great final
narrative of his Republic.
There he describes, in a mythological manner, the heavenly order of the
planets (including the sun and moon) and adds that on each of the
planetary circles, a siren sits, each one singing a tone, and “the
eight together form one harmony.” We have no details on this, since
this section is an encrypted secret text that has so far only been
partly interpreted.
The translation of the passage, however, contains an error, which has
barely been noticed until now: the use of the word “harmony.” The Greek
word Harmonia,
in the original text, had a meaning at that time nothing like our
present concept of harmony; it should correctly be translated as
“scale” (or octave). What Plato actually meant would be better
translated as “planetary scale.”
Of course, people knew this in ancient times, and there is proof for
it. Such planetary scales, i.e. assignments of tones to planets in the
form of scales, existed in the late Classical period (we know of at
least five different ones) and were continually rewritten and preserved
into the Christian middle ages; indeed, Isidore of Seville (ca. 600)
even invented a new version. As a second proof that Plato was really
referring to a scale, we have evaluated his description of the creation
of the world's soul in his later dialog, the Timaeus, which-likewise approached as a secret text-also yields a scale as its solution.
These scales were also known in the late middle ages, and in the school
of Chartres, whose learned monks were strongly influenced by the Timaeus-the
one Platonic dialog that was at least partially known in the middle
ages. The belief was that the world's soul was synonymous with the Holy
Ghost, whereby the proportions and consonances of the scale were
responsible for the beauty and stability of the world's structure.
This longevity of the cosmic scales is actually surprising, since the
idea of planets giving off tones was sharply criticized even in ancient
times, indeed by none other than Plato's most famous student,
Aristotle. In his writing “On the Heavens” (in four books), he first
proposes the idea, prevalent at the time, of heavenly bodies truly
giving off tones, only to refute the argument, concluding thus: “Indeed
the reason why we do not hear, and show in our bodies none of the
effects of violent force, is easily given: it is that there is no
noise.”
This criticism was obviously little heeded in ancient times; it was
only brought to light at the time of high scholarship in the 13th century, when the West became aware of Aristotle's writings and thus also the cited opinion on the planetary scales.
The effects were manifested above all among music theorists, who had taken the idea of a “musica mundana,” a cosmic music with laws of proportion, from Boethius via the ancients, naturally inspired by Plato. In the 14th century
this grew to a lively controversy, in the course of which the old idea
of true acoustic phenomena in the cosmos faded further and further into
the background, while another idea caught on: that this alleged music
of the spheres actually consisted only of spiritual laws, arithmetical
and musical laws of proportion, like the ones already known to be the
foundations of earthly music. It could be seen that these laws produced
a gentle and beautiful harmony of the heavens, or that through them,
beauty and perfection were qualities of the heavens.
The final result of this debate was that thereafter-especially in the
Renaissance-the existence of real cosmic tones was denied, and instead
a philosophical and aesthetic “universal harmony” was adopted, whereby
henceforth a modified concept of harmony was applied, which is well
known to us. But the grave mistake that was finally made, and whose
perpetrator is unknown, was to shove this modern concept of harmony
back into ancient times, where the word-as noted above-had a completely
different meaning, so that erroneous ideas in this regard are
widespread today.
Now, admittedly, it is clear that Plato was not referring to real tones
from the spheres in the texts cited, but that these were symbols, as
they had customarily been for the Pythagoreans, to whose influence
these secret texts explicitly referred. The extent of this “harmonic
symbolism,” described by Albert von Thimus, must now be restricted once again, since Thimus took his hypotheses much too far;
yet Plato's texts belong indisputably to the true foundations of this
domain. We can only guess at what Plato intended to express
symbolically, but it is a good guess that he was referring to the
existence of harmonic principles as important components of the cosmos,
as was discussed even earlier in other sophisticated cultures (albeit in different forms and without proven connections).
The first person to recognize the symbolic character of the versions of
the harmony of the spheres common at the time was Johannes Kepler
(1571-1630), who had set it as his life goal to prove the background
behind these old ideas scientifically, and who eventually found this
proof. We must present this fact here as given; but some evidence exists that Kepler was well aware of the peculiarity of his procedure.
It should first be emphasized that Kepler remained skeptical about the symbolism, and also refuted Plato's Timaeus scale. Various remarks by him on this subject are preserved for us, e.g. the following:
“Nothing is proven through symbols, nothing hidden will be revealed in
the philosophy of nature with the help of geometric symbols. Only
things already known can be set in relation.” Kepler's verdict on
Fludd, one of the Renaissance scholars who knew all about universal
harmony but explained it unscientifically, is also typical: “One can see that he is satisfied with incomprehensible puzzle-pictures of reality, whereas I
start with these and bring things covered in the darkness of nature
straight into the bright light of knowledge. His is the task of the
chemist, the hermeticist, the paracelsist, while mine is the task of
the mathematician.”
But the title of the work in which he published his proof is even more revealing: Harmonices mundi libri V-and not Harmoniae mundi...! Max Caspar translates this correctly into Weltharmonik,
and here it should also be clear that harmony and harmonics are
completely different concepts. Harmonics is a neutral scientific method
of perception-neutral because all dissonances are inseparably connected
to proportions-while the word “harmony” has an exclusively positive
meaning and applies mainly to aesthetic realms. Nonetheless, there is a
connection between the two concepts: since harmony, strictly speaking,
assumes a plurality of objects whose relationship is perceived as
pleasing, and since, on the other hand, through Kepler in astronomy and
through present-day fundamental harmonic research
in all sciences, a significant prevalence of consonances-and therefore
pleasing perceptions-is proven with the natural laws of harmonics, this
condition can be described as harmony.
b) “Zehn Jahre harmonikale Grundlagenforschung,” Schriften über Harmonik no. 1, Bern 1976