Theory of harmony

455 Pages·1978·23.12 MB·English

by  Arnold Schoenberg

THEORYO F
HARMONY
ARNOLD
SCHOENBERG
Translatedb y
ROYE . CARTER
UNIVERSITYO F CALIFORNIAP RESS
BERKELEY LOS ANGELES
CONTENTS
TRANSLATOR,S PREFACE PAGE XlI1
PREFACE TO THE FIRST EDITION I
PREFACE TO THE THIRD EDITION 4
I THEORY OR SYSTEMO F PRESENTATIONI z
il THE METHOD OF TEACHINGH ARMONY rj
m CONSONANCEA ND DISSONANCE 18
IV THE MAJORM ODE AND THE DIATONIC
CHORDS 2j
The DiatonicT riads 3r, Spacingth e Chords3 3, Connectiono f the Dia-
tonic Primary and SecondaryT riads 18, Connection of the Diatonic
Primary and SecondaryT riads in Short Phrases4 z,The VIIth Degree4 6,
The Inversionso f the Triads ;2, a The Sixth Chord 5y , ParallelO ctaves
and Fifths 6o, Connectiono f the Triads with the Sixth Chords,t he Sixth
Chords with the Triads and the Sixth Chordsw ith One Another 7r,
6 The Six-FourC hord7 5, SeventhC hords8 r, Inversionso f the Seventh
Chords8 9, Connectiono f SeventhC hordsw ith One Another9 z
V THE MINOR MODE
The DiatonicT riadsi n Minor 99, fnversiono f the Triadsi n Minor ro;,
SeventhC hords and their Inversionsi n Minor ro8
VI CONNECTIONO F CHORDST HAT HAVE NO
COMMON TONE (HARMONISCHES BAND) rtz
VII SOMED IRECTIONSF OR OBTAININGB ETTER
PROGRESSIONSC;O NCERNINGM ELODIC
CONDUCT OF THE TWO OUTER VOICES;
THEN CONCERNINGC LOSESC, ADENCES,
DECEPTIVEC ADENCESA, ND THE SIX-FOUR
CHORD IN THE CADENCE ttt
Guidelinesfo r usingt heM eanss of ar Introducedr z3,C losesa nd Cadences
rz;, DeceptiveC adencers3 6, The Six-FourC hord in the Cadencer4 3
VIII FREERT REATMENT OF VII IN MAJOR AND
MINOR 146
rX MODULATION rto
X CONTENTS
X SECONDARYD OMINANTSA ND OTHER NON-
DIATONIC CHORDSD ERIVEDF ROM THE
CHURCH MODES r7t
Guidelinesr 88, Conceming the Diminished SeventhC hord r9z, Guide-
lines for the Use of the DiminishedS eventhC hord zor
)(I RHYTHM (TAKT) AND HARMONY 2oz
XII MODULATIONS: CONTINUATION 2cl7
To the Third and Fourth CirclesU pward zo7,To the Third and Fourth
CirclesD ownward zr8
XIII RELATIONSHIPT O THE MINOR SUB-
DOMINANT zz2
Guidelinesz zy
XMT THE FRONTIERS OF TONALITY More aboutt he
diminished seventh chord; then about the augmented triad; fur-
ther: the augmented six-five, four-three, and two chords and the
augmented sixth chord (ofthe IInd degreea nd on other degrees).
Some other alterations of the IInd degree;t he samea lterations on
other degrees.C onnections of altered and vagrant chords 48
The AugmentedT riad z4r, AugmentedS ix-Five, Four-Three, Two, and
Sixth Chords,a nd SomeO ther Vagrant Chords 245
XV MODULATION TO THE IInd, Vth,A ND VIth
CIRCLESO F FIFTHS,T O THE VIIth AND VIIIth,
AND ALSO TO MORE CLOSELYR ELATED
CIRCLESB Y SEGMENTSA ND THROUGH
INTERMEDIATE KEYS 268
Fifth andS ixthC ircleso f Fifthsz z6
XVI CHORALE HARMONIZATION 286
Cadence(sSc hl,lsse3)o 1
'NON-HARMONIC'TONES
XVII rog
SuspensionD,o ubleS uspensioent,c .,P assingT ones,C hangingT ones,
Anticipation3s3 1
XVIII A FE\T REMARKS CONCERNING NINTH
CHORDS }4,
XIx SOME ADDITIONS AND SCHEMATIC
PRESENTATIONS TO ROUND OUT THE
SYSTEM 350
Alterationso f Triads, SeventhC hords,a nd Ninth Chords 3;o, Abbrevia-
tion of SetP atternsT hrough Omissiono f IntermediateS teps3 59,T riads
Connectedw ith All Other Triadsa nd SeventhC hords;a lso,A ll Seventh
Chordsw ith One Another 36o,S omeO ther Details:P ossibilitieos f the
CONTENTS Xi
AscendingS eventh;B assefso r the DiminishedS eventhC hord; a Chord of
Mozart;a n Eight-Part Chord 36y, Additional Schemesfo r Modulating
369,S omeA dditionalD etails3 8o,C oncerningF luctuatinga ndS uspended
Tonality 383,T he ChromaticS calea sa Basisf or Tonaliry 384
XX THE WHOLE-TONES CALEA ND RELATED
FIVE AND SIX-PARTC HORDS 3go
XxI CHORDSC ONSTRUCTEDIN FOURTHS
J99
XXII AESTHETICE VALUATION OF CHORDSW ITH
SIX OR MORET ONES
APPENDIX 42J
TOPICAL INDEX 43t
INDEX OF NAMES 44r
TRANSLATOR'PSR EFACE
Shortly after the revised edition of Arnold Schoenberg's Theory of Harmony
was published, his pupil and friend, Erwin Stein, assembleda Practical Guide to
Sc/zoenlerg's THEORY OF HARMONY: A Handbook for Teachers and
Pupils.r In his Preface, Stein stated the purpos€ of his Guide as follows:
TIis Guidei s designedt o facilitatei nstruction from Schoenberg'sT ieorjr of Har-
nony. ln view of the abundanceo f ideasa nd the great amount of spacet aken by
theoreticald erivationsa nd justificationso f harmonicp henomenab, y polemicala rgu-
ments,a nd by criticismso f the usuals ystemo f instruction,t he useo f that book may
have beeni nconvenientf or many a pupil who wantedm erely to learn or review the
handicrafto f harmony,a nd for many a teacherw ho only wanteda faciles urveyo f the
materialt o be taught.T \is Guides hould remedyt hat inconvenienceI.t leadst hrough
the courseo f instructiona nd indicateso nly thoset hingst he pupil must unquesdonably
learn.s
Schoenbergi ntroduced the Guide with a few comments of his own (appear-
ing at the head of Stein's Preface). He himself had instigated the writing of the
Guide; yet he could not gladly approve its stated purpose. His comments,
characteristically sardonic, include the following:
My Theoryo f Harmonyi s obviously much too long. Once its author is out of the
way - the living obstaclet o iudicious cutting - three quarterso f the text must then
surely go by the board.
For my part, this Guiderwrittena t my own behest,i s an attemptt o makee vent he
remaining quarter unnecessary.. . . One need only work diligently through this
Guide, forthriehtly taking what little is worth keeping; that way one can leavem y
entire Theoryo f Harmonya lone,u nchanged.s
The Guide, in outline form, cites page and line of Schoenberg's text where
the pupil or teacherm ay find the nameso f chords,i nstructionsf or building and
connecting them, pertinent examples,a nd suggestede xercises.T hese things the
'must
pupil unquestionably learn'; he may, if he chooses,i gnore all the rest. He
may ignore the prefaces, the first three chapters, and the first section of the
fourth, as well as the last chapter and many sentences,p aragraphs, and pages
from other chapters.R oughly estimated,t he unessentiapl ortions make up at
least one third of Schoenberg's treatise.
Yet, Schoenberg insisted throughout his Theory of Harmony that the pupil
L Praktiscfur Lei{aden 7u SchdnbergsH armonielehre:e in Hilfsbuchf ir Lehrer ud
Sch,nle(rV ienna: Universal-Edition,n ,d.). Stein'sP refacei s datedM arch, 1923.
z lbid., p. 1. I lb;d.
xtv
must unquestionably learn more than mere chords and rules for manipulating
them. It is true, his chief aim was to present the uaft of harmony, the harmonic
usage that had evolved prior to r9oo, and to present it as systematically as
possible, leading the pupil step by step toward mastery of that craft. Neverthe-
less, Schoenbergc ould not be satisfied with showing the pupil ion, something
'how',
is done; the teacher and pupil should search behind and beyond tlle
trying to find what it is, and why it is so, and indeed, whether it need be so.
Schoenbergu sed his harmony text as a vehicle for publishing his views, not
only on the origins, evolution, and implications of harmonic practice, but also
. . . on more complexr elationships. . . on the similaritiesa nd relationshipsb etween
artistic creationa nd other human activities,o n the connectionsb etweent he natural
world outsideo urselvesa nd the participatingo r observings ubject.l
Indeed, practically every topic, be it the major scaleo r the minor, be it parallel
fifths and octaves,n on-harmonic tones, modulation, or the minor subdominant,
leadsh im into wide-ranging speculationso n nature, art, and culture, and vigor-
ous attacks upon ossified or irrational aesthetics.T his prefacet o a translation of
the Harmonielehrei s hardly the place to discussS choenberg'ss peculations,b ut
it is perhapsn ot amiss to mention here one of the many writers who have done
'The
so. In his essay, Speculative Content of Schoenberg's Harmonielehre'rA
Professor John F. Spratt has ably summarized a number of Schoenberg'sm ain
ideas and addressed himself in particular to Schoenberg's attitudes toward
nature and culture. Professor Spratt views Schoenberg
. . . asa determiniswt ith respectto nature,a relativistw ith regardt o culture,a Spinozan
naturalisti n the senseo f regardingn aturea sa n exemplarys ystema nd regardingi nfer-
encef rom naturea s a vital force in culturerg
and concludest hat, in his considerabler everencef or nature and natural law, and
in spite of his cultural relativism, Schoenbergc learly remained within the Pla-
'No
tonic tradition of rationalism. law is eternal except as it removes itself from
the world of transientp henomena.'a
All these digressions from the strictly practical aim of his textbook Schoen-
berg justified on grounds that he was searching, as the pupil should search,f or
explanation. That the pupil should learn so to search - this Schoenberg con-
sidered his most important teaching. Hence, he could not give his unqualified
blessing to the Practical Guide.
From the 6rst chapter to the last, Schoenberge xplicitly renounced any claim
that he was writing a 'theory' of harmony or a 't*teory' of anything at all - at
least, not a systematict heory. But even if he did aim at a systematicp edagogical
presentation rather than a systematic theory, his presentation is nevertheless
saturated with theory, with speculation (the roots of both words denoted
'looking'and 'seeing', 'search');
and Schoenbergi ndeede xhorts us to thus the
only English translation of the Harmonielehre available heretofore, that of
I Infra, p. 17. 8 CurrentM usicology,X I (r97r), pp. 8i-8.
t lbid., p. 84. I lbid., p.88.
xv
Robert D. W. Adams, is entided Theory of Harmony,r as is the present trans-
lation. Yet Professor Adams, intending his translation as a practical student
edition, followed Erwin Stein's Guide, included only 'the essentials- explana-
tions, directions, examples' - and thus omitted from the Theory of Harmony
virnrally all of Schoenberg'st heoretical commentary.r
This new, complete translation grew out of the conviction that the abundance
'essential'
of Schoenberg'st heorizing, speculation, and polemics is no less than
the purely technical material. In fact, he so interwove the practical with the
theoretical that the one is incomplete without the other. For example, he de-
cried the usual exercisesb y which a pupil is supposed to learn harmony; the
realization of given figured bassesa nd the harmonization of given melodies. If
we would understand why he objected to such exercises,w hat alternatives he
recommended, and why he recommended these, we must read his theoretical
commentary together with his instructions on how to proceed.
Schoenberg's Theory of Harmony is indeed his seminal theoretical work. In
his later textbookss he was able to keep his theoretical commentary to a mini-
mum by simply referring the reader back to his earlier work. Moreover, he gave
expression inhis Theory of Harmony to a number of the notions that have most
excited the rwentieth-century musical world. Most obviously, there is the pro-
position that the system of major-minor tonaliry is no necessity of music, no
natural law - even if it is partially founded upon the natural laws of harmonics;
it is rather a convention, once viable, now exhausted,n ow undoubtedly to be
'tonalities'
modified or replaced by other conventions, perhaps by of rwelve
'tone
tones. Then there is the fascination with colour' (see the last two pageso f
the text); there is the notion that musical order may be manifest in many pre-
viously inconceivable ways; and there is the very questioning of the need for
order in music.
r (New York: PhilosophicalL ibrary, r948).The title Harmonielehrhea sb eenv ari-
'Manual',' Textbook',
ously translateda s'Treatiseo n Harmony',a nd or'Theory of
Harmony'. A Lehre can be a theory; it is, essentially,t he collection of facts, laws,
opinions,a nd theoriest aughtw ithit a certainf ield of learning.T extbookso f harmony
in Germang enerallyb eart he title, Harmonielehrea,s thosei n English are quite often
simply entitled Harmotty.T his, the most generalt itle, would perhapsb e the most
accuratet ranslationo f Schoenberg'sti tle; but sincet he book is far more theoretical
than the usual textbook of harmony, and sincei t is conrmonly cited in English as
Schoenberg'Ts hcoryo f Harmonyritwx deemeda ppropriateto retaint hat title for this
'Harmonielehre'
new translation.W ithin the text, however,t he word has beenv ari-
'instruction'
ously translateda, ccordingt o its context,a s or'course in harmony' and
the like, or'harmonic theory'.
8 Adams,i bid., p. xr.
s Mo&ls for Begilners in CompositionN, ew York G. Schirmer, r94z; Sructural
Functions of Earmony, New York: W. W, Norton, ry14; Preliminary Exercisesi n
CounterpoinLt,o ndon: Fabera nd Faber, 1963;a r,dF undamentalosf Musical Composi-
rrbz, London: Fabera nd Faber, t967.S eea lso his Style andf dea (LeonardS tein,e d.,
London: Fabera nd Faber, l97y): this volume of selectede ssays(w ritten by Schoen-
berg beveen I9o9 and r95l) containsm any referencetso topicsd iscussedin Theoryo f
Harmony.
xvl
This translation is based on the third, revised (improved) and enlarged
edition, completed in rgzr and published in ryzz. The first edition was pub-
lished in r9rr.r Since the appearanceo f the revised edition, it has been re-
printed a number of times. The last copyright date is ry49. The latest reprint
was edited by Josef Rufer, whose Preface is dated Autumn, 1966.A s noted in
his Prefacet o the seventh editionr2 Rufer made a few minor alterations follow-
'Handexemplar
ing Schoenberg'sm arginal notes (dated March, rgzz) in a mit
Fehlervormerkungen' (author's copy, indicating errata) and in addition deleted
four of Schoenberg'sf ootnotes. These alterations were not made in the present
translation, but they are cited at the pertinent places by translator's footnotes.
Rufer also corrected typographical errors in the examplesa nd made a few minor
revisions in their figuration. The examplesh ere have been revised according to
Rufer's correctionsa nd revisions.
ft is noteworthy that Schoenberg wrote the original edition of his Theory of
Harmony during approximately the same years in which he composed such
'The
works as the Three Piano Pieces,O p. t r, Book of the Hanging Gardens',
Op. ,t, the Five Piecesf or Orchestra,O p. 16, and Etwartung, Op. 17 - his
'atonal'
first works. Moreover, the revision of his book coincided approxi-
mately with the composition of the Five Piano Pieces,O p. ,j, the Serenade,
Op. .4, and the Suite for Piano, Op. - the first piecesi n which he ventured
'Method "l
his of composing with twelve tones which are related only with one
another.' Thus, it is perhapsn ot amisst o say that theset wo editions mark the
beginning and the end of the most critical period in Schoenberg'sa rtistic
career, the period in which, having finally assertedh is independencef rom the
old laws of tonaliry, he sought the stability of a new law.
The facts cited above can quite naturaily arouse one's curiosity as to what
changes he may have made in revising his Theory of Harmony. Here it must
suffice, first, to affirm that Schoenberg'sg eneral statementsi n his Prefacet o the
third editions accurately summarize the differences between the two editions,
and secondly,t o cite a few of the more important changes.
The changesr ange from substitution of other words, or even merely other
punctuation, to the extensiver evision of whole chapters (e.g. Chapters XI,
XVII, and XXI). Schoenberge nlargedv arious sectionss ubstantially,i n addi-
'Guidelines'
tion to the he specifically mentioned in the Preface. As is perhaps
to be expected,t he changesh e found necessaryw ere most often in the specula-
tive or polemical passagesm, any of which are longer in the later edition. Many
of his ideasw ere of coursec learert o him in ryzt than they had been in rgrI;
hence, they are more clearly expressed.A few passages,it must be admitted,
seeml essc lear in the revision. The essentials,t he principles set forth in the first
edition, remain intact in the third. One might describet he edition of rgzI as
merely a polisheda nd expandedv ersion of that of r9r r. The earlierm ight even
be viewed as a rough draft of the later.
However interesting the changesS choenberg saw fit to make, we should of
r Both editionsw ere publishedi n Vienna by Universal-Edition.
2 ffienna: Universal-Edition),p . fX. " I&o, pp.4-t.
xvlr
course also take note of those portions that remained unchanged. For example,
'Aesthetic
in the last chapter, Evaluation of Chords with Six or More Tones',
'Consonance
and in the third, and Dissonance',h e made only a few minor re-
visions. In Chapter IV, on the other hand, Schoenbergs o extendedh is footnote
on the more minute subdivision of the octave that it is now almost a chapter in
itself.l In the revised edition he went on in this footnote to deny that further
subdivision of the octave was necessarya s the next step beyond the tonal (dia-
tonic-chromatic) system. He went on to argue for the use of twelve tones,
elaborated polyphonically, as preferable, at least for some time, to further pro-
liferation of tones within the octave. Finer subdivision of the octave Schoen-
berg did not accept as, at that time, technologically feasibleo r culturally neces-
sary.
'The
Section 8 of Chapter XIX, entitled Chromatic Scale as a Basis for
'after
Tonality', was added to the first edition as an afterthought, completing
the book.' In the first part of this section,i n both editions, Schoenbergs um-
marized the principles of his Theory of Harmony. Then he went on to discuss
some minor chords that are remote from the key and suggestedt wo ways one
can relate, for example,m inor triads on dlr rb, f#, af, and b to the key of C
major. He then continued (pug +l+ of the first edition, page 387 of this trans-
lation):
A third and more significantw ay, however,w ould be to work out an idea already
mentionedi n this book: to baseo ur thought, not on the sevent ones of the major
scale,r ather,o n the rwelveo f the chromatics cale.
Then, in the first edition, having thus arived at the topic indicatedb y the title
of this section,h e simply dismissedt he topic by saying that'a future theory will
undoubtedly follow that coursel it would thereby reach the only correct solu-
tion to this otherwise difficult problem.' The chapter then ended with a short
paragraph merely repeating a point he had made earlier, that all chords can be
'
vagrant', even triads.
The title of this section therefore seems unjustified in the first edition.
Whatever the reasonf or the lamee nding in r9r r, he did continuei n the revised
edition. Instead of the hasty appeal to some future theory, Schoenbergn ow
pursued the topic indicatedi n his title, at which he had just arrived in r9r r, by
'such
outlining how a theory could begin.'2
Now, after that outline Schoenbergc oncluded the chapter by stating rwo of
the assumptions that underlie both his book and his music that the evolution
of harmonic theory had reached a frontier it could not cross, at least not for a
while; and that, therefore, music now stood at the door to a new polyphonic
'harmonies
era, in which, as in past times, will be a product of the voice leading:
justified solely by the melodic lines!'8
In the edition of r9r r, again in Chapter IV (p. 3r), he wrote:
It should not be said that order, clariry, and comprehensibilityc an impair beauty,
' Irfro, Appendix, pp. 421-r. ' I4fro, pp. 382-9.
3 Infra, p. 389.
xviii
but they are not a necessarfya ctor without which therew ould be no beauty;t hey are
merelya n accidentala, circumstantiafla ctor.F or naturei s alsob eautifule venw hen we
do not undetstandh er, and where shes eemsto us unordered.
He rewrote this passagea s follows:
This is not to say that somef urure work of art may do without order, clarity, and
comprehensibiliryb, ut that not merelyw hat we conceivea ss uchd eservesth esen ames.
For naturei s also beautiful.. . .1
Schoenberg seemst o have said in rgrr that order in music is unnecessary,a t
leasta s far as beauty is concerned,a nd in rgzr that it is necessaryb ut can be con-
ceived much more variously than is commonly assumed. Perhaps the latter
statement merely makes clear what he had intended to say in the first edition.
However that may be, he maintained in both editions that the listener's interest
in order and beauty surpassest hat of the composer, and that order and beauty
may be attributes, not of the music, but of the listener's perception. Yet, his
efforts during those years (c. r9o9-zr) to define the order, or to createo rder, in
'atonal'
his works led him to devise a method which, pursued to its logical con-
clusions,c ould perhapsc reatet otal order in a piece of music. Of course this
possibility of total order, theoretically attainable by rigorous application of
serial methods to all aspectso f music, did not seemt o interest Schoenberga s
'Method
it hass ome subsequenct omposers.H e did, neverthelessi,n vent the of
composing with twelve tones which are related only with one another' and
thereby demonstrated that Schoenberg, the composer, was, after all, looking
'order,
for some explainable clarity, and comprehensibility'in his music.
Schoenberg undoubtedly referred to such statements as that quoted above
from the original edition when he wrote (in ry4g) of exaggerationi nhis Theory
of Harmony, of the intoxicating
enthusiasmo f having freedm usic from the shackleso f tonaliry. . . . In fact, I myself
and my pupils Anton von Weberna ndA lban Berg,a nd evenA lois Hiiba believedt hat
now musicc ould renouncem otivic features[a sw ell] andr emainc oherenta nd compre-
hensiblen everthelesIs.
For the edition of r9rr, toward the end of Chapter XXI,'Chords Con-
structed in Fourths', Schoenberg wrote a long footnote attacking aesthetic
dogma and the aestheticiansa nd theorists who try to preserve that dogma. In
the revised edition this footnote, thoroughly reworked and greatly expanded,
appearsa s text, as the last secrion ofthe chapter; and for the revised edition he
also wrote a new footnoters discussing and denouncing the use of the word
'atonal'
and its implications. In fact, he mentioned that word only twice in his
Theory of Harmony (the other instance is on page rz8). This is after all a text-
'atonal'
book of taditional, tonal harmony and has nothing to do with his and
twelve-tone music. Nothing to do, that is, explicitly. But with this book (and
t I&q pp. 29-1,c..
s'My Evolution',M usical QuarterlyrXXXVIII, No. 4, October,rgj2, pp. t2+-J.
The articlew as completedi n August, 1949.
t It o, Appendix,p . 4rz.