<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 content="text/html;charset=UTF-8" http-equiv="content-type" /> <title>History of Harmonics - Haase - Leibniz & Kayser.html</title> <style type="text/css"><!-- #toc, .toc, .mw-warning { border: 1px solid #aaa; background-color: #f9f9f9; padding: 5px; font-size: 95%; } #toc h2, .toc h2 { display: inline; border: none; padding: 0; font-size: 100%; font-weight: bold; } #toc #toctitle, .toc #toctitle, #toc .toctitle, .toc .toctitle { text-align: center; } #toc ul, .toc ul { list-style-type: none; list-style-image: none; margin-left: 0; padding-left: 0; text-align: left; } #toc ul ul, .toc ul ul { margin: 0 0 0 2em; } #toc .toctoggle, .toc .toctoggle { font-size: 94%; }@media print, projection, embossed { body { padding-top:1.0000in; padding-bottom:1.0000in; padding-left:1.2500in; padding-right:1.2500in; } } body { text-indent:0in; text-align:left; font-weight:normal; text-decoration:none; font-variant:normal; color:#000000; font-size:12pt; font-style:normal; widows:2; font-family:'Times New Roman'; } table { } td { border-collapse:collapse; text-align:left; vertical-align:top; } p, h1, h2, h3, li { color:#000000; font-family:'Times New Roman'; font-size:12pt; text-align:left; vertical-align:normal; } *.footnote_text { font-size:10pt; } *.footnote_reference { font-size:10pt; vertical-align:super; } --></style> </head> <body> <div> <div style="text-align: center;" dir="ltr"><span style="font-weight: bold;" lang="en-US" xml:lang="en-US"> <table style="border-collapse: collapse;" width="600" cellspacing="0" cellpadding="3" bordercolor="#000000" border="0"><tbody><tr><td width="100%" valign="top"> <div><span style="font-weight: bold;" lang="en-US" xml:lang="en-US"></span> <div style="text-align: center;" dir="ltr"><span style="font-weight: bold;" lang="en-US" xml:lang="en-US"><br /> Research on Leibniz at the Hans Kayser Institute for Fundamental Harmonic Research</span></div> <p style="text-align: center;" dir="ltr"><span style="font-weight: bold;" lang="en-US" xml:lang="en-US"></span><span lang="en-US" xml:lang="en-US">By Rudolf Haase</span></p> <p style="text-align: center;" dir="ltr"><span lang="en-US" xml:lang="en-US">Translated by Ariel Godwin</span></p> <p style="text-align: center;" dir="ltr"><span lang="en-US" xml:lang="en-US">Essay from the Newsletter of the Vienna Academy of Music, 1/1984</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US">The Author was summoned to Vienna for the purpose of scientific work on Gottfried Wilhelm von Leibniz (1646-1716). He had already written articles on Hans Kayser and Johannes Kepler for the encyclopedia </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Music in History and Present Times</span><span lang="en-US" xml:lang="en-US"> (MGG),</span><span id="footnote_ref-1" class="footnote_reference"><a href="#footnote_anchor-1">1</a></span><span lang="en-US" xml:lang="en-US"> and was considered a specialist in the Pythagorean harmonic tradition, and was therefore called upon to write an article on Leibniz for the MGG.</span><span id="footnote_ref-2" class="footnote_reference"><a href="#footnote_anchor-2">2</a></span><span lang="en-US" xml:lang="en-US"> This was not entirely self-evident, and was actually based only on a quote from Leibniz that is famous in musicology: “musica est exercitium arithmeticae occultum nescientis se numerare animi.”</span><span id="footnote_ref-3" class="footnote_reference"><a href="#footnote_anchor-3">3</a></span><span lang="en-US" xml:lang="en-US"> This sentence, in which the emphasis is on the word </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">unconscious</span><span lang="en-US" xml:lang="en-US"> (directed against the ideas of Descartes), allows for a connection of Pythagorean and Platonic ideas to an innate musical disposition of the human soul on the basis of mathematical laws (interval proportions), and it is likely that Leibniz had further knowledge on music theory.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> The intensive study of Leibniz's works and the secondary literature soon revealed that no one else had tackled this question yet, and therefore extensive preparatory work was required. As a result, it was finally concluded that only relatively few statements on music and music theory existed, in contrast with a multitude of testimonies from the Pythagorean tradition on the subject of a “universal harmony.” This led to these ideas being expanded beyond the reference in the MGG article, and a few essays,</span><span id="footnote_ref-4" class="footnote_reference"><a href="#footnote_anchor-4">4</a></span><span lang="en-US" xml:lang="en-US"> into a book: </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Leibniz and Music: A Contribution to the History of Harmonic Symbolism</span><span lang="en-US" xml:lang="en-US">.</span><span id="footnote_ref-5" class="footnote_reference"><a href="#footnote_anchor-5">5</a></span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> After the calling to Vienna (1965) and the founding of the Institute (1967), studies on Leibniz were continued; a chapter of the </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">History of Harmonic Pythagoreanism</span><span id="footnote_ref-6" class="footnote_reference"><a href="#footnote_anchor-6">6</a></span><span lang="en-US" xml:lang="en-US"> was dedicated to Leibniz, and an article was written for </span><span style="font-style: italic;" lang="en-US" xml:lang="en-US">Grove's Dictionary of Music and Musicians</span><span lang="en-US" xml:lang="en-US">.</span><span id="footnote_ref-7" class="footnote_reference"><a href="#footnote_anchor-7">7</a></span><span lang="en-US" xml:lang="en-US"> The results of the studies were finally summarized in a report from the 2</span><span style="vertical-align: super;" lang="en-US" xml:lang="en-US">nd</span><span lang="en-US" xml:lang="en-US"> International Congress on Leibniz, 1972, in Hanover.</span><span id="footnote_ref-8" class="footnote_reference"><a href="#footnote_anchor-8">8</a></span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> This collection contained two parts. In the first, it was reported that Leibniz gave many demonstrations for the assumption of a universal harmony, but that unlike Kepler he did not use interval proportions as a basis, although Leibniz was familiar with this “universal harmonics.”</span><span id="footnote_ref-9" class="footnote_reference"><a href="#footnote_anchor-9">9</a></span><span lang="en-US" xml:lang="en-US"> Rather, this idea emerges in a sort of abstract form, transferred from the realm of natural philosophy to that of metaphysics. In this interrelation, the concept of harmony plays an important role, standing right at the center of Leibniz's philosophy, often substituted with other concepts of similar meaning (parallelism, mirroring, singing in unison, rhyme, correspondence, chords, sympathy, etc.), and finally developed to its highest point in the famous concept of prestabilized harmony,</span><span id="footnote_ref-10" class="footnote_reference"><a href="#footnote_anchor-10">10</a></span><span lang="en-US" xml:lang="en-US"> that harmony of body and soul determined by God which Leibniz transferred analogically into other domains and thus built into a comprehensive metaphysical universal harmony.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> The second part of the report describes how Leibniz was also aware of the study of proportion in music theory, which had already been closely connected with the concept of universal harmony, so that it was actually surprising that he did not also apply it together with his ideas on harmony. In an attempt to answer this question, the hypothesis was put forward that Leibniz had planned a synthesis of the two components, but was not able to take them any further; various remarks (written and oral) shortly before his death can be interpreted to indicate this.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> Studying Leibniz had brought another fact to light, which now had to be pursued. As was shown in the catalog of Leibniz's letters, published in 1899,</span><span id="footnote_ref-11" class="footnote_reference"><a href="#footnote_anchor-11">11</a></span><span lang="en-US" xml:lang="en-US"> there was an extensive correspondence with a certain Conrad Henfling, the content of which dealt exclusively with music theory, but which had not yet been published. From this it was clear from the outset of the research that another gap had to be filled, and that all previous statements on the subject “Leibniz and music” must be incomplete. This was also discussed at the 2</span><span style="vertical-align: super;" lang="en-US" xml:lang="en-US">nd</span><span lang="en-US" xml:lang="en-US"> international congress on Leibniz, and the result was that the director of the Leibniz Archives at the Niedersachsen State Library in Hanover, where all of Leibniz's legacy is preserved, asked the Author to undertake the editing of Leibniz's music-related writings, the major part of which was the correspondence with Henfling. A cursory examination, along with the assurance of the Leibniz Archive that the handwriting (very difficult to read) could be sent to Vienna in “plain text,” led to the acceptance of this task.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> Unfortunately, it soon became evident that the promise of delivering the texts in deciphered form could not be kept (except for one long letter in Latin from Henfling); but the Author's wife, Ursula Haase, decided to take on the task of transcribing this correspondence, mostly in French, from photocopies of the letters. The other assistants of the Institute, Leopold Spitzer and later Werner Schulze, were also involved in the difficult and time-consuming editing work, which took many years.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> While the transcription progressed slowly, the primary task was the solution of an important problem, namely that of finding information on the previously completely unknown Conrad Henfling. This was difficult, because no reference to him existed in any modern musicological literature. After a long search, sufficient information on him was found, and the results published.</span><span id="footnote_ref-12" class="footnote_reference"><a href="#footnote_anchor-12">12</a></span><span lang="en-US" xml:lang="en-US"> They are briefly summarized here.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> Conrad Henfling lived from 1648 to 1716 in Ansbach, and was a court counselor to the Margrave of Brandenburg-Ansbach, with whose daughter Caroline he had close contact. In 1705 she became electoral princess of Hanover (and in 1727, Queen of England). Leibniz lived in Hanover at the time, and he and Henfling became acquainted through the highly educated princess, leading to their correspondence between 1705 and 1711. The content of this correspondence relates mainly to music theory, which Henfling presents in the form of a long letter in Latin to Leibniz. Henfling's views are very idiosyncratic; this is due not only to the complexity of his letter, but even more to the non-pedagogical and sometimes completely incomprehensible nature of his writing. He asks many questions, and Leibniz finally calls in an expert, Alphonse des Vignoles, for advice. This leads Henfling to work towards improvement, and although not all obscurities are resolved, Leibniz decides to recommend a publication, which actually happens in 1710.</span><span id="footnote_ref-13" class="footnote_reference"><a href="#footnote_anchor-13">13</a></span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> This publication, as well as Leibniz's patronage, leads one to suppose that Henfling's name must have been known and preserved for posterity. But this was not the case. Johann Mattheson does mention him a few times; but in one of these cases there is a confusion of names, the background of which is extremely complicated. Finally, a method of tempering developed by Henfling was attributed to his contemporary in Ansbach, Georg Heinrich Bümler (1669-1745), and has been handed down under his name,</span><span id="footnote_ref-14" class="footnote_reference"><a href="#footnote_anchor-14">14</a></span><span lang="en-US" xml:lang="en-US"> while Henfling was already forgotten by the end of the Baroque period.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> Admittedly, clearing up Henfling's identity and his role in the history of music theory was only a byproduct of the actual work of editing, which continued gradually and finally led to the publication of the correspondence.</span><span id="footnote_ref-15" class="footnote_reference"><a href="#footnote_anchor-15">15</a></span><span lang="en-US" xml:lang="en-US"> The volume contains 27 documents with numerous annotations; an extensive commentary was also necessary, making up half the length of the publication, since many problems had to be explained. At the center is the music theory developed by Henfling, which he explains in the aforementioned Latin letter. To be precise, the core of the debate is a new method of tempering.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> This method is based on the application of multiple roots, and it yields an astonishing precision for 10-digit numbers, as is shown by comparison with the most prevalent temperings of the period. The calculations only work with the numbers 2, 3, and 5, thus avoiding the number 7, whose applicability in music theory was widely discussed at the time (and also in the correspondence). Henfling not only provides the values for a 12-step tempering, but also develops 19-, 31-, and 50-step subdivisions of the octave with equal precision, compiling them all in complicated and extensive tables based on the division of a monochord. Incidentally, in the justification of Henfling's method, virtually all other tempering methods known at the time (Huygens, Sauveur, etc.) are discussed. There is a very original further proposal by Henfling regarding the renaming of the familiar interval terms. He knew, very correctly, that the traditional theory of steps actually began with an error in reasoning, namely designating the keynote of a scale as a “prime” (1</span><span style="vertical-align: super;" lang="en-US" xml:lang="en-US">st</span><span lang="en-US" xml:lang="en-US"> step), although the sound is not an interval, not a step. Henfling suggests the term “nulla” instead, and based on this, he develops a highly different new terminology, which is one of the greatest complexities of his Latin letter.</span></p> <p style="text-align: left;" dir="ltr"><span lang="en-US" xml:lang="en-US"> The publication of the correspondence between Leibniz and Henfling finally makes possible the summarization of all aspects of the topic “Leibniz and music.” It is now clear that Leibniz must have at least had the knowledge of music theory that he uses in discussion with Henfling, which we have already summarized. But Leibniz did not get his knowledge only through Henfling; his answers suggest a considerable expertise in the field, which he must have acquired earlier and through which he is entirely on par with Henfling in their discussion. Leibniz even makes a few hints about this; but sadly, the details of his studies on music theory are not known-unless there is an as yet untranscribed remainder of his legacy that will one day give us information on this. Regardless, we must respectfully conclude that Leibniz, the great philosopher, mathematician, and universally learned man, the internationally famous savant of the Baroque period, possessed knowledge of the highest order in the domain of music theory.</span></p> <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"> R. Haase: a) “Kayser, Hans” in: Musik in Geschichte und Gegenwart, vol. 7, Kassel 1958;</span></p> <p><span lang="en-US" xml:lang="en-US"><br /> b) “Kepler, Johannes,” ibid.</span></p> <p style="text-align: left;" dir="ltr" awml:style="Footnote Text" class="footnote_text"><span id="footnote_anchor-2" class="footnote_reference"><a href="#footnote_ref-2">2</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> R. Haase: “Leibniz, Gottfried Wilhelm,” in: MGG vol. 8, Kassel 1960</span></p> <p style="text-align: left;" dir="ltr" awml:style="Footnote Text" class="footnote_text"><span id="footnote_anchor-3" class="footnote_reference"><a href="#footnote_ref-3">3</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> G.W. Leibniz: Epistolae ad diversos (ed. Chr. Kortholt), Leipzig 1734, p. 240ff (“Music is a hidden arithmetical exercise of the spirit unconscious of number”)</span></p> <p style="text-align: left;" dir="ltr" awml:style="Footnote Text" class="footnote_text"><span id="footnote_anchor-4" class="footnote_reference"><a href="#footnote_ref-4">4</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> R. Haase: a) “Leibniz und die pythagoreisch-harmonikale Tradition,” in: Antaios, vol. 5, no. 4, Stuttgart 1962;</span></p> <p><span lang="en-US" xml:lang="en-US"><br /> b) “Harmonikale Gedanken bei Leibniz,” in: Zeitschrift für Ganzheitsforschung, yr. 6, vol. 4, Vienna 1962;</span></p> <p><span lang="en-US" xml:lang="en-US"><br /> c) “Leibniz und die Musiktheorie,” in: Österreichische Musikzeitschrift, yr. 27, vol. 10, Vienna 1972;</span></p> <p><span lang="en-US" xml:lang="en-US"><br /> d) “Leibniz und die harmonikale Tradition,” in: Musikerziehung, yr. 26, vol. 2, Vienna 1972</span></p> <p style="text-align: left;" dir="ltr" awml:style="Footnote Text" class="footnote_text"><span id="footnote_anchor-5" class="footnote_reference"><a href="#footnote_ref-5">5</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> R. Haase: Leibniz und die Musik. Ein Beitrag zur Geschichte der harmonikalen Symbolik, Hommerich bei Köln, 1963</span></p> <p style="text-align: left;" dir="ltr" awml:style="Footnote Text" class="footnote_text"><span id="footnote_anchor-6" class="footnote_reference"><a href="#footnote_ref-6">6</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> R. Haase: Geschichte des harmonikalen Pythagoreismus, Vienna 1969</span></p> <p style="text-align: left;" dir="ltr" awml:style="Footnote Text" class="footnote_text"><span id="footnote_anchor-7" class="footnote_reference"><a href="#footnote_ref-7">7</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> R. Haase: “Leibniz, Gottfried Wilhelm,” in: Grove's Dictionary of Music and Musicians, vol. 10, London 1980</span></p> <p style="text-align: left;" dir="ltr" awml:style="Footnote Text" class="footnote_text"><span id="footnote_anchor-8" class="footnote_reference"><a href="#footnote_ref-8">8</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> R. Haase: “Leibniz und die harmonikale Tradition,” in: Akten des II. Internationalen Leibniz-Kongresses Hannover, vol. 1, Wiesbaden 1973</span></p> <p style="text-align: left;" dir="ltr" awml:style="Footnote Text" class="footnote_text"><span id="footnote_anchor-9" class="footnote_reference"><a href="#footnote_ref-9">9</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> J. Kepler: Weltharmonik (tr. and ed. by M. Caspar), Darmstadt 1984</span></p> <p style="text-align: left;" dir="ltr" awml:style="Footnote Text" class="footnote_text"><span id="footnote_anchor-10" class="footnote_reference"><a href="#footnote_ref-10">10</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> R. Habs: Kleinere philosophische Schriften von G.W. Leibniz, Leipzig 1883, p. 170 ff.</span></p> <p style="text-align: left;" dir="ltr" awml:style="Footnote Text" class="footnote_text"><span id="footnote_anchor-11" class="footnote_reference"><a href="#footnote_ref-11">11</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> E. Bodemann: Der Briefwechsel des Gottfried Wilhelm Leibniz in der königlichen öffentlichen Bibliothek zu Hannover, Hanover 1889</span></p> <p style="text-align: left;" dir="ltr" awml:style="Footnote Text" class="footnote_text"><span id="footnote_anchor-12" class="footnote_reference"><a href="#footnote_ref-12">12</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> R. Haase: “Korrespondenten von G.W. Leibniz, 3. Conrad Henfling,” in: Studia Leibnitiana, vol. IX/1, Wiesbaden 1977</span></p> <p style="text-align: left;" dir="ltr" awml:style="Footnote Text" class="footnote_text"><span id="footnote_anchor-13" class="footnote_reference"><a href="#footnote_ref-13">13</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> “C. Henflingii Epistola de novo suo Systemate Musico,” in: Miscellanea Berolinensia, vol. 1, Berlin 1710</span></p> <p style="text-align: left;" dir="ltr" awml:style="Footnote Text" class="footnote_text"><span id="footnote_anchor-14" class="footnote_reference"><a href="#footnote_ref-14">14</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> F. Krautwurst: “Bümler, Georg Heinrich,” in: MGG, vol. 15 supplement, Kassel 1973</span></p> <p style="text-align: left;" dir="ltr" awml:style="Footnote Text" class="footnote_text"><span id="footnote_anchor-15" class="footnote_reference"><a href="#footnote_ref-15">15</a></span><span style="font-size: 12pt;" lang="en-US" xml:lang="en-US"> R. Haase (ed.): Der Briefwechsel zwischen Leibniz und Conrad Henfling. Ein Beitrag zur Musiktheorie des 17. Jahrhunderts, Frankfurt 1982 (Veröffentlichungen des Leibniz-Archivs 9)</span></p> </div> </div></td></tr></tbody></table></span></div></div> </body> </html></div>
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