<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 lang="en" xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"> <head> </head> <body> <p> <table style="border-collapse: collapse;" bordercolor="#000000" cellspacing="0" cellpadding="3" width="600" border="0"> <tbody> <tr> <td valign="top" width="100%"> <div> <?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE html PUBLIC "-//ABISOURCE//DTD XHTML plus AWML 2.2//EN" "http://www.abisource.com/2004/xhtml-awml/xhtml-awml.mod"> <html xmlns="http://www.w3.org/1999/xhtml" xmlns:awml="http://www.abisource.com/2004/xhtml-awml/"> <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>Cosmology & Cosmogony - I Ching.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; } --> </style> </head> <body> <div> <p dir="ltr" style="text-align:left"><span style="font-weight:bold;font-style:italic" xml:lang="en-US" lang="en-US">§50.8. The I Ching Diagram</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> One of the most remarkable books of humankind is the Chinese </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US">, the “Book of Changes.” It was originally made up only of marks, consisting of unbroken - and broken - - lines; this fact, and possibly more importantly the respect and high veneration for the commentaries and legends surrounding the book in the most ancient times of Chinese intellectual history, allowed it to escape the great book burnings of Qin Shi Huang. In the introduction to his translation of the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US"> (Jena, Diederichs, 1924, 2 vols.), R. Wilhelm writes: </span></p> <p dir="ltr" style="text-align:justify"></p> <p dir="ltr" style="text-align:justify;margin-right:0.4160in;margin-left:0.5194in"><span style="font-size:11pt" xml:lang="en-US" lang="en-US">“Up to modern times, the most distinguished Chinese scholars study it. Almost all the great and important ideas that have emerged for over 3,000 years of ancient Chinese history have in part been inspired by this book, and in part have had an influence on its further clarification, so that one can reasonably state that the most mature wisdom of the millennia is worked into the </span><span style="font-style:italic;font-size:11pt" xml:lang="en-US" lang="en-US">I Ching</span><span style="font-size:11pt" xml:lang="en-US" lang="en-US">. Its existence is attributed to the four holy, mythical figures, meaning that its age spans all of living history. The eight basic signs [see below] do not even have names in the Chinese language, and thus it has been assumed that they are foreign in origin. The version of the </span><span style="font-style:italic;font-size:11pt" xml:lang="en-US" lang="en-US">I Ching</span><span style="font-size:11pt" xml:lang="en-US" lang="en-US"> that we have today goes back to Confucius, who was approximately contemporary with Pythagoras, Buddha, and Lao Tzu (ca. 600 b.c.). Confucius meditated upon the diagrams, wrote down his thoughts, surely preserving yet older interpretations, and thus over the course of the centuries there finally emerged a great commentary, which only in modern times was separated from the tangled mass of superstitious marginalia that had crept in, and which now can be shared as a unified whole with our European thought.”</span></p> <p dir="ltr" style="text-align:justify"></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> There are two basic ideas in the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US">. One is the idea of change, i.e. the continual change of all relationships in a world of opposites: Yang = light, male, heaven, and Yin = dark, female, earth. The other idea is the ideology. Everything that happens is the image-concept, i.e. the effect of an image, an idea, in the invisible.</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> In these two fundamental thoughts, Confucius and Lao Tzu completely agree. Lao Tzu, in his 42</span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">nd</span><span xml:lang="en-US" lang="en-US"> speech, writes: “One has brought forth two, two has brought forth three,” to which one of the old Confucian commentators remarks: “These words mean: One has divided itself into Yin = the female principle and Yang = the male principle. These two have joined, and from their union, harmony emerges (as the 3</span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">rd</span><span xml:lang="en-US" lang="en-US">). The exhalation of harmony (Ki-ho), however, compressing itself, has produced all beings” (Thimus, </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Harmonikale Symbolik</span><span xml:lang="en-US" lang="en-US"> I, 80 and 193). Later in his 42</span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">nd</span><span xml:lang="en-US" lang="en-US"> speech, Lao Tzu writes: “All beings flee from stasis and seek movement. An empty breath, connecting things, generates harmony.” Even more descriptive are the words right at the beginning of the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Tao Te Ching</span><span xml:lang="en-US" lang="en-US">: “The nameless Nothing is the originator of heaven and earth ... the endless Nothing can only be seen in its invisible spiritual existence, the finite Something is seen in the form of its limitation. These two opposites are one because of their primordial existence, only they are designated in different ways. Both are called depths. They are depths, twofold depths. That is the gate to all extrasensory things” (from Thimus I, 193-194).</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> We also learn (Thimus I, 81) that the “Tao” (inadequately translated as “understanding,” “sense,” “path,” “right way,” etc.) stands on these two principles Yang and Yin as something no longer adherent to the corporeal, purely rational, and intelligible. The Tao is also known as Chang-ti, the highest lord of heaven = God. Thus we can add the following to the beginning of the “P”:</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:center"><img alt="" src="/EZ/kayser2/kayser2/imagelibrary/Cosmo_IChing/0.png" /></p> <p dir="ltr" style="text-align:center"><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">Figure 464</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US">in order to find these basic ideas of Chinese philosophy once again in precise harmonic correspondence. A. von Thimus had the idea of bringing this identity (I, 83 ff.), the principles Yang and Yin, for which the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US"> uses an unbroken - and broken - - line, in connection with the reciprocal partial-tone series. Namely, in the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US"> the following four images, the Se-Siang, are constructed from these lines:</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:center"><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">--</span><span xml:lang="en-US" lang="en-US"> </span><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">- -</span><span xml:lang="en-US" lang="en-US"> </span><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">-</span><span xml:lang="en-US" lang="en-US">-</span><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">-</span><span xml:lang="en-US" lang="en-US"> </span><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">-</span><span xml:lang="en-US" lang="en-US"> </span><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">-</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> Since Confucius, in his commentaries, identifies these images with “Siang,” i.e. mutuality, reciprocity-a reciprocity from which the entire system of the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US"> hexagrams is built-the idea of the model of the reciprocal “P” suggests itself in these first four Se-Siang:</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:center"><img alt="" src="/EZ/kayser2/kayser2/imagelibrary/Cosmo_IChing/1.png" /></p> <p dir="ltr" style="text-align:center"><span style="font-style:italic" xml:lang="en-US" lang="en-US">The four basic images (Se-Siang = reciprocities)</span></p> <p dir="ltr" style="text-align:center"><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">Figure 465</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> The “Se-Siang” are thus to be assessed as the four </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">basic tendencies</span><span xml:lang="en-US" lang="en-US"> from which the system of the world comes, surrounded by the heavenly number of the “great Yang” </span><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">--</span><span xml:lang="en-US" lang="en-US"> and the earthly number of the “great Yin” </span><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">-</span><span xml:lang="en-US" lang="en-US"> </span><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">-</span><span xml:lang="en-US" lang="en-US"> and completed by the two permeating tendencies that realize the structure of the world, the “small Yang” </span><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">- -</span><span xml:lang="en-US" lang="en-US"> and the “small Yin” </span><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">-</span><span xml:lang="en-US" lang="en-US">-</span><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">-</span><span xml:lang="en-US" lang="en-US">.</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> From these four primal signs, the famous eight trigrams are constructed, through the addition of new lines; they are then the basis for the hexagrams of the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US"> that emerge through their permutation. These eight signs, which are not images of things, but images of tendencies of relation and change (</span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US"> = the Book of Changes), have the following arrangement and meaning, according to R. Wilhelm, Vol. I, p. V (see the table below).</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> From these diagrammatic roots, out of which the coupling of each pair yields 64 combinations, the hexagrams of the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US"> are constructed. For harmonic analysis, we choose from these the four that A. Amiot gives as the basis for the elicitation of the Chinese tone-system, in his “Mémoire sur la musique des Chinois,” in </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Mémoires concernant le chinois</span><span xml:lang="en-US" lang="en-US">, vol. 6, Paris 1779 (from Thimus I, 86):</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:center"><img alt="" src="/EZ/kayser2/kayser2/imagelibrary/Cosmo_IChing/2.png" /></p> <p dir="ltr" style="text-align:center"><img alt="" src="/EZ/kayser2/kayser2/imagelibrary/Cosmo_IChing/3.png" /></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:left"><span xml:lang="en-US" lang="en-US"> Thimus (I, 87 ff.) now proceeds by using for the unbroken lines of the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Kien</span><span xml:lang="en-US" lang="en-US"> the product of a · b · c · d · e · f, or</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:center"><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">a · b · c · d · e · f</span></p> <p dir="ltr" style="text-align:center"><span xml:lang="en-US" lang="en-US">1</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:left"><span xml:lang="en-US" lang="en-US">and for the broken lines of the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Kouen</span><span xml:lang="en-US" lang="en-US">, the corresponding reciprocal term</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:center"><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">______1______</span></p> <p dir="ltr" style="text-align:center"><span xml:lang="en-US" lang="en-US">a · b · c · d · e · f</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> In the ancient Hebrew book of </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Sepher Jezirah</span><span xml:lang="en-US" lang="en-US">, Ch. 4 reads: “Two letters build 2 houses, 3 build 6 houses, 4 build 24 houses, 5 build 120 houses, 6 build 720 houses, and from there it goes on, and think what the mouth cannot speak and the ear cannot hear.” If one substitutes for a b c d e f the first numbers of the number-series as first product one obtains the factorial number 6! = 720, and for the second reciprocal product, the fraction </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">6!</span><span xml:lang="en-US" lang="en-US"> = </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">720</span><span xml:lang="en-US" lang="en-US"> as a numeric expression for the hexagrams </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Kien</span><span xml:lang="en-US" lang="en-US"> and </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Kouen</span><span xml:lang="en-US" lang="en-US">. Regarding the number 720, the 11</span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">th</span><span xml:lang="en-US" lang="en-US"> verse from the unity song of Dirghatama from the hymns of</span><span style="font-style:italic" xml:lang="en-US" lang="en-US"> </span><span xml:lang="en-US" lang="en-US">the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Rig Veda </span><span xml:lang="en-US" lang="en-US">appears to me to be relevant:</span></p> <p dir="ltr" style="text-align:justify"></p> <p dir="ltr" style="text-align:left;margin-left:1.2986in"><span xml:lang="en-US" lang="en-US">“With twelve of the spokes, because they never age,</span></p> <p dir="ltr" style="text-align:left;margin-left:1.2986in"><span xml:lang="en-US" lang="en-US">The wheel of order surrounds the heavens;</span></p> <p dir="ltr" style="text-align:left;margin-left:1.2986in"><span xml:lang="en-US" lang="en-US">On it, O Agni! stand, as twin pairs,</span></p> <p dir="ltr" style="text-align:left;margin-left:1.2986in"><span xml:lang="en-US" lang="en-US">The number of seven hundred and twenty suns.”</span></p> <p dir="ltr" style="text-align:right"><span xml:lang="en-US" lang="en-US">(Deussen, </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Allgemeine Geschichte der Philosophie</span><span xml:lang="en-US" lang="en-US">, Vol. I, 1894, part 1, p. 111).</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:left"><span xml:lang="en-US" lang="en-US"> The two middle hexagrams then have the value</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:center"><img alt="" src="/EZ/kayser2/kayser2/imagelibrary/Cosmo_IChing/4.png" /><span style="font-weight:bold" xml:lang="en-US" lang="en-US"><br /></span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> If one now sets the tone </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">d</span><span xml:lang="en-US" lang="en-US"> as generator tone for </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US"> (for reasons of symmetry of accidentals, instead of </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">c</span><span xml:lang="en-US" lang="en-US">), then the above four hexagrams get the tone-values:</span></p> <p dir="ltr" style="text-align:left"></p> <table cellpadding="0" border="1" rules="all" style="width:100%;border:0.80pt;border-collapse:collapse;empty-cells:show;table-layout:fixed;border-style:solid"> <colgroup> <col /> <col /> <col /> <col /> </colgroup> <tbody style="border:inherit"> <tr style="border:inherit"> <td style="padding: 0.00pt 2.16pt;background-color:#ffffff;color:#000000;border:0.00pt solid #000000"> <p dir="ltr" style="text-align:center"><span style="vertical-align:super" xml:lang="en-US" lang="en-US">720</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">gis</span><span xml:lang="en-US" lang="en-US">ˆ</span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">9</span></p> </td> <td style="padding: 0.00pt 2.16pt;background-color:#ffffff;color:#000000;border:0.00pt solid #000000"> <p dir="ltr" style="text-align:center"><span style="vertical-align:super" xml:lang="en-US" lang="en-US">48</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">15</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">b</span><span xml:lang="en-US" lang="en-US">ˆ</span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">2</span></p> </td> <td style="padding: 0.00pt 2.16pt;background-color:#ffffff;color:#000000;border:0.00pt solid #000000"> <p dir="ltr" style="text-align:center"><span style="vertical-align:super" xml:lang="en-US" lang="en-US">15</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">48</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">fis</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">2</span></p> </td> <td style="padding: 0.00pt 2.16pt;background-color:#ffffff;color:#000000;border:0.00pt solid #000000"> <p dir="ltr" style="text-align:center"><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">720</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">as</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">10</span></p> </td> </tr> <tr style="border:inherit"> <td style="padding: 0.00pt 2.16pt;background-color:#ffffff;color:#000000;border:0.00pt solid #000000"> <p dir="ltr" style="text-align:center"><span style="font-style:italic" xml:lang="en-US" lang="en-US">Kien</span></p> </td> <td style="padding: 0.00pt 2.16pt;background-color:#ffffff;color:#000000;border:0.00pt solid #000000"> <p dir="ltr" style="text-align:center"><span style="font-style:italic" xml:lang="en-US" lang="en-US">Weiki</span></p> </td> <td style="padding: 0.00pt 2.16pt;background-color:#ffffff;color:#000000;border:0.00pt solid #000000"> <p dir="ltr" style="text-align:center"><span style="font-style:italic" xml:lang="en-US" lang="en-US">Kiki</span></p> </td> <td style="padding: 0.00pt 2.16pt;background-color:#ffffff;color:#000000;border:0.00pt solid #000000"> <p dir="ltr" style="text-align:center"><span style="font-style:italic" xml:lang="en-US" lang="en-US">Kouen</span></p> </td> </tr> </tbody> </table> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US">i.e. in the “heavenly number,” </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">720</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">, and the “earthly number, </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">720</span><span xml:lang="en-US" lang="en-US">, the two imaginary poles of an “inaudible harmony” (</span><span style="font-family:'Tahoma'" xml:lang="en-US" lang="en-US">̔</span><span xml:lang="el-GR" lang="el-GR">αρμονία</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-family:'Tahoma'" xml:lang="en-US" lang="en-US">̕</span><span xml:lang="el-GR" lang="el-GR">αφανής</span><span xml:lang="en-US" lang="en-US">) and in the two ratios </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">48</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">15</span><span xml:lang="en-US" lang="en-US"> and </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">15</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">48</span><span xml:lang="en-US" lang="en-US"> the two poles of a scale to be projected from the imaginary into this “real” space. There are two ways of obtaining this. Either we build from the imaginary poles through the “way up” in duodecimal (octave plus fifth) intervals, thus via the circle of fifths (interval power-series of the fifth), whereby we admittedly “land” on the ratio 729:</span></p> <p dir="ltr" style="text-align:justify"></p> <table cellpadding="0" border="1" rules="all" style="width:100%;border:0.80pt;border-collapse:collapse;empty-cells:show;table-layout:fixed;border-style:solid"> <colgroup> <col /> <col /> <col /> </colgroup> <tbody style="border:inherit"> <tr style="border:inherit"> <td style="padding: 0.00pt 2.16pt;background-color:#ffffff;color:#000000;border:0.00pt solid #000000;border-right-width:0.03pt"> <p dir="ltr" style="text-align:center"><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">/</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">729</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">as</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">ˇ</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">10</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">/</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">243</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">es</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">ˇ</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">8</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">/</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">81</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">b</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">ˇ</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">7</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">/</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">27 </span><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">f</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">5</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">/</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">9</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">c</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">3</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">/</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">3</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">g</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">2</span></p> </td> <td style="padding: 0.00pt 2.16pt;background-color:#ffffff;color:#000000;border:0.03pt solid #000000;border-top-width:0.50pt"> <p dir="ltr" style="text-align:center"><span style="font-size:10pt" xml:lang="en-US" lang="en-US">1 </span><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">d</span></p> </td> <td style="padding: 0.00pt 2.16pt;background-color:#ffffff;color:#000000;border:0.00pt solid #000000;border-left-width:0.03pt"> <p dir="ltr" style="text-align:center"><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">3</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">/</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">a</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">ˆ</span><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">9</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">/</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">e</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">ˆ</span><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">3</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">27</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">/</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">h</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">ˆ</span><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">4</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">81</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">/</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">fis</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">ˆˆ</span><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">6</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">243</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">/</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">cis</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">ˆˆ</span><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">8</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">729</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">/</span><span style="font-size:10pt;vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">gis</span><span style="font-size:10pt" xml:lang="en-US" lang="en-US">ˆˆ</span><span style="font-size:10pt;vertical-align:super" xml:lang="en-US" lang="en-US">9</span></p> </td> </tr> </tbody> </table> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:left"><span xml:lang="en-US" lang="en-US">which, reduced by octaves, yields the chromatic scale:</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:center"><span style="font-weight:bold" xml:lang="en-US" lang="en-US">as</span><span xml:lang="en-US" lang="en-US">ˇ </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">a</span><span xml:lang="en-US" lang="en-US">ˆ </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">b</span><span xml:lang="en-US" lang="en-US">ˇ </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">h</span><span xml:lang="en-US" lang="en-US">ˆ </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">c</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">cis</span><span xml:lang="en-US" lang="en-US">ˆˆ </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">d</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">es</span><span xml:lang="en-US" lang="en-US">ˇ </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">e</span><span xml:lang="en-US" lang="en-US">ˆ </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">f</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">fis</span><span xml:lang="en-US" lang="en-US">ˆˆ </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">g</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">gis</span><span xml:lang="en-US" lang="en-US">ˆˆ</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> With tempering of </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">as</span><span xml:lang="en-US" lang="en-US"> and </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">gis</span><span xml:lang="en-US" lang="en-US">ˆ, we have the “scale of 12 Lu” of Chinese music, and Thimus remarks on this (I, 89) that the system of this scale “moves into those modulatory limits (alterations) beyond which the Classical composers of the 16</span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">th</span><span xml:lang="en-US" lang="en-US"> century did not go in their application of chromatics.” Or else, we start from the two “real” poles, which for </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">d</span><span xml:lang="en-US" lang="en-US"> have the values </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">48</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">15</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">b</span><span xml:lang="en-US" lang="en-US">ˆ</span><span style="font-family:'Symbol'" xml:lang="en-US" lang="en-US"></span><span xml:lang="en-US" lang="en-US"> and </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">15</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">48</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">fis</span><span style="font-family:'Tahoma'" xml:lang="en-US" lang="en-US">,,</span><span xml:lang="en-US" lang="en-US"> and construct, upwards or downwards in fourth steps, the series:</span></p> <p dir="ltr" style="text-align:left"></p> <table cellpadding="0" border="1" rules="all" style="width:100%;border:0.80pt;border-collapse:collapse;empty-cells:show;table-layout:fixed;border-style:solid"> <colgroup> <col /> <col /> <col /> </colgroup> <tbody style="border:inherit"> <tr style="border:inherit"> <td style="padding: 0.00pt 2.16pt;background-color:#ffffff;color:#000000;border:0.00pt solid #000000;border-right-width:0.03pt"> <p dir="ltr" style="text-align:center"><span style="vertical-align:super" xml:lang="en-US" lang="en-US">81</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">256</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">fis</span><span xml:lang="en-US" lang="en-US">ˆˆ</span><span style="font-family:'Tahoma'" xml:lang="en-US" lang="en-US">,,</span><span xml:lang="en-US" lang="en-US"> </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">27</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">64</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">h</span><span xml:lang="en-US" lang="en-US">ˆ</span><span style="font-family:'Tahoma'" xml:lang="en-US" lang="en-US">,,</span><span xml:lang="en-US" lang="en-US"> </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">9</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">16</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">e</span><span xml:lang="en-US" lang="en-US">ˆ</span><span style="font-family:'Tahoma'" xml:lang="en-US" lang="en-US">,,</span><span xml:lang="en-US" lang="en-US"> </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">3</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">4</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">a</span><span xml:lang="en-US" lang="en-US">ˆ</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">1</span></p> </td> <td style="padding: 0.00pt 2.16pt;background-color:#ffffff;color:#000000;border:0.03pt solid #000000;border-top-width:0.50pt"> <p dir="ltr" style="text-align:center"><span style="font-size:10pt" xml:lang="en-US" lang="en-US">1 </span><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">d</span></p> </td> <td style="padding: 0.00pt 2.16pt;background-color:#ffffff;color:#000000;border:0.00pt solid #000000;border-left-width:0.03pt"> <p dir="ltr" style="text-align:center"><span style="vertical-align:super" xml:lang="en-US" lang="en-US">4</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">3</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">g</span><span xml:lang="en-US" lang="en-US"> </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">16</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">9</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">c</span><span xml:lang="en-US" lang="en-US">ˆ′ </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">64</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">27</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">f</span><span xml:lang="en-US" lang="en-US">ˆ′ </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">256</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">81</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">b</span><span xml:lang="en-US" lang="en-US">ˇˇ′′</span></p> </td> </tr> </tbody> </table> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:left"><span xml:lang="en-US" lang="en-US">which, after octave transposition, yields the nine-step scale:</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:center"><span style="font-weight:bold" xml:lang="en-US" lang="en-US">a</span><span xml:lang="en-US" lang="en-US">ˆ </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">b</span><span xml:lang="en-US" lang="en-US">ˇˇ </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">h</span><span xml:lang="en-US" lang="en-US">ˆ </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">c</span><span xml:lang="en-US" lang="en-US">ˆ </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">d e</span><span xml:lang="en-US" lang="en-US">ˆ </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">f</span><span xml:lang="en-US" lang="en-US">ˆ </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">fis</span><span xml:lang="en-US" lang="en-US">ˆˆ </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">g</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> These nine steps, with the elimination of </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">b</span><span xml:lang="en-US" lang="en-US"> and </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">fis</span><span xml:lang="en-US" lang="en-US">, contain the diatonic (</span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">C</span><span xml:lang="en-US" lang="en-US">-major) scale, but precisely these two chromatic steps </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">b</span><span xml:lang="en-US" lang="en-US"> and </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">fis</span><span xml:lang="en-US" lang="en-US"> were necessary, as Thimus explains (I, 90), to represent the so-called octave-categories of the system of the eight Gregorian church modes within the steps of the natural key-signature (without alteration of the clef), as well as within the so-called </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">musica ficta</span><span xml:lang="en-US" lang="en-US"> of the signatures with a sharp and a flat in the Guidonian tone-system. From these analyses, it can already be seen that the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US"> hexagrams are the expression of a general regularity in musical terms.</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> However, by means of harmonic analysis, we can explore this regularity further. For this, we return once more to the eight primal signs (</span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Koua</span><span xml:lang="en-US" lang="en-US"> = primal signs)-see Table 466.</span></p> <p dir="ltr" style="text-align:center"></p> <p dir="ltr" style="text-align:center"><img alt="" src="/EZ/kayser2/kayser2/imagelibrary/Cosmo_IChing/5.png" /></p> <p dir="ltr" style="text-align:center"><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">Figure 466</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> Category I lists the eight signs with their names. They are analyzed according to Chinese usage from bottom to top; we set the whole lines equal to the whole numbers, the broken lines equal to their reciprocals. Categories II to IV attempt to harmonically analyze the individual triads a b c through insertion of various number values (V belongs to IV and simply gives the logarithms of IV). Category II proceeds according to Thimus's scheme, and sets a = 1, b = 2, c = 3 for the straight lines and </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">a</span><span xml:lang="en-US" lang="en-US"> = </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">, </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">b</span><span xml:lang="en-US" lang="en-US"> = </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">2</span><span xml:lang="en-US" lang="en-US">, and </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">c</span><span xml:lang="en-US" lang="en-US"> = </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">3</span><span xml:lang="en-US" lang="en-US"> for the broken lines. The insertion of tone-values stands under the sign of the fifth intervals </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">g</span><span xml:lang="en-US" lang="en-US"> and </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">f </span><span xml:lang="en-US" lang="en-US">(here we return to using </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">c</span><span xml:lang="en-US" lang="en-US"> as generator-tone), the “father” designated as </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">g</span><span style="font-family:'Symbol'" xml:lang="en-US" lang="en-US"></span><span xml:lang="en-US" lang="en-US">, the “mother” as </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">f</span><span style="font-family:'Tahoma'" xml:lang="en-US" lang="en-US">,,,</span><span xml:lang="en-US" lang="en-US">. In the ratio of the “children” an agreement of character of the first son with the mother is shown, a similarity of the second son with the mother, and a similarity of the third son with the father; the first daughter is identical in character with the father, whereas the second is similar to the father and the third is similar to the mother. Regarding the “character identity,” however, it must be remarked that since the Chinese also assign a meaning to the location of every line, e.g. the “identity” of father </span><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">===</span><span xml:lang="en-US" lang="en-US"> and first daughter </span><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">=</span><span xml:lang="en-US" lang="en-US">=</span><span style="text-decoration:underline" xml:lang="en-US" lang="en-US">=</span><span xml:lang="en-US" lang="en-US"> is inwardly present (both the value </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">g</span><span style="font-family:'Symbol'" xml:lang="en-US" lang="en-US"></span><span xml:lang="en-US" lang="en-US">), but is different in terms of its “material” spatial structure. The formula of the father is 1 · 2 · 3, that of the first daughter is </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">2 </span><span xml:lang="en-US" lang="en-US">· 2 · 3-identical as tone-value, but different in the octave and the character of the lines, as well as their </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">situs </span><span xml:lang="en-US" lang="en-US">= location. This observation should be kept in mind with all further identities.</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> We come closer to the “family relationship” of these eight signatures through the fifth-analysis of category III. This was well known in Chinese harmonics, and therefore we may use it without scruples. Here, father and mother have the ratio to the generator-tone </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">c</span><span xml:lang="en-US" lang="en-US"> of the minor third and sixth (</span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">a</span><span xml:lang="en-US" lang="en-US">ˆ) and (</span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">es</span><span xml:lang="en-US" lang="en-US">ˇ)-whereby we are reminded of the third as the “gender tone.” Son and daughter here emphasize the three identical values: the fifths </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">f</span><span xml:lang="en-US" lang="en-US"> and </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">g</span><span xml:lang="en-US" lang="en-US">.</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> Most interesting, however, is the analysis of category IV. Here I have inserted the first, second, and third powers of the fifths, i.e. the potentiation that is known to us from the Pythagorean scale and that plays such an important role in Plato's </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Timaeus</span><span xml:lang="en-US" lang="en-US">. It seems likely to me that this was known of and used in ancient Chinese harmonics, since fundamentally it only consists of very simple multiplication. But this is irrelevant to the results of our analysis, since the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US"> diagram gives psychical forms in bar-notation, which we can elicit in other ways with harmonic methods. Here the father- and mother-principle returns in the extreme ratios </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">729</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">fis</span><span xml:lang="en-US" lang="en-US"> and </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">729</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">ges</span><span xml:lang="en-US" lang="en-US">, whose logarithms 510 and 490 only differ by 20 units (reduced by octaves), which their enharmonic character shows, although one is very high (heaven-number) and the other very low (earth-number). This number 729 is otherwise almost twice the number of days in the year (2 × 365 = 730) and thus has symbolic-cosmic significance. The progression of the “sons” climbs upwards in the whole-tone steps </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">c b</span><span xml:lang="en-US" lang="en-US">ˇ </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">as</span><span xml:lang="en-US" lang="en-US">ˇ, the progression of the “daughters” in analogous whole-tone steps </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">c d e</span><span xml:lang="en-US" lang="en-US">ˆ. If we arrange the tones of the “family” of eight scalewise, the result is the strange scale:</span></p> <p dir="ltr" style="text-align:center"></p> <p dir="ltr" style="text-align:center"><img alt="" src="/EZ/kayser2/kayser2/imagelibrary/Cosmo_IChing/6.png" /></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US">so, a definite </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">whole-tone scale</span><span xml:lang="en-US" lang="en-US"> of completely symmetrical “genealogical” construction: parents in the middle, daughters to the left, sons to the right. Moreover, the intervals of this whole-tone scale emerge from the important steps we know of: the major whole-tone of type </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">9</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">8</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">d</span><span xml:lang="en-US" lang="en-US"> 170, and the minor whole-tone of nearly </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">10</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">9</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">d</span><span xml:lang="en-US" lang="en-US">ˇ 152-again, two enharmonic steps-whereas the enharmonic middle interval of the “parents” has 19 log units, an interval that is very close to the so-called synthetic comma of 18 log units (</span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">80</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">81</span><span xml:lang="en-US" lang="en-US"> or </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">81</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">80</span><span xml:lang="en-US" lang="en-US">), and thus once again shows its harmonic-rational significance.</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> I began by investigating all the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US"> hexagrams (from R. Wilhelm's edition) according to the Thimusian scheme (table 466, category II), and calculated the number- and tone-value for every hexagram. The result is that all 64 hexagrams yield only the following ten values in multiple repetitions-here I present them arranged in numerical terms, as well as in musical notation:</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:center"><img alt="" src="/EZ/kayser2/kayser2/imagelibrary/Cosmo_IChing/7.png" /></p> <p dir="ltr" style="text-align:center"><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">Figure 467</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US">This is a chromatic scale without the main steps </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">c f</span><span xml:lang="en-US" lang="en-US"> and </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">g</span><span xml:lang="en-US" lang="en-US">. The many “identities” must naturally be observed from the above viewpoint of the various “locations” of the lines; thus all hexagrams of equal harmonic value are still different in themselves.</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> But the fruitfulness of our analysis of categories IV (and V) in Table 466 allows us to suppose that with this power-analysis we can come closer to finding the inner psychic meaning of the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US"> hexagrams than with the too-simple Thimusian method. Unfortunately, I have not yet found the time to calculate all 64 hexagrams according to this scheme, and therefore can only note the results for the first four (Fig. 468).</span></p> <p dir="ltr" style="text-align:center"></p> <p dir="ltr" style="text-align:center"><img alt="" src="/EZ/kayser2/kayser2/imagelibrary/Cosmo_IChing/8.png" /></p> <p dir="ltr" style="text-align:center"><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">Figure 468</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> 1. Twice the “father” becomes the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Kiän </span><span xml:lang="en-US" lang="en-US">hexagram, the creator. The total value is </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">his </span><span xml:lang="en-US" lang="en-US">log 020, a step that is enharmonic to the generator-tone </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">c</span><span xml:lang="en-US" lang="en-US">.</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> 2. Twice the “mother” becomes the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Kun</span><span xml:lang="en-US" lang="en-US"> hexagram, the receiver. The total value is </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">deses </span><span xml:lang="en-US" lang="en-US">log 980, likewise an enharmonic step to </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">c</span><span xml:lang="en-US" lang="en-US">. The generating and receiving principle, as above in the trigrams of “father” and “mother,” is in an enharmonic relationship, albeit not directly in itself, but rather in terms of an imaginary </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">c</span><span xml:lang="en-US" lang="en-US"> that creates both, i.e. unity. All remaining values of the other hexagrams will show, as for 3 and 4, total values built from two independent trigram values, i.e. a psychic unity. Even if different hexagrams should exhibit identical tone-number characters on the outside, still the inner structure of their step-building is different. This is somewhat comparable to the tone-</span><span style="font-style:italic" xml:lang="en-US" lang="en-US">locations </span><span xml:lang="en-US" lang="en-US">in the “P” system, where, for example, </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">2</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">c</span><span style="font-family:'Symbol'" xml:lang="en-US" lang="en-US"></span><span xml:lang="en-US" lang="en-US"> </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">4</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">2</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">c</span><span style="font-family:'Symbol'" xml:lang="en-US" lang="en-US"></span><span xml:lang="en-US" lang="en-US"> </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">6</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">3</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">c</span><span style="font-family:'Symbol'" xml:lang="en-US" lang="en-US"></span><span xml:lang="en-US" lang="en-US"> etc. are not different in themselves, but are different in the tone-</span><span style="font-style:italic" xml:lang="en-US" lang="en-US">location</span><span xml:lang="en-US" lang="en-US">, i.e. the place in the configuration space.</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> Those who know and “practice” the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US"> will wonder what has been gained for the understanding of this book with this type of harmonic analysis. Each of its hexagrams has, in any case, a title (see the titles of the first four ones just discussed), each has enough commentaries on its “meaning,” etc. But this is not in “tones,” but in a conceptual speech that we can understand. Through various modifications and combinations of these hexagrams, the imagination and intuition are given full rein.</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> But let us take </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">ad exemplum</span><span xml:lang="en-US" lang="en-US"> only the first two hexagrams, </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Kiän</span><span xml:lang="en-US" lang="en-US"> = the creative and </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Kun</span><span xml:lang="en-US" lang="en-US"> = the receptive. In Wilhelm's edition, much is written about these two concepts, more or less describing and interpreting the concepts of the “creative” and the “receptive,” furnishing them with rules and modes of conduct, etc. The harmonic analysis, however, gives the reasons, in a precise and concrete way, for why in these signs the “creative” is connected with the “heavens,” the great light with the “masculine,” etc.; why the “receptive” is connected with the “earth,” “small,” “dark,” “feminine,” etc.: in the trigrams, the appearance of the “gender interval,” the third; the peculiar enharmonic equivalence of both principles; that they are “of one flesh” yet different in essence; the assignment of the undivided lines to </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US"> → </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">∞</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">, the endlessly large, the light, heaven, and the divided lines </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">∞</span><span xml:lang="en-US" lang="en-US"> ←</span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US"> to the limited small, dark, receptive; the remarkable number 729 and its closeness to twice the number of days in the year. In contrast to the non-committalness, the stark claims (whose antiquity is indeed honorable, but tells us nothing about the effective truth content) of the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US"> commentators, harmonic analysis thus reveals the reasons and leads these reasons back to a value-emphasized number-system, from which views of other domains are possible.</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> Naturally, a sensitivity to a differentiated tone- and interval-perception, a thoroughly trained psychical grasp of the characteristic steps through the ear (in monochord experiments), and spiritual insight into the symbolism of these steps that emerges from this, are central to harmonic analyses of this type. Anyone who inherently has, or has developed, an ear for this will also be able to judge whether the analyses of the further 64 </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US"> diagrams show similar results. It is this sensitivity, this “sixth sense” of akróasis, that lies at the root of all harmonic investigations, thoughts, and perceptions, and I can imagine that in future times, there may be an ingenious harmonist who will concentrate the basics of harmonics in a book similar to the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US">.</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:left"><span style="font-weight:bold;font-style:italic" xml:lang="en-US" lang="en-US">§50.9. Advice for the Harmonic Analysis of Number Symbols</span><span xml:lang="en-US" lang="en-US"> </span><span style="font-weight:bold" xml:lang="en-US" lang="en-US">(cf. §50.4)</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> This chapter in itself far exceeds the space permitted by the limits of a textbook. But the domain of number symbolism itself is enormously large, and treated (and here very meagerly) in the strict scientific sense as something simply “historical,” “folkloric,” etc., while, as is shown by the above examples and all the work of A. von Thimus, there is still an almost inexhaustible field of harmonic research at our disposal. Therefore, I thought I should show a few concrete examples of how and by what means harmonic analysis should proceed here. The “uninitiated” will admittedly find the analyses of the </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">I Ching</span><span xml:lang="en-US" lang="en-US"> diagrams very complicated; but anyone who has solidly worked through this book up to this point will be impressed by the simplicity of these investigations.</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> We have seen not only that the tone-numbers, intervals, selections such as scales, interval powers, etc. can and should be used for the analysis of number symbolism, but that also the harmonic configuration space (“P” and its modifications) must be taken into consideration. In my essay on Pythagoras, for example, the interpretation of the Pythagorean number-cosmos was only possible by means of analogies with the polar “P”, which however hit the target. One should carefully note the possible approaches from case to case, and not give oneself up to haphazard tone-analysis. In many cases, harmonics will fail, and then it is better to be content with a negative result than to use harmonics like a straitjacket. With the relics of the ancient number-harmonics, we must not forget-as Thimus noted again and again regarding the ancient sources-that in ancient wisdom, especially in its Gnostic form, much was kept deliberately secret, and thus often misunderstood and wrongly recorded later. The first task, then, is to separate the wheat from the chaff, as far as possible; only then will harmonic analysis have meaning and purpose.</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:left"><span style="font-weight:bold;font-style:italic" xml:lang="en-US" lang="en-US">§50.10. “Life-Numbers”</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> Since the belief in a significance of certain “life-numbers” is widespread, and certain temporal-spatial periodicities and rhythms are also not to be repudiated, I will give a simple overview here of how one must proceed with the harmonic analysis of such “numbers.” The method has already been mentioned in my </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Abhandlungen</span><span xml:lang="en-US" lang="en-US">, pp. 49-50.</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> One should draw up a table similar to Fig. 469, which is simply an “overtone series” dissolved into interval constants and powers-naturally those who hope to live 100 years can lengthen it as much as they wish beyond the ratio 81.</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> Suppose we analyze the dates of our own lives from the viewpoint of this scheme, first purely biologically. It may appear that the individual spaces of the interval constants are equal in value amongst themselves, despite respective doubling of their periods. What we biologically “experience” between the first and second year is thus equal in value to what we experience between the second and the fourth, the fourth and the eighth, the eighth and sixteenth, etc. The same goes for the fifth-octaves 3, 6, 12 ..., the third-octaves 5, 10, 20, etc. A closer examination will also ascribe certain intervals to periods of a definite type, for example, the seventh-octave 7, 14, 28, 56 to a sexual type, etc. But not only the biological, also the psychical and spiritual “stations” of our life appear to consolidate in these harmonic “numbers.” I myself have found peculiar equivalents with regard to important stages of life. There are apparently “octave-,” “third-,” etc. breaks, which are connected with important changes in our fate, or which provoke them. Any reader can easily perform his own analyses here, on himself, his family, etc. No extensive investigations of this type have yet been made. One can further imagine that some important event in life also makes the relevant life-number “independent,” i.e. changes it to </span><span style="vertical-align:super" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US">/</span><span style="vertical-align:sub" xml:lang="en-US" lang="en-US">1</span><span xml:lang="en-US" lang="en-US"> and from there on the intervals follow autonomously. Furthermore, the predominant intervallic </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">character</span><span xml:lang="en-US" lang="en-US"> of the life in question could be retrospectively defined and studied from the data obtained; for example, the relevant intervals within a family, a line of ancestors, or simply between two or more different life-number successions could be consonant or dissonant. These are no Utopias; but the investigation of such connections requires particular assiduousness and strict disavowal of all “augury,” since one can never know or say with precision to what extent, for example, a certain life-number is autonomous and radiates out into the future. But for insight into a biological-psychic arrangement of every life's fate, this method appears to me from my own experience to be </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">retrospectively</span><span xml:lang="en-US" lang="en-US"> important. (The oldest testimony to the significance of the number 7 in human stages of life is in the elegy of the “Hebdomad” of Solon. He prescribes at age 7 the second teeth, at 14 puberty, at 21 beard growth, at 28 the maximum bodily strength, at 35 the time to marry and have children, at 42 the full formation of character, at 49 and 56, thus through 2 hebdomads, the mature development of understanding and discourse, in the ninth hebdomad their deterioration, and in the tenth, preparation for the end.)</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:center"><img alt="" src="/EZ/kayser2/kayser2/imagelibrary/Cosmo_IChing/9.png" /></p> <p dir="ltr" style="text-align:center"><img alt="" src="/EZ/kayser2/kayser2/imagelibrary/Cosmo_IChing/10.png" /></p> <p dir="ltr" style="text-align:center"><span style="font-weight:bold;font-size:10pt" xml:lang="en-US" lang="en-US">Figure 469</span></p> <p dir="ltr" style="text-align:left"></p> <p dir="ltr" style="text-align:left"><span style="font-weight:bold;font-style:italic" xml:lang="en-US" lang="en-US">§50.11. Bibliography</span></p> <p dir="ltr" style="text-align:justify"><span xml:lang="en-US" lang="en-US"> Besides the works named in the text: for 2: §4 of this text; H. Kayser, </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Hörende Mensch</span><span xml:lang="en-US" lang="en-US">, 29ff., 133, 233; </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Klang</span><span xml:lang="en-US" lang="en-US">, 34-39. For 3: </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Hörende Mensch</span><span xml:lang="en-US" lang="en-US">, 131 ff.; </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Grundriß</span><span xml:lang="en-US" lang="en-US">, 265. For 5: </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Grundriß</span><span xml:lang="en-US" lang="en-US">, 265 ff. Further: F.C. Endres, </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Die Zahl in Mystik und Glauben der Naturvölker</span><span xml:lang="en-US" lang="en-US">, Zürich 1935; Erich Bischoff: </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Babylonisch Astrales im Weltbilde des Talmuds und Midrasch</span><span xml:lang="en-US" lang="en-US">, Leipzig 1907; </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Mystik und Magie der Zahlen</span><span xml:lang="en-US" lang="en-US">, Berlin 1920; </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Die Elemente der Kabbalah</span><span xml:lang="en-US" lang="en-US">, 2 vols., Berlin 1914. O. Fischer: </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Der Urspruch des Judentums im Lichte alttestamentlicher Zahlensymbolik</span><span xml:lang="en-US" lang="en-US">, Leipzig 1917; </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Orientalische und greichische Zahlensymbolik</span><span xml:lang="en-US" lang="en-US">, 1918. H. Jennings: </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Die Rosenkreuzer</span><span xml:lang="en-US" lang="en-US">, Berlin 1912 (caution!); Julius Stenzel: </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Zahl und Gestalt bei Platon und Aristoteles</span><span xml:lang="en-US" lang="en-US">, Berlin 1924. For 6: H. Kayser: </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Grundriß</span><span xml:lang="en-US" lang="en-US">, 203 ff. For 7: L.B. Hellenbach: </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Die Magie der Zahlen</span><span xml:lang="en-US" lang="en-US">, Leipzig 1925 (caution!). F. Maack: </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Die Heilige Mathesis</span><span xml:lang="en-US" lang="en-US">, Leipzig 1924. Franz Dornseiff: </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Das Alphabet in Mystik und Magie</span><span xml:lang="en-US" lang="en-US">, Leipzig 1922. For 7: H. Kayser: </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Grundriß</span><span xml:lang="en-US" lang="en-US">, 164 ff. For 5: there is rich material which we have not mentioned (except for the Hebdomad of Solon), with bibliography, in Franz Boll: </span><span style="font-style:italic" xml:lang="en-US" lang="en-US">Die Lebensalter</span><span xml:lang="en-US" lang="en-US">, Berlin and Leipzig 1913 (especially on the number seven).</span></p> <p dir="ltr" style="text-align:left"></p> <p></p> </div> </body> </html> </div></td></tr></tbody></table></p> </body> </html></div>
History of Harmonics
Ancient Civilizations
Haase - Hermann Bahr & Harmonic Thought
Haase - Leibniz & Kayser
Summary of History
Harmonics & Mathematics
Magic Squares
Number Distribution
Number Symbolism
Fractal Harmonies
Harmonics & Geometry
Musical Ratios
Parabola, Hyperbola, Ellipse
The Proportions
Tone Spirals & Tone Curves
Harmonics & Astronomy
Kepler
Haase on Plato's Harmony of The Spheres
Harmony of The Spheres
Kepler`s Platonic Solids
Planetary Harmonics
Cosmology & Cosmogony
Harmonic Cosmogony
I Ching
Pythagoreanism
Robert Fludd
Robert Fludd Images
Octaves & Spirals
Harmonics & Architecture
Harmonics & Architecture
Architectural Examples
Harmonics & Language
Harmonics & Language
Harmonics & Symbolism
Cosmic Harmony in Symbolism
Doctrine of Correspondences
Harmonics as Symbolism
Hermann Hesse & The Glass Bead Game
Gann & Financial Markets
Partial Tone Diagram & Square of 9
Polar Diagrams & Spiral Charts
Harmonics in Nature
Human Canon
Animals
Plants
Snow Crystals
Harmonics & Music Theory
Harmonics as a Science
Interference
Harmonic Theories & Diagrams
Thought as a Sense
Color & Partial-Tone Coordinates
The Lambdoma
Lambdoma Applications
The Monochord
Library & Resources
Hans Kayser Biography
Hans Kayser's Horoscope
Rudolf Haase Biography
Bibliography of Kayser's Works
Bookstore
Law of the Cosmos
Natural Architecture
The Textbook of Harmonics
News - May 2010
February 2008 Newsletter
Links
