<div id="LayerE10" style="visibility: visible; overflow: visible; z-index:0; left:10px; top:5px; position:absolute; "><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> <div> <div style="text-align: center;" dir="ltr"><span style="font-weight: bold;" lang="en-US" xml:lang="en-US"></span><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 align="center"></div> <div> <div style="text-align: center;" dir="ltr"><span style="font-weight: bold;" lang="en-US" xml:lang="en-US"><span style="font-weight: bold;" lang="en-US" xml:lang="en-US"><span lang="en-US" xml:lang="en-US"><br /> <img width="500" height="392" title="" alt="" src="../kayser2/imagelibrary/Nature/Snow_crystals.jpg" /></span></span></span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US"></span></div> <div style="text-align: center;" dir="ltr"><span style="font-weight: bold;" lang="en-US" xml:lang="en-US"><br /> Variations in the Forms of Snowflakes</span></div> <p style="text-align: center;" dir="ltr"><span style="font-weight: bold;" lang="en-US" xml:lang="en-US"><span lang="en-US" xml:lang="en-US"></span></span></p> <p style="text-align: center;" dir="ltr"><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">from: </span><span style="font-weight: bold; font-style: italic;" lang="en-US" xml:lang="en-US">Atlas der Krystalformen </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">by Victor Goldschmidt (1853-1933)</span><span id="footnote_ref-1" class="footnote_reference"><a href="#footnote_anchor-1">1<br /> </a></span><span lang="en-US" xml:lang="en-US"></span></p> <div style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US">In his observations of geometric structures in nature, Johannes Kepler also studied snowflakes and their six-pointed forms, and presented his ideas on this in the small volume </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">A New Year's Gift, or On Six-Cornered Snow</span><span lang="en-US" xml:lang="en-US">. Here, in addition to causal “scientific” considerations, he makes more morphological observations, such as comparing the six-pointed form of the snowflake and the six-petaled flowers of the lily family, and contrasting these with the five-petaled blossoms of fruit trees-and seeks to draw conclusions on the natural qualities of these plants thus revealed.</span></div> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US">Image 4, however, is not from Kepler, but is much more recent: it is from Victor Goldschmidt's </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Atlas der Krystalformen</span><span lang="en-US" xml:lang="en-US">. Just as Kepler is famous as an astronomer, but hardly anyone knows that the results of his studies emerged in the course of a search for the musical harmony of the universe, so the </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Atlas der Krystalformen</span><span lang="en-US" xml:lang="en-US"> is known as the standard work of this crystallographer, but it is little known that Goldschmidt studied the connections between crystallography and harmonics: in his book </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Über Harmonie und Complication</span><span lang="en-US" xml:lang="en-US">, he investigates analogous phenomena in music, colors, and various domains of nature, on the basis of a fundamental law he developed from crystallography.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> It was above all the works of Victor Goldschmidt, along with those of Kepler and Thimus, that inspired Hans Kayser's work-Kayser reestablished harmonics as we know it today and presented it in a new form for our times.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> The commentary on Images 17 and 18 also relates to Goldschmidt's system of “complication.”</span></p> <div style="text-align: left;" align="center" dir="ltr"><span lang="en-US" xml:lang="en-US">Peter Neubäcker<br /> </span></div> <div style="text-align: left;" align="center" dir="ltr"><span lang="en-US" xml:lang="en-US"><br /> </span> <div align="center"><span style="font-weight: bold;" lang="en-US" xml:lang="en-US"> <span style="font-weight: bold;" lang="en-US" xml:lang="en-US">Image 4</span></span><br /> </div></div> <div style="text-align: left;" align="center" dir="ltr"><span lang="en-US" xml:lang="en-US"> </span></div> <div style="text-align: left;" align="center" dir="ltr"><span lang="en-US" xml:lang="en-US"> </span><img src="../kayser2/imagelibrary/Nature/0.jpg" alt="" /><span lang="en-US" xml:lang="en-US"><br /> </span></div> <p> </p> <div> <p style="text-align: left;" dir="ltr" awml:style="Footnote Text" class="footnote_text"><span id="footnote_anchor-1" class="footnote_reference"><a href="#footnote_ref-1">1</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> Translator's note: This was Victor Mordechai Goldschmidt, not to be confused with Victor Moritz Goldschmidt (1888-1947), another chemist and crystallographer.</span></p> </div></div></td></tr></tbody></table> </span></div> <div style="text-align: center;" dir="ltr"><span style="font-weight: bold;" lang="en-US" xml:lang="en-US"></span></div></div></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
