TONAL VOICE-LEADING in SCHOENBERG's OPUS 1 5 Grace

TONAL VOICE-LEADING IN

SCHOENBERG'S OPUS 15

Grace A. L. McNab

B. Mus., The University of British Columbia, 1979

A THESIS SUBMITTED IN PARTIAL FULFILMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF MUSIC

THE FACULTY OF GRADUATE STUDIES

Department of Music

We accept this thesis as conforming

to the required standard

THE UNIVERSITY OF BRITISH COLUMBIA

April 1982

© Grace A. L. McNab, 1982 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.

Department of Music

The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3

Date March 2b, 1982

DE-6 (3/81) V ii

ABSTRACT

This study deals with the processes of tonal

counterpoint inherent in the songs of Schoenberg's Opus 15i

"Book of the Hanging Gardens" and, by implication, in

related works.

Chapter I, "The Concept of Harmonic Voice", introduces

the conceptual key to the manner of investigation presented

herein. Simply stated, "harmonic voices" consist of the

strongly-directed, predictable motions by semitone and

whole-tone, and the common-tone connections which occur from

one chord to the next in a tonal progression. Examples of

strongly-directed motions are the rising of the leading-

tone and falling of the minor seventh of a dominant-seventh

chord, and the diverging motions present when an augmented

sixth progresses to an octave on the dominant. To show

how the harmonic voice concept may be applied in analysis,

passages from Opus 6, Number k are examined.

Chapter II, "Harmonic Procedures Which Minimize

Diatonic-Chromatic Differences", deals with specific types

of harmonic voice motion which are common to chromatic passages and simpler, more overtly tonal ones. The lack of

importance which the harmonic voice concept attributes to

the presence or absence of the root of a chord is emphasized.

The harmonic procedures discussed come under the following

subject headings: "The Tritone-Substitute", "The Minor- iii

Seventh/Augmented-Sixth Potential of 'Whole-tone' Chords",

"Double-Neighbor Pairs in 'Whole-tone* and Other Contexts",

"The Minor-Third Relationship", and "The Minor-Second

Relationship". Passages from songs of Opus 3i 6, 12, and

14 are analyzed.

Chapter III is a detailed analysis of Opus 1$,

Number 5$ which applies the harmonic voice concept and attempts to expose the harmonic devices dealt with in

Chapter II.

Chapter IV is a detailed analysis of Opus 15,

Number 11.

Signature of Thesis Supervisor iv

CONTENTS

ABSTRACT ii

LIST OF ILLUSTRATIONS -v

EXPLANATION OF GRAPHIC SYMBOLS USED IN THE

ANALYTICAL SKETCHES x

ACKNOWLEDGEMENT xi

CHAPTER I. THE CONCEPT OF HARMONIC VOICE 1

CHAPTER II. HARMONIC PROCEDURES WHICH MINIMIZE DIATONIC-CHROMATIC DIFFERENCES 18 The Tritone-Substitute (18)—The Minor-Seventh/ Augmented-Sixth Potential of "Whole-tone" chords (24)—Double-Neighbor Pairs in "Whole-tone" and Other Contexts (30)—The Minor-Third Relationship (45)—The Minor-Second Relationship (59) CHAPTER III. AN ANALYSIS OF OPUS 15, NUMBER 5 . . . 70

CHAPTER IV. AN ANALYSIS OF OPUS 15, NUMBER 11 ... 109

CONCLUSION 157

FOOTNOTES 160

SELECTED BIBLIOGRAPHY 161 V

LIST OF ILLUSTRATIONS

1.0. Opus 6, Number 4, "Verlassen", measures 158. . . 5 1.1. , untitled 6 1.2. , untitled 6 1.3* i untitled 6 1.4. , Progression suggested in measures 3-4. 7 1.5* , Reduction of Example 1.4. . . 7 1.6. , measures 9-12 8 1.7- measures 32-33 9 1.8. , measures 43-45 9 1.9. , untitled 10 1.10. , Vocal line, measures 5-6. . . 10 1.11. , untitled 11 1.12. , measures 4-6 11 1.13. t untitled 12 1.14. , untitled 12 1.15. , untitled 13 1.16. , measures 16-18* 13 1.17. , measures 20-22 14 1.18. , measures 35-43 14

2.0. The harmonic-linear paradox 18 2.1. Opus 6, Number 3t measures 4-6 19 2.2. , untitled 20 2.3. , measures 21-23 22 2.4. , measures 13-16 23 2.5' , Harmonic voice summary of Example 2.4 24 2.6. (quotes from Harmonielehre) 25 2.7. Opus 6, Number 3, measures 24-26 27 2.8. Opus 12, Number 2, measures 43-44 28 2.9. , measures 50-52 29 2.10. , untitled 30 2.11. , untitled 30 2.12. Opus 14, Number 1, measures 6-8 31 2.13. Opus 6, Number 7» measures 58-65 32 2.14. , untitled 32 2.15. , Harmonic overstatement, measures 58-65. ' 33 2.16. , untitled ,. . 33 2.17. , untitled 33 2.18. Opus 14, Number 1, measures 1-3 35 2.19. , First progression suggested, measures 1-3 35 2.20. , untitled 36 vi

2.21. Opus 14, Number 1, second progression suggested, measures 1-3 37 2.22. , untitled 37 2.23. , Essential content of measures 1-3 38 2.24. (quote from Harmonielehre) 38 2.25. (quote from Harmonielehre) . . 40 2.26. untitled 41 2.27. Opus 14, Number 1, measures 5-8 41 2.28. , Traditional progression resembling Example 2.27 42 2.29. , "Fourth" and "Whole-tone" versions of TS(V7/V) 43 2.30. , measures 19-22 43 2.31. , untitled 44 2.32. , untitled 44 2.33' » Long-range manifestation of double-neighbor pair, D - C 45 2.34. Motion between adjacent dominant-seventh chords along the "minor-third ladder" 46 2.35. Motion between tritone-related dominant-seventh chords 46 2.36. Opus 6, Number 2, measures 1-14 48 2.37« » clashing voice-leadings in measure 7« 50 2.38. , The turn to B-flat minor at the . beginning of measure 10 51 2.39. , Pre-dominant and dominant functions in C-flat,in measure 10 52 2.40. , Brief appearance of C-flat in measure 11 52 2.41. Opus 12, -Number-,1, untitled 53 2.42. ' , measures 32-42 54 2.43. , untitled 55 2.44. , untitled 55 2.45. , measures 36-38 56 2.46. , measures 39-42 57 2.47. , Long-range viio7 functions in D and D-flat 58 2.48. Double-neighbor and minor-seventh functions of ehharmonically equivalent chords 59 2.49. Double interpretation of an augmented triad. . . 60 2.50. Opus 12, Number 1, measures 4-12 61 2.51. , untitled 62 2.52. , Harmonic voice sketch of measures 4 to 12 of "Jane Grey". 63 2.53' t Hypothetical antecedent phrase, analogous to measures 5 to 8 of "Jane Grey", but which remains in D minor 64 2.54. , More complex phrase, including elements which suggest F major, as in "Jane Grey" in measure 6 64 2.55' t Hypothetical resolution to D-flat major 65 2.56. , Hypothetical resolution to D minor. . 65 vii

2.57' Opus 12, Number 1, harmonic progression analogous to that in measures 9 and 10, but with D as the • tonic instead of D-flat 66 2.58. . , The hypothetical consequent phrase, which remains in D minor 67 2.59' . Hypothetical close, measures 11 and 12. 67 2.60. , A possible shift back to D minor in measures 10 and 11. 68 2.61. , Return to D minor at the last moment, in measure 12. 69 3.0. Harmonic relationships in Opus 15, Number S> • • 70 3.1. Opus 15, Number 5 71 3.2. Tonics in Opus 15, Number 5. 73 3.3. Measures 1-2, first stage of recomposition. . . 74 3.4. Second stage of recomposition. 74 3»5« Measures 1-2, final stage of recomposition, resulting in progression along the cycle of fifths 75 3.6. Measures 3-4 75 3>7« "4-3" motion in measure 3 and a similar inference in measure 5 77 3.8. Measures 5-6, approach to V7 of D. 77 3.9. Measures 5-6 in harmonic voice notation. ... 78 3.10. Prototypical approach to V7 of D 78 3.11. untitled 79 3.12. untitled 79 3.13. untitled 79 3.14. untitled 80 3.15' Rhythmic patterns of the vocal line in measures 1-2, 3-4, 5-6, and 7-9 82 3.16. Comparison of the melodic contour of the vocal phrase in measures 5-6 with that in 7-9 82 3.17. Hypothetical two-measure vocal phrase. .... 83 3.18. Two-measure groups in the piano accompaniment, measures 7-8 and 9-10. 83 3.19. Harmonic voice summary of measures 7-10. ... 84 3.20. Prototypical progressions having the same outer voices as in the ultimate reduction of measures 9 and 10. 85 3.21. untitled 85 3.22. The hint of TS(V7/v) in D, brought on by the pitches B-flat, D, and G-sharp in measure 10. . 86 3.23. The equivalence between l|>7 of B-flat and TS(V7/V) of D 87 3.24. The hint of V7 of B in measure 10 87 3.25. Continuation of Example 3.14 from page 80. ... 88 3.26. The prolongation of a B-flat major-minor-seventh chord in measures 10 to 12 89 3.27. The vocal phrases of measures 1-2 and 13-15. . . 90 3.28. untitled 92 3.29. untitled „ 92 3.30. Harmonic voice summary of measures I3-I5, to be. compared with Example 3.29 93 viii

Double appoggiatura figures from measures 6 and 8, and measure 14. 94 3.32. Measures 1-3 and 13-15 compared. 95 3.33. Continuation of Example 3.25, page 80 96 3.34. untitled 96 3«35' Measures 15 to 18; the suggestion of a cadence to the B tonic. 97 3.36. Measure 14, beats 2 and 3» and measures 15 to 16; the suggestion of V-I progressions in B. ... 99 307' The "deceptive" cadence effect in measures 14-15 and 17-18 99 3.38. untitled 100 3.39. The vocal line in measures 16 to 18. 100 3.40. Measures 15-18, with emphasis upon the B-flat- related harmonic voices. 101 3.41. Functional harmony in relation to G in measures 15-18 104 3.42. The amalgamation of Examples 3-35, 3.40, and 3.41 105 3.43. The "whole-tone" chord of measures 16-18, and the presence therein of the roots, thirds, and sev• enths of major-minor-seventh chords on B, F, and G. 106 3.44. Harmonic voice summary of Opus 15i Number 5* • • 10? 3.45. untitled 108

4.0. Harmonic voice motions from B-flat to B-natural and D-flat to D-natural in measure 1...... 110 4.1. Opus 15, Number 11 Ill 4.2. untitled 114 4.3. untitled 114 4.4. untitled 115 4.5. untitled 115 4.6. The functions TS(V7/V) and V7 in F-sharp. ... 117 4.7. untitled 118 4.8. untitled 119 4.9. untitled 120 4.10. untitled 121 4.11. untitled 121 4.12. The hint of v/lY and IV in F-sharp, in measures 7 and 8 122 4.13. untitled ,. 123 4.14. Minor triads moving to diminished triads in measures 1 and 8, resulting in the functions viio7 and viio7/V in F-sharp, respectively. . . 124 4.15« Harmonic voice summary, measures 8-12. . . . . 125 4.16. untitled 127 4.17. untitled 127 4.18. Piano, left hand of measures 2 to 5...... 127 4.19. Close-up of structures (b) and (c) 128 4.20. untitled 128 4.21. untitled 129 4.22. untitled 131 ix

4.23« Melodic parallel between measures 1-5 and 13-16 133 4.24. Harmonic voice summary, measures 13-14 134 4.25. Double-neighbor "fourth" chords in the piano treble of measure 14 135 4.26. untitled 137 4.27. untitled 138 4.28. untitled 138 4.29. Progression along the cycle of fifths in measures 15 and 16 140 4.30. untitled 142 4.31. untitled 142 4.32. untitled 143 4.33. untitled 143 4.34. untitled 145 4.35» Harmonic voice summary of the vocal and piano parts in measures 16 to 19 • 146 4.36. The expectation of a "4-3" resolution in measures 16-17 148 4.37. untitled 149 4.38. untitled 149 4.39. Approach to dominant-seventh of F-sharp, comparable to events in measures 16 to 19. • • 150 4.40. untitled 150 4.41. Hypothetical and actual runs compared. .... 151 4.42. untitled 152 4.43. untitled 153 4.44. (1) The embellishment of I by ii7 and #ii?f as in measures 8 and 9; (2) The traditional cadence along the cycle of fifths. 154 4.45. Harmonic voice summary of measures 21-24. ... 155

5.0. Two "equivalent" progressions along the cycle of fifths in C 158 X

EXPLANATION OF GRAPHIC SYMBOLS USED

IN THE ANALYTICAL SKETCHES

1. X in place of a note-head. This means that the pitch is implied. The justification for the implicit presence of a given pitch will be made during the discussion of the sketch in which that pitch appears.

2. Diagonal lines drawn through regular or "X" note-heads ( >#" and ,^*f ). These serve to mark the end of a harmonic voice which is carried on in another octave or not at all.

3. Stems. These are occasionally used to aid in the differentiation of harmonic voices. The same direction of stem indicates membership in the same harmonic voice. However, sometimes where several voices are in operation, more than one may be given upward or downward stems, so that one must look for the proper semi-, whole-, and common-tone connections which characterize allcharmonic voices, in addition to observing the directions of stems. k. Ties. These join pitches which continue to sound either because they are reiterated or because they are actually sustained.

5. Brackets or parentheses ( H or ( ) ). These are used at the end of a sketch to enclose a chord which is not actually stated in the passage with which the sketch deals, but which helps the reader to grasp the harmonic context in which the sketch is conceived. The chord in brackets or parentheses might arrive within the next few measures, or never occur.

6. "TS". This stands for "tritone-substitute". The term is explained on pages 18-20. xi

ACKNOWLEDGEMENT

I wish to express my gratitude to Wallace Berry, my thesis supervisor, whose thorough scrutiny of my

tentative analyses led to their clarification, and whose

suggestions concerning general matters of style and

organization were invaluable. I also extend my sincerest

thanks to William Benjamin, whose interest in my work gave me the confidence to complete this study.

The excerpts of Schoenberg's works which appear in

this thesis are used by permission of Belmont Music Publishers,

Los Angeles, California 90049- 1

CHAPTER I

THE CONCEPT OF "HARMONIC VOICE"

The analytical sketches in this study rely upon a procedure of simplification designed to bring registrally, rhythmically, and harmonically complex music into a form which is more easily accessible to the tonally trained ear.

Involved in this procedure are three ways of manipulating the music: the first eliminates octave doublings and dis• placements so that each pitch-class is represented by one pitch; the second regulates the rhythmic activity by verti• cally stacking arpeggiated chords and eliminating repeated pitches so that a chorale-like texture results; the third, and most important, introduces registral changes which make apparent the common-, semi-, and whole-tone connections be• tween adjacent vertical structures in a way which is logical

in terms of tonal counterpoint. These three manipulations rob the music of everything but its harmonic-contrapuntal

interest, and yet, the pieces of Opus 15 withstand such

treatment wellt many of the analytical sketches may be per•

formed with musical conviction, providing powerful testimony

to the intensity with which underlying tonal progressions af•

fect the emotions of the listener/performer.

The third of the aforementioned manipulations results 2 in the concept of "harmonic voice". The term is intended to blur the distinction often made between harmony and counter• point as the "vertical" and "horizontal" aspects of music.

According to this distinction, we evaluate the harmonic func• tion of a chord by determining i.ts root; if this cannot be done, we try to justify the chord as part of a contrapuntal motion which, depending upon the composer and the work, we may or may not expect to reflect the consonance/dissonance concepts of conventional tonality. Analyses which are root• ed in this way of thinking tend to consist of progressions of discrete chords represented by Roman numerals; linking the chords are uncertain structures considered to be of linear origin. As we become accustomed to certain specific types of linearally-conceived structures, we feel the need to give them status as legitimate harmonies. The fact that we would consider a question such as whether the "correct" root of an augmented-sixth chord which prepares a dominant is the supertonic, the sub-dominant, or even the sub-mediant, exemplifies our desire to transfer a structure from the linear world to the harmonic once it has become familiar to us in a certain tonal context.

Ways of describing music which rely upon harmonic- contrapuntal distinctions are, perhaps, adequate in cases where most vertical structures fall without question into the "harmonic" category; however, in Schoenberg's music be• tween Opus 1 and Opus 15, root progressions, particularly at the foreground, are not usually made obvious by a bass line 3 or by the presence of purely conventional chords. Therefore, if we wish to determine the roots of chords, they must some• times be inferred from complexes of semi- and whole-tonal voice-leading with which they are associated. A simple ex• ample would be that m M. is inferred from when 4 A o the latter appears in a suitable context, namely a passage which at least hints at a C tonality. In this case, the in• ferred root progression contributes the pitch G towards a third harmonic voice, the resulting three being

It is important to note that the progression of roots, which is G to C in this case, does not comprise a single harmonic voice? rather, each root is part of whichever harmonic voice leads to and/or follows from it by common-, semi-, or whole- tone succession. Inferring a root progression results in the implication of further harmonic voices which may be com• pleted to form the three- or four-part texture required to display triads and seventh chords in full. This process of inferring and completing a progression is useful when one is dealing with Schoenberg's sparser textures, and might be de• scribed aptly as "harmonic overstatement". It is also use• ful in the context of a thick texture in which only certain 4 of the voices follow typical tonal patterns, or in which patterns associated with more than one familiar progression seem to be combined; in such cases, the voices implying the progression(s) which one desires to emphasize may be extract• ed from the total texture and additional voices inferred to complete it(them) where necessary.

The following sample analysis serves to introduce the concept of harmonic voice as it will be applied to pieces from Opus 15• particularly with regard to the drawing out of tonal progressions from voice-leading complexes which im• ply them.

How do we hear the opening measures of Opus 6, Number

4, "Verlassen"? Although some would interpret measures 1 to

6 as expressing only one harmonic function (i in E-flat minor), subtle foreground progressions are inferrable from the motion of the harmonic voices over the E-flat pedal-point. Further• more, these progressions are fitting for the opening measures of a piece, consisting of motion through tonic, dominant-pre• paratory, and dominant functions—after the fashion of the typical introductory progressions, I-IV-V? and I-ii7-v7.

The two harmonic voices which are repeated for the first five measures of the piece are shown in Example 1.1; Example 1.2 shows the slightly altered version of those voices which oc• curs in measure 6; Example 1.3 shows the tonal progression which we are reminded of when we hear the preceding two Ex• amples . 5

Example 1.0: Opus 6,-Number 4, "Verlassen", measures 1-8. 6

Example 1.1: (Example 1.3: 7'

measures 1 to 5 > v

r y Example 1.2* ? * Iff ^sZb \1 1V E^-i V7/VI 1 or v? ii7

tjX If N

M Iff bf^Jf

measure 6

A harmonic progression very similar to that shown in

Example 1.3 is suggested when the vocal phrase of measures 3

and 4 is stated above the two harmonic voices of Example 1.1.

This progression, which is shown in Example 1.4, differs from

that in Example 1.3 only in the substitutions of B-double-flat

for B-flat and D-double-flat for D-flat, which are made to

create a similar emphasis in the accompaniment upon A-natural

and C-natural to that which exists inaithe vocal phrase. It

should be noted that the whole-notes in Example 1.4 represent

the pitch-classes found in the vocal phrase of measures 3 and

The effect created when one sings the vocal phrase while performing Example 1.4 is truly one of harmonic over• statement, as can be verified by analysis of that example and re• ference to other passages in "Verlassen". In Example 1.5» a reductive procedure has been applied to Example 1.4 which

suggests that one harmony, certainly not i in E-flat minor,

is being prolonged.

Example 1.4: Progression suggested in measures 3-4.

/ /

$0 1 ty* 4°=

Example 1.5: Reduction of Example 1.4

/Example 1.5 contains all of the pitch-classes of the vocal phrase in measures 3 and 4, with the exception of E-flat; in addition, it contains the important motion from E to D with which the vocal phrase begins, making it, in effect, a chordal 8

version of the vocal phrase. This creates a strong case for

the appropriateness of the inferred B-double-flat and D-double-

flat at the beginning of measure 3 and suggests that like in•

ferences might be made, in retrospect, at the beginnings of

measures 1 and 2. The resulting interpretation of measures

1 to 3 as representing D major-minor-seventh chords embel•

lished with upper-neighbor-tone motions from E to D is

strongly supported by the appearance, in measures 9 and 11

respectively, of similarly treated A and G-flat major-

minor-seventh chords (Example 1.6). Furthermore, later pas-

Example 1.6: Opus 6, Number 4, measures 9-12'

h-4f ». Err y r r mir das Herz veip - . dortr _

a - len wa ,J h hj JH=J vm | fc f|3 % i J.. j) Jr • «p fcK 11> L I IT- —1 If*—$• $4 JjJ InIj j jjjj—1 i

iJN'.b,i, - • h 1 N =tea \— 4— 1 "' ¥ die Lip pe spra ch ke in rt _ si e Ab - schieds - wo

/ J'. hi, , 1 j-

14 8' # =ri f t> F il 12 - _/

—r-p—| j~— | "t ^ "~~— [il Example 1.6, continued measures 1 to 3 measure 9 measure 11

sages in the song reveal fully realized implications of the

D major-minor-seventh harmony which were inherent in the ini• tial harmonic voices of Example 1.1 (Examples 1.7 and 1.8).

2 Example 1.7: Opus 6, Number 4, measures 3+33«

Example 1.8« Opus 6, Number 4, measures 43-45.

Langsam.

Was war minrr ddei r pran-gen-de

\pp 11 iJWJj) hi. - - 10

The D major-minor-seventh chord with minor-ninth which occurs in measures 33 and 43-44 relates to the ^ version of D major- minor- seventh which occurs over the E-flat pedal-point in the initial measures of the piece by a simple exchange of out er voices (Example 1.9)• The juxtaposition of these two ex• pressions of D-major-minor-seventh harmony which occurs in measure 44 and 45 of Example 1.8 makes their relationship clear.

^Example 1.9*

* y*- f4- f-^

measures 1-6 3,2-03 45-48 43-44

Wher.eas the first vocal phrase, in measure 3 and 4, enabled us to infer the progression in Example 1.4, the second vocal phrase connotes a slightly different foreground progression due to the presence of C-flat at the beginning of measure 5« The second vocal phrase is shown in Example

1.10.

Example 1.10: Vocal line, measures 5-6.

. r , j n f—6—^ «* iw 4 ) 11

During measures 1 to 5, a definite sense of E-flat as the tonic is created through the prevailing E-flat pedal-point and the foreground harmonic progression in E-flat minor inferred in Example 1.3 (page 6); resulting from this is the listener's desire to hear the chromatically rising harmonic voice (Example

1.11)

reach B-flat, forming a perfect fifth with the E-flat pedal- point, on the first beat of each new measure. Therefore, the

C-flat which initiates the vocal phrase in measure 5 is heard as an upper neighbor to B-flat and, when aurally connected with

A-natural from measure 4 and the minor third, E-flat - G-flat, with which it occurs on the first beat of measure 5» results in the hint of an augmented-sixth function embellishing the brief E-flat major harmony which follows (Example 1.12).

Example 1.12: Opus 6, Number 4, measures 4-6. Shown are those pitches from which the "harmonic overstatement"' in the following portion of this example is inferred. the

Pfo t 1* b. b, 12

Example 1.12, continued.

Harmonic overstatement of Opus 6, Number 4, measure 4-6.

7 7 7 E-flat: Aug6 — j iv — V /VI--l) — iv — V or ii7 or ii7

In addition to the local augmented-sixth function

which occurs at the beginning of measure 5» the entire meas•

ure can be heard as expressing the chord in Example 1.13*

Example 1.13s

As shown in Example 1.14, the outer voices of measure 5 range

from C-flat to G-flat and G-flat to A-natural, both being accom•

panied by the constant E-flat pedal-point. The resultant chord,

Example 1.14: **1 to with its enharmonic equivalent (Example 1.1$),

Example 1.15s K . ^

is important throughout the piece in a variety of ways: (1) it

establishes a voice-leading connection between the important

D major-minor-seventh chord and the major version of the tonic

triad, E-flat (Example 1.16, and Example 1.12 from the end of

measure k to beat 2 of measure $); (2) it embellishes the domi-

Example 1.16: Opus 6, Number 4, measures 16-18.

; nant-seventh of E-flat (Example 1.17); (3) it is given a hint

of emphasis as a tonic in the middle of the piece (Example 1.18). 14

Example 1.17« measures 20-22'

E-flats V#5 Aug 6

E-flat V -Aug 6 s #5' '#5

Example 1.18» measures 35-43.

H- u- ..1 |l>, lltUl y . > Iff) P 1? * a 4 sam Pas - sen! is 35 jfr

(continued on page 15) Example 1.18, continued.

Man - lich wur - de die Welt nun .•v nnr^r itf 33 .^F-T^

.—.

C-flats V' I I^7 V^_ passing to V7 (VI) ii

#7 v? - passing to V 16

The voice-leading which connects the C-flat chord of

measure 41 with the D major-minor-seventh chord of measure

43, C-flat to C-natural and E-flat to D, exemplifies a par•

ticular affinity of Schoenberg for connecting chords whose

roots lie a minor-third apart; it should he noted that Ex•

ample 1.4 of page 7 depicts one complete progression in•

ferred from harmonic voices in the opening measures of

„ "Verlassen", revealing a harmonic sequence consisting of

7 7 chords connected in this manner (GI* to E^ and F7 to D7).

Henceforth, the term "minor-third relationship" will he ap•

plied to this type of connection; it will be treated as a

separate topic later, as its role in Opus 15 is very impor

tant.

Example 1.18 displays harmonic voice notation as it

generally will be applied to Opus 15* One problem arising

from this type of notation must be mentioned: pitches which

may move in either of two directions, such as the fifths of

chords moving along the cycle of fifths, involve an ambigui•

ty which cannot be resolved here. Of the greatest concern

in this study are those pitches which are strongly directed,

such as the major thirds and minor sevenths of chords moving

along the cycle of fifths. In cases where the tendency of

a pitch is less specific, the analytical sketches will show

both possible motions, assuming that, in an abstract sense,

both may be said to occur.

The concept of harmonic voice, as illustrated in the

preceding examples, leads to a certain kind of equality be- 17 tween diatonic and chromatic progressions, since the common-, semi-, and whole-tone connections which both possess, as op• posed to the roots which supposedly lend greater harmonic va• lidity to diatonic progressions, are emphasized. This "equal• ity" is exploited by Schoenberg through several general har• monic procedures, all of which are found in profusion in the

Opus 15 songs. These procedures will now be introduced in context of earlier, more overtly tonal songs, where they may be assimilated readily in preparation for approaching their less explicit occurrences in Opus 1$. 18

CHAPTER II

HARMONIC PROCEDURES WHICH MINIMIZE

DIATONIC-CHROMATIC DIFFERENCES

The Tritone-Substitute

The most basic potential which the tritone possesses is to imply a local dominant-seventh function having one of two possible roots, themselves lying a tritone apart. Hence, the paradox exists that descending perfect fifths and descend• ing semitones are simultaneously implied as the roots of chromatically descending tritones, the former being associat• ed with everything that is "harmonic" and the latter with everything that is "linear".

Example 2.0s The harmonic-linear paradox

Two cycles of fifths, Two chains of semitones, a tritone aparts a tritone apart:

-A tP**—b» ^—at, —i' —

—^ ~- — 7 Possible rootst Possible roots: i -* N # />' mw

Possible roots: Possible roots: 1 —t -h-P# - « =#=— 19

This conflict between the harmonic and the linear is resolved in Schoenberg's music, since he freely interchanges

the two roots attributable to a given tritone, leaving it to

that tritone to define the location along the cycle of fifths

in whichever key is being implied at the moment.

An excellent example of the interchangeability of roots which lie a tritone apart is found in Opus 6, Number 3» "Mad-

chenlied".

Example 2.1s Opus 6, Number 3» measures 4-6.

In this example, roots of chords are shown as stemmed pitches, below the four harmonic voices. In measures 5 and 6,

D and A-flat, the two possible roots of the tritone, F-sharp/

G-flat - C, are stated, prolonging a dominant function in G.

The A-flat major-minor-seventh chord which occurs halfway 20 through measure 5 can be called the "tritone-substitute" of 7 V of G, since it contains the tritone formed by the third and seventh of V, with the alternate root thereof, A-flat.

The tritone-substitute of a given chord henceforth will be indicated by a "TS", followed by the Roman numeral represent• ing the harmonic function of that chord, as in measure 5 of

Example 2.1.

Vacillation between a chord and its tritone-substitute represents no change in harmonic function when we think in terms of harmonic voice motions rather than root progressions.

The most strongly directed harmonic voice motions which occur 7 during a progression from V to I are those from the leading- tone to the tonic and the subdominant to the mediant pitches} these motions are also present in a progression from TS(V^) to I. Furthermore, absolute identity of pitch-class content between any major-minor-seventh chord and its tritone-substi• tute may be achieved simply by lowering the fifths of each chord, making them diminished; since, in terms of harmonic voice motion, the fifths and roots of major-minor-seventh chords are not strongly directed, as are the thirds and sev• enths, such altering of fifths has no important effect on the harmonic voice motions which issue from such chords.

In Example 2.1, the symbol, "ii'?", which is used to represent the chord (Example 2.2) Example 2.2«

in measures 3 and k is intentionally made more general than it 21

might be. The passage in question presents us with inflec•

tions of both the major and minor modes of G, raising the is•

sue of which mode governs the indication of chromatic altera•

tions to chords beside their corresponding Roman numerals. In

Example 2.1, one is tempted to specify the mode of G as major because the opening tonality of "Madchenlied" is E minor and

a shift to the relative major key is such a common harmonic gesture; however, the ii'7 function in measures 3 and 4 is dia•

tonic to the minor mode of G, a fact which is indicative of

Schoenberg's casual attitude toward major/minor distinctions.

We would be placing far greater emphasis upon such distinctions than the composer if we insisted upon specifying the key as G major and the function as "iiuZ". Instead, the "neutral" sym- 7 bol, "iif", suffices, and we understand the key to be a mixture of G major and minor at this point in the piece.

In Example 2.1, the concept of the tritone-substitute was introduced with the specific function, TSfV'7). This func• tion is not to be confused with that of the "Neapolitan" chord, which does not contain the crucial tritone needed to resolve to the root and third of the tonic triad and, therefore, re• tains the quality of a pre-dominant harmonic stage, or a true

"1?II". For example, a "Neapolitan-to-v''" progression occurs later in "Madchenlied". In measure 21, one has the sense of two separate harmonic functions, the first pre-dominant and the next dominant (Example 2.3)} this situation is completely different from that in Example 2.1, where a playful tossing back and forth of D and A-flat beneath the constant F-sharp/

G-flat and C prolonged a purely dominant function. 22

Example 2.3* Opus 6, Number 3, measures 21-23.

Ct |? II V7 1 V7/IV IV

The tritone-substitute with which we have been long•

est aquainted is, of course, the augmented-sixth chord which

prepares the dominant, of TS(V'Vv). It is distinguishable

from VI of the minor mode or JPVI of the major because, unlike

those triads, it contains the same tritone as V^/V; since

the most important harmonic voice motions which proceed from

V^/V do so from its third and seventh, which form this tritone,

TS(V'V'V) may be said to have essentially the same harmonic

function as V?/V.

The distinction between TSCV^/V) and the sub-mediant

chord is made in examples 2.4 and 2.5» which are taken from

Opus 3» Number 2, "Die Aufgeregten". Initially, the D major- minor-seventh harmony is measure 13 has a dominant function, 23

since G minor is strongly suggested as the tonic key during

the opening measures of the piece* however, in relation to G-

flat, which is tonicized by the progression, ii7-V7-I, in meas•

ures 15 and 16, the same D major-minor-seventh harmony repre•

sents the function TS(V7/v) (Example 2.4). What prevents us

Example 2.4t Opus 6, Number 3, measures I3-I6.

und ein hoi - derSchmetterling zer-riss den a - zirr - - neaTrack Iin

G: V

GJ? t |>VI vi ii7 V7 1

from hearing a direct progression from TS(V7/v) to V7 in G-flat

is the occurrence of the simple D major triad, without its mi•

nor seventh, halfway through measure 14; this chord functions 24

as Wl of G-flat and moves through vi and ii7 to reach V7 in

measure 15• This local, diatonic approach to V7 of G-flat

weakens the more distant relationship between the tritone, C -

F-sharp/G-flat, of TS(V7/V) and the root and third, D-flat and

F, of V which links measure 13 to measure 16. A harmonic

voice summary of this passage is presented in Example 2.5» in

order to clarify points made in Example 2.4.

Example 2.5* Harmonic voice summary of Example 2.4.

13 1 i4 15 0 ? r —*

G: TS^-V7, TS^J-V7 TS(V^)-V—

7 7 G|P« V£ -TS(|5).IZ -TS(^) TSt|^)-^VI—vi—ii V —I 11 ll

The Minor-Seventh/Augmented-Sixth Potential

of "Whole-tone" Chords

In the "Harmonielehre , Schoenberg emphasizes the ar•

rival at whole-tone sounds through common compositional de• vices, such as melodic motion between tones of augmented triads

and certain seventh chords, arid chromatic alteration of conven•

tional chords. He illustrates this view with several examples,

the most important of which are quoted in Example 2.6.1 25

Example 2.6s (from Schoenberg)

(i) Examples from Harmonielehre which depict melo• dic motion between pitches of an augmented triad, resulting in a whole-tone collection.

318 |l^t e lite j_«ULi U ^ ^

(ii) Further examples, depicting melodic motion between pitches of major-minor-seventh chords with raised or missing fifths.

bi=jj= aipb:i 3CT 319

(iii) Examples showing the function of a "whole-tone" chord as a dominant-seventh with both raised and lowered fifths, and its derivation through the chromatic alteration of a ninth chord.

1° " 322 < 323 EBB 3fc 26

Example 2.6, continued (iv) The complete "whole-tone" chord, as shown in • Schoenberg's Ex. 321.

Schoenberg describes our aural gathering of a whole- tone collection into a chord thusi

[TheH derivation [of a whole-tone collection through melodic motion between chord pitches] reflects the way in which our ear draws analogies (kombiniert)t it connects like things, it sets widely separated events adjacent to one another and adjacent events over one another. Once the three figures of three tones shown in Examples 318a, b, and c are actually used, they

soon move closer to one another (3l8d)2and finally sound together at the same time (321).

It is clear that Schoenberg did not think of a whole- tone collection as a prefabricated scale or chord .which a com• poser' decided to use, but as an outgrowth of certain harmonic and melodic procedures. Specifically of concern in this study are those harmonic procedures which involve major-minor-sev• enth and augmented-sixth chords in "whole-tone" passages of works of Schoenberg.

A simple example of a dominant-functioning passage which contains a whole-tone collection is found in Opus 6, Number 3»

"Madchenlied" (Example 2.7). At different points in Opus 12,

Number 2, "Der verlorene Haufen", the two who&e-tone collec•

7 tions function as TS(V7A) in C-sharp and V in E-flat (a dom• inant-preparing augmented-sixth chord and a dominant-seventh chord, respectively) (Examples 2.8 and 2.9). It is important 2? to understand that, when a complete whole-tone collection is harmonically interpreted (that is, all six members of the col• lection are actually or implicitly present simultaneously), six separate harmonic voices are present, each of which resolves to a particular member of the following harmony. Even though whole-tone collections are often accumulated during melodic whole-tone passages, as in examples 2.7, 2.8, and 2.9» one must guard against interpreting a whole-tone scale as a single har• monic voice; instead, each new member of the scale (i.e. of

the collection) must be interpreted as belonging to a different harmonic voice, if the scale, indeed, functions as a chord.

Example 2.7« Opus 6, Number 3» measures 24-26,

Es V7 1 (Vr has major ninth, and raised and lowered fifths) 28

Example 2.8: Opus 12, Number 2, measures 43-44.

j wird die Mau - er vom Bo - den ge - fegt sein

yesante <—T

fs **» I*

TS(V7/V) v*5—vii7—I

A more traditional version of measures

it*

7* *f* ™ 31 ~ '

C#s TS(V7/V) 29

Example 2.9« Opus 12, Number 2, measures 50-52.

7 E|?S V I (with major-ninth, raised and lowered fifths)

pf the whole-tone's two possible interpretations, as

a major second (minor seventh) and a diminished third (augment•

ed sixth), the latter is especially important in context of

Opus 15. Since the term "augmented-sixth chord" is still chief ly used to describe a dominant preparation in tonal music, whil

Schoenberg uses augmented-sixth chords in many other contexts,

and because Schoenberg's choices of inner voices within the

augmented-sixth frame are often unconventional, the more gener•

al term "double-neighbor chord" has been 'chosen as an alterna•

tive; likewise, the interval of an augmented sixth, or a dimin•

ished third, will often be referred to as a "double-neighbor 30

pair".

By the time of Opus 15, the resolution of a double-

neighbor pair to a unison or octave has become an exceeding•

ly common way of approaching a structurally important pitch-

class. We will now examine the double-neighbor relationship,

not only in context of whole-tone collections, but also with

respect to "fourth chords" and ordinary minor-seventh and aug•

mented-sixth chords.

Double-Neighbor Pairs in "Whole-tone"

and Other Contexts

Excellent examples of the double-neighbor relationship

and its connection with the whole-tone collections are found

in Opus 14, Number 1, "Ich darf nicht dankend". In measures

6 and 7, the motive given as Example 2.10,

Example 2.10:

"tand its transposition (Example 2.11),

Example 2.11:

create a harmonic progression from TStV^/V) to V7 in F-sharp,

as shown in Example 2.12. Although the local behavior of these

two motives is identical, save that one embellishes C-sharp with

its double-neighbor pair and the other does so for C-natural, 31 in the larger context of functional harmony in F-sharp, corres• ponding parts of the motives are weighted differently. The C- natural which is embellished by the double-neighbor pair, B -

C-sharp, in the second motive, is merely a lower neighbor to the C-sharp of the tonic ^ chord in measure 7; therefore, the additional function of B - C-sharp as the seventh and root of V' in F-sharp becomes the most important one. There is no such ambiguity regarding the double-neighbor pair, C - D, contained in the first motive, as it functions only in TS(V7/v),

Example 2.12s Opus 14, Number 1, measures 6-8.

F#s TS(V7/V)—V 7 TS(V7)- I

(at "*", a decorative TS(V7/V)) 32

The final measures of Opus 6, Number 7* "Lockung", ex•

emplify a double-neighbor pair, in the context of an ordinary

TS(V7), which resolves conspicuously, de-emphasizing its har• monic origin in favor of the simple, skeletal resolution of

a diminished third to a unison (Example 2.13)• Example 2.13: Opus 6, Number 7, measures 58-65 •

[The complete harmonic context of the double-neighbor pair, D - F-flat, can be inferred from the preceding measures.

The progression in measures 58 and 59 from V7 of G-flat to n Vy^ of E-flat involves three harmonic voice motions: C-flat

to B-flat, F to F-flat, and D-flat to D, the latter two of

which eventually converge on the tonic pitch, E-flat. A

sketch of the most important harmonic voices in measures 58

to 65 is given in Example 2.14.

Example 2.14:

58 59 60 61 62 63-4 65 n» t>» b>__y* t*

E|>, 1^—^^-—^-—^ TS(v7)~i;or i 33

The more detailed harmonic overstatement of measures

58 to 65 given in Example 2.15 reveals that the dominant

pitch, B-flat, is also embellished by its double-neighbor

pair, A - C-flat, although a complete TS(V7/V) function is

not present.

Example 2.15: Harmonic overstatement, measures 58-65 (B-flat embellished by its double-neighbor pair at points "*").

% OR X

58 59 60 -61 -62" 63 64 65" Ebijrz—vZ—yx_ V#5 III viiS? TS(V7) i or I 3 III III (orni#5)

Of special interest in Example 2.15 is the particular

context in which the double-neighbor pair, A - C-flat, does

occur, namely that of the harmonic structure in Example 2.16.

Example 2.16:

This chord prepares TS(V7») as would a ii7 chord prepare a true

dominant-seventh (Example 2.I7). Therefore, the double neigh-

Example 2.1?: -b y^wi V r

possible actual j

1 *l 0. "At ii V' —I E|?:TS(V7)-I 34 bor pair, A - C-flat, has a subtle, additional function as the major second (or minor seventh) in a chord which directly pre• cedes TS(V?) along the cycle of fifths in A, the tonic a tritone away from E-flat. This is an especially fine example of what might be called the "double-neighbor/minor seventh" dichotomy.

An aspect of Schoenberg's harmonic vocabulary which plays an important role in Opus 15 and which reveals another facet of the double-neighbor relationship may be introduced, facetiously, by the "equation", "4 + 4 = 6 or 7". The implication of the e- quation is that two perfect fourths stacked one upon the other are sometimes better thought of as a simple double-neighbor or minor-seventh chord, rather than as a "fourth chord". This is because the interval framing such a structure exhibits strong voice-leading tendencies (in Opus 15 and earlier works) which one easily hears in tonal terms: semi-tonal convergence of the outer voices suggests a root progression down a minor third, of• ten to another seventh chord, and semi-tonal divergence suggests an augmented-sixth or double-neighbor resolution. Both voice- leading patterns are so familiar to the tonally-trained listener that they can override the less familiar activity of inner voic• es in certain contexts.

In measures 1 to 3 of Opus 14, Number 1, familiar sounds result from the presence of harmonic voice motions found in two traditional progressions? The first involves a converging minor seventh which, in Schoenberg's score, frames a "fourth chord",

A - D - G. The function of this chord may be shown to parallel that of a major-minor seventh chord on A. Example 2.18 quotes the passage in question and provides a simplification thereof. 35

Example 2.18s Opus 14, Number 1, measures 1-3

Langsam (J)

Ich darf nicfat

1 p

i r mi i T— i ' i ^ t|» f

The first traditional progression with which the pas• sage in Example 2.18 has harmonic voices in common suggests a turn from the dominant of a major key to that of its relative minor; Example 2.19 shows the traditional progres• sion and Example 2.20 the harmonic voices which it shares with the opening of Opus 14, Number 1.

Example 2.19s First progression suggested, measures 1-3-

B: V7/y..__Y7 — y7—V7—v7-—I or i III III 36

Example 2.20:

1 I rb—1 - i II I

1 1 2 A: — ' J ! —/ 1 1— h\ - B:> V7/V-— V7 —--V7—V7—V7 1 III III

During the actual listening process, Example 2.20 pre• cedes Example 2.19: our tonal expectations cause us to focus upon certain harmonic voices in the music, and then we are moved to discover in what context those voices have become familiar. The three-chord cadential approach to B, "V7/m -

V7 - I or i", is clearly implied by the converging pair of har• monic voices beginning with the minor seventh, A-G. Associ• ating the chromatic descent from G-sharp to G in the upper voice with motion along the cycle of fifths yields the func• tion, V7/v in D, which completes Example 2.19. Example 2.19 is not meant to be a translation of what we actually hear; it is merely a characteristic tonal context in which some of the more conspicuous harmonic voices of the opening of Opus 14, -

Number 1 could be felt to participate, and which may, somehow, underly the experience of measures 1 to 3.

The same is true of the second tonal progression which one might recall upon hearing the same passage; this time, a double-neighbor pair is involved, rather than a converging mi• nor seventh. The complete progression is shown in Example 2.21, and the harmonic voices from which it is inferred in Example 37

2.22. Example 2.21: Second progression suggested, measures 1-3.

it, m " "I ' . B: I r -iv7—TS(vI)-V, iv7-TS(y2)-V 1 or i V V

Example 2.22: (Pitches actually present)

1 rfJ) , i \ 1 1 ^==;

" * 4* 1 ^ j /- - =F= • V——" s 1

, In this case, we interpret the function of the first chord of measure 1, V7/iv in B, from its tritone, A - D-sharp.

We infer the resolution to iv when G appears in measure 2, even though E-natural is missed and we immediately hear the aug• mented version of the sixth, G - E-sharp, which characterizes the TS(V7/V) function in B. We hear the resolution of this double-neighbor pair to F-sharp in measure 3 when G disappears.

Combining the harmonic voices of Examples 2.20 and 2.22 yields the essential content of the first three measures of 38

"Ich darf nicht dankend" (Example 2.23)1 completing the case which has been made, through Examples 2.19 to 2.22, for the powerful influence which familiar voice-leading patterns ex• ert on the listening experience.

Example 2.23: Essential content of measures l-O •

I Jt 1 1 .1 to \i 4| #1 J?i- \

Examples 2.19 and 2.20 also made a case for thinking

of the "fourth chord", A - D - G, as V7/lII in B, the function

which we would normally attribute to the seventh chord, A - C-

sharp - E - G. Although Schoenberg did use the term, "fourth

chord", some of his examples from the Harmonielehre reveal

that he, too, thought of such structures as potential seventh 3 and double-neighbor chords.

Example 2.24: (Arrows have been added to Schoenberg's examples to show the progress of minor sevenths and double- neighbor pairs.)

—1 --ybb Kto£__»?L» 1 _o r" 332 —«.» : 0

" li" i^L [ ^»y~r \, 1 —->o Pr-O _o —^-b-po or ^t>x$ —^7 n—— ~™ W*F-^ = ^ —"—<>— 39

The general principles in Example 2.24 are that a dou• ble-neighbor pair embellishes the root or fifth of a triad,

and that a minor seventh converges chromatically (if not par•

ticipating in a "vii7" - I progression such as begins the ex•

ample). In Opus 15» fourth chords whose double-neighbor pairs

embellish the roots or fifths of major and minor triads are particularly important} the generalization may be made that such chords often suggest the functions TS(V7) and TS(V7/V), respectively, as the fourth chords share common double-neigh• bor pairs with the tertian chords having those functions.

Further examples from the Harmonielehre o involving larger chords consisting of three stacked perfect fourths ra• ther than two, display some possible harmonic voice motions to and from fourth chords which reinforce the idea that a double-neighbor pair (or a minor seventh) can, of itself, suggest a harmonic function in the absence of the tritone

/ • x 4 which would define that function (Example 2.25).

In Example 2.25, arrows have been added to Schoenberg's examples which lead to and from the double-neighbor pairs or minor sevenths which are responsible for the suggested har• monic functions below certain chords. Even in such brief contexts as these, it is apparent that where a double-neigh• bor pair resolves to the root of a major or minor triad, a local TS(V7) function may be inferred (Schoenberg's examples

333a and b, and 33^). In addition, a TS(V7/v) function could be suggested where the object of the double-neighbor embel• lishment is the fifth of the following chord (Schoenberg's 40

f Example 2.25* ( rom Schoenberg)

a) b) C)

v7'? i(D) A 'P# root root

~7L "' 7 ~rti'5 Mi! —V* ""55 334 y —1, (g j

7 yjf -TS (v'O-i v' T'J (V )?_ I TS(v'? A>? example 333c). Where there is no double-neighbor resolution, the minor seventh can imply a local dominant function in re• lation to the following chord (when the upper member of the seventh falls but the lower remains, as in Schoenberg's exam• ple 333d, first measure), or hint at a root progression down a minor third (when the seventh converges chromatically as in Schoenberg's example 333<*» second measure).

The use of the symbol "TS" to describe the function of a chord which contains no tritone may, at first, seem problematic; however, examination of a hypothetical, two- voiced progression such as is presented in Example 2.26 veri• fies that double-neighbor pairs and minor sevenths can conjure up the same harmonic images as do tritones, in addition to 41

specifying whether the original root of the suggested harmonic

function is present, or its tritone-suhstitute. This justifies

the use of symbols such as TS(V7) and TS(V7/V) to describe the

functions of certain fourth chords.

Example 2.26: [Note minor sevenths/double neighbors and tritones at points (X).]

A fourth chord which suggests the function TS(V7/v) in F-sharp is found in measure 5 of Opus lk, Number 1. Rein• forcing such an interpretation of the chord, which consists of the pitches D, G, and C from the piano, with A from the vocal line, is the fact that a tertian version of the same harmonic function, TS(V7/V),' directly follows it-(Example 2.27)

Example 2.27: Opus 14, Number 1, measures 5-8 42

Example 2.27» continued.

7 7 F#: TS(V7A) V —TS(V ) r-I (discounting CD)

Example 2.28: Traditional progression resembling 2.27.

/ri ' "" ~

0:—Jl-J tf *K4 II S ^ 7^ J5r*=

7 F#: TS(V7A) V 1

Example 2.28 shows the traditional progression which

Example 2.27 resembles. The greater complexity of the latter

is in part the result of the two-fold function of the pitches

C-sharp and B in measure 6, already mentioned during the dis•

cussion of double-neighbor pairs in whole-tone contexts. Two

staves have been used in Example 2.27 to show both functions

clearly: the uppermost staff shows the conventional behavior of C-sharp and B as a minor seventh, with B descending to A

and C-sharp remaining; the lowest staff shows the double- neighbor function, with the resolution of both C-sharp and

B to C-natural in measure 7.

The important double-neighbor pair in this passage, however, is D - C. It appears in both the "fourth-chord"

and "whole-tone" versions of TS(V?/v), and is responsible for determining their single function (Example 2.29).

Example 2.29s "Fourth" and "Whole-tone" versions of TS(V7/V).

• «1

The same function, TS(V''/V)» is made more explicit in the similar passage which occurs later in the song, shown in Example 2.30. In this case, the double-neighbor pair, D -

C, immediately reaches its goal of C-sharp in measure 20.

Example 2.30: Opus 14, Number 1, measures 19-22. The tonic ^ chord which arrives at that time resolves to the expected V7 almost conventionally; however, the third of the dominant-seventh chord, E-sharp, is missing as a result of the transposition of the motive from measure 6 (Example 2.31) up a whole tone (Example 2.32).

Example 2.31:

Example 2.32:

Of course", this does not change the harmonic function of the motive, V in F-sharp, since, at either transposition, it is part of the same whole-tone collection (C-sharp, D- sharp, E-sharp, G, A, and B). The transposition does, how• ever, result in a new, local double-neighbor relationship.

The pair, C-sharp - D -sharp, now embellishes D-natural where

B - C-sharp formerly embellished C-natural. These two double- neighbor embellishments form a long-range manifestation of the double-neighbor pair, D - C, and its goal of C-sharp, as depicted in Example 2.33. 45

Example 2.33* Long-range manifestation of the double- neighbor pair, D - C

If double-neighbor pairs and minor sevenths are impor• tant in local chord connections, they are indispensable in the connection of key areas. Two specific intervallic relation• ships between keys, which directly depend upon the double- neighbor/minor seventh dichotomy, are conspicuous in Opus 15 and earlier songst those of the minor third and minor second.

Discussion of these relationships will be the final concern of this chapter.

The Minor Third-Relationship

Schoenberg's practice of hinting at two, three, or all four keys whose tonics trace out a diminished-seventh chord hinges around the relationship between the dominant-sevenths of those keys. The motion of harmonic voices within any pair of dominant-seventh chords in such a complex of four is of two basic types:

(i) that between adjacent dominant-seventh chords along the "minor-third ladder", which involves motion from a minor seventh (major second) to a minor sixth (major third) and vice versa (Example 2.34); and

(ii) that between non-adjacent dominant-sevenths in the sequence of minor thirds, or those which are tritone- related, which would involve motion from a perfect fifth

(fourth) to a perfect fourth (fifth )(Example 2.35).

Example 2.34s Motion between adjacent dominant- seventh chords along the "minor-third ladder"

Example 2.35: Motion between tritone-related dominant- seventh chords 47

Going on the principle that the tritone and the minor

seventh (with its potential to he a double-neighbor pair) are

the crucial intervals, at least one of which should be pres•

ent in a chord for it to suggest some harmonic function along

a cycle of fifths in a highly chromatic context, the harmonic voice motions in Example 2.34 must be considered functionally

much more significant than those in Example 2.35. In the case of the latter, there is a common tritone between members of each dominant-seventh pair, and the possibility exists for the root and seventh of one dominant chord to act as the dou• ble-neighbor pair to the tonic of the other. Both of these factors, which together form the essence of the tritone-sub• stitute relationship, make the strong implication of a change of harmonic function simply through the voice-leading in Ex• ample 2.35 an unlikely event. Of course, where both of the tonics corresponding to a tritone-related dominant-seventh pair are suggested, two separate V' functions may emerge des• pite the common tritone between them.

An important example of the minor-third relationship, which involves three of the four possible dominant-seventh chords and their respective tonics, is found in Opus 6, Num• ber 2, "Alles". The main tonal center of the piece is A-flat

(with strong minor inflections), but emphasis upon C-flat and

F as subsidiary centers is clear. By measure 14, all three of these tonics have emerged, as revealed in Example 2.36.

In summary, measures 1 to 6 are concerned with the A- flat center, measures 7 to 11 with a mixture of A-flat and C- flat, and measures 12 to 14 with F. 48

Example 2.365 Opus 6, Number 2, measures 1-14.

Gesang Lass uns Doch die

Klavier •

fait die Han - de_ in den har - ten Stei gen durch den

JWI>JLTO|>JLPI!!- 49

Example 2.36, continued.

Harmonic voice summary of measures 1-14.

i do Ju 1 k*- 4-1 4 1 W U 1

•I 1). Jn> , =

0 — , 10 7 '1 1: 1 J

1 V ' ^fcF. + \ ^(Hb 14 | 11

/ ^r-^ " ' 5 _T Y 1 :

The most striking of the minor-third relationships in

"Alles" is that between the A-flat and C-flat key areas. The first hint of C-flat occurs at the end of measure 6, where a progression from ii to V7 in that key is heard; however, with the beginning of measure 7% a shift back to V of A-flat is initiated, causing confusion as it clashes with motion between V and I in C-flat which is trying to proceed simultane•

ously. The two voice-leading patterns being pitted against

one another are shown in Example 2.37*

Example 2.37* Clashing voice-leadings in measure 7. \

Although the conflict between C-flat and A-flat is

most obvious in measures 7 and 8, where the dominant-seventh

chords of those keys are actually stated simultaneously, it

is continued until measure 12 through foreground subtleties

which are not visible in Example 2.36. In measure 9. for in•

stance, a progression from ii7 to V7 in C-flat is suggested,

but where the resolution to I should occur (at the beginning

of measure 10), a turn to B-flat minor, or ii in A-flat,

takes place (Example 2.38). Even during measure 10, where

a return to A-flat through its ii7 and V7 seems imminent, pre• dominant and dominant functions in C-flat are perceived in the

foreground (Example 2.39). Finally, in measure 11, where A-

flat re-emerges, C-flat also appears briefly before its domi• nant-seventh chord leads to V7 of F by the tritone-substitute

relationship (Example 2.40).

Though Examples 2.36 to 2.40,from Opus 6, Number 2,

concerned references made to three minor-third-related tonics,

Example 2.39s Pre-dominant and dominant functions in C-flat in measure 10 .

geht das Heim - wen

C-flatJ

Example 2.40: Brief appearance of C-flat in measure 11.

auf den Zehn JihlSpJ?^ JH-

I and V7 in C-flat.

I V 53 the introduction of dominant-seventh chords in a minor-third sequence could serve other musical purposes. One such pur• pose would be to prolong either or both of two diminished- seventh chords: type (i) is that which would function as

o7 vii in any of the four potential tonic keys suggested by the dominant-seventh chords, and type (ii) is that a semi• tone lower, which is traced out by the roots of the four dom• inants. A clear example of prolongation of a type (i) dimin• ished-seventh chord is found in Opus 12, Number 1, "Jane Grey".

At the same place, a less persuasive case might even be made for the prolongation of the corresponding type (ii) chord.

The passage in question, which begins with the last half of measure 32 and continues to measure 42, is the bridge to and statement of the fourth verse of the ballade (Example 2.42).

For the sake of this discussion, let it be accepted that the tonality of "Jane Grey" is a mixture of D and D-flat/

C-sharp (which will be elaborated upon in the next section of this chapter).

From the beginning of the passage until measure 36,

the diminished-seventh chord shown as Example 2.41, Example 2.41:

is prolonged in the piano treble; it will be referred to sim•

ply as (i). The chord which will be called (ii) is formed

in the piano bass by the alternating roots of four dominant- 54

Ex-ample 2.42-; Opus 12, Number 1, measures 32-42. 55

seventh-minor-ninth chords, in which (i) would serve as the four upper members (Example 2.4-3).

Example 2.43s mm

The long-range function of (i) can be shown to be vii°7

in D; however, more locally, it works with C and F-sharp from

(ii) to form V7 and TS(V7) chords in F, which resolve to i in measure 36, as shown in Example 2.44. It is only in measure

Example 2.44s

. n . ^ ~ - _-

' 32 33 5*? i i =e*4 •—b* t& \<=*=

Fs V7 and TS(V7) i

42 that D appears as the tonic and the implications of (i) as

its vii07 are realized.

Preventing a direct connection between (i) and the ton•

ic in measure 42 are measures 37 to 41, which are completely

concerned with harmonic functions in C-sharp/D-flat, rather

than D. Measures 37 and 38 introduce V7 of D-flat and hint 7 7

at the relative key, B-flat, with the progression, iif to V

of vi (Example 2.45); measures 29 to 41 (second beat) proceed 56 through a very traditional preparation of and arrival at a cadential 1^ in D-flat (Example 2.46) which, however, goes astray and leads to a novel combination of dominant elements in both D-flat and D by the end of measure 41. The harmonic

Example 2.45: Opus 12, Number 1, measures 36-38.

ii7- V7 V7 of vi 57

Example 2.46: Opus 12, Number 1, measures 39-42.

structure at (x) in Example 2.46 contains three pitches of vii°7 in D-flat (E-flat, G-flat, and A, or B-double-flat); if C-natural were substituted for C-sharp as the fourth mem• ber of this structure, a conventional resolution to I in D- flat could take place over the bar-line to measure 42. How• ever, three of the pitches at (x) suggest a dominant func• tion in Dt C-sharp, E-flat, and A. The double-neighbor pair, C-sharp - E-flat, is characteristic of TS(V7), and A, of course, is the dominant pitch of D; these three pitches are responsible for the sudden, and somewhat unconvincing, resolution of the (x) chord to i in D.

The resolution to D in measure 42 does not allow one to forget the strong harmonic functions in D-flat which oc- 58

cupied measures 37 to 41, nor does it answer the question of how the D-flat passage relates to chords (i) and (ii) of measures 32 to 36. Examples 2.44 and 2.45 showed how (i) led to an F minor chord, or iii in D-flat; the same examples reveal something more subtle about (ii), with respect to D-

flat. When V7 of D-flat is introduced in measure 37, we re•

cognize that its tritone, C - G-flat, has been present since measure 32, in the form of alternating roots to chord (i),

C and F-sharp; the possibility of interpreting (ii) as a sub• tle hint of vii°7 in D-flat, despite its linear disposition over measures 32 to 36, must be allowed, in view of the ob• vious harmonic voice connections between C and D-flat, and

G-flat and F. Example 2.47 depicts what was referred to on page 53 as the "less persuasive case...for the prolongation O 7 of...(ii)" (as vii ' of D-flat) along with the long-range function of (i) as vii07 of D. o7 Example 2.47: Long-range vii ' functions in D and D-flat .

Ds vii ' (x) i

In summary, the passage from "Jane Grey" may be said 59 to emphasize the link between four minor-third-related major- minor-seventh chords» the presence of the upper three mem• bers of each in a common diminished-seventh chord, chord (i).

This link enabled the four chords to be used to express the o7 single function, vii ' in D. The passage from "Alles", dis• cussed previously, emphasized the individual dominant-seventh functions of three minor-third-related chords by the appear• ances of their respective tonics. Through the two passages, examples of both the collective and separate functioning of major-minor-seventh chords in a minor-third sequence are re• vealed.

The Minor-Second Relationship"^

Schoenberg connects semitonally-related keys by means of two basic types of harmonic double interpretation. The first relies upon the identity between V7 of a given key and

TS(V7/V) of that a semi-tone lower, and its corollary, the equality of V7/V in the lower key to TS(V7) in the upper.

Example 2.48t This type of double interpretation con• trasts the double-neighbor and minor-seventh functions of en- harmonically equivalent chords.

_D~* V^='I C#TTS_("^—J^I DTTS~(T7)^lC DJ?:^ «V7

The second type involves the interpretation of a given aug• mented triad as I#5 in the lower key, and either as V#5 or i with suspended leading-tone in the upper (Example 2.49).

Characteristic of the minor-second relationship in 60

Example 2.4-9« Double interpretation of an augmented triad.

C#s I#5 Ds V#5 or i

Schoenberg's music is that elements of functional harmony in both keys appear alternately, and even proceed simultaneously, yet a general Roman numeral analysis frequently can be done which actually overlooks the fact that two keys are being im• plied and still makes tonal sense. This testifies to the as• tounding degree of integration between the two keys which

Schoenberg achieves.

The work which depicts most strikingly the minor-sec• ond relationship, accomplished through the two types of dou• ble interpretation just introduced, is Opus 12. Both songs,

"Jane Grey" and "Der verlorene Haufen", are based upon the minor-second-related tonic pair, D - C-sharp/D-flat. In each song, D is the initial and final tonic, but substantial passag• es are best interpreted in C-sharp or D-flati additional tonics are hinted at by the minor-third relationship between domi• nant-seventh chords discussed in the preceding section of this chapter.

The important keys in "Jane Grey" may be diagrammed thus t D_ (F) (B>)- pi (This sketch does not represent an order of occurrence, since 61

the tonics fade in and out; it is only meant to show the

main minor-second and subsidiary minor-third relationships.)

Measures k to 12 of "Jane Grey" will be dealt with in this

regard.

Example 2.50» Opus 12, Number 1, "Jane Grey", meas• ures k to 12.

Sie fiihr - ten Urn durch den grau - enn Hof, daB ihm seui Spriich ge

br - ni - g ii Grey.

' espress.

¥ f^rF^^r" u ' q—rffc-1 ^4 ^ espress.

Measures 5 to 12, inclusive, to which the first stan•

za of poetry is set, contain elements of all four of the keys in the aforementioned diagram (page 60). The simple,

two-times-two-measure structure of the passage harbours a

correspondingly simply harmonic scheme, barring the fact

that one's point of tonal reference subtly shifts from D 62 to F, then D-flat, and finally, B-flat, in the course of eight measures of music. Example 2.51 shows the harmonic scheme of measures 4 to 12; the tonic(s) to which each Roman numeral applies may change, but it must be emphasized that the passage, as a whole, creates the same basic effect, in terms of musical "rhetoric", as it would if the harmonic scheme were applied to a single tonic.

Example 2.51: Dots (...) indicate that a given tonic is in effect. Note the mixture of D and D-flat at measure 8.

Measure: 4— -,5— 6—, 7—8—-, 9—10—, 11—12—,

Function: hl-V7,i—V7--, I—V—, I-IV-ii-, l£-v7-I—,

(F : ) (D i ) (D>« ) (B>i )

A sketch of the harmonic voices in measures k to 12 which clarifies the roles of the two most important tonics,

D and D-flat, is given in Example 2.52, page 63.

We can describe this passage from "Jane Grey" subjec• tively, in terms of general musical gestures and correspond• ing, traditional progressions which would be found in a harmonically simpler, but similarly structured stanza of a song.

First, measure 4 ends the introduction with a very fam• iliar approach to the D minor tonic: the progression from

(or the "Neapolitan-sixth" chord) to V7. Then, there is a four-measure antecedent phrase (measures 5 to 8), followed by a balancing consequent phrase (measures 9 to 12). Both phras- 63

Example 2.52» Harmonic voice sketch of measures 4 to 12 of "Jane Grey". The upper system relates to the tonics D and F, and the lower system to D-flat and B-flat. Square brackets show how the music corresponds to the individual lines of poetry.

7 7 7 D T—ii —(V?) —I#5-iv -ii -TS (^5-it" (no 3) ii'-VI

B^t (v#5?) es may be halved, resulting in four two-measure groupss 5-6, 7-8, 9-10, and 11-12.

The first half of the antecedent phrase might be de• scribed as the tentative departure from the tonic, and the second half as the decisive departure, the latter ending in a semi-cadence. A simple, prototypical antecedent phrase which captures the essence of the harmonic events in meas• ures 5 to 8 while staying within one tonic key is given-in

Example 2.53; a slightly more complex phrase which comes closer to the actual events in "Jane Grey" by including a 64 hint of the relative major key in its second measure appears in Example 2.54.

Example 2.53' Hypothetical, simpler antecedent phrase, analogous to measures 5 to 8 of "Jane Grey", but which re• mains in D minor.

D: i-—VI ii' V i____XZ V' 1 V Example 2.54« More complex phrase, including elements which suggest F major, as in "Jane Grey" in measure 6.

-D-i—i—- -V I— -V7/V—.-y7 F Comparison of Example 2.54 with the corresponding por• tion of Example 2.52 on page 63 reveals the only significant difference between the two; it is that D-flat rather than D appears where the tonic is supposed to return in preparation for the semi-cadence (at the beginning of measure 7) in the earlier example. Example 2.52 also shows that the dominant in

measure 8 is interpretable in both D-flat and Dr With res• pect to D-flat, the leading-tone, C, is emphasized, having been prepared in measure 7 by the progression from I to ii7 in D-flat, which made D-flat the dissonant seventh; in addi• tion, measure 8 contains implications of the dominant of D, 65 in the form of the pitches A, C-sharp, and E. Further ele• ments which add to the sense of a dominant function in D are the B-flat (present in vii07 of D) and the F/E-sharp (present in V#5) found in the piano treble in measure 8.

The resolution to the D-flat augmented triad in meas• ure 9 may be seen as a compromise between "pure" resolutions in D-flat major and D minor which might have taken place as shown in ixamples 2.55 and 2.56, respectively.

Example 2.55' Hypothetical resolution to D-flat major.

? !• 5i V 1

1 ' 'V i I I I

—lj?pJ 1 I ft

(8)' (< [ -^rr -h '1 UrU \ 1

Example 2.56« Hypothetical resolution to D minor. 66

The general musical gestures in the consequent phrase of measures 9 to 12 are clear. The first half of the phrase represents a harmonic intensification which prepares for the final and most dramatic arrival at the dominant [with motion from the tonic to the subdominant, followed by the pre-^dominant functions, ii7 and TS(V7/V)]} the second half involves the final cadence itself, beginning typically, with a tonic

^ chord which one expects to resolve to V and then I.

To compose a simpler version of the first half of the consequent phrase, we need not change significantly the pro• gression in the piece which is shown in Example 2.52, except to have it occur in D instead of D-flat, so that the music follows logically from Example 2.54. This is done in Exam• ple 2.5?.

Example 2.57t Harmonic progression analogous to that in measures 9 and 10, but with D as the tonic instead of D- flat.

D: 7 i —7i?v -i'v —ii —TS(^£)— *V .

(**V7/iv has been substituted for the continued I#5 of 2.52)

The final cadence which one would expect to follow

from Example 2.57 appears in Example 2.58, which shows the

complete, hypothetical consequent phrase. Comparing this phrase with measures 9 to 12 of Example 2.52, we find essen• tially the same progression of harmonies up to and including 67 the first half of measure 11, except that it is happening in

D minor rather than D-flat major in the hypothetical phrase.

In the last half of measure 11, a turn to B-flat takes place in the original music which is omitted in Example 2.58.

Example 2.58: The hypothetical consequent phrase, which remains in D minor (analogous to measures 9-12).

X) • #f SI »-S- -•• # - lio) (12) <5> V > (11) #— -J-o* v' =. 1

7 D: i — XL — IV ii -Ts<^)~i<;—_v? i IV

Cadence

The actual consequent phrase would he identical to

Example 2.58, save the substitution of D for D-flat as the

tonic in the latter, if measure 11 of "Jane Grey" proceeded

from the D-flat ^ chord as depicted in Example 2.59«

Example 2.59: Hypothetical close in D-flat (analogous to measures 11 and 12).

tee die scho - ne Ko -

(ID

3 fi£ 68

Example 2.59» continued

Harmonic voice summary of the hypothetical close

Although the consequent phrase, in its original form,

is clearly in D-flat, a shift back to, D could be achieved

simply, on two occasions during measures 9 to 12. The first

is in measure 10, where the progression from ii to TS(V?/v)

in D-flat bears some similarity to that from to V7 in D

which occurred in measure 4; the minor alterations of G-flat

to G-natural and C-natural to C-sharp in the two chords, res•

pectively, would enable a smooth resolution to a D minor ^

chord to take/place at the beginning of measure 11, as

shown in Example 2.60. The second occasion is in measure

Example 2.60t A possible shift back to D minor in measures 10 and 11.

If* (10) (ID

12, where the double-neighbor pair, E-flat and C-sharp, re•

solves to D, the third of a B-flat major triad; the same 69

double-neighbor resolution might have been part of a progres•

sion from TS(V7) to i in D (Example 2.61).

Example 2.61J Return to D minor at the last moment, in measure 12.

Of the examples dealing with this passage from "Jane Grey" (2.52 to 2.60), several manifest one of the basic types of double interpretation set out in Examples 2.48 and

2.49 of pages 59 and 60. The former type, which relies upon the double-neighbor/minor seventh dichotomy, is apparent in

Examples 2.59 and 2.60, which concern the equivalence be• tween V7/v in D-flat and TS(V7) in D; the latter type arises in Examples 2.55 and 2.56, which deal with the equivalence between I#5 in D-flat and i, with suspended leading-tone, in

D. 70

CHAPTER III

AN ANALYSIS OF OPUS 15, NUMBER '§

The most important harmonic relationships in Opus 15,

Number 5 are summarized in Example 3*0. This example is not meant to depict the chronological order of events in the piece, but to map in abstract form the crucial harmonic con• nections which characterize the music. (A reproduction of the entire piece appears in Example 3.1, pages 71 and 72.)

Example 3.0« Harmonic relationships in Opus 15t Number 5*

With regard to tonal centres, it is B and D which are most strongly suggested? the latter never actually appears, but its presence is felt due to convincing preparations of its dominant, which fails to resolve to D. The pitches G and B-flat become important when the harmonic functions of 71

Example 3»1« °Pus 15* Number 5. 72

Example 3»lt continued . 73

TS(V7/V) in B and D are emphasized enough for their alter• nate identities as major-minor-seventh chords on the roots

G and B-flat to be recognized. In the last half of the piece, G and B-flat are given the stature of hinted tonics,

although their main functions prove to be as members of the

unstable harmonic structures in which they appear in Example

3«0. Example 3*2 is derived from 3.0, and shows the pitches

which achieve some degree of tonic status during the piece.

Example 3.2t Tonics in Opus 15, Number 5 (Notice the similarity between this example and that at the bottom of page 60, which mapped the tonal centres in Opus 12, Number 1.)

G- B^

-D

The first phrase of the piece, comprising measures 1

and 2, introduces B as a tonic. The harmonic progression in these measures bears overt resemblance to, and serves the

same purpose as would, one along the cycle of fifths in B

from V'/ii to i. This can be shown by recomposing the phrase

in several stages, the first of which involves simplifying

the vocal line to show its basic descent from F-sharp to D,

as shown in Example 3-3. In the next stage, having noticed that the E and D of

.the vocal line are displaced one chord to the left from what

would be the proper alignment for a cadence from TS(V7) to i

in B, we correct the situation (Example 3.4).

Finally, we introduce G-sharp as the root of the first

chord in measure 1, having allowed its tritone, C/B-sharp - 74

F-sharp, to determine its function as V7/ii in B; in addi• tion, we restore V7/V and V7 to their traditional forms.

The result is the prototypical progression shown in Example

3»5» first in notation which emphasized the root movements, and then in harmonic voice notation (page 75).

Example 3*3* Measures 1-2, first stage of recomposition. Etwas langsam (J ca 66} Gesang Sa - get mir, auf wel-chem Pfa - de Di - tea moi sur quel - le rou - te

H Sir Klavier p El

Example 3*4* Second stage of recomposition.

Bi r7/y————TS(V7) — i 75

Example 3.5s Measures 1-2, final stage of recomposition, resulting in a progression along the cycle of fifths.

Following this arrival at the tonic, B, is a progres• sion to the dominant of D, which is completed by measure 6.

Since the minor mode of B rather than the major was suggest• ed in measures 1 and 2, this progression has the effect of a turn to the "relative major", even though D major, or mi• nor, never appears. Crucial to the progression to V7 of D is the motion from TS(V7/V) in B to the same function in D, which occurs in measures 3 and 4. A summary of these meas• ures is given in Example 3*6.

Example 3*6* Measures 3-k. 76

Example 3.6, continued

Measures 3-4: whole-notes are those present in the vocal line.

of B of D

The chord which ultimately functions as TS(V7/V) in D

is shown in (i) and (ii) of Example 3.6 as a B-flat major-mi• nor-seventh chord; this notation is consistent with the

chord's more local function, V7/blI in D. This function be•

comes apparent with the beginning of measure 5t where |?II of

D appears; the substitution of A for G does not obscure the

bll function, but recalls the appoggiatura from the raised

fourth to the third of the G major-minor-seventh chord in

measure 3t as shown in Example 3*7• 77

Example 3.7 s "4-3" motion in measure 3 and a similar inference in measure 5•

The chord of measure 5 marks the beginning of a most familiar approach to V? of D. Example 3*8 extracts the relevant pitches from the music, leaving them in their original registers, while 3.9 rearranges the pitches registrally to yield the same progression in harmonic voice nota• tion.

Example 3.8t Measures 5-6, approach to V7 of D (Whole notes indicate which pitch-classes are found in the vocal line.)

dafi. irh aus der reieh - sten La . de zar mes - se - crets trk - sors pour el - le ii nut znrtem Ausdruck 78

Example 3.9« Measures 5-6 in harmonic voice notation.

Eliminating the F-sharp and E-flat of the first chord in measure 6, which may be interpreted as a suspended and pas• sing tone,, respectively, and omitting the minor ninth of V7 of D allows the proto$ypical progression of Example 3.10 to emerge.

Example 3.10J Prototypical approach to V7 of D .

3 T Dl' til V7/hl rj TS(V7/V) V'

The semi-cadence from TS(V7/V) to V7 in D ends a six- measure passage consisting of Ithree very basic harmonic ges•

tures*

(1) the approach and V-I cadence to a tonic (measures 1 and 2);

(2) the destabilization of that tonic pitch through the introduction of the leading-tone to the domi• nant, which forces the tonic down to its leading- tone (measures 3 and 4); (it should be noted that this process is usually initiated to achieve a re• solution from V7/V to V, as shown in Example 3.11* 79

although the actual situation in measures 3 and k involves the descent from the tonic, B, to B- flat rather than A-sharp, and a progression from TS(V7/V) in B to TS(V7/V) in D, as in Example 3.12);

.Example 3.11s

^Example 3.12:

(3) a shift to the dominant of the relative major, resulting in the further descent of the original leading-tone by a semitone to the new dominant pitch (Example 3.13).

Example 3.13: 80

The three gestures just described occur in three and four harmonic voices. Of these voices, the ones which in• volve the progress of the original tonic pitch, B, are par• ticularly important, since that pitch was introduced to us as the first tonally stable point in the music, however fleetingly. The harmonic voice shown by the beamed pitches of Exam• ple 3*13 receives the impetus to descend two semitones from its initially stable B in the following way (Example 3.14).

Example 3.14» Note the tritones at the points (X).

The two tritones, at the points (X), are the sonorities which motivate the first six measures of Opus 15* Number 5» the B-flat of the beamed voice is the result of the first tri• tone, and the A that of the second. The tritones occur with• in TS(V?/v) functions in B and D, respectively, those func^ tions having been introduced at the outset of this discus• sion as fundamental to the piece. Having now made the obser• vation that these functions collaborate to bring the origin• al tonic pitch, B, down two semitones, our concerns in the continued discussion of the piece must include a study of how this process is reversed, since, indeed, we find ascend• ing chromatic motion back to B by the end of the piece. 81

In terms of pitch alone, measures 7 and 8 have essen•

tially the same meaning as do measures 5 and 6 s therefore,

it may seem strange not to have included them in the dis•

cussion of the earlier two measures. However, measures 7

and 8 play an entirely new role in terms of musical dis•

course, in addition to whatever effect they might have as

an echo of measures 5 and 6. They initiate a four-measure

passage which diminishes the sense of semi-cadence we might

feel at the end of measure 8. The momentum which brings in measure 9 stems chiefly from the vocal part, which is in mid-phrase during measure 8, having broken away from the es•

tablished two-measure grouping which is carried on in the

accompaniment, and with which it was synchronized in the

first six measures of the piece. What frees the vocal line

from the two-measure grouping is the elongation of the

rhythmic pattern which it stated in measures 1-2, 3-4, and

5-6i the specific result of this is that the line one ex•

pects the vocal* part to complete in measures 7 and 8 ac•

tually lasts into measure 9» as shown in Example 3-15*

Example 3'158 Rhythmic patterns of the vocal line in measures 1-2, 3-4, 5-6, and 7-9 •

1-2:

3-4:

5-6:

7-9 s 82

Of course, it is more than the obvious one-to-one cor•

respondence between the pitches of the vocal line in meas•

ures 7-9 and those of the three preceding vocal phrases

which justifies interpreting the three-measure fourth phrase

as an elongated version of a two-measure phrase. The strik•

ing similarity of melodic contour between the vocal phrases

of measures 5-6 and 7-9 fortifies such an interpretation

(Example 3.16)^ as does the fact that the accompaniment in measures 7^8 is almost identical to that in measures 5-6.

Example 3.16: Comparison of the melodic contour of the vocal phrase in measures 5-6 with that in 7-9*

measure 789

The most convincing way of illustrating the rhythmic distortion of the fourth vocal phrase, however, is to remove it. To have the phrase take place in two measures rather than three, and to follow a rhythmic pattern similar to those of the first three phrases proves fascinating; we find that remarkable coincidences of pitch content exist between the hypothetical, shorter vocal phrase and its accompaniment in measures 7-8 (Example 3.I7).

The two-measure version of the fourth vocal phrase n creates a definite semi-cadence with the arrival of V' of D 83

Example 3«17« Hypothetical two-measure vocal phrase, created by compressing the material of measures 7-9 into 7-8» curved lines show pitch-class correspondences between the vocal line and the accompaniment.

\}L j 1 > ^ ^ — Op J «L- (8> (7) J \ \

lire-

^—

— —/-— l \ r •f 1 ^ 1 in measure 8, and is entirely compatible with the measure groupings of 7-8 and 9-10 suggested by the melodic structure of the accompaniment (Example 3.18). The actual three-meas-

Example 3'18s Two-measure groups in the piano accom• paniment.

measures 7-8

measures 9-10

ure vocal phrase must work against the contrasting two meas• ure groups of Example 18, which are reinforced by the har• monic functions in measures 7-8 and 9-10. Measure 9 may be said to represent a harmonic "catch-step", which essentially repeats the harmonic function of measure 8 with renewed pur• pose, the only change being that TS(V^) of D replaces the pre• ceding V?. The resulting sense is of two surges of harmonic 84 activity, moving forward as in the numerical sequence 12 3,

3 4 5 (Example 3.19).

Example 3.19* Harmonic voice summary of measures 7-10 (Note that measure 10 represents the beginning of a new vocal phrase as well as the end of a two-measure group in the accom paniment: the latter of these aspects is relevent to this ex- 85

The outer voices of the three chords in measures 9 and 10 of Example 3-19 characterize the conventional progressions from a IV^7 or ii7 chord through TS(V7/V) to l£ of B-flat which are shown in Example 3*20. However, the actual pro- Example 3'20J Prototypical progressions with the same outer voices as in the ultimate reduction of measures 9 and 10 which appears in Example 3«19«

gression during measures 9 and 10 differs in two ways from those of Example 3.20.

The first is that the presence of A as one of the most important pitches in measure 9» in combination with E-flat, creates some sense of a dominant function in B-flat; the pro• gressions of Example 3»20 have the stationary tonic as one of their most significant features. The vocal line in measure 9 actually states the tritone of V7 of B-flat, A - E-flat, and its resolution to B-flat and D, a gesture which foreshadows the appearance of B-flat harmony in measure 10 and emphasizes n the suggestion of V' in B-flat which comes with the chord in

Example 3.21. 86

The second difference between the harmonic progression

in measures 9 and 10 and the prototypes of Example 3.20 stems

from the premature arrival of the note D in measure 10; it is

brought in simultaneously with the double-neighbor pair, F-

sharp/G-flat - E, before the pair resolves to F, rather than occurring,as one might expect, with F on the third beat of measure 10. Therefore, the harmonic structure occupying • beats 1 and 2 of measure 10 contains not only the crucial pitches of TS(V7/V) in B-flat (F-sharp, B-flat, and E), but also those of TS(V7/V) in D (B-flat, the "early" D, and G- sharp). Since B-flat, D, and G-sharp appeared in measures 5 and 7 as TS( in D, when they return in measure 10, im• mediately following TS(V7) in D, we are aware of their po• tential to assume the earlier function once more, and to re• solve to the tonic or dominant chord of D as shown in Example

3.22.

7 Example 3.22t The hint of TS(V /y) in D, brought on by the pitches B-flat, D, and G-sharp in measure 10.

7 7 / \ .Df TS(V ) TS(V A)~- .-.-.-Jai_--__yl . 87

Measure 10 is important in expressing the link between

B-flat and D key areas which was emphasized at the outset of

this discussion, and is recalled in Example 3.23.

Example 3«23: The equivalence between lb7 of B-flat and TS(V7/V) of D.

A reminder of the first tonic of the piece, B, and

its relation to B-flat is present in measure 10, in the form of TS(V7/V) of B-flat, which could also act as V7 of B. The passage from measure 7 to 10 might even be said to hint at a shift from the dominant of D to that of B, as represented in

Example 3'24, until the double-neighbor resolution of F-sharp and E to F takes place at the end of measure 10, proving B-

Example 3.24: The hint of V7 of B in measure 10.

' / r~ Op \i i\ 8 9 10 / 1 V DT 11- - TS ( -B: V7? flat to be the goal rather than B.

We may now add to the sketch begun in Example 3*14 of page 80, which traced the progress of the harmonic voice that commenced on the tonic, B, and fell through B-flat to A by measure 6. We see that the descent from B-flat to A is sim- 88

ply repeated in measures 7-8, but that it is reversed in measures 9-10 (Example 3.25).

Example 3»25« Continuation of Example 3.14 from page 80; the progress of the harmonic voice from the initial tonic, B, through B-flat and A, and now back to B-flat. Crucial tritones at "(X)". —

Measures 10, 11, and the beginning of 12 are complete• ly concerned with the embellishment of I^7 in B-flat by TS

(v7/v ), as Example 3*26 shows. A "whole-tone" version of

TS(V7/V) occurs, which includes D (in place of the more con• ventional C-sharp/D-flat) and G-sharp, in addition to the cru• cial pitches, F-sharp/G-flat, B-flat, and E. This results in the stationary tonic (B-flat) and its third (D) being held throughout measures ISO to 12, and in our hearing B-flat har• mony as prolonged for the duration of the passage. The func• tions I^7 and TS(V7/v) refer only to the very local relation• ship expressed in these measures, as the arrival at measure

13 suggests the function V7 of E-flat for the B-flat major- minor-seventh chord, as in measures 4 to 8 (Example 3*26).

As was done in measures 4 and 7, G is inferred to com• plete the E-flat major chord of measure 13. Since G is de• picted as such a structurally important pitch, its inference in Example 3*26 must be justified. 89

Example 3.26: The prolongation of a B-flat major-minor- seventh chord in measures 10 to 12, its embellishment by TS (V7/V) of B-flat, and its resolution as V7 of E-flat to I in measure 13•

J* 9

rrrrn

• - •- —- - — — . - . - -

^— 1 —- - >-• E : V7-

(At the points **, the B-flat major-minor-seventh chord is embellished by TS(V7/V) of B-flat.) 90

A most convincing point can be made regarding the im•

plicit presence of G in the vocal line, on the first beat of measure 13« The vocal phrase beginning in that measure bears

a marked resemblance to that with which the piece began; Ex•

ample 3*27 compares the two phrases.

Example 3*27* The vocal phrases of measures 1-2 and 13-15-

Measures 1-2:

-^TJ-T-— \f\) a. #* \r— .tJ if " H r r

measures 13-15

The important differences between these two phrases

are:

(i) the transposition up a semitone of the measure 13 phrase;

(ii) the greater length of the measure 13 phrase, caus• ed by the insertion of E-natural between F and E- flat and the addition of D to the end of the phrase;

(iii) the omission of the first pitch of the measure 13 phrase, which would be G. to correspond to the F- sharp of measure 1. The third item of difference argues for the inference of G

tinder discussion. In addition to this, expectation of G re•

sults from the prolongation of the B-flat major-minor-seventh

chord from measures 10 to 12, and becomes intensified by cer•

tain events at the end of measure 12s the harmonic voice be•

ginning with the E and F in the vocal line is continued by

E-sharp and F-sharp in the piano treble, and the latter two 91 pitches are stated in octaves, resulting in a strong, chro• matic rise toward G. This makes the A of measure 13 sound like an appoggiatura to G. All of these factors, combined with the actual:presence of G at the beginning of measure 7 in the vocal line (where the same chord occurs in the accom• paniment as begins measure 13)1 allow G to be inferred.

There is irony in the three differences between the vocal phrases of measures 1-2 and 13-15 mentioned on page 90.

It lies in the fact that the second and third factors repre• sent adjustments to the later phrase which contradict its transposition up a semitone and make it more similar to the phrase of measures 1-2 in terms of pitch-class content. We recall that the first vocal phrase descended from F-sharp to

D in two stages, F-sharp to F, and E to D, and that this oc• curred as part of a progression along the cycle of fifths in

B from V^/ii to i. In measures I3-I5, the transposed phrase still descends from F-sharp to D and thereby allows for a similar harmonic progression, due to the modifications shown in Example 3*28. This example compares the vocal phrase in measures 13-15 with a hypothetical, exact transposition of the phrase in measures 1-2, as well as with the original open• ing phrase.

Since the harmonic progression accompanying the first vocal phrase [line (iii) of Example 3.28, page 92] arrives on the tonic, B, the new phrase in measures 13-15 has the poten• tial to return to that tonic with a similar progression. Be• ginning with the progression in measure 13 from an E-flat ma• jor chord to TS(V?) of E-flat, which supports the inferred G 92

Example 3.28$ Line (i) shows the exact transposition up a semitone of the vocal phrase from measures 1-2, line (ii) the actual phrase of measures 13-15i and line (iii) that of measures 1-2. Notice that the omission of the initial G and the additions of E and D which are made in line (ii) serve to make it more similar to line (iii).

• 1w Line 4 0 k— ^r—k i Y—1 (ii) hi w I

Line (iii) 3£

and the actual F-sharp of the vocal line, one can easily imagine a continuation to V7/v of B occurring where the voice states F/E-sharp. The connection between TS(V7) of E-flat and

V'/V °f B would be a simple one of minor-third-related seventh chords, as shown in Example 3.29. Example 3.29s

4 13 (15)

•J-^^ZmL~u-_ 1. Hypothetical continuation E|?, I-—TS(V7) 7 Bs r /V- (i) 93

The progression in Example 3.29 is surprisingly like what actually happens. Measure 14 presents V7 and a hint of

I^7 in B, supporting the E and E-flat/D-sharp of the voice, n as Example 3'30 indicates. However, V of B is not prepared

Example 3*30' Harmonic voice summary of measures 13- 15» to be compared with Example 3«29«

daB ich mei - ne Wan ge brei te, et sous ses pieds im pla - ca ties

ML •e-

XJ)P etteas drfingend 14 15

i>fr?t ft

F7 4' y ^4 *1

.E^i I—-TS(V7) B: V7- ;|?7 TS(V7/V) (PII of D, relative key to B) 94

by V7/V as in Example 3.29; instead the same double appog-

giatura (to the fifth and seventh) of V7 occurs as that which

embellished V7 of D in measures 6 and 8 (Example 3.31).

Example 3«3l« Double appoggiatura figures from meas• ures 6 and 8, and measure 14.

m.6,8s V7 of D m.l4i V7 of B

It is important to note that, by not preparing V7 of

B with V7/V, Schoenberg prolongs the leading-tone, B-flat/A- sharp, for longer, avoiding resolving it until the tonic harmony arrives at the end of measure 14. (In Example 3.29, which does use the V7/V to approach V7, B-flat moves to B at the beginning of measure 14, and back to A-sharp for V7 before the more important rise to B at the end of the measure.)

With the third beat of measure 14, the two crucial harmonic voice motions of a V7-I cadence in B occur (E to E^ flat/D-sharp, and B-flat/A-sharp to B). The former motion is stated in voice and piano, and the latter appears in the highest voice of the accompaniment, rendering both conspicuous despite the conflicting presence of C-sharp and G in the tonic

7 chord, held over from V ^9)# The brief tonic harmony passes immediately to TS(V7/V) at the beginning of measure 15, a progression which resembles that from the end of measure 2 into measure 3. The main difference between the two is that the tonic harmony of measure 2 ended the first vocal phrase and the TS( V7/V) of measure 3 "began the next, while, in meas- 95

ures lk and 15, the extended vocal phrase encompasses both

the tonic and TS(V7/V) functions. A comparision of measures

1-3 and 13-15 is made in Example 3.32.

Example 3*32: Measures 1-3 and 13-15 compared; stemmed half-notes are those found in the main descent of the vocal line in each passage. Common to both passages is the progres• sion: V7---I- —TS(V?/V) in B. measures 1-3

measures 13-15 (v7/v)

The arrival at TS(V7/V) in measure 15 marks the return of B-flat/A-sharp to B, and what follows is essentially a coda. Example 3*25 of page 88, which depicted the long-range progress of the harmonic voice beginning with the tonic B of measure 2, may now be dontinued as in Example 3«33« The hy• pothetical, bracketed portion of Example 3-33 is included to clarify the effect which the TS(V /V) chord of measure 15 potentially has; approached by the dominant-seventh chord of

B, it substitutes for the tonic, enabling motion from the leading-tone to the tonic to occur while the supporting har• monic progression actually regresses from the dominant to the function which immediately precedes it along the cycle of 96

fifths in B. This makes us anticipate another approach of

Example 3'33* Continuation of Example 3.25, page 88; the return to the tonic, B, of the harmonic voice which began there in measure 2. The important tritones are at the points (X).

(X) (X) , (X) (X)( 0 4 1 r— s-fa-^

*y ^V^f >f'f ff>f I m. 2 3 4-5 6 7 8 9 10 14 15 expected? the tonic which will prove to be a conclusive V^-I cadence, as shown in the brackets.

Certain pitches in* the last four measures of the piece constitute a rather obscure version of the expected attempt to achieve a cadence on the B tonic. The initial step toward this resolution is the convergence of the tritone of TS(V7/V),

B - F/E-sharp, back to F-sharp - A-sharp of V7. This essen• tially occurs in the course of measures 16 and 17, although pitches which contradict the sense of V of B which would re• sult from the bare resolution seen as Example 3*34,

Example 3.34:

are also present. Extracting only those pitches which parti• cipate in harmonic functions which, in isolation, are inter- 97 pretable with respect to B yields a progression from TS(V7/V) through V to I (Example 3.35).

s Example 3'35 Measures 15 to 18; the suggestion of a cadence to the B tonic. 98

Obviously, so much else occurs in measures 15 to 18 which does not support a cadential feeling in B that one hears only a hint of the progression shown in Example 3»35» however, this hint is worthy of discussion because of the abundance of harmonic voice motion throughout the piece which points to B as a tonic and to D as a related key. (One hesitates to specify the modes of these keys, but the fact that B occurs first, in measure 2, where its minor mode is suggested, argues for the conventional minor/relative-major interpretation of B and D.)

Whether considered in context of a cadence to B or not, the emphasis upon B-flat/A-sharp in the last three measures of the piece is undeniable, as is the ultimate re• solution of that pitch to B. Also undeniable is the impor• tance of the major third, B-flat - G-flat, which is gradually achieved by the fall of B to B-flat in measure 15 and the rise of F to G-flat in the following measure. As a final argument for the presence of an obscured V-I cadence in B at the end of the piece, a parallel may be drawn between the final two chords and those upon beats 2 and 3 of measure 14.

In measure 14, we heard a progression from V' of B through a brief I^7, with the latter function represented by the pitches B, E-flat/D-sharp, and A. The final "tonic" chord in measure 18 also contains these three pitches.

Naturally, the presence of A in the final chord destabilizes any tonic implications in B, but it does draw attention to the similarity between the final cadence and the much clearer progression from V7 to I^7 in measure 14. Measure 14 and the 99

final cadence are compared in Example 3«36.

Example 3.36: Measure 14, beats 2 and 3, and measures l^ to 16; the suggestion of V-I progressions in B. (Stemmed pitches are those found in the vocal line.)

One might also hear a reference to the progression from

V7 in measure 14 to TS(V7/V) in measure 15 in the final cadence.

In both progressions, the leading-tone resolves to the tonic,

but one has the sense of a "deceptive" cadence due to the

emphasis upon G in the harmony which supports the tonic pitch.

In the final cadence, though, the absence of F in the second

.chord suggests an ordinary V-VI progression, rather than V-

TS(V7/V), as shown in Example 3.37.

Example 3.37: The "deceptive" cadence effect in meas• ures 14-15 and 17-18.

The material in measures 15 to 18 which is left un•

accounted for in the preceding "B" interpretation is directed 100

toward two other tonal centres, B-flat and G (members of the

original complex, G-B-flat-B-D, introduced at the outset of

this discussion). We will deal first with those harmonic

voice motions relevant to a "B-flat" interpretation of the

last four measures of the piece.

To consider B-flat-related harmonic voices, we must

first return to the parallel drawn in Example 3-32 between

measures 1 to 3 and 13 to 15. That example ended with cor•

responding TS(V7/v) chords, but could have extended to include

one further chord into measures 3 and 15 (Example 3'38).

Example 3.38:

\7- y 1

In measure 3t the above chord was interpreted as V of

J?II in D, on the strength of the events which followed in measure 4: here, in measure 15» it is still heard primarily

as a B-flat chord, but instead of its being followed by J5ll 7 and V of D, elements of its own dominant are introduced.

This is most obvious in the vocal part, which is essentially

concerned with the pitches F, E-flat, and A throughout meas• ures 16 to 18 (Example 3.39). Example 3'39* The vocal line in measures 16 to 18 . 101

On the second beats of measures 16 and 17» where E-

flat occurs in the vocal line, the piano accompaniment sup•

plies A, forming the tritone of V7 of B-flat. In alternation

with these statements of E-flat - A are chords containing the

pitches C and B-flat, to which the tritone would resolve in

a V'-I cadence in B-flat. In Example 3'40, the harmonic

voices which participate in tonic and dominant functions in

B-flat from measures 15 to 18 are presented} the example

should be compared with Example 3«35t which did the same for

functions in B.

Example 3*40: Measures 15-18, with emphasis upon the B-flat-related harmonic voices .

mel un ter Ih - rer Soh W ten - drai~ mon hum - ble jou

-> fr* * ^ „ *» _ ' 4* i nit n*: ' ^ - -tjr-= G rVs— -b-^ fi— li

fe^- 1 V [ t> ^~

BK vi£~ I V7 TS(V7) 102

Example 3.40 proves to be easier to hear than Example

3.25 when the two are compared. This is because the main harmonic voice of 3.40, which involves B-flat and A, is actu• ally treated as a voice in the music, and appears as the high• est part in the accompaniment, whereas the correspondingly important harmonic voice of 3.25, involving A-sharp and B, is obscured. Several octave transfers are required to derive the latter, and furthermore, B-flat/A-sharp and B are heard simultaneously on the tied-over third beats of measures I5i

16, and l?t thwarting the sense of harmonic voice motion from one pitch to the other which Example 3*25 suggests occurs over the bar-lines.

The validity of Example 3'25 would depend heavily upon the precedent set from the beginning of the piece that B is relevant as a tonic center, while Example 3'40 is self-explan• atory despite the lack of precedent of B-flat as a tonic.

However, additional remarks are necessary for a full understanding of Example 3*40. It will have been noted, no doubt,that the motions from B-flat to A in measures 15-16 and 16-17 are shown to be supported by progressions from I to V7 in B-flat, whereas the final cadence is interpreted as

I to TS(V7). The distinction between V7 and TS(V7) is exag• gerated in Example 3'40; although the final cadence does dis• play the only overt motion from B-flat to B, the latter pitch is still present each of the two preceding times that B-flat descends to A for V7 of B-flat. This means that the V7 chords actually have lowered fifths, making them distinguishable from

TS(V7) only if one judges F to be of greater importance than B. 103

Such a judgement is made in Example 3'40 because the vocal line emphasizes F, and not B, and because V7 is the more immediate of the two functions.

The third tonal center which was said to be implied in measures 15 to 18 is G. The case for this tonic rests upon three statements of the perfect fifth, D to G, the last of which is accompanied by direct harmonic voice motion from

F-sharp to G. The fundamental weakness in this case stems from the familiarity which we have developed with the chord,

in the role of TS(V7/V) in B, based upon occurrences of that function in measures 3 and 15' If we are able to listen to the last four measures of music in context of a proposed G tonic, then the pitches of the above chord which appear at the beginning of measures 16, 17, and 18 (G, B, and F) may be said to represent I^7 in G: the final chord of the piece could be interpreted as the complete I chord. In alternation with the I^7 chords would be dominant chords implied by the pitches

D and F-sharp. Example 3.42 depicts the functional harmony in G which can be inferred from measures 15 to 18.

Having considered three interpretations of measures 15 to 18, each biased in support of a different tonal center, it is necessary to consider their interrelation and to determine what general principles make such diversity possible in a sin• gle passage. The examples to be referred to in this regard are 305i 3«40, and 3.41, which dealt with B, B-flat, and G, 104 respectively (see pages 971 101, and 104 for these examples).

Example 3.41: Functional harmony in relation to G in measures 15-18.

1(?7 v#5 1^7 -v#5 lv

The simplest way of observing how examples 3'35» 3'40

and 3'41 interrelate is to place the furthest reductions in

each example in a column and "sum" them up on a fourth staff

to show the full complexes of pitches from which they have been drawn. This should result in something close to the

actual score, but condensed into harmonic voice notation (see

Example 3.42, page 105).

Example 3'42 presents two basic structures: an aug• mented triad, and a five-pitch, "whole-tone" chord. The lat•

ter contains the roots, thirds, and sevenths of three differ•

ent major-minor-seventh chords, making either the minor-sev•

enth or double-neighbor function of any one of them a possible 105

Example 3.42: The amalgamation of Examples 3.35, 3.40, and 3.41. on the fourth staff, the important augmented triad is labelled "A", and the "whole-tone" chord "WT".

From 3-35«

7 7 — - B~i—s TS( v 7v •) -mr—~ v#5- - - - TS"( v /v") v#5- — i ^

From 3.40 : I v' I#5— TS(V7)

From 3.41: *{ iff f1}^?

G: v#5- • l)?7 v#5—i'

i r

"Total1

1 " " -___WTinffp _ AA - ,---,-WM«PT -AA WT«rTm (nt * o F)

interpretation of the entire structure (Example 3«43)« The

augmented triad is interpreted as a different major triad

with raised fifth in each of its inversions; on an F-sharp

root, it is V#5 in B (3*35); on B-flat, I#5 in B-flat (3-40);

and on D, V#5 in G (3.41).

To close this discussion of Opus 15i Number 5i a sketch of the entire piece, in two levels, is presented in

Example 3.44 on page 107. The first level is simply a union of the examples presented hitherto; the second recognizes areas of prolongation suggested by the absence of motion in 106

Example 3«43s The "whole-tone" chord of measures 16- 18, and the presence therein of the roots, thirds, and sev• enths of major-minor-seventh chords on B, F, and G.

the uppermost harmonic voice, which begins on the first tonic of the piece, B. The progress of this voice was traced in examples 3.14 (page 80), 3.25 (page 88), and 303 (page 96); its placement above the others in level two of Example 3*44 is to emphasize its role in defining the structure of the piece. The upper voice is acted upon by other voices, which force it to move up or down by forming tritones with it. The fact that it moves less often than the lower voices suggests that it waits until the stress of dissonance placed upon it is so intolerable as to demand motion.

For example, the stress upon the initial B results from E-sharp/F in measure 3» and B descends to B-flat to re• lieve it; skipping to measure 9» the pitch A of the upper 107

Example 3«^s Harmonic voice summary of Opus 15» Number 5» 108

voice is pressured by the introduction of E-flat, and reacts

by rising .back to B-flat; in turn, the pitch E in measure 14

forces B-flat/A-sharp up to B once more. The only motion of

the upper harmonic voice which is not dictated by the direct

formation of a tritone with one of its members is the descent

from B-flat to A which occurs over measures 4 to 6 and is re•

peated in 7 to 8; interestingly, this motion is also the only

one which might be considered partially unsuccessful, since

B-flat does remain as the minor-ninth of V7 of D, with the A

which may be said to replace it on a more fundamental level.

One might be tempted to show B-flat as prolonged through measures 4 to 14, making the motion in the upper voice a

simple lower-neighbor figure, B - B-flat/A-sharp - B. The

supporting harmonic progression for this figure which occurs

in Opus 15» Number 5 is shown on the first staff of Example

3»45» The second staff shows a conventional progression which might be expected to accompany such an upper voice in a more traditionally tonal piece.

Example 3.45:

measure: 2 3 5,7 6,8 10-12 14 15 109

CHAPTER IV

AN ANALYSIS OF OPUS 15, NUMBER 11

The opening measure of Opus 15» Number 11 presents a

B-flat minor triad, stated explicitly in the piano treble and

supported subtly in the bass. The progress of this chord to

the C-sharp/D-flat major-minor-seventh chord of measure 5

depends on a single harmonic voice motion—that from B-flat

to B-natural. This motion actually occurs in measure 1, with

the final pitch of the sixteenth-note run in the bass clef, a

C-flatj however, the true arrival of the C-sharp/D-flat chord

is delayed by the motion from D-flat to D-natural which occurs

at the end of measure 1. Example 4.0 shows both of these harmonic voice motions. (So that individual examples may be

seen in context of the entire piece, a reproduction of Opus

15, Number 11 is provided on pages 111 and 112, in Example 4.1.)

The reader will have noticed that the pitches of the

B-flat minor triad which are extracted from the sixteenth-

note run and included in levels 1 and 2 of Example 4.0 (page

110) are not uniformly emphasized either by the manner in

which the run is beamed or by the way in which it aligns with

the beats of measure 1. However, an aural connection is

certainly made between the pitches in the right-hand portion

of the piano accompaniment and their repetitions in different 110

octaves in the left. The following points suggest why we make such a connection, beyond the basic reason that we perceive octave-related pitches as being similar.

(1) A B-flat minor triad is the first complete, three- Ill 112

Example 4.1, continued. 113 voiced harmony we hear. The first interval in the sixteenth- note run which allows us to discern the presence of more than one harmonic voice in the piano bass is the first that is greater than a whole-tone—the major third, F to D-flat. Its two pitches must be interpreted as belonging to different har• monic voices by the definition of harmonic voice presented in

Chapter I. With the B-flat of the piano treble, F and D-flat form the first structure in three harmonic voices: a B-flat minor triad. Because of further statements of these three pitch-classes, we hear them as prolonged until new members of their respective harmonic voices contradict them, as do the

C-flat/B-natural and D-natural which occur later in the meas• ure.

(2) Pitch-class repetitions in the sixteenth-note run emphasize the B-flat minor triad. The point at which the sixteenth-note run first repeats a pitch-class is in the second quarter of beat 2, where G-flat moves to F, as it did an octave higher at the beginning of the run. The two pitches were interpreted as an upper neighbor and its resolution to the fifth of the B-flat minor triad when they first occurred; the same interpretation is valid for their second appearance, an octave lower, as it coincides with D-flat of the piano treble and the memory of B-flat is still fresh. The only other pitch-class which is stated more than once in the six• teenth-note run is C-flat/B-natural, but the first of its two statements is effectively cancelled out by the more important

B-flat to which it leads, the latter pitch being the second

B-flat which is heard as well as the root of the prevailing 114 harmony. Even if we include the pitches of the piano treble in our search, we find no pitch-class repetition save that of members of the B-flat minor triad (and the upper neighbor to its fifth, G-flat/F-sharp, mentioned above).

Example 4.2 is essentially the same as level 3 of

Example 4.0s the single addition of G-flat as an upper neighbor to F has been made. The importance of G-flat is thus suggested at an early stage in the piece; it will prove to be the tonal center of the entire work in the course of this analysis.

Example 4.2s

The chord (Example_A.3)_,

Example 4.3$

of measure 2,issues from what precedes it in two ways. First, it continues to build the diminished chord which thus far consists of B, D, and F (Example 4.4). The presence of G- sharp with B and F in measure 2, along with the still-fresh sound of D-natural from measure 1, causes the new pitch, E- natural to sound like an upper neighbor which may yet re• solve back to D, as shown in Example 4.4.

The second element of derivation of the chord of measure 2 involves tonal harmonic voice motion of a different 115

Example 4.4:

new voice enters

E as an upper neighbor to D

—^ 3$ ^

sort than that shown in Example 4.4. The major third, E - G-

sharp, is the final member of a chain of thirds which has

moved by descending perfect fifths as shown in Example 4.5.^

Example 4.5*

Level 1 PP

Level 2

Level 3 116

The harmonic overstatement of the chain of thirds which is shown in levels 2 and 3 of Example 4.5 is vaguely audible when one listens to measures 1 and 2 of the piece. However, at the point "**", Example 4.5 distorts what is actually heard in an effort to project the chain of thirds as repre• sentative of complete triads moving in traditional fashion along the cycle of fifths. The G-flat included at the point

is not actually heard, and thwarting any sense of a C-flat major triad which the major third, C-flat - E-flat, might itself create is the presence of F-natural in the right hand of the piano accompaniment, followed by D-natural. The F- and

D-naturals serve to cancel out G-flat and C-flat, respectively, being newer members of the same harmonic voices as G-flat and

C-flat. However, it would be inconsistent not to acknowledge the function of E-flat as a leading-tone to the E-natural of measure 2, in addition to its more immediate submission to

D-natural at the end of measure 1, since similar functions were attributed to the corresponding pitches, F and B-flat, of the preceding major thirds (they were shown to rise to

G-flat and C-flat/B-natural, respectively, in Example 4.5)'

Of course, the two inferred derivations for the measure 2 chord must be reconciled; in order to do this, we must look ahead to measure 5» as that is where the function of the measure 2 chord becomes clear.

The progression in measures 3 to 5 overtly suggests the functions TS(V7/v) and V7 in F-sharp. The former function, which is suggested by the double-neighbor pair D - C, lacks F- 117 sharp and, instead, contains C-sharp and F/E-sharp, pitches which anticipate the dominant-seventh function which is to come; Example 4.6 shows both of these functions.

Example 4.6: The functions TS(V7/V) and V7 in F-sharp in measures 3-5 • 118

Level 1 of Example 4.6 shows the individual path of

every harmonic voice in measures 2 to 5» beginning from the

diminished triad, B - D - F, achieved by the end of measure

1. The simple facts about measure 2 are that B and F con•

tinue from measure 1 and that a new harmonic voice begins on

G-sharp. Complications stem from the double function of E-

natural as (i) an upper neighbor to the D-natural which would

complete a vii ' of F-sharp, and (ii) as a passing tone to E-

sharp of the soon-to-be-achieved dominant-seventh of F-sharp.

This multiplicity of purpose is represented on level 1 by the

inclusion of a D-natural tied over from measure 1 and shown

to sound implicitly with the E-natural. This D-natural carries

over to that of measure 3 which functions in the double-neigh•

bor pair, D- C/B-sharp, which prepares the root of V7 of F-

sharp. The case for its implicit presence in measure 2 will be strengthened when we observe measures 13 and 20, in which

D actually occurs with the measure 2 chord, later in this

analysis. At present, it rests upon the listener's awareness, when hearing Example 4.6, of the two important harmonic voice motions (Example 4.?),

Example 4.7: J\

which characterize the preparation of a dominant by TS(V7/v); as level 3 of Example 4.6 shows, these two harmonic voices strive toward the root of Vf of F-sharp, whereas all of the

other voices enter and remain upon pitches of that V7 chord,

anticipating its ultimate arrival in measure 5« This results

in the arpeggiation of V7 of F-sharp (from E-sharp/F through

G-sharp to C-sharp) which we see clearly in Example 4.6,

levels 2 and 3i and which urges us to simplify measures 1 to

5 further in order to emphasize the function V7 of F-sharp.

This is done in Example 4.8, which eliminates the TS(V7/V)

function in favor of the prematurely-arriving pitches of V7

which oppose it.

Example 4.8:

F#: iii—vii

We may now interpret the diminished triad, B - D - F,

which arose from the initial B-flat minor harmony of measure

1 as the first indication of vii07 in F-sharp which becomes

V7 when D moves to C-sharp/D-flat in measures 4 and 5- We now find that it matters little whether the measure 2 chord is interpreted as an E major triad (with an implied minor

07 seventh, D-natural, from measure 1) or simply as vii ' of F- 7 sharp: the former chord would function as V of the relative key to F-sharp (A), turning directly to V7 of F-sharp with the

"minor-third connection" of seventh chords discussed in

Chapter I (Example 4.9). Since V7 of F-sharp and V7 of A share the same diminished-seventh "axis" of B - D - F/E-sharp 120

Example 4.9:

F#: relative key, A

G-sharp, Example 4.9 can be said to be just as much concerned with the dominant function of F-sharp as is 4.8, only to re• present a slightly different preparation of that dominant, involving a hint at the minor-third-related key of A resulting from the flexibility of vii

The role of the pitches D-flat and F/E-sharp in the first five measures of this piece is now clear: they are the common tones between the initial B-flat minor triad and the goal chord, C-sharp major-minor-seventh, of measure 5*

Example 4.10 is the final simplification of this portion of the piece, and it shows that the goal chord is being prepared from the very first measure.

In measure 6, our expectation of a resolution to F- sharp harmony is furthered by the breaking away of a chro- n matically descending line from the root of Vf which states C- 121

Example 4.10:

"m. "1

m. 1 5 natural and G-flat (or B-sharp and B-natural); the ear reaches for B-flat/A-sharp, but does not yet find it (Example 4.11).

m 5 6

We do hear E-sharp/F split into two harmonic voices, resolv• ing to E-natural and F-sharp in measure 7, after the fashion of a typical leading-tone which moves to the tonic and the immediately-generated, lowered seventh of the next chord along the cycle of fifths (with the difference that the 122

lowered seventh, E, actually occurs "before the tonic, F-sharp).

This results in the barest hint of ll?7 or V/lV in F-sharp

which, interestingly, does resolve in the next measure to a

briefly suggested IV (Example 4.12).

Example 4.12: The hint of V/lV and IV in F-sharp, in measures 7 and 8.

/) PPP

3 . _ .

G /F#: V7 V7/IV IV

(ignoring C# pedal point)

Example 4.12 shows that the role of the E-natural and F-

sharp of measure 7 in announcing the entry of the first vocal phrase is a product not only of timbral and rhythmic devices

(the distinctive quality of the high octaves and the three- beat duration of F-sharp), but also of a coherent tonal rela•

tionship. In measure 8, we find that attributing the subdom-

inant function to the beginning of the vocal phrase was essen• tially correct: the music from the beginning of measure 8 to the end of beat 1 in measure 9 constitutes an attempt to reach an F-sharp ^ chord by means of the traditional, embel• lishing progression, ii7 - #ii7 - 1^, this being entirely 123 compatible with the initial sense of subdominant harmony in measure 8. Example 4.13 shows the approach to an implied 1^ in F-sharp; it also shows that the C-sharp pedal-point may n be heard to combine with the ii function of measure 8 to 11 7 suggest V ^ , in view of the emphasis already placed upon V of F-sharp in measures 5 and 6.

Example 4.13:

Als wir hin-ter dem be - bliiin - ten TToc 'o Nous a - vions fran-chi la por-te fleu - ri

G |?/F#: IV (until - - i i7~-—-# -—- - „" -—(if) I AH over C# pedal-point

G|?/F#: ii7 #ii7 or (with the C#, viio?/V • V9-11 suggested) 124

From Example 4.13, a similarity between measures 8 and

1 is discernible. In both measures, the root and third of a minor triad are raised by semitones to create diminished triads. This comparison draws attention to the fact that a step backward along the cycle of fifths in F-sharp has taken place since the beginning of the piece: whereas in measure 1, the diminished triad, B - D - F, was suggestive o7 of vii ' of F-sharp, in measure 8, the pitches A, C, and E- flat participate in vii f/V in F-sharp,,(Example 4.14). In Example 4.14: Minor triads moving to diminished triads in measures 1 and 8, resulting in the functions viio7 and viio7/V in F-sharp, respectively.

. Measure 1: - Measure 8 (vocal line):

(partial) (partial) fact, measures 8 through 12 deal essentially with different expressions of pre-dominant harmony in F-sharp which only briefly bring in the dominant in measure 11, before departing from it immediately. Pre-dominant harmony is expressed in the forms of V7/V, TS(V7/v), and the already-mentioned vii07, all of which appear in the sketch of measures 8 to 12 in

Example 4.15, page 125. This example warrants a step-by-step explanation as a great deal of harmonic overstatement takes place within it; for this purpose, letters from (a) to (k) have been placed below the harmonic structures. Structures 125 126

Example 4.15» continued.

if7 7 'ft f p *c war den uns er - dach - dsais - tu, pro . mes

(i) (i) (j)

(a) and (b) have already been discussed in Example 4.13; in that example, (b) was described as a decorative -"#ii7" of an implied tonic harmony in F-sharp, with the proviso that it has the potential to be heard as viio7/v in F-sharp. Indeed, the latter function is clear when we look to the first quarter of measure 11, which is represented by structure (i) of Example.4.15 on page 126; however, the interim structures are intriguing. Structures (c) and (d) are inferred from the segment of the vocal line (Example 4.16), 127

Example 4.16: . ----- —,

which, played out of context, suggests motion along the cycle of fifths from pre-dominant to dominant harmony in either F- sharp or C, as shown in Example 4.17, and recalls the left- hand portion of the piano accompaniment in measures 2 to 5

(Example 4.18).

Example 4.17:

7 1^ Of* ' $Vv^te TS /v) 7 - 7 7 F#: (V V C: ii —y ' (D and C as double-neighbor) (D and C as minor 7th)

Example 4.18: Piano, left hand of measures 2 to 5

m. u -t^>—5 • [Mr

In measures 2 to 5» the stages of harmonic function were pre-dominant and dominant in F-sharp; the interval D - C was said to imply the function TS(V7/V) (although the pre• dominant tritone, C - G-flat/F-sharp, was not present), arid the interval B - F/E-sharp was said to participate in the o7 function vii ' of F-sharp. In measure 9* essentially the same interpretation is made: again, D - C suggests the pre•

dominant stage, continuing from the immediately preceding viio7/V as would a traditional TS(V7/V) save the sounding of

F-natural which counteracts the ongoing F-sharp pedal point. 128

This is shown in the close-up of structures (b) and (c) in

Example 4.19. As for the interval, B - F/E-sharp, it is still

Example 4.19s Close-up of structures (b) and (c).

-is — • : , -41 x

^—

(b) (c) to ??

.-•1

Udt*., fcr—7 ""T1^—

7 7 F#: Vji°7—TS(XZ) [ v or vii° ] V v heard as implying the diminished-seventh chord, B - D - F - A-

flat, shown as structure (d) in Example 4.15? however, the 7 resolution to V of F-sharp which occurred in measure 5 when D-natural descended to D-flat/C-sharp does not recur in meas• ure 9« Instead, the diminished-seventh chord, structure (d), behaves as an embellishment of V7/V, structure (e). This is

shown in Example 4.20, which is a close-up of structures (d) and (e)). ? Example 4.20: Notice that (cl) embellishes (e) as would (b) of Example 4.19 embellish a tonic chord in F-sharp.

(d) (e) 129

Structures (f) and (g) of Example 4.15 are made to

appear more distinct from one another than is actually the

case in the music, for as we hear the final pitch of the vo•

cal phrase in measure 10, E-natural, which completes the

fleetingly heard C major triad, we also hear the whole of

structure (g). The C major triad is stated separately, as

structure (f), to emphasize its relationship to structures

F-sharp, and is therefore the prime candidate for one of

Schoenberg's hints of an alternate tonic, as the juxtaposition

of structures (c), (d), and (f) suggests (Example 4.21).

Example 4.21:

V Urn h- Wm ! /v> —n-—- ufcr» k. "\ i ^— (;y^d)J

Structures (g) through (i) were dealt with when meas•

ures 2 to 5 were discussed (Examples 4.6 to 4.10, pages 117-

122). However, their treatment in measures 10 and 11 differs

slightly with respect to the ordering of the structures in

time. Whereas in measures 2 to 5 we heard the order of struc•

tures as (h), (g), (h), (i), and eliminated the second (h) to

simplify the analysis, in measures 10 and 11, we hear only

(g)» (h), and (i). Furthermore, the (g) and (h) of measure

10 are made less distinct from one another by the presence of

E-natural from the vocal line in (g). Still, structure (g)

represents a pre-dominant function in F-sharp, because of the 130 interval D - C/B-sharp which is so important to the TS(V7/V) function; this function is suggested despite the presence of

C-sharp and F/E-sharp in the piano treble, pitches which anticipate the subsequent dominant function in F-sharp. The inferred G-sharp of structure (g) is included to complete the path of the harmonic voice which stated G-natural in structure

(f); this is a valid act of harmonic overstatement since G- natural may certainly not be heard as sustained through structure (g), which is a combination of the double-neighbor pair, D - C/B-sharp, and anticipations of the C-sharp triad to which the pair will progress in measure 11.

Structure (h), as in measures 2 to 4, represents an essentially dominant function in F-sharp, although,as was previously shown in Example 4.9 of page 120, there exists a hint of the dominant of A as well. Again, D-natural is in• cluded as a product of harmonic overstatement, justified by the fact that the D-natural of structure (g) must fall to

D-flat/C-sharp of structure (i) and may therefore be thought to remain implicitly through the intermediate structure (h).

The pitches contained in the box drawn in Example 4.15 are those which are to become members of structure (i), and which occur earlier, anticipating the dominant function in F-

sharp. This means that those pitches not included in the box which participate in structures (g) and (h) provide us with

a concise summary of the harmonic voice activity which actually progresses to the dominant. We can discern two two-voiced processes, occurring simultaneously, which provide a striking

testimony to the importance of two concepts introduced in 131

Chapter II as fundamental to Schoenberg's harmonic language: the expansion of a double-neighbor pair (augmented sixth) to an octave, and the contraction of a minor seventh to a minor sixth which suggests motion between minor-third-related dom• inant-seventh chords (Example 4.22).

Example 4.22:

From structure-: Cg) (h) (I) "Harmonic voice prototype

From structure: (g) (h) (i) Harmonic voice prototype

Structure (i) of Example 4.15, the dominant-seventh of the implied tonic, F-sharp, still does not achieve a resolu•

tion, although with structure (k) we receive a vague hint of one. Proceeding in detail from the beginning of measure 11, we find that structure (i) is prolonged for the measure, with neighbor-tone motion from the inferred fifth of the chord, G-

sharp, to A and back, and the embellishment of the seventh,

B, with its upper-neighbor, C.

Structure (j) is a product of harmonic overstatement. 7

Having interpreted the root, third, and seventh of V of F-

sharp as prolonged until the end of measure 11, we find that

the strong motion from G-sharp through G-natural to F-sharp

and C-sharp (in the piano treble) suggests that E-sharp/F is 132 no longer present, but has resolved as well to F-sharp, as

indicated in Example 4.15. Stretching the harmonic over•

statement to its limit, we might also sense that B from

structure (i) falls implicitly to A (or A-sharp) with the arrival of structure (k), resulting in the latter structure's suggestion of a momentary F-sharp ^ chord.

With the appearance of structure (k), the TS(V7/V) function is reinstated. We may infer the presence of F- sharp and A in structure (k), held over from (j). The D- sharp which becomes added to structure (j) creates a local double-neighbor embellishment of the subsequent D-natural, since D-sharp is heard between two statements of C-sharp in the vocal line.

Measures 11 and 12 may be summarized by structures (i) and (k) alone, if one finds that (j) involves too radical an assumption of harmonic overstatement; however, structure (j) is necessary if one wishes to be very specific about the path n of every harmonic voice of V of F-sharp and to account for all of the pitches in the music. With the slow tempo of the piece, one can indeed hear hints of the overstated version of measures 11 and 12 presented in Example 4.15«

In measure 13, an altered recapitulation of measures 1 to 5 begins. The same upper voice which occupied the piano accompaniment in those measures may be traced in measures 13 to 16, although the harmonic pacing and content differ in the two passages (Example 4.23). Despite the similarity of melo• dic contour between measures 1 to 5 and 13 to 16, the harmonic progression which occurs during the earlier passage is rushed 133

Example 4.23: Melodic parallel between measures 1-5 and 13-16.

! 1 ^4 If — 1 #^ y*y w; 13 14 15 16

into two measures,13 and 14, after which B-flat minor harmony returns and entirely new harmonic events follow. Example

4.24, page 134, presents a harmonic voice summary of measures

13 and 14. In level 1, the right- and left-hand parts of the piano accompaniment have been brought closer together and the harmonic structures which parallel those of measures 1 to

5 have been circled? no attempt has been made on this level to show complete harmonic voices. The right-hand portion of the accompaniment in measure 14 has been simplified in the following way: the first halves of the first three beats of the measure are interpreted as embellishments of the second halves, because they involve arpeggiated "fourth chords" whose double-neighbor pairs embellish the pitch-classes B,

F, and B-flat, as shown in Example 4.25 on page 135«

The parallel between measures 13 and 14 and 1 to 5 must be discussed in detail. The first structure circled on level 1 of Example 4.24 is the B-flat minor triad which appears in the piano bass in measure 13; this chord, of course, 134 135

Example 4.25s Double-neighbor "fourth" chords in the piano treble of measure;, 14,': embellishing B - F and B- flat s F.

parallels that found in the piano treble in measure 1. The

second structure circled, at the end of measure 13» parallels

that of measure 2, with the exception that an actual D-natural

is now present where it was only inferred in measure 2. This

chord is shown to be approached in a rather complex way on level 2 of Example 4.24: the portion of the chord which is

an E major triad results most importantly from the harmonic voice motions from E-flat/D-sharp to E and A to A-flat/G- sharp which appear in the vocal line and the piano treble, respectively; in addition to these motions, B is approached by B-flat in the piano treble, and the G of the vocal line may be heard as the lower neighbor of G-sharp/A-flat of the piano treble; finally, the C-natural of the vocal line may be interpreted as cancelled out once B-natural occurs. All of these motions, occurring simultaneously, result in the two 136 three-voiced structures shown in the vocal and treble piano

staves of level 2, Example 4.24. The remaining pitches of

the chord in question, D and F in the piano bass, stem from

the initial B-flat minor triad of measure 13' As in measure

1, D-flat rises to D-natural and B-flat is less directly- replaced by B-natural. (B-flat and B-natural are the first

and final pitches, respectively, of measure 13») The impor•

tant difference between measure 13 and measures 1-2, that

the later measure is a compressed version of the harmonic

events of the earlier two, is vital to the case made for

the implicit presence of D-natural in the measure 2 chord

(page 118)i in measure 13» one actually hears the measure

2 chord entering while D-natural is still sounding. We

will find similiar circumstances later, in measure 20.

The third structure circled on level 1 of Example

4.24 is essentially a C-sharp minor-seventh chord with both

major and minor third, or the same chord as was just heard,

save the lowering of D-natural to C-sharp. This structure

does not quite correspond to the C-sharp major-minor-seventh

chord of measure 5; it seems, rather, to combine that chord

with the measure 2 chord, by including E-natural.

This suggests a compression of the events from measure 2 to

measure 5» omitting the hint of TS(Y7/V) which was heard in

measure 3.

As in measures 1 to 5» we may say that the most im•

portant harmonic voice motion' in measures 13 and 14 is that

from the B-flat introduced as the root of a minor triad to

the B-natural which becomes the seventh of a chord which is 137 potentially V7 of F-sharp. The importance of the tritone, B -

F/E-sharp, in the last half of measure 13 and the first half of 14 is clear, as is the common-tone relationship between the D-flat from the B-flat minor triad beginning measure 13 and the C-sharp of the C-sharp minor triad in the next meas• ure. Example 4.10 of page 121 is reproduced as Example 4.26, as it serves also to summarize measure 13 and the first half of 14.

Example 4.26:

We must consider an important, motivic matter from

the beginning of measure 13—that of the now familiar raising,

by semitones, of the roots and thirds of minor triads to form

diminished ones. In addition to the related occurrences of

this harmonic event in measures 1 and 13, which have just

been dealt with, the same event was presented in the vocal

line of measure 8, beginning from an A-flat minor triad.

Now, in measures 13 and 14, we find several minor triads,

all of which exhibit the tendency to become diminished through

raising of their roots and thirds. Examination of the vocal

line alone in these measures yields the "minor to diminished"

pattern, occurring in a chain-like fashion which lasts almost

two complete segments (Example 4.27). 138

Example 4.27s ^1 IFF .—1.3 minor ..minor..

(diminished?) ToimThis n^H

Of course, the manner in which the voice presents the triads emphasizes the minor ones on C and C-sharp; how• ever, it is interesting that we do hear the pitches of the second diminished triad, D, F, and G-sharp, as very important during the second and third beats of measure 14. They parti• cipate in a vaguely hinted B-flat major-minor-seventh chord when, during the second beat of measure 14, harmonic voice motion from B-natural to B-flat takes place. But for this motion, the diminished-seventh chord, B - D - F - G-sharp, is prolonged by statements of the "minor to diminished" pattern on B-flat and C-sharp, as shown in Example 4.28.

Example 4.28:

l.3_ 14

Moreover, the minor-third relationship of major-minor-seventh chords introduced in Chapter II is again apparent; referring 139 now to level 3 of Example 4.24, page 134, we see that, by- means of this minor-third relationship, Schoenberg returns to B-flat minor harmony from the C-sharp-oriented structure at the beginning of measure 14.

The hint of a B-flat major-minor-seventh chord which precedes the B-flat minor triad at the end of measure 14 is very significant in view of the events to take place in measures 15 and 16. We find that a progression along the cycle of fifths occurs, moving through B-flat and E-flat structures to culminate in the arrival at an A-flat structure at the beginning of measure 16 which functions as V/v in F-

sharp. This progression is initiated in measure 15 when the

B-flat minor triad which begins that measure becomes a major- minor- seventh chord in earnest (we recall the hint in the preceding measure which has just been discussed?). The pro•

gression is shown in Example 4.29-

Level 1 of Example 4.29 (page 140) shows which pitches participate in the progression along the cycle of fifths, and how they are interpreted as aurally grouped together: the

four main harmonic structures have been labelled with the

letters (a), (b), (c), and (d) for easier reference. Looking

at level 1, and the score above it, one can see that the D-

natural which makes structure (b) a major-minor-seventh

chord is considered to come from D-flat, the third of the B-

flat minor triad labelled (a). The past two occurrences of

the B-flat minor triad (measures 1 and 13) involved not only

this rise from D-flat to D-natural, but also harmonic voice

motion from B-flat to B-natural which was obscured by registral 140

Example 4.29: Progression along the cycle of fifths in measures. 15 and 16.

Level ~*'2T

=r| —Ht* ,J tJ ¥= IMLBS — r b 5 | 3?

-^bii— -1 | 13—12?

(a) -fbf (d- 141

discrepancies between the B-flat and B-natural; in this case,

B-flat shows no sign-whatsoever of moving to B-natural, but

rather, appears twiceiin the thirty-second note pattern of

the piano accompaniment. The perfect fifth, B-flat - F, is

strong right up until structure (c) arrives, so we do not

hear, as in measures 1 and 13, the suggestion of a dominant-

seventh chord in F-sharp, which depends upon the tritone,

B-natural - F.

Structure (c) is special in that it suggests two

harmonic functions. The first is a chord on an E-flat bass,

which would be "pre-pre-dominant" in F-sharp. To make

structure (c) into a conventional version of an E-flat chord,

we must infer a G-flat or natural (and possibly a D-flat) as

shown in Example 4.30. We justify this inference of G-flat

or natural by assuming that the seventh of structure (b),

A-flat/G=sharp, would normally tend to fall to one of those

pitches. The version of structures (a) to (d) shown in

Example 4.30 is supported by the bass line of the accompani•

ment, which moves overtly in perfect fifths from B-flat,

through E-flat, to A-flat, embellishing each of those pitches

with its own dominant. However, if we focus our attention

upon the notes of the piano treble, we are encouraged to

look at structure (c) quite differently.

The understanding of structure (c) as an E-flat chord

required interpreting the pitches F, A, and C of the piano

treble as passing tones to the seventh, ninth and eleventh

of the subsequent V7/V chord; however, in terms of actual pitch-class content, structure (c) is surely a dominant- 142

Example 4.30:

(a) (b) **(c)** (d)

seventh chord in relation to the preceding B-flat structures,

(a) and (t>). Example 4.31, then, suggests an interpretation of measures 15 and 16 which ignores the emphasis placed upon

E-flat in the bass of structure (c) in favor of a more literal approach relying upon pitch-class content. The version

Example 4.31:

(a) (b) (c) (d)

shown in Example 4.31 shows a minor-third relationship be• tween structures (c) and (d) rather than a fifth relationship.

Measures 13 to 16 were first introduced, with Example

4.23 of page 133» as the melodic parallel of measures 1 to 5.

Now that we have dealt with the harmonic content of both pas• sages, we can compare the respective roles of the similar upper voice melodies in their different harmonic contexts.

This is done in Example 4.32, page 143. We can see from this example that the point at which the position of the melodies in the harmonic structures begins to differ in the 143

Example 4.32: Beams show the parallel melodies .

~\2 3 If- '

13 14 15

two passages is in measures 2 and 14; whereas G-sharp has a stable role throughout measure 2, as the third of either the vii°7 or ?V'/relative key aspects of the chord in Example

4.33.

Example 4.33:

G-sharp in measure 14 gives up that role to become the fifth of a C-sharp-rooted chord (the role taken by the G-sharp of measure 5)t and goes on to become the seventh of a B-flat major-minor-seventh chord. With the C-sharp structure of

measure 14 comes the completion of the harmonic events

which parallel measures 1 to 5; the B-flat chord which

follows represents the beginning of new harmonic events, 144 although the melodic events parallel to measures 1 to 5 occupy the music until measure 16.

The most striking difference between any two roles taken by corresponding melodic pitches in their respective harmonic contexts is found where the C-natural of measure

4 parallels that of measure 1$. In the former case, C- natural is merely the lower neighbor to the C-sharp of V

in F-sharp and is forced to sound with its intended pitch of resolution. In the latter case, however, C-natural is more important thannC-sharp: although C-sharp appears to have returned at the end of measure 15, we find that C- natural recurs in measure 16 and remains as a vital part of

the pre-dominant harmony in measures 17 and 18 which leads

to the dominant-seventh of F-sharp in measure 19• The C-

sharp at the end of measure 15 proves to be an upper neighbor

to the third of V/V in F-sharp, and behaves traditionally, in

a 4-3 motion over the A-flat/G-sharp root.

The events which occur from measure 16 to measure 19

serve to prolong C-natural as the leading-tone to C-sharp,

placing it in the context of pre-dominant harmonic structures.

We immediately hear the similarity between this passage and

that from measure 8 to measure 12, which also dealt with pre•

dominant harmonic structures and featured C-natural as a

very important pitch of the vocal line. The prolongation of

C-natural in measures 16 to 19 actually begins with the state•

ment of that pitch in the middle of measure 15/ From that

point on, C-natural appears every measure in the same octave

and participates in a most basic pre-dominant structure: the 145 double-neighbor pair, D - C, which is emphasized in measures

16, 17, and 18, as shown in Example 4.35 on page 146.

The double-neighbor pairs found in the vocal line are part of larger harmonic structures which function as TS(V7/V), as sketch 1 of Example 4.35 reveals. In measure 16, TS( V7A) is heard to resolve very briefly when the pitches E and C- sharp occur, but is immediately brought back by the voice's leap from D to G over the bar-line to measure 1?. Measure 17 presents the complete whole-tone version of TS(V7/V); "the pitches of the vocal line can be rearranged so that the double-neighbor pair, D - C, frames the whole-tone collection as in Example 4.34. In measure 18, TS(V7/V) again disappears for an instant when we are given a hint of tonic harmony, after which viio7/V and TS(V7/V) bring in the V7 of measure 19.

Example 4.34s

The piano accompaniment also displays the double- neighbor pair, D - C, in context of pre-dominant harmonic structures. However, the tertian and whole-tone character of the vocal line is contrasted by the emphasis upon fourths in the accompaniment. The fourths arise from the thirty- second-note passage of measure 15» in which B-flat, E-flat, and A-flat were embellished from below with their dominants.

Where the sketch of the piano accompaniment in Example 4.35 begins, we find the fourth E-flat - A-flat, which represents U6 147

V/V in F-sharp. Immediately following is the fourth D - G, which represents the intensification of that pre-dominant function and brings us one half-step closer to the goal pitch, C-sharp, changing the harmonic function to TS(V7/V) when heard in conjunction with the vocal line, which supplies the necessary C.

An additional harmonic implication to those of

TS(V7/V) and V found in the vocal line in measure 16 arises from the emphasis upon G and the high E-sharp in the accompan• iment. G alone would present us with no complexity, since it could be said to participate in the "fourth type" of double- neighbor chord (introduced in Chapter II), D - G - C, which functions as TS(V7/V) in F-sharp; however the presence of E- sharp with G in the piano throughout most of measure 16, and the conspicuous resolution of E-sharp to F-sharp forms a new double-neighbor complex—G - E-sharp to F-sharp. This com• plex is not at all incompatible with the previously discussed one of D - C to C-sharp; in fact, it simply creates the im• pression of a suspended fourth (Example 4.36) when heard with the vocal line's TS(V7/V) and V structures, which increases one's expectation of the third, E-sharp.

In the sketch of the accompaniment in Example 4.35» the double-neighbor pairs D - C and G - E-sharp are shown to resolve simultaneously to C-sharp and F-sharp. Whereas we could now expect a 4-3 resolution to E-sharp and a complete

Vf structure, this does not occur: instead, the vocal part makes a leap from D to C, and when this is heard with the

still-sounding, high F-sharp of the accompaniment, TS(V7/V) 148

Example 4.36: The expectation of a "4-3" resolution in measures 16-17 .

be TO m ben wir -be-gan^ nen, ^/we&n wir^leis nur an uns

-3? 16 (17) 2! ^ see* results.

When the fourth, G - C, of the piano accompaniment

in measure 17 occurs, it contributes its more important., upper pitch to the TS(¥7/V) function being expressed in the vocal line; in addition, it forms the complete double- neighbor "fourth" chord, D - G - C, if heard as a continu• ation of the fourth, D - G, in measure 16 of the accompani• ment. Arguing for this accumulation of fourths over measures

16 and 17 is the appearance of E-flat and A-flat in the latter measure. Whether or not we can hear a long-range relationship between the D - G of measure 16 and this

E-flat - A-flat, it is indisputable that harmonic voice motion from the strongly-emphasized D-natural of the vocal line to the E-flat takes place. Furthermore, the vocal line states C-flat simultaneously with the fourth, E-flat -

A-flat, in the piano, giving one the sense that TS(V7/v), which has occupied measure 17 thus far, has regressed to a supertonic triad as shown in Example 4.37.

The regression to ii shown in Example 4.37 is, of 149

course, immediately reversed in measure 18: in this measure,

the piano accompaniment quickly reinstates the double-

neighbor pair, D - C, and goes on to state the chord

(Example 4.38)

Example 4.38: > '•

7 which, as previously, anticipates the arrival of V of F- o7

sharp by its similarity to vii 'min that key. The vocal

line is less hasty, dwelling upon its pre-dominant pitches

until the true arrival of V' of F-sharp in measure 19• The

final three pitches of this vocal phrase summarize what has

been a three-measure preoccupation with the double-neighbor

pair D - C and its function, TS(V7/V). We may compare measures 16 to 19 with the prototypical dominant approach

shown in Example 4.39, 7

The truly unusual aspect of the music from the V

chord of measure 19 on is that the dominant-seventh of F- 150 3

Example 4.39* Approach to dominant-seventh of F- sharp, comparable to events in measures 16 to 19.

Analogous to: 16 1? 18 19

sharp, which we have supposedly been awaiting since measure

15 presented V7/v, is not treated as a goal chord by

Schoenberg; rather, he uses it to lead into measure 20, where the chord shown as Example 4.40

Example 4.40: /~ ~(V ]

appears. Whereas the dominant-seventh of F-sharp in measure

19 occurred on an off-beat, the measure 20 chord occurs on beat one; whereas the dominant-seventh chord lasted two and one-half beats, the chord of measure 20 lasts seven. Such facts obscure the effect which the dominant-seventh might have as a true goal chord. Harmonically, what was achieved in measure 19 is now clouded; however, the measure 20 chord

07 still suggests vii ' of F-sharp and a crucial alteration is made in the sixteenth-note run of the piano bass which fur• thers such an interpretation. We may show this alteration by presenting the sixteenth-note run as it would be if it were an exact transposition of the original run stated in measure 1, and comparing this version to the run used by

Schoenberg. This is done in Example 4.41. 151

Example 4.41: Hypothetical and actual runs compared.

—Hypo the ti c ai run

Ac_tual_run ,

7 q ' UJ j q^ ^ iJ j" hj j H ^

The hypothetical sixteenth-note run shown in Example

4.41 lacks one important feature which is present in

Schoenberg's altered version in measure 20: the run which

Schoenberg uses ends on the leading-tone to F-sharp, and thereby helps to maintain the tritone of the dominant- seventh chord achieved in measure 19 until the middle of measure 21. Schoenberg's run also sets up the pitches of

07 vii ' of F-sharp to begin the second and third groups of sixteenth-notes, so that those pitches are noticed not only because they double the pitches contained in the measure 20 chord, but also because they occur at points of slight rhythmic emphasis in the run. Example 4.42 presents an interpretation of measures 20 and 21 which shows how the sixteenth-note run prolongs a dominant function in F-sharp.

In Example 4.42, pitches present in the measure 20 chord are shown to be aurally accumulated as we hear the sixteenth-note run. These pitches, G-sharp, D-natural, and

F-natural, all occur at conspicuous points in the run. G- sharp first occurs after the sustained upper neighbor, A- 152

Example 4.42:

,natural, and is stated for the second time, an octave lower, on the first beat of measure 21s D-natural occurs on beat four of measure 20, and again as the lowest pitch of the run in measure 21j F-natural is the final pitch of the run.

These pitches, when heard with the sustained B-natural in the piano treble and the C-flat of the vocal line, function as vii°7 of F-sharp. o7

Schoenberg suggests the resolution of vii ' to I in measure 21, where the vocal line descends from C-flat to B- flat just after the low F-natural of the piano bass has 153 moved to F-sharp, as shown in Example 4.43. However, the B-

Example 4.43

from end of run flat is so momentary that when it proceeds to A-flat and E- flat, we forge.t it in favor of the A-flat minor triad formed by those pitches and the preceding G-flats. As in measures

8 and 9, the A-flat minor triad functions as ii in F-sharp; the presence of F-sharp and G-sharp in the piano anticipate the tonic function which could occur if the ii chord behaved in one of the two common ways shown in Example 4.44. We find, upon listening to the last four measures of the piece, that

Example 4.44(a) fairly accurately represents the musical events which occur. However, a more detailed study of these final measures is in order; it will depict the exact path of each harmonic voice which operates in measures 21 to 24. The reader should refer to Example 4.45 during the following discussion (page 155)'

Level 1 of Example 4.45 harmonically overstates the last four measures of the piece. The initial sonority of that level is comprised of the B-natural/C-flat of the vocal line, the chord B - E - G-sharp of the piano treble, and the final three pitches of the sixteenth-note run in the piano 154

Example 4.44:

(1) The embellishment of I by ii7 and #ii7, as in measures 8 and 9»

•tr.

(2) The traditional cadence along the cycle of fifths.

bass (D, F, and G-sharp) as well as the implied pitches,

D-natural and G-sharp, which were accumulated in the course of the sixteenth-note run in the preceding measure. When the tritone, E-sharp - B, contracts to F-sharp and A-sharp on the third beat of measure 21, the harmonic overstatement depicts, implied motions in other harmonic voices: D-natural is shown to pass to C-sharp, although the latter pitch only occurs on beat four of the measure and does so four and five octaves away; E-natural is shown to move to D-sharp, which occurs on the last half of beat two in the vocal line, al• though the former pitch actually remains until beat four

(the E-natural occurred more than four beats ago. and has received no reinforcement through additional occurrences 155

Example 4.45: Harmonic voice summary of measures 21-24.

j> j1 w a> b n uSo ver - blie-best jdu mi^r lang zu Sei ten. Que ta pre - sence e - tait forte et dou

21 25=

since then, whereas D-sharp is clearly a very important pitch in the vocal line and is stated in the same octave as the fading E-natural so as to detract from it in the strongest way possible). These harmonic voice motions, 156

both real and implied, result in the second sonority shown

on level 1 of Example 4.45- The only harmonic voice motions

which take place from this point on are those from B-natural

to B-sharp and G-sharp to G-double-sharp; D-sharp is shown

to remain implicitly throughout measures 22 and 23 as the

fifth of the supertonic-seventh structure with raised root

and third.

Level 2 of Example 4.45 eliminates all octave doublings

and simplifies the music registrally, as in comparable reductions throughout this study. The inferred resolution

of B-sharp to C-sharp and that of G-double-sharp to A-sharp

complete the tonic triad by implication. 157

CONCLUSION

The analyses of Opus 15» Number 5 and Number 11, presented in chapters III and IV are intended to contribute to the understanding of Schoenberg's music in two ways: first, they attempt to demonstrate that certain fundamental processes of tonal counterpoint, particularly as they operate in nineteenth-century harmonic contexts, are a basis for the tonal coherence still perceived in Opus 15; second, the analyses serve as concrete examples of a practical analytical

"method", involving the concept of harmonic voice, which makes the aforementioned processes readily apparent.

In Chapter II, specific ways in which these processes are felt to underly Schoenberg's music prior to and during

Opus 15 were introduced under several subject headings:

"The Tritone Substitute", "The Minor-Seventh/Augmented-

Sixth Potential of 'Whole-tone' Chords", and "Double- neighbor Pairs in 'Whole-tone' and Other Contexts" were a few such headings. However, all of the topics discussed in

Chapter II seem to stem from a single, most basic concept.

It is the concept that the root of a chord need not be present for its function to be effective, and that the root may be inferred from the tritone which is perceived to represent the major-third and minor-seventh of the chord.

(Further to this concept is the idea that, in the absence of a tritone, a minor seventh or augmented sixth may suggest a 158 harmonic function or its tritone substitute.) Such a

concept results in an essential equality of meaning between

chord progressions which might once have been distinguished

from one another by the adjectives "harmonic" and "linearv,

or even "diatonic" and "chromatic".

Example 5«0s Two "equivalent" progressions along the cycle of fifths in C.

."The ramifications of a concept of harmony which allows the two progressions shown in Example 5.0 to be considered functionally equal harmonic motions along the cycle of fifths are extreme with respect to the analysis of highly chromatic, tonally fluctuating music. A useful over• simplification or summary of these ramifications would be to say that, with the adoption of this concept of tritone- determined function, many harmonic structures which previous•

ly might have, been tossed off as being of purely linear origin, with therefore attenuated functional meaning (i.e., the "meaning" commonly denoted by Roman numerals), may now be considered as truly "harmonic".

Of course, the concept of harmonic voice, and the development of a notational system which emphasizes step• wise motions common to progressions which might otherwise 159

be considered different in terms of the harmonic-versus- linear distinction was a necessary outgrowth of the author's belief that, in some sense, Schoenberg's music could be

considered a purely harmonic music, and explored from that standpoint with interesting results. It remains to be determined what further uses the harmonic voice concept might have in analysis, and for which idioms it might be suitable. With respect to the rest of Opus 15, which could not be dealt with in a work of this narrow scope, the follow• ing songs lend themselves especially well to the analytical approach demonstrated in this study: numbers 2, 3i 4, 9>

10, 12, and 15* However, it is my opinion that all of

Opus 15, and later works by Schoenberg, might be explored valuably using the harmonic voice concept. 160

FOOTNOTES

"''Arnold Schoenberg, Theory of Harmony, trans. Roy E. Carter (Los Angeles: University of California Press, 1978), pp. 391-2.

2Ibid., p. 392.

3Ibid., p. 404.

^Ibid., p. 405.

^Thomas Clifton mentions Schoenberg's use of key areas a semitone apart, referring to it as the "semitone relation" in his dissertation, "Types of ambiguity in Schoenberg's tonal compositions" (Ph.D. dissertation, Stanford University, 1966), p. 8.

^David Lewin points out this pattern of major thirds in his artical, "Toward the Analysis of a Schoenberg Song," Perspectives of New Music (Fall-Winter l973/sPring-Summer 1974), p. 55- 161

SELECTED BIBLIOGRAPHY

Benjamin, William E. "Pitch-Class Counterpoint in Tonal Music." In Music Theory: Special Topics, pp. 1-32. Edited by Richmond Browne. New York: Academic Press Inc., 1981. Clifton, Thomas James. "Types of ambiguity in Schoenberg's tonal compositions." Ph.D. dissertation, Stanford University, I966.

Cone, Edward T. "Sound and Syntax: An Introduction to Schoenberg's Harmony." Perspectives of New Music (Fall-Winter 197*0* 21-W. Friedheim, Philip Alan. "Tonality and structure in the early works of Schoenberg." Thesis, New York University, I963. Lewin, David. "Toward the Analysis of a Schoenberg Song (Opus 15 No. XI)." Perspectives of New Music (Fall-Winter 1973/Spring-Summer 1974)* 43-86.

Martin, Henry. "A Structural Model for Schoenberg's Per verlorene Haufen, Opus 12/2." In Theory Only 3 TJune 1977)* 4-22. Schoenberg, Arnold. Theory of Harmony. Translated by Roy E. Carter. Los Angeles: University of California Press, 1978. Schoenberg, Arnold. Structural Functions of Harmony. New York: W. W. Norton & Company, Inc., 1954; revised ed., edited by Leonard Stein, New York: W. W. Norton & Company, Inc., I969. Wintle, W. "Schoenberg's harmony: theory and practice." Journal of the Arnold Schoenberg Institute 4:1 (1980): 50-67.