<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 & Symbolism - Doctrine of Correspondences.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> <p 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"> Harmonics as a Doctrine of Correspondences</span> <p style="text-align: left;" dir="ltr"><span style="font-weight: bold; font-style: italic;" lang="en-US" xml:lang="en-US">Jakob Böhme</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> The second founding pillar of akróasis is </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Harmonics as a doctrine of correspondences</span><span lang="en-US" xml:lang="en-US">. We can characterize today's predominantly haptified mode of scientific thought with one of the many sayings of the deep and sharp-</span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">sensed philosophus teutonicus</span><span lang="en-US" xml:lang="en-US"> Jakob Böhme: “For that is the law of conceivability, that it does not emerge in the inconceivable.”</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"> But there is another kind of thought, or rather another attitude of our thought and feeling, which is structured differently, and precisely for that reason exists outside the merely conceivable, the conceptual: the doctrine of correspondences. In my book </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Akróasis</span><span lang="en-US" xml:lang="en-US">,</span><span class="footnote_reference" id="footnote_ref-2"><a href="#footnote_anchor-2">2</a></span><span lang="en-US" xml:lang="en-US"> I tried to depict this mode of thought in connection with Ernst Cassirer. Admittedly I find his chosen term, “mythical” thought, too broad, since mythology already crosses over into symbolism, which latter covers deeper areas than are possible for a mere doctrine of correspondences. Despite this, we will use this term.</span></p> <p style="text-align: left;" dir="ltr"><span style="font-weight: bold; font-style: italic;" lang="en-US" xml:lang="en-US">Ernst Cassirer; “Mythical” Thought</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> The philosopher Ernst Cassirer contrasts the conceptual form of “mythical” thought with modern scientific thought. He characterizes mythical thought as associative thought, in which individual analogies relate to each other in external, often arbitrary ways. “The Mythos, as long as it does not remain in the realm of undefined ideas and emotions, but develops in objective forms, is also a kind of form-giving, a direction peculiar to objectivization, which in a very specific way contains the 'synthesis of the manifold,' the integration and reciprocal arrangement of the sensory elements.”</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"> The most primitive form here is totemism, “which is not merely a principle of social structure, but a universal principle of world-arrangement, and thus includes worldview and world-understanding. Not only the tendrils of the root, but the entire universe ... is put, by the totemistic way of thinking, in groups, which are connected to one another or separated from one another through certain kinds of relationships.” For the Zuni people, for example, there is a “septuarchy,” a sevenfold arrangement of their entire thought and lifestyle: “The Zuni village is divided into seven areas corresponding to the seven directions: North, West, South, East, the upper and lower worlds, and lastly the center of the world. Not only every separate clan of the race, but also every animate or inanimate being, every thing, every process, every element, and every definite time period, belongs to one of these seven areas ... every spatial domain has its own specific color, number, etc.”</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"> The principle is the same in astrological thought, and in mythology in general, which always latches onto a “material part” of the world (the cosmic egg of the Orphics, the primordial ash tree of the Germans, etc.) and then links association to association in a chain, in which causality (cause and effect) merely plays an external role of interrelationship. The mythical worldview is statically, spatially oriented, and thus predestined for rigid images and symbols.</span></p> <p style="text-align: left;" dir="ltr"><span style="font-weight: bold; font-style: italic;" lang="en-US" xml:lang="en-US">Scientific Thought</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> The modern scientific worldview is completely different: “The form of the scientific explanation of nature, the main principles of which have stood irreversible since the Renaissance, since Galileo and Kepler, mainly consists of unraveling all Being into Becoming, into spatial-temporal relationships, and using the laws of these relationships as a basis.”</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"> Further: “In the mathematical theory of natural events, which expresses these ideas the most purely and completely, all content and all events must first be converted into a complex of quantities that are generally regarded as changeable from moment to moment, in order for the explanation to be accessible at all. The task of the theory, then, is to ascertain how all these changes affect and dictate each other.”</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"> And: “That is why our modern scientific thought, in order to be able to conceive of any kind of Being, must first relate it to elementary changes and, as it were, break it down into them. The form of the whole, as it is present for sensory perception or for pure observation, disappears: in its place is the idea of a specific regulation of Being.”</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"> And then, Cassirer compares modern thought to astrology, as one of the models of mythical thought: “The unity that modern science seeks is the unity of the natural law as a purely functional law; for astrology it is the unity of a constant and pervasive condition, a structure of the universe.”</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"> And at another point: “Science's idea of law find such a correspondence [between two psychic elements], not where [as in mythology] the elements somehow correspond to one another, and where they can be mutually connected within a definite scheme, but instead where specific quantitative changes of the one dictate those of the other, according to a universal rule.”</span><span class="footnote_reference" id="footnote_ref-9"><a href="#footnote_anchor-9">9</a></span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> We should pay special attention to this last sentence. What Cassirer means by “scientific thought,” of course, does not apply only to science, but </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">mutatis mutandis</span><span lang="en-US" xml:lang="en-US"> to all modern thought, including philosophy (“philosophy as a science”), art, and religious studies, since causal-functional thought plays the lead role in these domains as well.</span></p> <p style="text-align: left;" dir="ltr"><span style="font-weight: bold; font-style: italic;" lang="en-US" xml:lang="en-US">Relationship of Harmonics to “Mythical” Thought</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> Harmonics and mythical thought immediately appear to be closely linked. Harmonics is also a discipline of correspondences; every harmonic value-form is, so to speak, a convex lens for a whole series of coordinations, which have little or nothing to do with each other outside the lens. But it is precisely this image in the convex lens that brings the fundamental difference between mythical and harmonic thought into focus. According to Cassirer, mythical thought always starts with some real image-concept (world-egg, primordial ash tree), and then adds further image-concepts onto it, which appear to our modern way of thinking, just like the initial symbol, to be more or less arbitrary connections, or at least external ones. Harmonics, on the other hand, does not begin its series of correspondences with any arbitrary symbol such as a world-egg, but with a harmonic value-form (prototype) whose initial theorem is anchored psychophysically in nature and in our psyche, and as such is suited to the criteria of understanding (number) and feeling (tone), and can thus be judged and evaluated abstractly and concretely. The correspondences radiate outwards from these convex lenses of harmonic value-forms as though toward the periphery of a circle. Viewed by themselves, </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">without</span><span lang="en-US" xml:lang="en-US"> the focus of the lens, they appear just as “arbitrary” as in Cassirer's mythological thought, but </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">with </span><span lang="en-US" xml:lang="en-US">the lens they are arranged in our causal way of thinking, and are a function of precisely these prototypes or value-forms. Here are some examples:</span></p> <p style="text-align: left;" dir="ltr"><span style="font-weight: bold; font-style: italic;" lang="en-US" xml:lang="en-US">Harmonic Examples of the Doctrine of Correspondences</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> The following facts are known: In the growth of crystal surfaces, the following numbers usually appear:</span></p> <p style="text-align: center;" dir="ltr"><span lang="en-US" xml:lang="en-US">... </span><span style="vertical-align: super;" lang="en-US" xml:lang="en-US">1</span><span lang="en-US" xml:lang="en-US">/</span><span style="vertical-align: sub;" lang="en-US" xml:lang="en-US">4</span><span lang="en-US" xml:lang="en-US"> </span><span style="vertical-align: super;" lang="en-US" xml:lang="en-US">1</span><span lang="en-US" xml:lang="en-US">/</span><span style="vertical-align: sub;" lang="en-US" xml:lang="en-US">2</span><span lang="en-US" xml:lang="en-US"> </span><span style="vertical-align: super;" lang="en-US" xml:lang="en-US">2</span><span lang="en-US" xml:lang="en-US">/</span><span style="vertical-align: sub;" lang="en-US" xml:lang="en-US">3</span><span lang="en-US" xml:lang="en-US"> 1 </span><span style="vertical-align: super;" lang="en-US" xml:lang="en-US">3</span><span lang="en-US" xml:lang="en-US">/</span><span style="vertical-align: sub;" lang="en-US" xml:lang="en-US">2</span><span lang="en-US" xml:lang="en-US"> 2 4 ...</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US">If we place beneath these numbers the tone-values:</span></p> <p style="text-align: center;" dir="ltr"><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">c</span><span style="font-family: 'Tahoma';" lang="en-US" xml:lang="en-US">,,</span><span lang="en-US" xml:lang="en-US"> </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">c</span><span style="font-family: 'Tahoma';" lang="en-US" xml:lang="en-US">,</span><span lang="en-US" xml:lang="en-US"> </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">f</span><span style="font-family: 'Tahoma';" lang="en-US" xml:lang="en-US">,</span><span lang="en-US" xml:lang="en-US"> </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">c g c</span><span lang="en-US" xml:lang="en-US">΄ </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">c</span><span lang="en-US" xml:lang="en-US">΄΄</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US">then in the tones </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">f c g</span><span lang="en-US" xml:lang="en-US"> we have the functions subdominant-tonic-dominant, upon whose movement the chords of Classical, Romantic, and modern music are based.</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"> If we imagine the inner movement of the cadence autonomously, as the positioning of thesis, antithesis, and synthesis, then we find ourselves in the domain of logic, where this triadic movement signifies the prototype of dialectic. Here, then, we have three instances from crystallography, music, and logic, which have nothing to do with each other practically, and cannot be derived from one another causally, but whose inner form or character is analogous and can be traced back correspondingly to the harmonic prototype of “step-dialectic” (in musical terms: cadencing).</span><span class="footnote_reference" id="footnote_ref-11"><a href="#footnote_anchor-11">11</a></span></p> <p style="text-align: justify; text-indent: 0.5in;" dir="ltr"><span lang="en-US" xml:lang="en-US">Another example: The blossom of the passionflower has five regularly divided stamens, upon each of which is a pistil, also regularly divided into three. 5 : 3 or 3 : 5 is the minor third, whose importance (as well as that of the major third) in the two-part singing of folk songs, and as a typical interval of “romantic harmonics,” is well known. If we imagine the third-interval autonomously-it is the fifth tone of the overtone series-the we remember the Greek letter E (= 5), which stood at the entrance of a temple at Delphi and about which Plutarch wrote an entire essay; we will also remember the pentacle, which produces the golden section, and so forth. Here, then, we have four instances from botany, music, mythology, and mathematics, which have nothing to do with one another factually and cannot be derived from one another causally, but whose inner form or character is analogous and can be traced back correspondingly to the harmonic prototype of the third-interval.</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> One might now ask: “What should I do with such correspondences? What is the advantage over the causal method?” As a harmonist, I will give the following answer:</span></p> <p style="text-align: left;" dir="ltr"><span style="font-weight: bold; font-style: italic;" lang="en-US" xml:lang="en-US"><br /> Causal and Correspondent Modes of Thought</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> The causal mode of thought leads all too often to a false certainty, to an attitude of self-evidence, to a sacrifice of experience in favor of established facts and laws. All great scholars and explorers of this thought (Max Planck, etc.) made it clear that any science is only ever approximately “true,” and that in pure scientific thought, no conclusive results or truths are to be expected. Moreover, for all these scholars, most of the experiential content was retained. But the great majority of their colleagues, and laypeople, came all too easily to believe, as regards science, that “truth” is to be found only here, within the causal-scientific mode of thought, and that when these truths are set before them, everything is completely clear and self-evident, and they have fundamentally “gotten there.”</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> While scientists are driven restlessly from one result to the next (Max Planck, in his speech at Vienna, March 3, 1929, spoke of the “goal, unreachable in principle, of a knowledge of true reality”), and an individual discovery is often able to shake up an entire, supposedly well-established “worldview” (case in point: classical and modern physics), the layman, and not only he, is stuck with the illusion that contemporary research produces conclusive truth, that it can be built upon, and that any doubt is forbidden, indeed utterly ridiculous. Since the current results of this research are believed to be “factual” and “objective,” and there is a panicking fear of “psychic” references or of trespassing into other domains, this “haptification” affects researchers and laypeople as an accumulation of scientific material that is lacking any psychic relationship to humanity as a whole, and leaves the seeker of truth fundamentally unsatisfied-regardless of the element of uncertainty that he sees and feels as a result of the continual “revisions” of the scientific worldview.</span><span class="footnote_reference" id="footnote_ref-12"><a href="#footnote_anchor-12">12</a></span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> The doctrines of correspondence, on the other hand-of which harmonics is only one of several-begin with experiential content (in the above examples, the dynamics of cadences and the psychic content of the third-interval) and then seek the domains in which satisfactory analogies to this primary experiential content can be found; in harmonics we call it prototype, or harmonic value-form. The thinking here is not aimed at cause and effect (proof), nor at a “goal unreachable in principle”; instead, the experiential content of the initial position is extended and transferred to the “corresponding” analogies. From this, a fundamentally different viewpoint emerges within our capability of perception. In scientific thought, we find a restless desire to know, pursuing an ever unattainable goal, connected to supposedly “conclusive” results and an ever sharper focus on pure logic as its tool. In the doctrines of correspondences, we find calm introspection and a hearkening to the convergence of fundamental prototypes and value-forms, connected to ideas in the Platonic sense, these ideas being focused upon the “</span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">intellectus archetypus</span><span lang="en-US" xml:lang="en-US">” (Kant) of our psyche.</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> Both modes of thinking and viewing, the scientific and the correspondent, arrive at truths, if we take “truth” to mean the appeasing of our striving for knowledge. But in the two cases, these truths are anchored and structured in different areas of our psychic capability. I personally would be wary of a face-off between the two domains. It is unquestionable that the causal-scientific way of thinking has its great and permanent uses, and will continue to have them. But it will have to get used to the fact that there are other approaches for our perception to the eliciting of the “truth,” and that if it really understands the serious doctrines of correspondences, it must see them only as siblings, working together with it to mediate the truth. And there is more: every doctrine of correspondences, if it is to be taken in earnest-which is why I use the word “serious”-must use “scientific” means to ensure that its starting positions are unobjectionable. Certainly we harmonists place great value in the fact that our theorems, upon which the prototypes and value-forms are built, are grounded in measure, number, and the usual criteria according to scientific methods. Only then may observation and listening be set free and give themselves up to meditation on the series of correspondences.</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> We will now resume the thread of the above discussion with Cassirer. For the real doctrines of correspondences, and especially for harmonics, there are not simple arbitrary assignations, as in mythical thought, but instead these assignations show themselves as causally supportable image-concepts of a specific psychophysical form: that of the relevant harmonic value-form. If we think this through correctly, and look again at Cassirer's definition of mythical thought, the question arises: shouldn't it be possible to understand all these assignations of mythical symbols and image-concepts-naturally only as far as concerns the real ancient universal images, and not obvious nonsense-in such a prototypical, value-formal way? Certainly, from the harmonic point of view much of so-called numerology is already psychologically dictated, emanating from certain tone-number forms already present in our psyche.</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"> For example, the above mentioned “septuarchy,” the sevenfold system of the Zunis, superficially seen as a “wild” totemic hierarchy of assignation, has a psychic foundation that is harmonic (7 as the first number of dissonance, the seven-step scale as a prototype). The same goes, among others, for the doctrine of astrological aspects, which has been explained since ancient times, and later by Kepler, by means of musical intervals, i.e. psychic forms. Furthermore, it can be harmonically proven that the “object concept” of the world ash tree, mentioned above by Cassirer, is based on the image-concept of the “tree” that is common to almost all mythologies and religions (tree of paradise, etc.): it can be elicited directly from dichotomy, i.e. the division of the “partial-tone coordinates,” and therefore corresponds to a specific fundamental structure of our psyche and our ability to think (dieresis of the Platonic ideas).</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"> Thus “mythical thought” would not be merely a kind of imperfect prelude to our modern scientific thought, but completely equal to it as a human endeavor for truth, albeit structurally different. Cassirer, moreover, comes to the similar conclusion, on the basis of his theory of the various “modalities” of our thinking ability, that the various forms of thinking are in a way equal, though differing in nature. Moreover, as appears from the passages quoted above, he makes his position clear on the pros and cons of the two types of thought: above all, modern thought must first “break apart” before it can rebuild, and even then it will arrive only at “certain rules of Being” whereby “certain quantities dictate other quantities following a universal law,” and “the form of the whole, as it is present for sensory perception or for pure contemplation, disappears.” Naturally Cassirer assumes, like all thinkers of his type, that modern science has conquered mythical thought, but that a true conquest of the latter must rest upon knowledge and acknowledgment of it, since no matter what, it is still there.</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> Harmonics, then, has an important mission: to reintroduce the “harmonic value-form” into scientific thought, not as an antiquated doctrine of correspondences to be conquered, but as a new psychic structure of our scientific perception, verifiable by means of number and causality. The mythologem, symbol, etc., thus appear not merely as a form of perception that once existed and was historically equivalent to our modern thinking, but is irrelevant today: rather they are just as important as this modern thinking and still of value today, always assuming one can understand them causally and fit them into modern ways of thought. This avoids, above all, the danger of the mythologems being swept under the rug. To banish spirits, one must first summon them; and harmonics may have a similar mission to fulfill in the domain of science as depth psychology has within psychology.</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> Besides this fundamental debate with Cassirer, from which I believe the new justification for a doctrine of correspondences emerges under harmonic auspices, there are at least two examples in modern times of correspondence-based thinking: Fechner's </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Zend-Avesta</span><span lang="en-US" xml:lang="en-US"> and modern Gestalt theory.</span></p> <p style="text-align: left;" dir="ltr"><span style="font-weight: bold; font-style: italic;" lang="en-US" xml:lang="en-US">Thomas Fechner</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> G. Thomas Fechner</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"> works primarily with analogies in his </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Zend-Avesta</span><span lang="en-US" xml:lang="en-US">.</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"> The earth, as a higher spiritual being, is in the middle between humans and God. The stars are conscious beings, the earth itself is an “angel.” </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Zend-Avesta </span><span lang="en-US" xml:lang="en-US">means “living word,” everything speaks to us, and the analogies rise in hierarchical stages from familiar things and concepts up to the highest peak: to God. “In the step-by-step construction of the world, there is always a fixed corporeal system from above, and thus a consciousness always encloses the world below, and keeps it connected with omniscience in God.”</span><span class="footnote_reference" id="footnote_ref-17"><a href="#footnote_anchor-17">17</a></span><span lang="en-US" xml:lang="en-US"> The natural science of Fechner's time shrugged its shoulders at this work and declared him a “muddlehead,” whilst for the theologians Fechner's thoughts were too “materialistic.” If we modern people regard his work without prejudice, we can see that the verdicts of both the scientists and theologians of 100 years ago were wrong: this is not merely a matter of knowledge or belief, but of a synthesis of both, on the basis of a different kind of thought, a gradation of correspondences. Asking, about such thoughts, “Is it all </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">true</span><span lang="en-US" xml:lang="en-US">, what Fechner says?” is like asking whether a work of art is “true.” All art produces analogies in the deepest sense, and all works of art stand upon the background of correspondences. I do not mean this in the sense of “allegorizing,” but entirely concretely with regard to the inner construction of the artwork itself. The formed idea is not realized in art by means of cause and effect (causality), nor by pure feeling forms (belief), but on the basis of correspondences of artistic inspirations and their evolutions. Here, the result is “truth” just as in Fechner's </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Zend-Avesta</span><span lang="en-US" xml:lang="en-US">; only this truth reaches into other levels of our capabilities of consciousness and contemplation than those of the scientific and religious attitudes.</span></p> <p style="text-align: left;" dir="ltr"><span style="font-weight: bold; font-style: italic;" lang="en-US" xml:lang="en-US">Gestalt Theory</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> Another type of correspondence thinking occurs in the various directions of modern Gestalt theory, Gestalt philosophy, and Gestalt psychology. In Gestalt psychology,</span><span class="footnote_reference" id="footnote_ref-18"><a href="#footnote_anchor-18">18</a></span><span lang="en-US" xml:lang="en-US"> for example, a series of “Gestalt laws” are elicited on the basis of certain predominantly optical phenomena, such as “the law of containment,” “the law of common movement,” “the law of the good curve or the common fate” (!) and others, which are not restricted to the initial domain, but have application and correspondence in all possible domains, and thus are fundamentally analogized. The advantage of Gestalt psychology over Fechner is that it bases its laws on definite experiential conditions and universalizes them abstractly-similarly to what harmonics does with its theorems and value-forms.</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> I gave these examples of modern correspondence-thinking only to show that harmonics as a doctrine of correspondences is in no way an anachronism today, and indeed is in respectable company. Its specific nuances, in comparison with the two doctrines mentioned above, would require similar explanations to those we have already expressed regarding Cassirer.</span></p> <p style="text-align: left;" dir="ltr"><span style="font-weight: bold; font-style: italic;" lang="en-US" xml:lang="en-US">The Difficulties of Doctrines of Correspondences</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> Of course, one must be aware of the general and specific difficulties of doctrines of correspondences. We are not on such “solid” ground here as exact scientists, logicians, or believers. Misunderstandings and mistakes are given wider leeway than on the hitherto trustworthy paths of familiar thought. To give the reader an impression of these difficulties, here are examples from my own works:</span></p> <p style="text-align: left;" dir="ltr"><span style="font-weight: bold; font-style: italic;" lang="en-US" xml:lang="en-US">Two Harmonic Examples</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> In </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Hörende Mensch</span><span lang="en-US" xml:lang="en-US">, p. 191 ff., and in </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Akróasis</span><span lang="en-US" xml:lang="en-US">, p. 132 ff., I compared the base 10 logarithms of the median planetary distances (average distance between the sun and Mercury = 1) with the most accurate primary senary base 2 partial-tone logarithms, and thus came upon an octave-reduced scale, half major, half minor in character, and upon a remarkable localization of the first enharmonic steps </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">d d</span><span lang="en-US" xml:lang="en-US">ˇ and </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">b b</span><span lang="en-US" xml:lang="en-US">ˇ. The shattered fragments that are asteroids are </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">between</span><span lang="en-US" xml:lang="en-US"> </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">d</span><span lang="en-US" xml:lang="en-US"> and </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">d</span><span lang="en-US" xml:lang="en-US">ˇ, Jupiter </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">outside</span><span lang="en-US" xml:lang="en-US"> </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">b</span><span lang="en-US" xml:lang="en-US"> and </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">b</span><span lang="en-US" xml:lang="en-US">ˇ, but still within the domain of the </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">b</span><span lang="en-US" xml:lang="en-US"> value. I concluded from this that the dangerous area within the first enharmonic domain of division must have resulted in the fate of the original asteroid-planet, which would otherwise be in the position of the major third; and I was reminded of the legend of Lucifer, the angel who was at first noblest of all, then was destroyed-while Jupiter remains outside the second enharmonic division zone. </span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> One of the first critics of this harmonic analysis argued as follows: it would be presumptuous to attribute the evil of the world to its fitting or not fitting into a </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">scale</span><span lang="en-US" xml:lang="en-US">! A scale has nothing to do with planets and their distances. My response-that Plato used the same analogy for his theory of the cosmos in his </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Timaeus</span><span lang="en-US" xml:lang="en-US"> scale-was answered thus: Plato, as an artist, was allowed to do this, meaning that with Plato one never knows where he stops being in earnest and where the fun begins. So, Plato was a joker-conveniently enough, whenever he is not understood today! See above for the evaluation of a harmonic analysis and the constitutive character of its correspondences as an answer to this objection.</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> Another, I believe, well-meaning critic made more pertinent objections. First, the connection of the tones to the median planetary distances is equivocal, since each of the 12 (tempered) tones of the scale has a variation breadth of </span><span style="vertical-align: super;" lang="en-US" xml:lang="en-US">1</span><span lang="en-US" xml:lang="en-US">/</span><span style="vertical-align: sub;" lang="en-US" xml:lang="en-US">12</span><span lang="en-US" xml:lang="en-US"> and thus other tones could lie within these tolerances; secondly, it is entirely clear that some kind of scale must arise from comparing 9 planets with 12 tones. The first objection is only valid if I am thinking in “tempered” terms, subtly introducing the concept of “variation breadth.” But in such analyses, harmonics thinks or perceives in terms of pure-tones, and thus the fifth and the octave have no “leeway” as intervals, as every string player knows when he tunes his instrument. There is only “variation breadth” in the intervals that follow afterward-third, second, etc.-and for these it is limited, certainly not </span><span style="vertical-align: super;" lang="en-US" xml:lang="en-US">1</span><span lang="en-US" xml:lang="en-US">/</span><span style="vertical-align: sub;" lang="en-US" xml:lang="en-US">12</span><span lang="en-US" xml:lang="en-US"> of the octave! The second objection would, again, be obvious from the point of view of “tempered” hearing, but absolutely not from the pure-tonal viewpoint. Because as it is clear that a scale, more or less, must emerge from 9 planets and 12 tones, thus it is evident that there must be senseless and sensible nuances of this (pure-tonal) scale. And it was the peculiar character of the scales I analyzed that set them apart from the other, senseless ones. The critic, however, either did not notice the most important part of my analysis, or else it appeared unimportant to him: first, the ratio of the two logarithm systems, base 10 : base 2, which harmonically signifies the interval of a third. But the third (5 or </span><span style="vertical-align: super;" lang="en-US" xml:lang="en-US">1</span><span lang="en-US" xml:lang="en-US">/</span><span style="vertical-align: sub;" lang="en-US" xml:lang="en-US">5</span><span lang="en-US" xml:lang="en-US">) is the number of the Earth in harmonic symbolism, the interval of type.</span><span class="footnote_reference" id="footnote_ref-19"><a href="#footnote_anchor-19">19</a></span><span lang="en-US" xml:lang="en-US"> And secondly, the location of the asteroids between the first two enharmonic steps, and the location of Jupiter near the second pair, which are always especially significant harmonically: compare to this the peculiar correspondence of the harmonic sphere of the head to the harmonic sexual sphere in the “sound-image of primal man,” §38a.2. For someone who thinks “uniformly,” i.e. temperedly here, and to whom correspondences such as the last two points mean nothing, this type of analysis is like an empty page with no clue how to begin.</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> A second example: my harmonic analysis of the Pythagorean triangle with the sides 3, 4, 5 and the square numbers 9, 16, 25, whose permutations yield the chromatic scale.</span><span class="footnote_reference" id="footnote_ref-20"><a href="#footnote_anchor-20">20</a></span><span lang="en-US" xml:lang="en-US"> Here the same critic objected that it “also works with other triangles,” if their sides have the triadic ratio 3 </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">f</span><span lang="en-US" xml:lang="en-US"> 4 </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">c</span><span lang="en-US" xml:lang="en-US"> 5 </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">as</span><span lang="en-US" xml:lang="en-US">, e.g. with a triangle with sides 4, 5, 6 and the squares 16, 25, 36, etc. Obviously it “also works” with these and many other triangles. As harmonists, however, we think not uniformly but morphologically, and thus, of course, the Pythagorean triangle with its primary and smallest triadic ratios 3, 4, 5 is </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">preferred</span><span lang="en-US" xml:lang="en-US"> over all others; its symbolism and importance for the measurements of ancient temples (right angles) is also relevant. If I do not think in terms of the form, i.e. not morphologically, but view other triangles as equal simply because they are triangles, then I can continue along these lines and say that in the infinite plethora of numbers, there must be some numbers from which I can build the numbers for a chromatic scale-which is correct!</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> So-as a brief response to the above objections-one gets nothing from the doctrine of correspondences without a certain </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">evaluation</span><span lang="en-US" xml:lang="en-US">. This evaluation can never come from the uniform concept of number or from logical conclusions alone, but must come from a formed number, namely the tone-number (as far as harmonics goes) and from a formal type of thinking that, while using logic and causality, does not rest upon concepts but on evaluations of these concepts, i.e. upon inner psychic formative tendencies. Every evaluation, however, brings research up out of mere factual analysis and has its true origin in a domain of ideas that are “no longer of this world.”</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> If, according to Plato's doctrine, the intellect, however sharp it may be (Today, rather than intellect, we might speak of purely scientific thought, founded only on logic and factual material), can have no direct access to the world of the knowledge of values</span><span class="footnote_reference" id="footnote_ref-21"><a href="#footnote_anchor-21">21</a></span><span lang="en-US" xml:lang="en-US"> (see the above quote from Jakob Böhme), then the doctrines of correspondences-of which harmonics is only one kind-will once again pave the indirect way to this world, even if they must be fertilized and propagated by values if the “Eros” in them is to be effective.</span></p> <p style="text-align: left; margin-left: 0.5194in;" dir="ltr"><span lang="en-US" xml:lang="en-US">“And he [Zeus] ordains the golden chain of ether;</span></p> <p style="text-align: left; margin-left: 0.5194in;" dir="ltr"><span lang="en-US" xml:lang="en-US">So that everything exists as one, and yet separate.”</span><span class="footnote_reference" id="footnote_ref-22"><a href="#footnote_anchor-22">22</a></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"> Aurora, 16, 39.</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"> Benno Schwabe-Verlag, Basel 1946; Gerd Hatje-Verlag, Stuttgart, 1947, p. 87 ff.</span></p> <p style="text-align: justify;" 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"> “Die Begriffsform im mythischen Denken,” in Studien der Bibliothek Warburg, Leipzig 1922, p. 7; Philosophie der symbolischen Formen, vol. II, Berlin 1925.</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"> Cassirer, Die Begriffsform, etc., pp. 17, 22-23.</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"> Op. cit., p. 32.</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"> Op. cit., p. 32.</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"> Op. cit., p. 33.</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"> Op. cit., p. 34.</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"> Op. cit., p. 44.</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"> See my Grundriß, p. 269.</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"> Ibid., p. 182 ff.</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"> See “Tagebuch vom Binntal” in my Abhandlungen.</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"> See §50.</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"> See Julius Stenzel, Zahl und Gestalt bei Plato und Aristoteles, 1924, p. 30 ff.</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 p. 45 ff.</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"> Zend-Avesta oder über die Dinge des Himmels und des Jenseits, vom Standpunkt der Naturbetrachtung, 2 vols., 1st ed., 1851; 3rd ed., 1906. See also the selection in Dom, Bücher deutscher Mystik.</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-17"><a href="#footnote_ref-17">17</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> Kurd Laßwitz: G. Th. Fechner, 1910, p. 60.</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-18"><a href="#footnote_ref-18">18</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> See David Katz, Gestaltpsychologie, 2nd ed., Benno Schwabe-Verlag, Basel, 1948.</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-19"><a href="#footnote_ref-19">19</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> See the interesting statements about the number 5 in Plutarch's essay On the E at Delphi.</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-20"><a href="#footnote_ref-20">20</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> Hörender Mensch, pp. 116-117 and §28a of this book.</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-21"><a href="#footnote_ref-21">21</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> Werner Jäger, Paideia, vol. II, 1944, p. 305.</span></p> <p style="text-align: left;" class="footnote_text" awml:style="Footnote Text" dir="ltr"><span class="footnote_reference" id="footnote_anchor-22"><a href="#footnote_ref-22">22</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> Hieros Logos of Orpheus-Pythagoras.</span></p> </div></div></td></tr></tbody></table><br /> </span></p></div> </body> </html></div>
