<div id="LayerE10" style="visibility: visible; overflow: visible; z-index:0; left:10px; top:5px; position:absolute; "><?xml version="1.0" encoding="iso-8859-1"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> <head> <!-- ======================================================= --> <!-- Created by AbiWord, a free, Open Source wordprocessor. --> <!-- For more information visit http://www.abisource.com. --> <!-- ======================================================= --> <meta http-equiv="content-type" content="text/html;charset=UTF-8" /> <title>Harmonics & Astronomy - Haase on Plato's Harmony of The Spheres.html</title> <style type="text/css"><!-- #toc, .toc, .mw-warning { border: 1px solid #aaa; background-color: #f9f9f9; padding: 5px; font-size: 95%; } #toc h2, .toc h2 { display: inline; border: none; padding: 0; font-size: 100%; font-weight: bold; } #toc #toctitle, .toc #toctitle, #toc .toctitle, .toc .toctitle { text-align: center; } #toc ul, .toc ul { list-style-type: none; list-style-image: none; margin-left: 0; padding-left: 0; text-align: left; } #toc ul ul, .toc ul ul { margin: 0 0 0 2em; } #toc .toctoggle, .toc .toctoggle { font-size: 94%; }@media print, projection, embossed { body { padding-top:1.0000in; padding-bottom:1.0000in; padding-left:1.2500in; padding-right:1.2500in; } } body { text-indent:0in; text-align:left; font-weight:normal; text-decoration:none; font-variant:normal; color:#000000; font-size:12pt; font-style:normal; widows:2; font-family:'Times New Roman'; } table { } td { border-collapse:collapse; text-align:left; vertical-align:top; } p, h1, h2, h3, li { color:#000000; font-family:'Times New Roman'; font-size:12pt; text-align:left; vertical-align:normal; } *.footnote_text { font-size:10pt; } *.footnote_reference { font-size:10pt; vertical-align:super; } --></style> </head> <body> <div> <div style="text-align: center;" dir="ltr"><span style="font-weight: bold;" lang="en-US" xml:lang="en-US"> <table style="border-collapse: collapse;" width="600" cellspacing="0" cellpadding="3" bordercolor="#000000" border="0"><tbody><tr><td width="100%" valign="top"> <div> <span style="font-weight: bold;" lang="en-US" xml:lang="en-US"> </span> <div style="text-align: center;" dir="ltr"><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">Remarks on Plato's “Harmony of the Spheres”</span></div> <p style="text-align: center;" dir="ltr"><span lang="en-US" xml:lang="en-US">By Rudolf Haase</span></p> <p style="text-align: center;" dir="ltr"><span lang="en-US" xml:lang="en-US">Translated by Ariel Godwin</span></p> <p style="text-align: center;" dir="ltr"><span lang="en-US" xml:lang="en-US">(Part of an introductory lecture)</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US">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.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> 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 </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Republic</span><span lang="en-US" xml:lang="en-US">.</span><span class="footnote_reference" id="footnote_ref-1"><a href="#footnote_anchor-1">1</a></span><span lang="en-US" xml:lang="en-US"> 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.</span><span class="footnote_reference" id="footnote_ref-2"><a href="#footnote_anchor-2">2</a></span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> 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 </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Harmonia</span><span lang="en-US" xml:lang="en-US">, 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.”</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> 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 </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Timaeus</span><span lang="en-US" xml:lang="en-US">,</span><span class="footnote_reference" id="footnote_ref-3"><a href="#footnote_anchor-3">3</a></span><span lang="en-US" xml:lang="en-US"> which-likewise approached as a secret text-also yields a scale as its solution.</span><span class="footnote_reference" id="footnote_ref-4"><a href="#footnote_anchor-4">4</a></span><span lang="en-US" xml:lang="en-US"> These scales were also known in the late middle ages, and in the school of Chartres, whose learned monks were strongly influenced by the </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Timaeus</span><span lang="en-US" xml:lang="en-US">-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.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> 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.”</span><span class="footnote_reference" id="footnote_ref-5"><a href="#footnote_anchor-5">5</a></span><span lang="en-US" xml:lang="en-US"> This criticism was obviously little heeded in ancient times; it was only brought to light at the time of high scholarship in the 13</span><span style="vertical-align: super;" lang="en-US" xml:lang="en-US">th</span><span lang="en-US" xml:lang="en-US"> century, when the West became aware of Aristotle's writings and thus also the cited opinion on the planetary scales.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> The effects were manifested above all among music theorists, who had taken the idea of a “</span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">musica mundana</span><span lang="en-US" xml:lang="en-US">,” a cosmic music with laws of proportion, from Boethius via the ancients, naturally inspired by Plato. In the 14</span><span style="vertical-align: super;" lang="en-US" xml:lang="en-US">th</span><span lang="en-US" xml:lang="en-US"> century</span><span class="footnote_reference" id="footnote_ref-6"><a href="#footnote_anchor-6">6</a></span><span lang="en-US" xml:lang="en-US"> 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.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> 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.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> 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,</span><span class="footnote_reference" id="footnote_ref-7"><a href="#footnote_anchor-7">7</a></span><span lang="en-US" xml:lang="en-US"> must now be restricted once again, since Thimus took his hypotheses much too far;</span><span class="footnote_reference" id="footnote_ref-8"><a href="#footnote_anchor-8">8</a></span><span lang="en-US" xml:lang="en-US"> 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</span><span class="footnote_reference" id="footnote_ref-9"><a href="#footnote_anchor-9">9</a></span><span lang="en-US" xml:lang="en-US"> (albeit in different forms and without proven connections).</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> 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.</span><span class="footnote_reference" id="footnote_ref-10"><a href="#footnote_anchor-10">10</a></span><span lang="en-US" xml:lang="en-US"> We must present this fact here as given;</span><span class="footnote_reference" id="footnote_ref-11"><a href="#footnote_anchor-11">11</a></span><span lang="en-US" xml:lang="en-US"> but some evidence exists that Kepler was well aware of the peculiarity of his procedure.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> It should first be emphasized that Kepler remained skeptical about the symbolism, and also refuted Plato's </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Timaeus</span><span lang="en-US" xml:lang="en-US"> scale. Various remarks by him on this subject are preserved for us, e.g. the following:</span><span class="footnote_reference" id="footnote_ref-12"><a href="#footnote_anchor-12">12</a></span><span lang="en-US" xml:lang="en-US"> “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:</span><span class="footnote_reference" id="footnote_ref-13"><a href="#footnote_anchor-13">13</a></span><span lang="en-US" xml:lang="en-US"> “One can see that </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">he</span><span lang="en-US" xml:lang="en-US"> is satisfied with incomprehensible puzzle-pictures of reality, whereas </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">I</span><span lang="en-US" xml:lang="en-US"> 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.”</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> But the title of the work in which he published his proof is even more revealing: </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Harmonices mundi libri V</span><span class="footnote_reference" id="footnote_ref-14"><a href="#footnote_anchor-14">14</a></span><span lang="en-US" xml:lang="en-US">-and not </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Harmoniae mundi</span><span lang="en-US" xml:lang="en-US">...! Max Caspar translates this correctly into </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Weltharmonik</span><span lang="en-US" xml:lang="en-US">,</span><span class="footnote_reference" id="footnote_ref-15"><a href="#footnote_anchor-15">15</a></span><span lang="en-US" xml:lang="en-US"> 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</span><span class="footnote_reference" id="footnote_ref-16"><a href="#footnote_anchor-16">16</a></span><span lang="en-US" xml:lang="en-US"> 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.</span></p> <p> </p> <div> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-1"><a href="#footnote_ref-1">1</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> Plato: Republic, 616B ff.</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-2"><a href="#footnote_ref-2">2</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> M. Schneider: “Die musikalischen Grundlagen der Sphärenharmonie,” in: Acta musicologica, vol. 32, Basel 1960</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-3"><a href="#footnote_ref-3">3</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> Plato: Timaeus, 35A ff.</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-4"><a href="#footnote_ref-4">4</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> R. Haase: “Harmonikale Synthese,” Vienna 1980 (Beiträge zur harmonikalen Grundlagenforschung, 12), p. 25 ff.</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-5"><a href="#footnote_ref-5">5</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> Aristotle: On the Heavens (tr. J.L. Stocks), book 1, part 9.</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-6"><a href="#footnote_ref-6">6</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> V. Zoubov: “Nicole Oresme et la musique,” in: Medieval and Renaissance Studies, 5, London 1961</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-7"><a href="#footnote_ref-7">7</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> A. v. Thimus: Die harmonikale Symbolik des Alterthums, 2 vols., Köln 1868-1876, reprint Hildesheim 1972</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-8"><a href="#footnote_ref-8">8</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> L. Spitzer: “Die harmonikale Symbolik des A. Frh. von Thimus. Ein Beitrag zur Geschichte der Harmonik,” Vienna 1978 (Beiträge zur harmonikalen Grundlagenforschung, 8)</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-9"><a href="#footnote_ref-9">9</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> M. Schneider: “Klangsymbolik in fremden Kulturen,” Vienna 1979 (Beiträge zur harmonikalen Grundlagenforschung, 11)</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-10"><a href="#footnote_ref-10">10</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> J. Kepler: Weltharmonik (tr. and ed. by M. Caspar), Darmstadt 1982</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-11"><a href="#footnote_ref-11">11</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> R. Haase: “Keplers Weltharmonik in Vergangenheit, Gegenwart und Zukunft,” in: Sudhoffs Archiv, vol. 57, no. 1, Wiesbaden 1973</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-12"><a href="#footnote_ref-12">12</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> J. Kepler, op. cit., Introduction, p. 26</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-13"><a href="#footnote_ref-13">13</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> J. Kepler, op. cit., p. 362</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-14"><a href="#footnote_ref-14">14</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> J. Kepler, Harmonices mundi libri V, Lincii 1619</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-15"><a href="#footnote_ref-15">15</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> See footnote 10</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-16"><a href="#footnote_ref-16">16</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> R. Haase: a) Der messbare Einklang. Grundzüge einer empirischen Weltharmonik, Edition Alpha, Stuttgart 1976;</span></p> <p><span lang="en-US" xml:lang="en-US"><br /> b) “Zehn Jahre harmonikale Grundlagenforschung,” Schriften über Harmonik no. 1, Bern 1976</span></p> </div></div></td></tr></tbody></table></span></div></div> </body> </html></div>
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