Table Of ContentSigfrid Karg-Elert’s
Precepts
on the
Polarity
of
Sound
and
Tonality
Complete Original German Text
and Illustrations Reprinted
with English Translation
by
Harold Fabrikant
and
Staffan Thuringer
iii
Original German text supplied as a facsimile by Anthony Caldicott
on behalf of the Karg-Elert Archive
from an original print of the edition by F.E.C. Leuckart, Leipzig 1931
held in the British Library, London
English Translation
by
Harold Fabrikant and Staffan Thuringer
2003 – 2007
Introduction
by
Harold Fabrikant
2006
Restoration of figures,
layout and printing:
Terry Truman
First published — October, 2007
By Dr Harold Fabrikant
37 Maxwell Grove
Caulfield. Victoria 3162
Australia
National Library of Australia Cataloguing-in-Publication Data
[Polaristische Klang- und Tonalitätslehre(Harmonologik) English]
Sigfrid Karg-Elert’s precepts on the polarity of sound and tonality.
ISBN 978-0-9804162-1-3 (CD-Rom version)
1. Polarization(Sound). 2. Tonality. 3. Harmony. 4. Music theory
I. Fabrikant, Harold. II. Thuringer, Staffan. III. Title.
781.25
This work is also available in a printed edition
complete with recorded examples CDs
ISBN 978-0-9804162-0-6
Please note that the English translation in this book is not subject to
copyright. On the condition that use of, or reference to, the translation
is suitably acknowledged by reference to the title of this work, and to
the translators, we welcome the use of this material.
iv
Foreword
It is a great privilege to be asked to provide a Foreword to this monumental
work, the result of many years' intensive study by Dr Harold Fabrikant, with
the invaluable assistance of Staffan Thuringer and Terry Truman. Ever since
I received the gift of Karg-Elert's Theory of Polarity photocopied and bound
through the good offices of the British Library, the concept of its being made
available to the English-speaking world has been an objective of the Karg-
Elert Archive. Such a project also received the enthusiastic support of our
late Vice-President, Dr Felix Aprahamian. As Karg-Elert's 'Letters to his
Australian Friends' (The Harmony of the Soul, published by Dr Fabrikant in
1996) make clear, the composer regarded an English version as 'an act of
culture'. Many years later, Karg-Elert's Australian friend and advocate, Dr
Arthur Nickson, wrote an essay on the composer in which he referred to the
Polarity book as 'a fully documented volume on Modern Harmony, which
would be of priceless value to musicians acquainted with the author's
original ideas on Tonality, Modulation, Enharmonic systems, and the Whole
Note and the Twelve Note experimental scales'. (The Harmony of the Soul, p.
96)
Those who admire, study and play the music of Karg-Elert are already
indebted to Dr Fabrikant for his outstanding work in the compilation of the
composer's letters in The Harmony of the Soul and also for completing the
translation of all the correspondence to Godfrey Sceats (Your Ever Grateful,
Devoted Friend, 2000) as well as that of the composer and his daughter
during his North American tour of 1932 (Everyone is Amazed, 2002). The
light which these collections shed on Karg-Elert's character and work has
now been even more fully enhanced by an achievement in musicology which
confirms the composer's own assertion: 'I know that I have, by this book,
gained a place in the history of music'.
Anthony Caldicott
Chairman, the Karg-Elert Archive
v
Contents
Acknowledgements ......................................................................................ix
Introduction ................................................................................................... x
Some Explanatory Notes ........................................................................ xviii
Karg-Elert’s Foreword ................................................................................. II
Main index ........................................................................................... IV – V
Alphabetical Index of composer’s musical texts ............................... VI - VII
First Part – Fundamental Introduction .......................................................... 1
Second Part – The System of Harmony in Polaristic Perception
Fifth relationship: Diatonality ........................................... 69
Third Part – The System of Harmony in Polaristic Perception
Third and Seventh Relationship: Chromatic Tonality ....... 173
vii
Acknowledgements
Several generous people have been essential in this prolonged project. Anthony
Caldicott of the Karg-Elert Archive was the first, showing me the photocopies of the entire
text held by the Archive in London. That was late in 2002 and I expressed dismay over my
difficulty in understanding the text and the exceedingly complicated illustrations. I resolved
to make a start but this came to very little. Only much later, as the work unfolded in 2003—
04 and it seemed likely completion would ultimately occur, did I ask Anthony Caldicott to
photocopy the complete book from the Archive’s copy and post the sheets across. This he
did, with great courtesy. Extra copies were made here, as there were now three people
needing access, all in different places. A copy of the facsimile edition by Peter Ewers was
purchased still later, a most fortunate acquisition.
In 2003, I was introduced to Staffan Thuringer in Melbourne and was delighted to find
him interested, even enthusiastic. Staffan, of Swedish origin, and also fluent in everyday
spoken German, has been a tower of strength. Without his invaluable assistance, the
translation would have been permanently abandoned.
Terry Truman in Adelaide represents another essential ingredient, responsible for
restoring all illustrations from second or third generation photocopies, a stupendous
undertaking, sufficient to test the patience of Job. He has also handled printing, layout and
binding. The magnificent appearance of the final work is all due to his care and attention to
the finest detail. Proof-reading has been my responsibility.
I am completely indebted to all these good friends. Here was truly a chain in which all
links had, by necessity, to withstand an equally high load and to do so over several years.
Special terms posed additional difficulties. I have been fortunate in the ready
assistance received from the staff of the Music Library at the University of Melbourne, where
I have been a frequent visitor. Of particular help has been the “Dictionary of Terms in
Music”, K.G. Saur, 1981, which the kindly librarians allowed me to retain for months at a
time. My own Collins German-English Dictionary, 1980, was of course in perpetual use.
Many passages have still posed great difficulty in translation. At times of uncertainty, I have
taken refuge in a more literal change into English, trying always to avoid corruption of K-E’s
intention in seeking something which seems more readable. I am aware that mistakes must
inevitably remain and for these I take sole responsibility. Readers are invited to make
comments in our wish to improve the work.
H.F., August 2006
ix
Introduction
Sigfrid Karg-Elert (‘K-E’ hereon), 1877—1933, was a supreme authority on harmony in
music. His numerous compositions furnish all the evidence needed in making such a
sweeping statement, for which I offer no apology. He sought the analysis of harmonies and
their sequences, representing them as symbols (or ‘grammalogues’, as he put it). This
implies his ability to pass such ideas over to others and, at first glance, suggests an excellent
teacher. That this was not the case will however unfold. The notion of symbols was not
entirely new but he extended it to an extreme degree. At the same time he developed
concepts of harmony which evolved from the foundations laid by 19th century German
musicologists; this formed a new science, their domain. He acknowledges his debt to some
of them in the body of the text, but immediately denigrates their contribution compared with
his present level of understanding! Moreover, his preface (pp. II—III) makes no mention of
their essential role, which will be presented in some detail later in this introduction.
Instead, K-E claims that in the early 1900s, intuition revealed to him the basic
proposition of polarity in music, viz., that the major and minor chords are natural
phenomena of equal importance. (By ‘natural’ he means the sound of the human voice or
acoustic musical instruments, not their synthetic counterpart.) Major and minor are
different from, and influence, each other but the names are misleading in suggesting one is
more important than the other.
In 1919, K-E became teacher of composition and theory at the Leipzig Conservatorium,
which was founded in 1843. In 1924 it was renamed Leipzig State Conservatorium and in
1927, the year he attained the age of 50, he was made a member of the Conservatorium
Senate. However, it was not until 1932 that he was elevated to professor. By then it was too
late to be more than a symbolic gesture for he was desperately ill, following an ill-advised
concert tour of North America in the first three months of that year. His decline continued
and death occurred in April 1933, aged only 55.
There was no shortage of German textbooks on harmony by the 1920s. But by then
K-E had already worked out his concepts of polarity sufficiently that this is what he taught.
He planned to publish these ideas but was greatly delayed, so that the preface (referred to
above) is dated Autumn 1930. It seems reasonable to assume that the content of the
published work and his lectures were at least similar, if not identical.
Throughout the 1920s, K-E was very close to his pupils. He was an extremely
colourful, outspoken eccentric and several pupils became his friends (even lovers); they were
frequent visitors at his home over long evenings, despite the needs of his faithful wife Minna
Louise (“Liesel”) Kretzschmar, 1890—1971, whom he married in 1910, and their beloved
daughter Katharina (“Katie” or “Kitty”), 1914—84. K-E’s enormous letter to the Nickson
circle in December 1923 claims that his students no longer have any trouble with their
theoretical studies(!):
“The giant province of Harmony, Modulation, Tonality and Atonality, and the
Phenomena of Sound from the many thousand-fold dissonance-colours, lie
before us like an open book — and everyone can read it and understand. I have
experienced it with my students when they arrive stuffed up with the dust of
Jadassohn’s dead documents — unload the whole mess within 10 minutes
and — new and free of prejudice climb into the Philosophy of Sounds of Cells
and of Cosmic Polarism. In only 14 days they are as if transformed and
Palestrina, Gesualdo and Monteverdi are as fluent for them as Debussy,
Scriabin or Schönberg. All the Masters simply obey a divine dictate, a cosmic
compulsion which in the case of us relatively egocentric beings cannot express
itself otherwise than through polarity.” (The Harmony of the Soul, 1996, p. 56)
K-E was however deluded. The students were so horrified by his hieroglyphics (even
more than his concepts) that some found the courage to petition the Conservatorium Senate,
seeking to have his teachings excluded from their examinations. Equally remarkable: the
x
Senate agreed and K-E’s material was never examined! (Ref. Sigfrid Karg-Elert und seine
Leipziger Schüler; von Bockel Verlag, Hamburg 1999, p. 31)
Meanwhile, K-E was committing his thoughts on polarity to paper. As early as 1923,
according to the letter mentioned above (p. 57), he planned an English edition, to be done
under his authority by Greta Bellmont in Australia, Nickson’s chief translator. He already
envisaged approaching Novello for publication, for they had put out the Lake Constance
Pastels, Op. 96, that year. Bellmont made only one return trip to Germany, in 1926, and
visited K-E when the subject of ‘polarity’ arose: “The big book which I am to translate is not
yet finished by the printer. I can see already how very interesting it will be.” (Harmony of
the Soul, p. 81) Bellmont’s diabetes became uncontrolled whilst she was in Germany and a
stay in hospital was necessary. She returned to Australia and died about 12 months later
(presumably from the same disease or its complications). The idea of an English version
died with her. K-E had already entered a contract with the Leipzig published Leuckart but as
the book grew in size and complexity, the proprietor, Martin Sander, decided to withdraw
from the agreement! K-E wrote to Bellmont in July 1926 of his misery:
“But this work — my life’s goal — has had ominous misfortune. 380
engraving plates, on which the International Firm C.G. Röder has worked for
exactly a whole year, and which are ready for printing (they look ravishingly
beautiful!), still lack about 80 pages on Atonality and 4ths and 6ths respectively
— and now that the work becomes considerably larger than originally agreed
upon, my publisher C.F. Leuckart (Martin Sander) has annulled the contract,
thus declaring it invalid. Since 1902, I have worked unswervingly, day and night,
on this gigantic work which on each page opens completely new spheres and
which is without doubt the Precepts of Harmony of the future, — and now . . . . . .
I stand before nothing!
I do not know what will happen: I cannot offer the work to another
publisher as 380 plates are already complete and belong to the publishing-house.
But the publisher is unable to start doing something with the torso and
furthermore he will not. The engraver and lithographer is demanding however
his approximately 5,000Mk manufacturing costs. He cannot be made good by
me but instead by the publisher, who again makes me liable for having exceeded
the limits of the contract. Well, a lawsuit in our dear Fatherland can run for 2—3
years. Lawyers also want to live . . . . . ” (Harmony of the Soul, pp. 82—83)
One can easily see what has happened. Sander agreed to publish a work which was
probably merely a plan or sketch, and then found he had a far larger, more mysterious
volume on his hands than business sense could accept. The engraver had had (was still
having) a frightful time in setting the type (all by hand in those days) and wanted payment.
The merest glance at this book reveals how ‘impossible’ was the task: not the text, but the
endless diagrams and legends with their hieroglyphics which would stun the readers.
Misprints there are, not surprisingly, even for such meticulous workers, some of which have
been corrected here wherever recognition has made this possible. The dispute did come to
the law courts where settlement was made; how K-E could find the money for this is
amazing. It seems likely that neither side came out as ‘winner’, more a compromise allowing
the work’s completion. K-E wrote to Sceats in March 1931 of that happy conclusion:
“On the 15th January I sold my Organ Symphony to C.F. Peters, and finally
my child of sorrow Polaritätslehre (Harmonologie) was published. I have
worked on this without pause since 1902. It is unfortunately an expensive
publication and will therefore have a limited circulation! But my work will not go
with me into the tomb. I know that I have, by this book, gained a place in the
history of music!!” (Your Ever Grateful, Devoted Friend, 2002, p. 31)
One is left to speculate how many copies were printed: perhaps a few hundred?
Economic conditions were appallingly bad in Germany and this ‘difficult’ text could never be
a best-seller in musical circles. To compound the position, two major events followed: (a)
the death of K-E in April 1933, leaving the way clear for rivals, especially Hermann Grabner
(v. infra) and (b) the inclusion of K-E’s name in the Nazi’s scurrilous pamphlet: ABC of Jews
xi
in Music. K-E may have looked the part but his father was Catholic and his mother
Lutheran; he was brought up Lutheran but swung towards Catholicism in the 1920s and
occasionally produced his own anti-Semitic remarks in his letters. Baptised Siegfried Karg,
he added his mother’s maiden name (Ehlert) with slightly altered spelling to give the
hyphenated Karg-Elert in 1902, when a piano instructor at the Magdeburg Conservatorium,
on the advice of the Director. A Jewish merchant in that city had the name Karger and they
were apprehensive the young musician might be confused with him; worse still, might be
thought to be Jewish himself. (Anti-Semitism was then well-entrenched in Germany; the
Nazis had merely to exploit it.) The inclusion of K-E’s name in the Nazi pamphlet was later
acknowledged to be wrong and it was removed, but irreparable damage may already have
occurred. Whether copies of the book were actually destroyed by the Nazis is uncertain.
Few came to English-speaking countries, e.g., a copy is held in the Library of Congress,
Washington, D.C. and the copy in the British Library, London, is probably the only one in
the U.K. Not one has been found in Australia. Nickson, writing in the 1950s, thought this
work, among others, had been lost:
“Mention should be made of the loss of much material left by the composer
after the World Wars, particularly of a fully documented volume on Modern
Harmony, which would be of priceless value to musicians acquainted with the
author’s original ideas on Tonality, Modulation, Enharmonic systems, and the
Whole Note and the Twelve Note experimental scales.” (Harmony of the Soul,
p. 96)
Comments such as Nickson’s, assuming the worth of K-E’s ‘polarity’ text, also come
from other quarters, their common features being a complete faith in K-E’s knowledge of
harmony, an assumption of his capacity to write a lucid text on the subject and ignorance of
the book’s actual content. Those who did see it in Germany in the 1930s were not so
enamoured. The work was judged unreadable and that remains the belief of some
contemporary Germans (Sigfrid Karg-Elert und seine Leipziger Schüler, p. 31). A major
difficulty lies in the symbols, which K-E, we must presume, found simplicity itself. Indeed,
they pose no problem where the harmony is straightforward (examples will be provided
below) but they become intolerable, meaningless to most of us as the complexity increases.
There is also a distressing degree of inconsistency. Most terms are defined but even these
may be difficult to follow. K-E attempts a format analogous to the great Oxford English
Dictionary, viz., explain the meaning of a word and then illustrate its use over the decades,
even centuries, by various writers. Thus an analytical text on harmony, not a practical
handbook for budding composers. A prodigious number of musical examples is provided,
many of great interest in themselves. K-E advances right up to atonality but includes
relatively few extracts from his own works, choosing instead his more famous
contemporaries and preceding composers. At the other end of the scale, Grabner’s texts
were standard reference works, evidently much easier to grasp; some came out in multiple
editions over several decades whilst K-E’s books were ignored.
In 2004, an enormous service has been carried out by the release of a facsimile edition
of ‘Polarity’ by the publisher Peter Ewers of Paderborn; a large preface is given by
Dr. Thomas Lipski (with English translation). Their source is a library copy in Weimar and
the volume is entitled: Sigfrid Karg-Elert — Die theoretischen Werke, ISBN 3-928243-16-0.
Two other works by K-E are included. Those fluent in German thus have had ready access
from 2004 and with the present translation, English readers may also avail themselves of the
work. That was of course K-E’s wish. He hints that readers should think deeply about his
concepts and argue a contradictory case if they feel so moved. Whatever we think of the
work, it represents the highest development of the polaristic concept and, if only for that
reason, is important historically. Of all the pupils of K-E, Paul Schenk (1899—1977) became
his leading advocate. He taught at the Leipzig State Conservatorium for several decades and
wrote some texts. Even Schenk, however, seems to place himself at a distance from the
polaristic viewpoint; in any case, he took it no further.
K-E’s preface to ‘Polarity’ is rather rambling and suggests his ideas were evolved on
philosophical grounds. There is, however, no possibility that he was unaware of the great
xii
musicologists still alive in Leipzig and of their fundamental work on polarity. In a footnote
(p. V) he refers us to a second text: Acoustic Regulation of Sound and Determination of
Function, Leipzig, 1930. He labels it ‘supplement’ or ‘complement’. Ewers gives a facsimile
of it in his work of 2004. Much shorter than ‘Polarity’ (96 pages vs. 327) it is given as an
exquisitely hand-written text with equally complicated diagrams and musical examples. In
the place where a preface is expected, a succinct summary is given, thus —
“Instead of a preface:
The number is the essence of all things (Pythagoras).
Relations in music truly seem to me the basic relations of nature.
The concept of mathematics is the most valid witness of idealism in nature; the
deep interrelation, the sympathy of the universe is its basis.
Pure mathematics is the notion of reason as universe. It appears in music
formally as revelation, as creative idealism (Novalis).”
To these, Lipski adds:
“The whole is more than the sum of its parts (Aristotle).”
{Pythagoras, ca. 582—ca. 500 B.C.; Novalis: pen-name of the German poet Friedrich von
Hardenberg, 1772—1801; Aristotle, 384—322 B.C.}
K-E thus wishes harmony to be placed on a scientific basis. He refers in the text to
Gioseffo Zarlino, 1517—90, whose work on harmony (published in 1558) stated “sine scientia
ars nihil est” — “without science, art is nothing”. Musicology arose in Germany during the
19th century; the major proponents even lived and taught in Leipzig. Here is some
background detail which unquestionably forms the basis of K-E’s work:
Hermann von Helmholtz, 1821—94, pursued medical studies in Berlin and graduated
in 1842, but also studied mathematics, physics and philosophy. He came to hold
professorships in anatomy, physiology and physics. Admittedly, the sum of knowledge then
was small compared with the present, but this was still an amazing achievement. His
research activity was maintained over a broad range. He invented the ophthalmoscope (still
in everyday use), created the fields of physiological optics and acoustics, and some aspects of
the science of electricity. He studied the anatomy of the human ear and founded works on
the physiology of hearing. Helmholtz explored the role of harmonics in timbre and that of
beats in consonance vs. dissonance. He published a text in 1863: Die Lehre von den
Tonempfindungen, embodying his principle studies on acoustics, which was translated into
English (1875) under the title: On the Sensation of Tone. In it was his nomenclature of pitch,
still the standard in Germany and employed by K-E in his ‘Polarity’, reproduced below. The
English equivalent is shown, plus the modification by Sir James Jeans (Science & Music,
1953) which combines the German treble designation with the English bass and, because of
this union, is used in the English text here:
Organ pipe length 32’ 16’ 8’ 4’ 2’ 1’ 6’’ 3’’ 11/2’’
Frequency (c.p.s.) 16 32 64 128 256 512 1024 2048 4096
Germany C’’ C’ C c c1 c2 c3 c4 c5
England CCCC CCC CC C c c1 c2 c3 c4
Jeans CCCC CCC CC C c1 c2 c3 c4 c5
In trying to explain harmony on scientific principles, Helmholtz immediately came into
difficulty with the minor chord, which he pronounced ambiguous and acoustically impure;
from that he concluded minor chords were inferior to their major counterpart. This however
struck him as nonsensical, obliging him to produce excuses in his writings. These failed to
solve the problem.
Gottfried Weber, 1779—1839 (q.v., p. 61), German composer and, more important,
theorist, whose published works appeared ca. 1820—30. He refined the work of earlier
xiii
writers to produce a simple system of chord representation, still in use. Thus capital (upper
case) letters denote major keys, small (lower case) letters the minor. Roman numerals
denote the scale degree (‘step theory’) on which a chord is based, e.g., v = the dominant.
Major/minor qualification of the step is represented by upper/lower case letters. Thus, the
following sequence:
“D: ii iv V I” represents, in D major: E minor triad, G minor triad, A major triad and
finally, D major triad. Weber was aware of the same triad appearing on different steps in
different keys, e.g., C major triad is C:I or a:III or G:IV, referring to this as “Mehrdeutigkeit”
(multiple meaning or ambiguity). This would be expanded by later writers.
Ernst Friedrich Richter, 1808—79, (q.v., p. 61) theorist, teacher and composer. He
came to Leipzig University in 1831 to study theology but soon turned to music. He became a
founding teacher of harmony and counterpoint at the Leipzig Conservatorium (1843) and
was also Thomas-Cantor from 1868, succeeding Hauptmann, when he was elected professor
at the Conservatorium. Richter’s Textbook of Harmony (1853) was adopted as the official
text at Leipzig. By 1953 it had gone through 36 editions and been translated into 9
languages! Richter followed closely Weber’s theories, adding refinements, e.g., to denote
augmented and diminished chords.
Moritz Hauptmann, 1792—1868, theorist, composer and teacher, born in Dresden.
Thomas-cantor from 1842, foundation teacher of theory and composition at the Leipzig
Conservatorium (1843) and a foundation member of the Bach Gesellschaft (1850). His text
of 1853 was not a practical but a philosophical account of musical events: major elements are
termed ‘unity’, ‘opposition’ or ‘re-union’ (= higher unity), depending on their degree in the
scale and whether major or minor. His source may have been Hegel’s philosophy but, in any
case, his theory is often labelled ‘Hegelian’. In it he conceives major and minor triads as
opposites, the major represented as ascending from the root and the minor descending from
the fifth (as if suspended from it). This concept is the very basis of ‘polarity’.
Arthur von Oettingen, 1836—1920, came from Dorpat, Livonia (now Tartu, Estonia).
His university training in Dorpat and Berlin was in physics, mathematics and physiology,
from 1853 to 1863! An associate professor of physics by 1865, he was already professor the
next year. At the same time he was a capable amateur musician (e.g., orchestra conductor).
His academic life was distinguished. In 1894 he retired from official university work and
settled in Leipzig where he was hon. prof. until 1919. Apart from his scientific articles, he
published a text on music theory in 1866 which won acclaim: System of Harmony in Dual
Development. It opposed the work of Helmholtz (1863) regarding the latter’s concept of
consonance vs. dissonance. Oettingen’s text was expanded further in 1913 as The Dual
System of Harmony (or Harmonic Dualism).
Even in 1866, Oettingen had developed further the idea of opposing major and minor
triads sharing a common note called “tonica” e.g., the major triad C-E-G, designated c+, is
mirrored by the minor triad F-A -C, designated co, where the two chords share a common C.
This gave rise to the terms Oberklang (upper sound) for the major triad and Unterklang
(lower sound) for the minor; in this example; ‘C Oberklang’ vs. ‘c Unterklang’. He also
postulated a “tonic major scale” (e.g., c1 to c2), mirrored by a “phonic scale” (in this instance,
e2 down to e1, which is the “common” [or melodic] minor scale of A minor from the
dominant. This aspect was not taken up by K-E but the concept of mirrored major/minor
triads is fundamental to his ‘polarity’, and that name will generally be used hereafter instead
of ‘dualism’.
In the body of the following text, ‘Oberklang’ is translated ‘upper sound’ or ‘upper
triad’. ‘Unterklang’ is translated ‘lower sound’ or ‘lower triad’, unless the context requires
otherwise, when ‘hanging triad’ is substituted.
Hugo Riemann, 1849—1919, German giant of musicology, the pre-eminent scholar in
music and teacher of his time. He was initially a capable pianist, trained in Berlin and
Tübingen, who came to Leipzig in 1871 and became acquainted with Oettingen’s dualism. He
left to take up various teaching posts elsewhere between 1876 and 1895, then returned to
Leipzig and was elevated to professor in 1901. He produced about 20 textbooks and had an
xiv
