<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>Harmonic Theories & Diagrams - The Monochord.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; } *.caption { font-size:10pt; font-weight:bold; margin-bottom:6pt; margin-top:6pt; } --></style> </head> <body> <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="left"></div> <div align="center"><img width="500" height="341" src="/EZ/kayser2/kayser2/imagelibrary/monochord.jpg" alt="" title="" /> </div> <div><span style="font-weight: bold;" lang="en-US" xml:lang="en-US"> </span></div> <div> <div align="center"><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">THE MONOCHORD</span></div> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> The harmonist's instrument for experimenting and measuring is the monochord: the one-stringed instrument (</span><span lang="el-GR" xml:lang="el-GR">το</span><span lang="en-US" xml:lang="en-US"> </span><span lang="el-GR" xml:lang="el-GR">μονόχορδον</span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">,</span><span lang="en-US" xml:lang="en-US"> from </span><span lang="el-GR" xml:lang="el-GR">μονος</span><span lang="en-US" xml:lang="en-US"> [monos] = one, and </span><span lang="el-GR" xml:lang="el-GR">χορδή</span><span lang="en-US" xml:lang="en-US"> [chorde] = string). In its simplest form, it consists of a board with a string of given length stretched on it between two bridges. For practical reasons, I envisage a thirteen-stringed monochord (for the analysis of a self-contained chromatic scale of twelve notes), with each string 1200 millimeters long. Thus the name “one-stringed” is, strictly speaking, no longer correct and would be better replaced with “sonometer,” “phonometer” (both meaning sound-gauge) or “polychord” (many-stringed). However, since all thirteen strings have the same length, thickness, and tension, and therefore give the same tone, we are in effect dealing with one and the same string. For this reason, and also for reasons of historical sentiment, we will retain the term “monochord.”</span></p> <p style="text-align: left;" dir="ltr"><span style="font-weight: bold; font-style: italic;" lang="en-US" xml:lang="en-US">§1a. Building a Monochord</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> One can easily build one's own monochord, or have it built by a carpenter or piano maker. I recommend making the chest out of planed spruce boards 123 cm long, 26 cm wide, and 10 cm high, firmly glued together.</span></p> <p style="text-align: center;" dir="ltr"><img alt="" src="../kayser2/imagelibrary/Theories/30.jpg" /></p> <p style="text-align: center; margin-bottom: 6pt; margin-top: 6pt;" class="caption" awml:style="Caption" dir="ltr"><span lang="en-US" xml:lang="en-US">Figure </span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> So that the chest will not bend under the relatively high tension in the strings, it is advisable for the upper soundboard to be 1 cm thick, and the lower one at least 2 cm thick. The thin headboards on each end should be reinforced with strong wood blocks 3-4 cm thick at the points where the nuts will be fixed. A thickness of 1 cm should suffice for the boards on the sides. On each side board, cut two sound holes about 4-5 cm in diameter. At each end of the top board, affix a brass nut 1.5 cm high, 1.5 cm wide, and 26 cm long, at an exact right angle to the length of the chest, so that between the two nuts there is a distance of precisely 120 cm (1200 mm). This precision is essential for precise tone analysis. Bridges for insertion beneath the strings, 11 mm high and with the cross section pictured in Fig. 1, should be cut from a rod of ash or hardwood, smoothed down by a carpenter. The insertion of the bridges must not result in the strings being pulled too taut; they should be just tight enough for the two divided parts of the string to sound clearly, without buzzing. If necessary, file small notches in the bridges. Place the 13 steel strings at equal distances from one another and fasten them, with ordinary piano tuning pins, onto the string boards at the head and foot of the monochord. With these pins, they can be tuned to the exact same note (here middle </span><span style="font-weight: bold;" lang="en-US" xml:lang="en-US">c</span><span lang="en-US" xml:lang="en-US">) with the aid of a tuning fork. The easiest and simplest way to make the strings sound is to pluck them. But the sound is better if the string is struck with a small felt-covered wooden hammer, which can be made easily.</span></p> <p style="text-align: left;" dir="ltr"><span style="font-weight: bold; font-style: italic;" lang="en-US" xml:lang="en-US">§1b. Dividing the Strings on the Monochord</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> For measuring divisions along a string 120 cm in length, it is best to use strips of millimeter paper 120 cm long, which can be fastened with pins under the strings between the brass nuts. Since we will be examining many different tone ratios, we will need a supply of replaceable paper strips, on which we will note the locations in question with lines and the appropriate tone and number signs. The methods of division will be specified in each case.</span></p> <p style="text-align: left;" dir="ltr"><span style="font-weight: bold; font-style: italic;" lang="en-US" xml:lang="en-US">§1c. Historical Remarks</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> The monochord is one of mankind's most venerable tools for scientific research, with a history going back into impenetrable antiquity. Its significance first comes to light with the Pythagoreans, who by means of the monochord made the discovery-an epoch-making one for Western scientific thought-that qualities (in this case, the hearing of tones) can be traced to quantities (measurement with numbers). “Modern natural science was born as empirical Pythagoreanism,” writes W. Windelband in his </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Lehrbuch der Geschichte der Philosophie</span><span lang="en-US" xml:lang="en-US"> (1935, p. 326). However, it should not be forgotten that for the Pythagoreans, the tracing of the qualitative to the quantitative, or as we harmonists would say, the path from tone to number, was only one aspect of this discovery. The other aspect was the transformation of quantity (string lengths on the monochord) into quality, i.e., of the measurable into the perceptible, the physical into the psychic, the number into the tone. For the ancients, this was a phenomenon at least equally wondrous, evoking their astonishment to a similar degree. Because of this dual aspect, the monochord soon became a kind of universal experimenting tool, a “canon” for psychophysical, scientific, and aesthetic investigations in the broadest sense. The monochord survived into the Middle Ages, though its use was increasingly restricted to investigations in music theory, and it finally served merely as an aid to precise intonation for choral singers, thereby becoming the direct precursor of the clavichord, harpsichord, and eventually the piano. Thus the monochord is, on the one hand, the prototype of the precise experiment in the natural sciences in the West, and on the other hand, the direct forerunner of that very instrument-the piano-to which all music is so greatly indebted for its enormous development.</span></p> <p style="text-align: left;" dir="ltr"><span style="font-weight: bold; font-style: italic;" lang="en-US" xml:lang="en-US">§1d. Bibliography</span></p> <p style="text-align: justify;" dir="ltr"><span lang="en-US" xml:lang="en-US"> Regarding the monochord, the best work, mainly historical and with further bibliographical sources, is Sigfrid Wantzloeben, </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Das Monochord als Instrument und als System,</span><span lang="en-US" xml:lang="en-US"> Halle, 1911. See also A. von Thimus, </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Das harmonikale Symbolik des Alterthums,</span><span lang="en-US" xml:lang="en-US"> I, 29-30; H. Kayser,</span><span style="font-style: italic;" lang="en-US" xml:lang="en-US"> Vom Klang der Welt</span><span lang="en-US" xml:lang="en-US">, 20, 50ff., 61, 78, 115, 149, 170; </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Abhandlungen,</span><span lang="en-US" xml:lang="en-US"> 87-88; </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Grundriß,</span><span lang="en-US" xml:lang="en-US"> 47, 54, 58, 64. [</span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">See the end of this book for full details of Kayser's works.</span><span lang="en-US" xml:lang="en-US">]</span></p></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> <p style="text-align: left;" dir="ltr"></p> </div> </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
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Octaves & Spirals
Harmonics & Architecture
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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
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Snow Crystals
Harmonics & Music Theory
Harmonics as a Science
Interference
Harmonic Theories & Diagrams
Thought as a Sense
Color & Partial-Tone Coordinates
The Lambdoma
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The Monochord
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