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Analisi Dumburton Oaks

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Analisi di Dumburton Oaks di Stravinsky
;,N OF THE DUMBARTON OAKS CONCERTO FOR CH/.MBER OHCHE3TRA BY IGOR STR1\ VINSKY Presented by James Daniel Dowdakin, Jr. To fulfill the thesis requirement for the degree of Master of Music Department of Theory Eastman School of Music of the University of Rochester June, 1953
Page 1: Analisi Dumburton Oaks





Presented by

James Daniel Dowdakin, Jr.

To fulfill the thesis requirement for the degree of

Master of Music

Department of Theory

Eastman School of Music

of the

University of Rochester

June, 1953

Page 2: Analisi Dumburton Oaks




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Page INTRODUCTION • • • • • • • • • • • • • • • • • • • • • 1

CHAPI'ER I. STRUCTtJRf:.L ANALYSIS • • • • • • • • • • •


CHAPTER III. HARMONY AND SCALES • • • • • • • • • • •




CHAPI'ER IV. MELODY, r.tiETER, AND REYTl-D\1 • • • • • • • • 95

CHAPTER V. SUYJlv!ARY AND CONCLUSIONS • • • • • • • • • 109

BIBLIOGRAPh"Y • • • • • • • • • • • • • • • • • • • • • 112

Page 4: Analisi Dumburton Oaks


On the back cover of the long playing recording 1

of the Dumbarton Oaks Concerto, Ingolf Dahl has given the

following information about its composition:

This work in three movements (Ttmpo giusto; Allegret~Q; Q2n ~) was written in the winter of 1937 and spring of 1938 in the French mountains and in Paris. Its full title reads: "Dumbarton Oaks; 8-V-38; Concerto in E flat for Chamber Orchestra." The instrumentation consists of 3 violins, 3 violas, 2 cellos, 2 double basses, flute, clarinet, bassoon, 2 French horns.

"Dumbarton Oaks" is the name of the Washing­ton estate of the Hon. Robert Woods Bliss, former United States Ambassador to the Argentine and Chair­man of the Visiting Committee of the Music Department of Harvard University. This estate was subsequently to become famous for rather less musical reasons, but in naming his work Stravinsky was obliquely dedicat­ing it to Mr. and Mrs. Bliss on the occasion of their thirtieth wedding anniversary. On this date (May a, 1938) it received its first performance under the di­rection of Nadia Boulanger at Dumbarton Oaks, and, almost simultaneously, its first Paris performance, under the direction of Stravinsky. • • • • • • • • • • • • • • • • • • • • • • • • • •

The Dumbarton Oaks Concerto followed chrono-logically the composer's sparkling and lighthearted ballet "Card Game" and preceded his monumental "Sym­phony in C". Both of these works are to some extent reflected in this Concerto. The ballet, in particu­lar, was the parent of the delicate ~ ~ ganse of the Concerto's second movement. The symphony, on the other handl is anticipated, thematically as well as structural y, in the Concerto's more richly textured outer movements.

1stravinsky, Igor, conducts the Dumbarton Oaks Festival Or.chestra in his Dumbarton Oaks Concerto. .Mercury Classics Recording, MG 10014.


Page 5: Analisi Dumburton Oaks

~vo terms used in the body of the thesis must be

explained here, e:md these are as follows: zero ... axial se­

ries, and poLlri ty of a series. The zero-axial series is

the term applied to a limited series of notes with no sin­

gle note of the series stressed as its tonic center. The

second term is best described in relation to the formDtion

of scales in the medieval modes. In this system all modes

employ the s~1.me series of tones wihh different tones de­

signated as final or tonic notes. These final notes <'re

supplied with standard mod,Jl cadence formulas which er;;pha­

size these particular tones. When mentioning the polarity

of a series in this work, it is implied that one pDrticu­

lar tone does receive more emphasis than any of the r·est,

and it is felt as the final of the scale bein£ used.


Page 6: Analisi Dumburton Oaks


First Movemen!t

The first movement is titled Tempo Giusto. The me­

tronome setting is J -:=. 152; this tempo is held throughout

the entire movement.

The plan of the movement is as follows:

1. Beginning to Figure 7: Introductory mate­

rial and presentation of the main motive of the first

movement derived from this material. The tonality is

basically E-flat major.

2. Figure 7 to Figure ll: Contrasting section.

The tonality is basically D major.

3. Figure 11 to Figure 20: Material from 1.

above comprises the transition to the fugal subject,

which is derived from the main motive. The fugue is in

C minor.

4. Figure 20 to Figure 25: Return of material

from the first section, altered and extended. The to­

nality is E-flat major.

5. Figure 25 to Figure 28: Coda. The tonali­

ty of the previous section is retained, but there is a

complete cessation of harmonic motion.

From Figure 28 to Figure 29 there is an eight

measure section consisting of linkin5 material between


Page 7: Analisi Dumburton Oaks

the first and second movements.

The best description of this type of composition

was given by Ingolf Dahl in his program notes describing

the Symphony in Three Movementsl. He calls this work

"another example of that additive construction, for the in­

vention of which Stravinsky is justly famous and which has

proved so influential on the younger composer. It is a

formal principle which conceives of music as the succes­

sion of clearly outlined blocks, or planes, which are uni­

fied and related through the continuity of a steadily and

logically evolving organic force."

The "logically evolving organic force" in the first

movement of the Dumbarton Oaks Concerto is the treatment of

the three note motive, ~-flat, ~' ~-flat (5·7-8 of the E­

flat major scale). This motive, or themes generated from

this motive, is found in every section of the movement.

The motive is found first in the flute line at the

begiru1ing, and later, at Figure 4, it is used independent­

ly. It undergoes a gradual decrease in range from Figure

5 to Figure 6 until its span has been reduced from a per­

fect fourth to a minor second. It appears at that point

concurrently with its original form. The smaller form of

the motive then proceeds to spread out again from Figure 6

to Figure ?.

lingolf Dghl, Program notes of the New York Philharmonic Society (January 20, 1946), Igor Stravinsky, Conductor.


Page 8: Analisi Dumburton Oaks

The contrasting section from Figure 7 to Figure 11

uses two forms of the main motive in a sequence as its

theme. 'I'he original motive is hidden in the texture of

this section, having four entrances in recognizable form

in the sub-section preceding Figure 11.

The motive is employed in the first fugal entrance

found two beats before Figure 13. The first tone, g, is

found in the cello and bass lines and marks the cadence

point of the transitional section. The violas enter with

Q-natural and £1 and then continue with the first complete

statement of the fugal subject.

In the section after Fig. 20, which follows the

fugue, the motive appears as it was used in its first solo

statement after Fig. 4. The instrumentation has been C:<l­

tered, and new elements have been included in addition to

the contrapuntal associate which was used in the first

statement. _F'inally, the motive is found as p<1rt of a seven­

tone ostinato (g, Q-flat, g_, &-flat, Q-flat, !l, &-flat) in

the Coda from Fig. 25 to Fig. 28.

As a general rule, the tonic note of the sc~le of a

section is the final tone of the primary motive as it is

used in that section. The flute line gives evidence of

this in the first two measures of the movement in its use

of the motive. The motive is also found in the flute line

in the fourth and fifth bars after the beginning. The sec­

tion from the beginning to Fig. 2 employs the seven tones


Page 9: Analisi Dumburton Oaks

of the E-flat major scale.

An altered form of the motive is found in this sec-

tion also; it is in the cl~rinet line in the second and third

b:.-irs after the beginning and in the second and third b&rs

after Fig. 1. This motive use is a fourth below the primary

form. See Ex. 1

Example 1. (I - Beginning) ~ I" I PI\I~AitY- ~r--....;.;.;. .. a..+...... MITIV'&. ~

~~r==.: ··=-==~=-==~~~-===·-==-~~=====~-==----=+· J.

.. ~ ..

• J


-61o 1\/..T E R.. £ I ~bt\~ __ MoTI t~ £..

Ifiaterial from the begi.!hning section is used and ex­

tended in the section from Fig. 2 to Fig. 3. 'Ihis section

is actually a modulation to the key of the first bar after

Fig. 3, C harmonic minor. The original key of E-Flat nL.jor

retur·ns in the second measure after Fie:;. 3. In the fourth

measure triads of ~-flat major and ~minor combine to intro­

duce the first solo statement of the motive at Fig. 4 in t.l::e

key of E-flat major.

Page 10: Analisi Dumburton Oaks

The motive is given three times in succession in

the first ~nd second measures after Fig. 4. Its accomra­

nyinc voice is actually a contrapuntal associate, since the

two lines are found in the return after Fig. 20.

Example 2. (I - Fig. 4) 1ll't M oT•v e. L:&l ,

. t

hfter the statement above in E-flst major, the mo­

tive is given twice in the key of I" h. rrnonic minor <st .§,­

naturctll, ,tl).

In the three measure section before Fig. s, there

are entrances of the primary motive in B-flat rrk'ljor, D-flc<t

major, ,snd G minor. These are outlined in ::xample 3.

measL:re Dfter Fig. 6, the primary :notive under[oes a gr<~­

duol decre2se in its span, beine reduced from a perfect


Page 11: Analisi Dumburton Oaks

fourth to a minor second. ExAmples of these reduction~ are

extracted from the score in Ex. 4.

From the third measure after Fig. 6 to Fig. 7 the

motive interval is exp~::.nded. ;,fter the flute gives two

statements of the motive in the minor second form in the

first two me,,;3ures after Fig. 6, it expands this fit_:ure to

a major second (~-flatl, ~-flatl) in the third measure.

The clarinet adopts the major second form (on ~-flat and

~-flat) at the beginning of the fifth mensure and sprec,ds

the interval to a major third on the next beat (g-flut to

12-flat) •

After Fig. 6 the horns D.nd bassoon make use of the

original motive and give a forecast of the openinc of the

fugue subject, w.,ich r.:lclkes its first entry at Fig. 13.

The bassoon end second horn are doubled in v.-.. o presenta-

tions of the mot-ive in the first o.nd second me'Jaures of

Ex. 5 below. The first horn enters on the upbeat of the

second me .. sure with a statement on the same tones in stret-

to fashion. iihile the first horn holds his fin.~l tone, the

bassoon line continues in the forecast of the furue subject.

'i.he first horn und bassoon follow this wi tl.L one more ,-Jt<~te-

ment of the motive doubled at the unison.


Page 12: Analisi Dumburton Oaks

5. (I - Fig. 6)

In the me:)sure preceding Fig. 7, the bassoon line

repeats once .::"gain its forecast of the fugue subject, but

this time the first horn follows with the principal motive

employed in the key of the next section. The first horn

continues with o statement of the subject of the contrus-

ting section. ;l close studJ of the new subject reveals

that it is the original motive plus the inverted retro­

grade form of the same motive. See Ex. 6.

Example 6. (I - Fig. 7)

GJ D--J L -~ F :::::=!= '- -~ ij1 ffJ I J 1 n J_)~_ogb£% r ...-

~.....__ , ~ 7

The section from Fig. 7 to Fig. 11 is in ternary

form ( 1\ - B - i.l), the pc.:rts indicated by eho.nges of sc<::<le.

The scale of the section from Fig. 7 through the fir st. :nea-

Page 13: Analisi Dumburton Oaks

sure aftt:r Fi,s. 8 is basicall.,- D mejor. /1 modulation occurs

in the second measure after Fi.t:. 8, ·which introduce:.:> the

scule of G major in the third measur-e. (This is an excmple

of an "enclosed-third 11 modulation; the tonic notes of the

three scales used in the section after Fig. 7, in the nwdu­

lation, &nd in the section followin[ this modulation in the

third measure after Fig. 8 give the following series:

D - B - G.)

;. repetition of material occurs in the first me;tsure

of the G scale. Tbis me.,sure is a f::;irly accurate cop,/ of

the finDl me.~.,sure of the D scale found after Fig. 8. l>'.l.Qst

of the lines have been dropped one step for the repeti tiort

in the nevJ scale on G. !1 modul<:,tion in the me.:lsure before

Fig. 9 brinr:s abollt the return at Fig. 9 of the m2teri<l

found ofter Fig. 7. i,fter two and one-h<::lf me.:~.;.;ures rkw

mc:.teriel is introduced. In the fourth me Jsure after ?ig. 9

a short passage of fourths is added to the running six­

teenths of the b:c;ssoon line. t.t this same point a broken


statement of the main motive appe.~~rs in the violin3. See Ex. 7.

Page 14: Analisi Dumburton Oaks

In the fifth ;ne··sure of Fig. 9 a simpler sc.:le is

announced by the int:rod'-.:.ction of g-natur :11. ~'<t Fie. 10

the b:,ssoon line becomes 8 series of fourth;_, in <-J six-tone

ostinato which continuE:,:; for four me: surea after Fig. 10.

The ton·.:lity of this section from Fig. 10 to Fig. 11 L;


The main :notive makes an appear;·~nce in the :;econd

<:md third ;neusures after Fig. 10. 'l'he first tone is 2_1,

found as the final note of a fi[;ure in the c lurinet. '..:'he

violins follow with the re.::;t of the motive an octave hi,t:her.

At the end of the fourth me .. sure of Pig. 10 the first t1NO

notes of t}& motive appear as a chord (~2, !-sharp?) ployed

sforzando in the violins and violes. The final tone (£~)

is he.;rd in the next measure. 'I'he same process is repeC~ted

at the end of the fifth measure of this section. See Ex. 8.

8. (I - Fig. 10) MoTIII!.


11 a :native

chord of the key of E-flat is he;rd, &Jnd cre:Jtes a cl~anLe

of scule to E-fl8t major. This chord is repeated at the

end of the first, second, and third me~-\sures of l"ig. 11.


Page 15: Analisi Dumburton Oaks

;:::xemple ~:;.

....___ /, general analysis of the section in D from Fit:. 7

to .F'ig. 11 is th:.;t it is in leading-tone relation tc tbe

section in E-flat mcJjor which follows ot Fig. 11.

The first three meusures .:,lfter Fig. 11 contnin con­

trapunt:, 1 lines derived from the m . ..~terinl found uft.er Fig.

2. In the fourth measure after Fig. 11 a close i~itction

of the section after Fig. 2 is begun. This continue0 to a

half cadence on a domin.:-_;,nt seventh chord on Q in the me,[~­

sure before Figure 12. This cadence chord is extended in

the next section from ,?ig. 1? to Fig. 13. ,-,t Fig. l~J the

fugue in C minor completes the suspended cadence. In the

parRllel ex:<mplf:) after Fig. 3, the Q dominant ~ievcntl1

chord occurred :i.n the mea sure before Fig. 3, and '.'<ns re­

solved in normc:~l fashion to C minor in the followinc ne;_,-


Vii th the reduction of the penultimate Cctde.c,ce cl1ord

to an octave .§ in the cellos und basses in the me:.;::.mr·e rre­

ceding Fig. 13, the first stc.ternent of the fugue subject,

which is quoted in Ex. 10, is begun. This octave 1 is also

the first tone of the subject, which is given in the violH

Page 16: Analisi Dumburton Oaks

line in the key of C melodic minor. Ex. 10 includes refer­

ences to the derivation of the melodic fragments of the

fugue subject.

(I - Fig. 13) C,Db,E"~ ~, F,c..,A-.,~,~b, 6

f"J•T'"' ,wultf~

r ~···----------The next entrance of the subject starts on £1, the

next note after the final note of the viola statement.

This statement is in F minor, and continues in normal fash­

ion until the end of the subject, where an eighth rest is

substituted for the final note. The last five notes of a

normal statement follow after this rest. The next two

statements are exact re-statements of the subject as given

in the viola line in Ex. 10. These occur in C minor (sixth

measure after Fig. 14) and F minor (third measure after

Fig. 15).

In the three measure section after Fig. 16, scales

on C and F are used concurrentlJ• The primary motive is

found in two forms in this section; it occurs in the violin

line in the scale on F as a filled-in interval of a fourth,

which is extended in the second and third measures; and also

in the cello line in the first measure after Fig. 16. In

this second use, it is an application of that portion of the


Page 17: Analisi Dumburton Oaks

fugal subject found in the viola line in the second complete

measure of EX. 10

11. (I - Fig. 16)

F1 "'~~~A, e•1 cJ "~ "~ e~ £

The two scales on F and C shown in Ex. 11 modulate

in the fourth measure after Fig. 16 to a scale on i\-flat;

this scale is found on the enclosed third between the two

original scales found in Ex. 11. The filled-in fourth form

of the motive, as found in the first measure of Ex. 11,

occurs in the viola line in the first measure of the new "-

flat scale ( . .::.ee Ex. 12). im incomplete statement of the

fugal subject moving from one instrument to another also

starts at this same point. (The three-measure section

which starts after Fig. 16 represents the first three notes

of the fugal subject in its use of the filled-in form of

the primary motive. The section quoted in Ex. 12 is a par­

tial statement of the fugue line found after the primary

motive. The relation of the actual subject to this section


Page 18: Analisi Dumburton Oaks

is shown in 12.)

Example 12. (I - e measures before Fig. 17)

F~!rltEM''U oFS"e.a&.c.-r ~

1--ffft-¥- - *-'~ ··~ '=n!-c· 2¥. ~:rJ@f'~ • ~ I r •

I • I f t

I I I ' I ' I ' I

I I ' : • I lW .

The motive appears in normal form after the exGmple

shown above. It is found in the cello line as shown in the

first and second measures of Ex. 13; however, this particu­

lar statement has two extensions. If the tied note (g) of

the cellos is resolved to the s-flC~tl of the violin line i.n

the next measure, and is continued in that line to the ~­

naturclll, the beginning of the fugal subject is he:::~rd, with

the violin portion in inversion. The other applic_;tion of

the motive is as the introductory portion of a complete

statement of the theme of the contrasting section as found

in Ex. 6. In the second measure of i.!:x. 13 the line moves

up from the .sa-flat in the cello to the viola £.1• From this

£.1 the line continues in the manner found in Ex. 6. Compare

Ex. 6 and Ex. 13.


Page 19: Analisi Dumburton Oaks




In the fourth measure after F'ig. 17 a one-measur·e

extension of the previous material serves £1S a modulation

<~1nd introduction to the new scale of E-flat minor. The

modulution is effected b.Y nn expanding figure in the upper

strines, as shown in Ex. 14.

Example 14. (I - 3 measures after Fig. 17)

The material found in the thi"'d and fourth measures of "x.

14 is repe:.:,ted essentially in the first two measureo r:fter

Fig. 18.

In the section from Fig. 18 to Fig. 20, the furue

material makes its final e1ppeurances. The fu&ue subject in

E-flat minor, ini tie ted by the horns in the third and fou.rth

measures of Ex. 14, is continued further in the second, third,

and fourth measures after I<,ig. 18. On the final note iu in:­

itation of the subject, founa in the fourth measure, ~-flatl

marks the entrance of another statement of the subject in

the key of R-flat minor.

Page 20: Analisi Dumburton Oaks

j,ll elements adopt the scale of -,-flat minor in the

measure before Fig. 19. In the second measure after Fig.

19 the new scale of B-flat minor begins to infiltra~e the

texture. The material in B-flat minor makes use of the fu-

gal subject in this shift of scales, gradually extendinr

its use from the primary motive, £..\S found in the first horn

in the first and second measures of i!:x. 15, to the larre

portion of the subject, as found in the winds in the third

o.nd fourth measures of this same example. With this entry

of the winds all elements are using the sc~.tle of B-fl:.'.t mi­

nor. The 'Ninds continue the subject until the third beat

of the fifth measure on g-flatl. This g-flatl in the VJinds

is the 1::: st tonefround in strict imitation of the fugue :.:>ub­

ject; however, the fugue subject is continued in another

manner in the violins and violas. /\t this point these in-

struments are heard in 8 portion of a scale line sp;:mning

a perfect fifth. This is to be considered an inversion,

both in direction and interval spanned, of the cllrom~~\t::.c

line of the fugal subject which moves downward :" perfect

fourth in the third and fourth measures at'ter Fig. 13.

Compare bX. 10 and Ex. 15.

t .. xample 15. (I - 2 measures <.:~fter Fig. s,e .1 ~c-r


Page 21: Analisi Dumburton Oaks

Two beats before Fig. 20 the first horn is heard on

.Q-fl<~t wiiict js ·th8 fir3t note of the primary r:1otive in E-

flat major which appears in the section :.:fter· Fig. 20. 'l'he

key of r::-flnt r:ttljor i:.> neld vlithout accidental:.; from .:'ir.

?0 to the end of the Cod:J at Fig. 28. This section fro!n

Fig. 20 ;JS f:-~r as Fig. 25 make.s use of mo.!terial found in

the first section of the composition from the berirmint_~ to

Fig. 7f it qualifies, therefore, as a recapitulation.

'I'he mElterial found in the five rne:..tsure s after .;:'ig.

20 is a re-statement of the muterial found in Ex. 2. '...'r;.e

chnnges are in the differin;~ orchestrationl and in t~ne addi-

tion ,,fter Fig. 20 of u stt;cc,::to cello .. :md bass line in

eighth notes. .~ince there is no modulation out of ~-flut

mnj or in this entire closiq; section, the movement. to /

minor expected in the third measure of this .Jection does

Example 16. (I - Fig. 20

lThe horn end bc:..~oon have the sociQte after Fi~ the violins these lines after Fig. 4.


Page 22: Analisi Dumburton Oaks

From the third meJsure after ~ig. 20 to Fig. 21 the

original m<~. terial of Ex. 2 is extended .::•nd developed. 'Ihe

running accompaniment(bassoon line) continues in a low

range, but, finally, moves upward scalewise in the measure

before Fig. 21. The staccato celJ..o.s and b-.iS6es continue in

eighth notes from Fig. 20 to 7i~. 21.


In the four-measure section after Fig. 21, all lines

stress portion.:; of the E-flat sc .. ~le or chords from the scc:le.

The bassoon line dictates tne h<,rmony of the section. lt

repeats n patter·n on the B-flc~t domim;nt seventh c!;or-.:t in -each of ti1e four me"''.sure.s. In its l~1st st~;tement, ·u:..icL.

leGds in to the section after Fig. 22, it gives a brief

st;;>,tement of tr1e primary motive (BB-flut, D, E-flat). - -In the next section found after Fig. 22, u ~or~ion

of ·t-he beginninL of the compo;.;i tion is developed. The rna-

terial found in the fourth me:.,sure ufter Fig. 1, -.:tnd ccu-

tinuin.c throue.:;h to Fit:. 2, is extended o.fter Fig. ~:2 f'r·o:c:

three rneDsures to 1 .. ive meusure.s in len[~th.

One be:. t be fort :B'ig. 23 the second horn begins "'

sto.tement of the pri:n ,ry motive in the key of E-flat r:Le.l or.

Tilis .>ection from Fig. 23 to Fig. 25 is G. re-stc.:te.:11ent,

w:i.th < new extension, of the m.::..terL.l found from J:'ig. 20

to Fig. 21. The extension is ended witl~ an ascend.int l~~-

flat mc;.jor scale;, which is hulted on the leiidinc tone by C).n

eighth rect. The resolution of this le<::..ding tone to ,g_­

fl2tl in the first ne~sure ufter Fig. 25 m3rks the be[in-

Page 23: Analisi Dumburton Oaks

nine of the Cod~. See Ex. 52.

sudden end to tLe nervot s h·_,rr:tordc novement of the previ.ous

sectioD. . , downwar·d-movinc scele line in the upper '"trings

is contr"; sted with a sevena.tone ostim: to in tr.e lower·

strirJ.fS \~l.icb. moves, within its r;:tn~:e, upw;:~rd. This osti­

n;:CJtO is ectu<1ll.;' two stc~te::;ent.:. of the tLree-note pri:n<:r J

moti v~c (Q.-fl. t, _gl, st-flntl) plus one other member· of tL.e

E-fl<:01t m~:.~jor tri£;u (g), whicr1 indic::1tes the beginnin.t of

each ostin~.1to gr·oup. The windc> and Lorn:J move dowm; rd on

choros of the key of E-flat mr::lj or, wldch move from one

chord membe1· to the next(with correspond!~, chanre._, ir:. i o­

sj tion of <Jll the other parts. One member of the cLur·,_, is

usu·-,llj fou~~1d ,ltered to creete C\ new chord, althouLL this

cilteration does not occur every time. See Ex. 40.

The section from 7ig. 27 to Fig. 28 is an exact

copy of the 8ection from Fig. 25 to .?ig. ~~6 with tl·le second

"'ection at .:.: softe:~ volume than the first. The Codd frou

Pig. ?5 to Fi[. 28, therefore, has its own form C .-B-, ) •

In the linking section fr-on~ Fig. 28 to .?ig. ~-~·,

a :noduL,tion occurs frorr; the E-flat nt::t~ or scc:1le of tLe first

movement to the key of F ffi3j or. '.::'his chord appe rG in t.l1e

sixth rne;_:sure after I<,ii.> 28. In the seventh t~no e it_ l:t,"

:ne:-;sur·es, the sinrle tone, E, is hecrd, doubled in oct: ve s.

'1'his is ti1c dor:dnant scale step of the B-flat sce.le u:::;ed in


Page 24: Analisi Dumburton Oaks

the second movement, and is also the first tone heard in

that movement. The indication attacca is found at the end

of this linking section.

second M9vement

The second movement is titled l\llegrettg; the metro­

nome setting is J':: 108, this tempo holding throughout the


The movement is in ternary form, its f:eneral outline

presented graphically as follows:

Graph I.

This movement is a model of simrlicity. Extensive

use is made of two and three-part writing; although ;:1ore

line enter occasionally, these usu~lly consist of tones re-

lated to the busic har·mony of the accompanir:1ent or to one

of the melodic lines. There are no ce:ses of the use of two

scales with different tonic notes at the same time, c.1s in

the first movement; in the second movement, however, the

moving or melody line can be found employing tones from one

portion of the scJle or selected tones from the sc~le, while

the accompaniment makes use of the remaininr tones, or ano­

ther selection of tones, or even :_;ll of tl1e tones of t..ds

sa me s c. i le •


Page 25: Analisi Dumburton Oaks


1~s evidenced by Graph I, the material found at the

outset of the movement (~ of Grnph I) returns in all sections

except the contrasting middle section (.£P. /1 study of the

manner in which this mDterial is used in the following sec­

tions will give a clear idea of the form of the movement.

The theme of the movement is begun without intr-o­

duction in the violas. :3ee t;x. 17. Its first tone (.fl) is

the upper boundary of the melody for four measures. TLe

first and second measures are repeated in the third ana

fourth me"'tsures with the only change found in the accompa­

niment. 'l'he bassoon tone (.§-flat) is found in a different

part of the meosuret

The leaps of a sixth in the fifth measure of ~.:.;x. 17

are related to the third (gl-fl) of the sixth measure in a

scalewise manner. If the sixths are given in inversion,

the following series of interlinked thirds develops:

,!2-flat - Q, £ - ~-flat, Q - l• In the sixth measure of Ex. 17 the line is extended

into a lower range (to ,5!), but it immediately swings bc\Ck

in a leap of a minor tenth (to £.2) to balance this. The

lower tone (A) is repeated in the next me.c:lsure by the accom­

paniment which resolves to Q•flat to form the cadence of

the phrase.

lThe simple accompaniment of the bassoon nnd cellos is gra­dually expanded in the first section from Fig. 29 to Fi£• 32. The b.::tssoon in:t:roduces sixteenth notes to the line, and finally becomes the only accompanying vioce in the se-

cond measure after .F'ig. 31.

Page 26: Analisi Dumburton Oaks

17 (II - Fig. 29)

-r--rr·· ±f ~-·- - -- - ~. - ,... __ ~-- --· -. ". . .. ··-· -

In the section from Fig. 30 to Fig. 31 the mater-ial

from the latter part of the first p.hrase group (final three

measures of Ex. 17) is extended and developed. The section

from Fig. 31 to the fifth me:::.sure after Fig. 31 makes use

of the melodic material found in the first four measures of

Ex. 17, again extended and developed.

In the fifth measure after Fig. 31, the line of the

melody and accompaniment come together on a unison (gl).

'I'he violins continue from this ,gl with members of the D m£1-

jor chord, the chord members (root, third, and fifth) orna­

mented by upper neighboring tones.

This D major chord does not anticipate the true to-

nality of the next section stnrting after Fig. 32. / s ~:hown

in Ex. 18, the tonality is changed to D minor in the first

measure after Fig. 32.

The section from Fig. 3? to Fig. 33 is a dialoeue

between the clarinet and the violins. In the first measure

of Ex. 18 the tones of a .£ minor triad, plus ]1-fl<.::t <-<nd £!­

natural, are heard in the melody line of the clarinet; the

violins re-state the clc...rinet phrase in the second measure


Page 27: Analisi Dumburton Oaks


with one tone altered. During this section the notes of the

accompc.niment played by the cellos are members of the .,.b;!. minor

triad. In the sixth me(;sure of Ex. 18, the violins .::mswer

the clarinet statement of the fifth me:-,sure with a three-

note fragment which, combined with the accomp<:miment note,

suggests a dominant function in an F scale. The new F scale

enters in the first measure after Fig. 33.

Example 18. (II - Fig. 32) ~

[!) VL..NS. L:UJ


!~ ~~~E?-EiEU~*~l1 :J!=,-i f

10 F > -The section in D minor found in Ex. 18 has thus

served in another "enclosed-third., modulation. The keys

employed in the sections after Figs. 31, 32, and 33 give

the following series of tonic notes; ~-flat, ~' L•

The section from Fig. 33 to Fig. 34 employs a com­

plex SC21le, its pola.ri ty establishing .E as the tonic note.

In its use of the two thirds of the sc:..;le ~!;;- flut and fl­

natural), the toncdity created is neither major nor minor,

but a combination of both. The melodic ~~terial found in

Ex. 17 is re-stated in this section using this F scale.

In the first measure after Fie. 34 new material en­

ters (section£. in Graph I). See Ex. 19. The flute has

Page 28: Analisi Dumburton Oaks

mEny repetitions of ~-flat and strengthens the feeling for

F minor ns the tonality. The melody line in the clerinet

in the four measures ofter Fig. 34 employs the .£::-flat r'lso.

J·\ re-stntement of material from the :first st: tement

of the theme in the F sc<~le, [JS found after :fig. 33, i;:;

found in the bu.ssoon line in the first four measures after

Fig. 35, In the fifth me<~sure after Fig. :35 the clari:1et

re-st_,tes in F major the melody found in the first me' :oure

plus one beat in the second measure of Ex. 17. This ere-

ates .::m emphasis in the two examples on the two thirds (6-

flat :,;_nd ;i-natural) of the F scale of this section, .. dnce

the lowe.st tone used in the first portion of the motive

(the first four measures after Fig. 35) is .6.-flt~t, and the

lowest tone found in the second series (in the fifth meu-

sure) is .,6-natural.

In the first me:;sure after .B'ig. 36 the bassoon

gives the theme in the major-minor form (descending to JJ.­

flat) found after Fig. 33. This is the fourth return of

Sl material of the graph in the first lHrge P<o~rt of t:r~is

movement. The section is brought to a cadence in the first


Page 29: Analisi Dumburton Oaks

meDsure o.fter :F'ig. 37 by an E minor chord. The third of

this chord (~-flntl) is supplied by the flute, and violins

Pizzacato, and the next section continues from this roint.

The flute once again stresses ,8-flat in this return of

section s of the graph. In the section after Fig. 37 the

clarinet line is altered slightly in order to empha;;.:;ize

the off-beats. It follows the same outline of the earlier

line as found in Ex. 19. In the fourth bar after Fig. ~j?

the bassoon makes another entrance using section !! as it

did after Fig. 35 in the first statement of section £•

This line continues with an extension through the first

measure after Fig. 38; the violins continue on alone in

the second me<lsure to close the large setion fl on :Q-fl;,t2•

The next three measures constitu~e the bridge to

the middle section (.12). With the exception of the firGt

~-flat pedal tone in the cellos and basses, this section

is a re-statement of the first three mensures after E'ig.

28 in the link between the first and second movements.

The diyisi strings are employed in both instances.

·:-he entrance of material g in Graph I is found in

the first me -'.sure after Fig. 39. The ostinato Of the cel­

los and basses expresses the tonality of the section (G

minor); the upper strings are found in another ostinato

implying an a minor chord, which produces a polychordal

effect. The detailed description of this ostinato will be

found in the section at the close of this chapter.


Page 30: Analisi Dumburton Oaks

The ;, .• ..;:lody is i:i ven to the clarinet, which lw s a

straight chromHtic series in sharp stuccc:lto fro:n g up to

g-flat in the second and third measures of Ex. 20.

Ex. 20.


G,~, B~C, 0

- Fig. 39)

cL. L.!NC. ~ r~ c, F, F~, cr,A II

This ascending chromatic line found in the clarinet seems

to have a rel2tion to the main theme of the second movement.

In the first statement of the main theme, the descendin,e::

chrome:J.tic line from ,t:1 to gl occurred. :Jee Ex. 17. The

ascending line in the second and third measures of Ex. 20

starts on g; it then proceeds upward a total of two minor

thirds, or twice the span of the theme as found in the first

four measures of Ex. 17. The clarinet series is shortE~ned

in the fourth and fifth me·:sure after Fig. 39, :.md extends

here fro:n 9. to g. This .series is repe:·;ted in i ._e sixth and

seventh measures by the clarinet and b<- ::>soon.

The quiet ostinato of the strines continues <";lone

for the first two measures after Fig. 40. In the tlh.ird mea­

sure the flute enters with em ornate subject wldch contuins

the primary motive of the first movement. The line exidts

in two rDnges, one having the tones ~ and !2,, c,nd the hi.rher


Page 31: Analisi Dumburton Oaks

one U3inL !i-fl,[jt and ~-flE:t. The motivE.! is found in two

more series t.h;:,t occur in the flute line in the third c::nd

fourth measure of Ex. 22; therefore, this appearance

seems more than coincidental. The flute line in the first

instance is shown in Ex. 21.

Example 21. (II - l measures sfter Fig. 40) ....

In the fourth chro:nD, t..ic

series from g up to~ is found in the clarinet 5lone. :n

the fifth and sixth measures, this series is supplieo. '.lith

its first tone (gl) by the upper strings; it is continued

in the cl.f'l.rinet and bc:,saoon.

In the first measure of Ex. 22 the flute begins a

line descending on chord tones. It leads into the remain­

ing two figures which include the reference to the mot5_ ve

from the first movement.

Example 22. (II - Fig. 41)

In the next section the ostinato continues alone nnd the

scale is changed from G minor to G major. i'£ter Fig. 43

the strines again return to G minor. In the first me .. sure


Page 32: Analisi Dumburton Oaks

the bassoon has an ascending ctu-omatic series from ,!i-nc:;tu­

ral to .s,-natural, and back to .s-flat. In the second ~ne<e,sure

it h<:;s a shorter series from f. to g-natur1:1l and again Q-

flat. This _s-flat is adopted by the string ostin<.lto in the

third mee:>sure <::fter Fig. 43 and, in combin::1tion with ]2.-flat,

g-flatl, and fl, creates a scc<le shift to B-flr:Jt minor.

This modification of the scale center indicates the entrance

of section ~ of the 11 portion of the movement.

Example 23. (II - Fig. 43)


The theme of section g is found in the clarinet. in

the third and fourth measures after F'ig. 43. ~:ee tile first

measure of Ex. 24. In the second me. sure of the ex<':l;::;·le

this statement is imitated a minor third lower; tllis form

is used in a stretto in the fourth and fifth me:.,sures of the

example. i~t the conclusion of the first statement of tj1e

theme of section g in the third measure of the example, the

flute ha3 an uscending line; this line is composed of :nem­

bers of the !!-flat major triad plus £, and is found lc .. ter

introducing a new section.


Page 33: Analisi Dumburton Oaks


Example 24. (II - 3 measures after

The flute sustains the final note (t_3) of the third

appe~Ojrance of its ascending line through the fourth :ne ··.Jure

after li'ig. 44. .i'tt the end of this measure the b<.tssoon leaps

a fourth :from ,g,l to ,tl, and the flute and bassoon re-st<~te

materie.l from the melodic line as found in Ex.l7. The CJ.C-

companiment is a po~chordal passage. See Zx. ?5.

Page 34: Analisi Dumburton Oaks

The fntrance of the solo cello on g-flo.tl in the

third measure after· Fig. 45 changes the scale from B-fl<·.t

major to B-flat minor. See upbeat to the first measure of

Ex. 26. The cello line continues in the first measur-e of

the example with the motive of section ~ , found in the

clarinet lin~ in the first und second measures of 2x. :·4.

'l'his cello line is developed in the following measures,

and is found in stretto in the fifth measure of Ex. :::'6.

The last three me<-::sures of the example make use of derived

forms of the line, and overlap in the final mec,sure v.i"Lh

the beginnin£ of large section ~1.

In the first mec:: sure o.fter Fig. 47 the violo.:c; <:re

heard in u recapitulation of the main theme (,61 ). m· • .dl.l:\

theme, found from Fig. 29 to one me.cisure before Fig. 3:~,

is repeated note for note until the lust note before u~

end of the entire section at Fig. 50, where an .fl is s,.lb­

stituted for a g_l.

The important addition to the recar,;itulG~.tion is the

flute line in thirty-second notes. It is usually bdsed on



Page 35: Analisi Dumburton Oaks

chords of B-flat major, but occasionully a scale line is

found, or a group of repeBted tones.

In the second measure of this florid line, the pri­

mary motive of the first movement makes another appear:mce.

The link to the bridging materiDl after Fig. 50 is

the final note of the flute pL.lssc;ge (g3). The tone lit/ of

the first three measures of the bridge is D major, and the

stringed instruments are used exclusivelJ only in these

first three mensures. In the fourth measure the strin,ed

instrurnent,s shift to an .§-flat chord which lws noi conrnon

tone in the previous chordJ the second horn enters at tilis

point on the lowest tone (§.-fl<:~t) of the cLord, ;:na . ustc:.ins

this tone into the next measure ·without the strin;:·s. In the

measure before Fig. 51 and the first measure after Fig. 51,

.c1ll the rest of the winds make entr:mces.

The sustained chords continue in E-fL1t ma.J or until

the third meDsure ~fter Fig. 51 where the key becomer) I:~ ...

flot mBj or. At this point a pl: ;gal cadence in B-fl;:;t ma,_! or

begins which reaches its resolution chor·d in the next :::e,,-

sure. The lower strinrs enter alone on a ~-fl.:;t major chord

in the last me:::sure, ana are joined by the upper ntrin,;,:s

Page 36: Analisi Dumburton Oaks

and the clarinet in the same chord repeated as the fin<:il

chord of the movement.

Tb;trd Movement

The third movement is titled Con Moto with a metro­

nome setting at J = 160. For the contrasting part (section

~ in Graph II below), a IeWQQ ~ ~ is indicated; the

metronome setting is .J : 100 for this section. /,t it.s com­

pletion +,e.:npQ I is found, and the original tempo is kept

from that point on to the end.

The movement is a five port Rondo; the outline of

the movement in graph form is ns follows:

Graph II.

A Cl' a "L I Fvr,u£ 'Ret~ .... s.i t io~ I a I


A c A I a"' I CooA I

The winds are predominant in the bulk of this move­

ment. The strings are found as accompnniment in all of the

sections except one, i. e., section~ in Graph II.

At the outset the movement employs a seven-tone se-


Page 37: Analisi Dumburton Oaks

ries bnsed on the E-flat major scale. The movement besins

in the brisk manner of a :3panish march. The main them€ is

found as n continuous line in the horns and bassoon from

the beginning through the seventh measure of ~;;x. 28. . t

this point an u-sharp breaks the ostinato of the basse.::;,

and a new scale resembling G minor is introduced.

v Ntf. e=:::::t~===-,pu ................ -......~ E~f ,,A!r, IJ~c, P


From Fig. 54 to Fig. 56 the previous section (:;X.

28) is repeated vvi th some al ter~~tion (section ~l). "i'he

first part in F~-flat major is essentially the same; hov:ever,

the G minor portion is altered considerably. This p~.irt

effects a modulBtion to the key of the third state::tent of

the motive in the section after Fig. 56 (section Q~)) •


Page 38: Analisi Dumburton Oaks

In the passage from Fig. 56 to Fig. 57, the section

found in Ex, 28 from the first to the eighth measure i;;

given in a series based on the G-flat major scale. In the

measure before Ii'ig, 57, the modulatory leading-tone (here

an iu\-natural) occurs in the basses to indicate a modula­

tion up a major third. See the seventh measure of Ex. :~.:.~.

The modulution to a B·flat minor series occurs in the ;aea­

sure after l''ig. 57, but the original melodic material, used

in the previous section from Fig. 56 to Fig. 57, is found

here once again on the same pitches. The dynamic indica­

tion for the section found after Fig. 57 is Forte ~)Ubi to.

At the conclusion of' this Forte passage, the first

statement of the fugue subject evolved from the main tl1eme

makes its appearance. The first half is begun in the tldrd

measure after Fig. 57 in the horns alone; all parts re­

enter in the fifth measure to mark the cadence of t:i1is 1)or­

tion. The horns continue in the sixth measure wi til the se­

cond part of the fugue subject, ·which again is brought to a

close by the rest of the ensemble.

'l'he f'ugue subject is quite closely rel<..<ted to tile

main theme. It can be discovered in any of the statements

of the main theme as the voice below the top voice in tile

texture. 'l'he first note is an extra tone which ru-:u:ne:::; the

scale of the subject; the part evolved from the main theme

begins on the second tone, which is a fifth Clbove the first.

'l'he bassoon line from the third to the fifth me ~i­

sures after Fig. 56 is a perfect fifth distant from the


Page 39: Analisi Dumburton Oaks

first statement of the subject found from t.l1e third through

the fifth me~·.sure after Fie. 57.

Example 29, (III- 3 measures after Fig. 56 [bassoon]; 3 measures after Fig. 57 [horns))

'l'he second portion of the fugue subject also hus

relntion to this same melodic fragment of the bassoon z>ound

in the section after Fig. 56. The line, as found in til.e

second horn part in the sixth meesure after Fig. 57, begins

with a leap of a major seventh; this is actuallJ the rdnor

second (~-flntl, R•flat) of the bassoon line in inversion.

The three notes at the beginning of the second horn portion

correspond to the second, third, and fourth tones in the

bassoon line above,

In the first measure c.:fter Fig. 58, the clarinet

repeats the first six tones found in the second horn line

in the two measures before Fig. 58 (second horn passage in

Example 29). On the fourth tone (g-flatl), the flute and

bassoon enter with the second statement of the fugue sub­

ject in the key of F minor. The clarinet continues its

line in counterpoint to this second stzJternent. The cl::::lri­

net part in the second and third measures after Fig. 58

is found in the bassoon part in the second and third mea­

sures after Fig. 59; it is used there as the contrapunt.;,l


Page 40: Analisi Dumburton Oaks

Dosociate for the second st,tement of the fugo.l sub(.ject in

F minor.

In the fifth me<:;sure after Fig. 58, the bassoon be­

gins n stotement of the fugue subject in B-flat minor; this

statement of the complete subject and the contrapuntc:.l <w­

sociate is the longest single stfltement, employing only re­

cognizable fugal material, found in the fugue section. The

second horn enters in the first me£<sure after Fig. 58 with

the subject in F minor. On the last beat of the third mea­

sure after Fig. 59, this portion of the fugue is ended by

the same materia.l which introduced it; the three mea:Jur·e

section which follows at this point is an abbreviut~stute­

ment of the first appearance of this material in the sec­

tion following Fig. 57.

The section after Fig. 60 serves to introduce the

next section of the fugue found after Fig. 61. The line in

the first violins after Fig. 60 is the retrograde form of

the flute and first horn line in the fourth and fifth .:ne -

sures after Fig. 59. See Ex. 30 below.

Exa~le 30. (III - 3 measures before Fig. 60 [horn]; S'ig. 60 L~ violilj)


r~W\1 IW=--13==,;~ -......,,


Page 41: Analisi Dumburton Oaks

The line LJ continued in the violins n.nd extends upw::tr'-~.

The scale beco~nes simpler in the fourth L1ea:.mre after /:L:.J•

60, Emd the \Jay is prepared for the final fugal section

which begins in the first me&sure after Fig. 61.

The fugue subject is be[:un in augmented for::1 in the

first horn, cellos, and bassoon in the key of D-fl<Jt ;lLJ or

(lst mec:1sure of t~. 31). The first horn line takes trli3

state:nent through the second portion of the fugue ancJ . .:.

complete stD.tement of the contrapuntul associate. 'l'L.e :>e­

cond entrance of the fugue subject is found in the seco.1d

horn line stBrting in the second measure of Ex. 31. '1:·.ii .. s

subject is in inversion, and extends through both .sections

of the subject to the first beat of the fourth me sur·E:.

The tonality of the second sti::itement in inversion is :--flat

minor. The violins and viol:::.s begin the third entr~mce of

the subject on the final note of the second subject in the

fourth mec:..sure of Ex. 31. This new stutement is in I.-Zlc:.:t

major, ~1nd extends to the end of the fifth me sure. .. i~e

fourth and final statement is found in the fifth r.1ec,;:;ure of

Ex. 31 in the cellos and basses. It is a complete .st t.e­

ment of the sub~ect in F minor, and extends throu.::)l t0 the

end of the sixth measure.


Page 42: Analisi Dumburton Oaks

Example 31.

In the section after· Fig. 63, two scales Gre pr!~sent

at the same time. They are r~-flat major and L-flat majorl.

'I'he melodic line of the section bears a strong rese.:nbl.J..:.-1ce

to the main theme of the movement. See Ex. 32.

lThe relation of these two scales will be studied in t1 ,e chapter on I~rmony and 3cales.


Page 43: Analisi Dumburton Oaks

(III - Fig. 63) I


In the section after Fig. 64 the melodic m;_~terin.l

becomes prectically ststic. Example 33 includes t.be entire

section from Fig. 64 to Fig. 65. The fin~.:~l mec-,sure of this

section was not included in the pocket edition of the .Jcore.

It is performed in the recording, hmnever.

Example 33. (III - Fig. 64)

17:'71 Ab .ScA'-f, ut"PeR.srAF,:: A~,B~,c,J>,Eb,f, <:-~G. l!e.:!J - - ....... ' I"'

'l'he entire section fro.::n Fig. 65 to Fig. 08 will be

considered in detail in the next section on Ostinoto. The

large section from Fig. 63 to Fig. 68 is the Retr3nsition

to section Q in Grnph II.


Page 44: Analisi Dumburton Oaks

The section from Fig. 68 to tvvo bt:.rs before Fi,.:. 70

is c. re-st~tement of the material found in Ex. 28; tL.e ::1<1-

teriul in thi.s section is a minor third higher, <:lnd uses

the scale of the earlier section transposed up to G-fle.t.

'rhe two measures before Fig. 70 are an extension Lmd aug-

ment.:::tion of the previous figure found in the fourth :ne ~­

sure after Fig. 69 (tenth me::sure of Ex. 28). This aug­

mented portion serves to slow the pace for the ~ ~

which follows.

':he first and second violins are found in a duet .:1t

the beginning of the Poco Meno section after Fig. 70. .·he

key of the section from Fig. 70 to Fig. 72 is C minor, '.nd

the simple accompaniment chords of the other instrur:1en ... s

are composed of members of the C minor triad. Exam_ple 3<i

shows the beginning of this section.

Example 34. (III - Fig. 70)

11dJ ?oGo M•b_" '- ---~~- ·--=-~·:1- -l.-:_---_·-----._ ;--


Page 45: Analisi Dumburton Oaks


The next section after Fig. 72 begins as a re-state­

ment, in the new key of B·flat minor, of the material found

in Ex. 34; in the third measure after Fig. 74 (lst measure

of Ex. 35), strettos are found using this melodic material.

Example 35. (III - 3 measures after Fig. 72)


The material of the stretto is extended in the first

two measures after Fig. 73; this leads to a section of sus­

tained chords, which recalls the linkint_; material found in

the closing portions of the first and second movements. This

extends from the third measure after Fig. 73 to Fig. 74 and

:f'emQO 1 again ...

In the section found after Fig. 74, a third deriva­

tion (a3 in Graph II) is found. The six-measure section

from Fig. 74 to Fig~ 75 represents the entire first state­

ment of the theme as found in Ex. 28. In the next section

from Fig. 75 to Fig. 77, the second portion of the m;:Jin

theme, as found from the eighth tr.LI'ough the eleventh mea-

Page 46: Analisi Dumburton Oaks

sures of Ex. 28, is developed. (This section from J.."~ig. 75

to Fig. 77 is repeated in the recording of the Concerto.)

The bridge to section £ of Graph II starts in the

first measure after ~.,ig. 77. Two scales of 11 minor and ;~

major exist in the section from Fig. 77 to Fig. 79; in each

of the scales the theme of section g is developing. When

the theme makes its appearance in the first me~sure after E,\1" ~

Fig. 79, the A scalest\dropped, and n new scc:\le on D is u.dop-

ted. In the section from Fig. 79 to Fig. 81 the new theme

is given one complete exposition. This is its only c:tp:~·ear­

ance in the entire movement. 'I'he horn begins the theme :J.nd

carries it into the fourth me:.:sure after Fig. 79. .·t this

point the flute continues with a Coda to the theme, and

completes the statement in the bar before .J:i'ig. 81. ..lee

Ex. 36 for the horn portion of this pc:~ssage.

Example 36. (III - Fig. 79)

D, c~ F; A, ~bJ '-, ob f L.


Page 47: Analisi Dumburton Oaks

In the first measure after Fig. 81 the fourth ver­

sion of the main theme Cs4 of Graph II) appeats; it is found

with a more LiCti ve accompaniment figure, an ostinato of two

beats duration in eighth notes. See Ex. 37.

~mple 37. (III - Fig. 81) uuu ~.~ ,

This section resembles the first statement of the mu.in

theme, as found in Ex. 28, in a form~l sense; however, the

second section does not modulate to G minor, but rem~dns

in the E-flat scale of the firot portion of this altered


In the section after Fig. 83, the m~dn t:neme ·is

c,ltered further. It is extended upward throughout tHis

section by consecutive scule steps. This section from ?ig.

83 to the end is the Coda of the movement; it consists en­

tirelJ of alterntions of the main theme. See Ex. 45.

From F'ig. 85 to the end of the movement the SC';le

employed is an E-flc:t ma,jor scale with two leading tones


Page 48: Analisi Dumburton Oaks

(.Q-flat and 12-naturo.l). In the section from Fig. 90 to the

end, the S!-flat major chord is used repeatedly with the '-ld­

ded tone, 12• This .seemd to be one final usa[;e of the pri­

mary motive of the first movement (]2-flat, Q, ~-flat).

Since the motive was detected in ~he second movement also,

it would indicate that the entire composition is cyclical

to this extent.


In the composition of the Durnbarton Oaks Concerto,

Stravinsky has made frequent use of the ostinato. .3ince the

device has been a basic part of his compositional technique

from the beginning, this usage is to be expected. He has

devised some new applications for the ostinato, which .:-:re

outlined in the next section.

His literal ostim.1ti (several exact repetitions of

a figure) are used in this composition as a block of the

form. They usually tend to hold the melodic elements to o.

specific range, or to a limited group of chord tones. The

rhythmic ostinato (several exact repetitions of a rhythmic

pattern while using various intervals) is also used.


The other group of ostinati, if this term is .::.:pplaed

in the freest sense, is made up of the pedal ostinati. The

pedo.l ostinato can be found as a sustained tone (pedal tone),

::1 sustained chord (pedal chord), or the rhythmically free

linear movement of a part which outlines the tones of a sin-

Page 49: Analisi Dumburton Oaks

gle chord against the melodic line. The first two of these

pedul ostin~ti will be discussed in the chapter on Harmony

and Scales; the last one .;ill be considered in the follow­

ing section.

The ostinato is used extensively in the first c:tnd

third movements. It is found mainly in section ~ of the

second movement. The use in this section is continuous,

since no measure from :B'ig. 39 to Fig. 47 is found without

some form of an ostinato, and usually two are present at

the same time. There is one other usage in the movement,

found in the accompaniment of the section ~ material.

Since there are numerous instances of ostinato usage

in the Concert9, the following discussion will consider each

movement separately in order that som~ conclusion about os­

tinato usage for each movemn~ may be drawn. In order to

facilitate this, mention will also be made of the ostinato

passages discussed in the previous portion of this chspter.

In the fifth me<:Jsure after Fig. s, a literal osti­

nato is found in the first violo. line; this ostinato wus

included in Ex. 4 as a part of the diminishing motive se-

ries. There are five repetitions of this form of the mo­

tive, and these repetitions are literal in the sequence of

tones chosen for the ostinnto; ho-wever, the rhythm is

slightly altered in the fir·st two series, as shown in Ex.

38 below.


Page 50: Analisi Dumburton Oaks

Example 38. (I - - 5 measures c;_fter- Fig. 5)

In the first measure after Fig. 6 there is a two-note (E, .Q) literal ostinato in sixteenths in the lower strings;

this is indicated in r~. 5.

The next example is another literal ostin,,to found

in the first four measures after Fig. 10. The discussion

of this basscfn ostinEtto in fourths is found in the fir3t

section of this chapter; the application of the ostinato

is shown in Ex. 8.

The ostinati found in the lower strint_ ,_ in the sec­

tions after Fig&. 12 and 13 are literal. They bear strong

resemblance to one another in the manner in which they ::~re

initiated. In the measure before F'ig. 12 the two notE: se­

ries (~-fLtt, .fl) occurs in the cellos and basses; this se­

ries is extended in the first measure after Fig. 12 (£;-fL,t,

,g, ,E), and is repented in the next measure. In the fourth

me0.sure the ostinato is found with one tone (Q) missing;

the leap (£-flo.t, E) remains, however, to identify the fi­

gure as a member of the ostinato.


Page 51: Analisi Dumburton Oaks

The next series after Fig. 13 is begun with the Q

of the lower strings in the measure before Fig. 13. As in

the previous series found after Fig. 12, the ostin_,.to has

only two members present at first (.Q, followed by .6-flat in

the first measure after Fig. 13). In the second and third

measures the ostinato is given for the first time in its

complete form (Q, ~-flDt, ~-flat). See Ex. 1~ This tl~ee-

note series is repe<?.ted with minor rhythmic variations un-

til the end of the third bar after Fig. 14 (five repetitions

occur). In the fourth and fifth measures after Fig. 10,

the ostinato is broken by a descending t~ee-note series

(.£, ~-flat, .6-flat) which leads to the next statement of

the fugue subject in the key of C minor (Q, ~natural, £,

and continuing in a normal statement of the fugue).

The next example found is classified as a pedal

ostinato. In the two mec:~sures before Fig. 18, the lovJer ' \;:\ ~

strillbs present three members of a ~-flatmajor/~eventh

chord (~flat, g,, and ,a-flat). In the two measures that

follow Fig. 18 these particular tones are used in a rlv­

th.mically free manner to outline the chord. The portion

of the fugue subject used in this section is restricted to

the first six tones because of this ped:~l ostinato. . ,ee

.2x. 14.

In the sections found from .F'ig. 21 to 22 and from

Fig. 23 to 24, examples of rhythmic ostinoto, which he1ve

characteristics of pedal ostin£~ti, are found. The ostinoto


Page 52: Analisi Dumburton Oaks

in Ex. 39 is from the first section after Fig. 21. The

second, after Fig. 23, is li.Uite similar in tree1tment, with

minor chcnges occurrin,in the double bass line.

Example 39. (I - Fig. 20)


In the four measure section after Fig. ?1, the bns­

soon line consists of a pedal ostinato which is nenrly liter­

al. 'l'his ostinato is componed of the four members of the

!a-flat major-minor seventh chord. An extra £!-fl·,t is c:dded

to the ostineto in the third measure, which labels it .:1s a

pedal ostinato instead of a literal one.

The ostinati found in the Codc.'t of the movement ex­

tend through its entire length form Fig. 25 to Fig. :?8.

There are two ostinati present nere. One is composed of

seven tones, and ia literal. The second one is composed

of three chords and is rhythmic. The note values of e~ch

chord member of this second ostinato are double the note

values employed in the seven-tone figure. 'l'his is an exam­

ple of polyrhythm in the combination of the two ostin::ti.

See Ex. 40 which follows.

Page 53: Analisi Dumburton Oaks


From this consideration of the ostinato us;.1ge in

the first movement, it will be noted that the use of liter­

al ostinati is more extensive than any other kind. iome

of these literal examr;les are found altered slirhtly, but

they remain more literal than anything else.

In the second movement the first use of an ostinGto

is found in the bassoon line in the last measure of ~x. 17;

the members of the ~-flat major chord are outlined here. A

rhyth.1nicully-free linear usaee continues until the fourth

meosure after Fig. 30, at which point a ,£-naturul L3 int.ro­

duced which breaks the ostinato. The same ped::1l ostinato

enters <;gain in the first measure after· fi'ig. 31, and conti­

nues until ... the fifth measure. In the return of this pc.:ss<:.<ge

from Fig. 47 to li'ig. 50, this ostinato is repeated exactly

with the exception of the last note (gl) for which a puuse

in all lines is substituted.

The important use of the ostinato is found in £ec- .

tion ,g of the movement. There are thirteen examples of os-


Page 54: Analisi Dumburton Oaks

tinato used in this section; since the entire section is

based on the ostinato, a full accounting of the method in

which it is employed in the section is nt:cessary. _;orne

of the ostinati have alreco1dy been mfmtioned in the section

describing the second movement.


Example 20 contains all elements of the two ostinu­

ti used without break from Fig. 39 to the meosure before Fi£>

42. At this point the three-note ostinato of the lower

strings has a ~-natural substituted for the ~-flat in the

chordal outline on Q in use since the first measure ,;.fter

Fig. 39; the upper strings continue in the usual mann~r un­

til the second measure after Fig. 42. .~;t this point they

break the original ostinato t and extend their· r, nge upwurd

in the implied key of D major from ~1 to ~2.

The upper strings return to a two chord ostin:to in

the first measure after Fig. 43. See :Sx. 23. The lower

strings again adopt the G minor chordal series.- In the

third measure after Fig. 43, the upper strings be£;in c~ new

two-chord ostinato. See Ex. 23. It has already been in­

dicuted that this change in ostinato marks the beginning of

section ~ in the second movement. This new ostinato in B­

flat minor in the upper strings continues until the fifth

measure ;.;.fter Fig. 44. It is accompanied throughout this

section by a pedal ostinoto in the lower strinrs. ,:;ee i!:x.


The strict two-chord ostinato of the upper strings,

Page 55: Analisi Dumburton Oaks

:ss found in Ex. 24, is chenged to the rhythm.ic ostimi.tO on

the .[ moj or cho.:·d as found in Ex. 25. This is an ex.~;;np le

of polyrhyth:nic ostin.:;to us<:tge corn.11on in the third movement.

The pedal ostinato becomes a sustained ped:.:l tone (£2.-:f'lat)

in the first measure of Ex. 25. Immediately followinr, this

in the fourth measure after Fig. 45, the ped~il ostinato of

the lower strings becomes a strict ostinato, consisti~u of

Em-flat and !}-flat alternating on every second beat. The

upper strings return to a two-chord ostinato at this sa:-.1e

point; the chordDl use1ge in this line becomes quite free

following this in the second mec:.sure of ::.:x. ~~6.

The final ostinato used in this section is a rhy­

thmic one; it is indic8ted in Ex. 41.

Example 41. (II - 4 measures after Fig. 46)

"F -.;F , (r= -.WJ (A') ~tnifJ:iffVJ~~-=ttL: -c~:

In the second movement twelve different ostinatio~t

used. Of this total, five were strict, one WQS a strict

rhythmic ostinato (Ex. 41), and the other six were vari­

ous types of pedal ostinati.

The third movement opens with an ostinato in the

lower strings. This is in groups of four chords, ::::i::iilsr

to the ostinato of the previous movement shown in Ex. <:5.

The plan of this ostinato is shown in Ex. 28; thi.s s<.~me


Page 56: Analisi Dumburton Oaks

tJpe of ostinbto is found in the sections efter Figs. 56,

57, und 68; it is an example of a strict rhythmic ostinQto.

The next section to make use of the ostinato is


from Fig. 65 to three measur~before Fig. 68. In this brief

section ten ostinati are found; the section is made ur n~nost

entirely of ostinato material. See Ex. 42.

Example 42. (III • Fig. 65)

3 ... 1---1 .,

Page 57: Analisi Dumburton Oaks

T!1e violin duet after Fig. 70 is accompanied by

two forms of ostinato. See Ex • .:.34. 1'he continuous eighth

note pc:ttern would be n strict two-beat ostinato, except

for the f~Jct that two sixteenths enter occasionally in the

place of one of the eighth notes; therefore, it must be

clnssed as a ped:Jl ostinato. 'I'he chords in the bass are

definitely classified as pedal ostinato; they occur ,:Jt ir­

regulnr intervals, and consist of members of the Q minor

triad. This Sc::me procedure is repeo.ted exactly in the sec­

tion following Fig. 72 in B-flat minor.

At the end of the B- flat minor section after Jig.

72, chords in the key of B-flat II13.jor create a two-beat os­

tinato in the strir~s; it is a strict ostinato, and accom­

panies the bassoon which outlines tones of the ~-flat mnjor

triad. :;ee 1st and 2nd measures of Ex. 43.

t.;xample 43. (III - 3 measures after Fig. 73)

In the third and flute ndopts

n ped.~,l ostinato which implies the g major chord; the bas­

soon outlines the £ major chord in another ped .. ,l ostinc.<.to.

The melOdJ line of this portion is in the key of G rnr:~j or.


Page 58: Analisi Dumburton Oaks

The next ostinato us<~ge is found in the section from

l',ig. 75 to Fig. 77; it is a rhythmic ostinato vdth two forms

as shown in Bx. 44. The section from Fig. 76 to Fig. 77 is

a repetition of the form of the fi~e mensures of this exam­

ple, on a new scale a fourth hiche~ than the first.

Example 44. (III - 1fg• 75) 17]) 'Ai.~ti'"i~' "'(~~~IS G~f.. G- t. '

... ~ :1

;'~ . Uif J:i• .... ., -.. ..... -~ ae.. I ·~ I r • _'li' ... Ill • • . .. ' .... t-' ,

ft .. ..,. 4f ' < _,_ , ,. I ' • ' ~ 'J ---··- --

r ~ ' ~r ~ ~ j ~ ~ s .( ij -

L1 1 ., • .. -+ Ji: -t ' . .I. .

• ··:; ; -:: ----~ 1 q~ :;t l-. 1 -l· l., _;;l. - • -ILl - ---- r---· ... t. -- ----.. -~ r-. ....... ;.,; ,., . ... u- ... •• ... I 7, ., ..

~- ... ;~~&TUff -~I-~~:· ".,-! ~,i~7 -(

~ - s i 't t 'I

I Jjfl l - •• r =t --'" .l. Ia .. - -\- -+ -- +r· -. '- ~~ .•r • . LJII .. . --f-

·1 i .. ~ 1 t p-t * L ' • .L . - ..

~- ~ • To A~+D - -'lhe next ostinDto i:.:~ a strict rhythrnic one; it is

found in the bassoon trills and cello pizzacalco not.cs in

the section following Fig. 79. See Ex. 36. These triJls

continue to the second me_,sure before the next section,

which begins after Fig. 81, for a total of nine reret~tions.

In the section fro:n Fig. 81 to Fig. 83, a .strict

ostinato is found in the accompaniment to tl~ia last rre­

sentationof tbe principal theme (.s4 of Graph II); tl!L; is

shown in Ex. 37. The section following t!lis after Fig. 83


Page 59: Analisi Dumburton Oaks

employs a rhythmic ostinato, :;"tg.:,in of tao-beats duration in

eighth notes. This outlines mony different chords u.sea in

the melodic structure; this continues until the fifth mea-

sure nfter Fig. 87. In combination with its predecesaor,

the strict ostinato found after I<,ig. 81, it comprizes the

largest block in the structure employing continuous 0~3ti­

nato (34~ measures). See Ex. 4~

Example 45, (III - Fig. 83)


;, very short strict ostine .. to is found in the section

in the first two me,.tsures after Fig. 90; this employ;3 F)n nn­

ticir.;ation of the final cadence chord c;u the beginning of

each ostinc:1to group. :3ee. Ex. 4&·


Page 60: Analisi Dumburton Oaks

, Example 46. ,,.,.._.,. ~


1'he final movement of the Concerto made the mo::~t

extensive use of ostinato. In all there were twenty-one

different ostinati; nine of these were literal, eig:;l .. t t·,ere

of the pedal group, and four were stri~t rhytrunic types.


Page 61: Analisi Dumburton Oaks


In the formation of a musicnl composition, the pro­

blem of ending one idea and beginning another continually

presents itself to the composer. The methods used to ac­

complish this are personal with every important composer;

in his solution of this compositional problem, Str<:lvinsky

makes use of certain basic formulas wLich will be consi­

dered in the following discussion.

The only three possible ways of handling the end

of one idea and the beginning of another are defined and

diagramed below:

1. Bring the first idea to a complete close be­

fore beginning the second idea.


2. Bring the first idea to a close and at the same

time begin the second idea (momentary elision).



Page 62: Analisi Dumburton Oaks

3. Before bringing the first ide:. to a close, enter

the second idea (overlap or elision).

The second and third types e.bove produce the most

continuity, ond are favored strongly by 3travinsky. The

first type, if used often, would create a section8liz<Jtion

of ideas.

The next problem to be considered in a Cddence is

the harmonic one; the relation of the penultimDte and finr:.Il

sonorities is tne prime factor in this problem. The compo­

ser must be aware of all the possibilities inherent in the

immediate vicinity of his cadence so that his use of t.Lis

material will create a convincing cadence.

'l'he discussion of cadences of the Concerto will be

approached from the standpoints of continuity and J:larmonic

and linec~r motion. Typical examples have been extr:"cted

from the score, and :..re discussed in the order of their :~p­

peurance. The examples will contain the h•:r:nonic scheme of

the codence, and will be diagramed to show the particular

method employed in the ending of one idea and the beginning

of the next. Following the example, other features of the

cadence will be discussed.


Page 63: Analisi Dumburton Oaks

Example 47. (I - 2 measures before Fig. 4)

This cadence occurs at the end of the introductory

.rn<.::.terial. The two cta'ds used concurrently are the §-fl·.,t

major triad and the Q minor triad. The E-fl<:~t major line

resolves into the accompaniment line, ;,;~nd the g minor line


is resolved in the first solo statement of the primc,ry motive.

It will be noted that all three members of the main motive

cun be found in this combination of chords which occurs be-

for Fig. 4.

Example 48. (I - 1 measure before Fig. 7)

Jtjt:~R==:t=~~~t=1==i:;:+.=::l!~!::j::::;!=:t:t=~ .. ~~rc . 0, E," F:ll, G,Grtl, ~~'~~I C:.ff

Page 64: Analisi Dumburton Oaks

The .@-fl<.lt in the lower strinrs is carried over into

the next section as an E-sharp. The !2-flat und _g-fl2t found

in the clarinet line are resolved after Fig. 4 to the enclo-

sed tone, _s-naturc:d, by the second horn and bassoon. 1'iLis

is nn example of the shift of orchestro.tion principle,

which is a favorite device of StrC1vinsky. In this shift,

an important principle of the orchestr.:1tor' s technique is

disregarded, namely, the ideD that old and new orchestr.l

colors must overlap by at least a quarter of n be~.t.

Example 49. (I - 2 measures 11)

In this example the b;::..ssoon line plays an important

pnrt in the shift of sc~les. In the fow . .ne;:sures 1.:;.::1.e-

div.tely following Fig. 10, the bassoon li.ne i~) a six-tone

ostin .. to in a D SC<lle. See Ex. 8. The tones employed in


Page 65: Analisi Dumburton Oaks

this ostinato are .£;, g, g, and g_l. If this series of

fourths is continued upward, r.>n E., B-flFtt, and E-flat I - 7

occur as the next three tones. There ure no E-naturals

found in the texture until the descending series of the

bossoon in the second measure of E.x. 49; therfore this

i-natural is to be considered the actual link between the

two sec.-des on D and E-flat. '1'he chord found immedic:,tely

after Fig. 11 includes the same members found in the chord

after Fig. 2; in both places these chords function <:ts long

suspended dominants. Of the two this one founo after .?ig.

11 is the longer, for with its extensions it does not

reach a tonic resolution until Fig. 13, the beginning of

the fugue in C minor.

Example 50. (I - 1 me.:-.sure



Page 66: Analisi Dumburton Oaks

The chromatic passing tone, ~flat in the basses,

Gerves as the connecting link in this cadence. The !Ili.'te­

rail to this point has employed members of a scGle which

basically resembles F minor. The g-flat resolves in two

directions chromatically to introduce members of the two

scales used in the three-measure passage after Fig. 16.

It resoves to g-naturc-:.1 in its own line, the dominant of

the scale of C major. It is resolved downward in the vio­

la line to .t:-natural, the tonic of the SC<.1le of F major.

It is, therefore, the reverse of the procedure found in

Ex. 48.

Example 51. (I - 2 measures before Fig. 20)

~--q .. ~~~· --I • -~ •

~p .. .- ~ - ---- . ··- - I" -v -2. - r '1

-""l ... ~ -· ·------··

c-.u .:hJ ··~~· ....... - J ., z. - 1? ~ -

I ~

l -· I ··,-;.=~ ··J,) ·' ·~--·

2 , ... --p-· - --~ ...

> • - r t-1 (S•tt ....... • - .. ..... '"' - u• ..!.. • ..-.

~h•ll' • -"" -· .. ,. - ; - ·-


Page 67: Analisi Dumburton Oaks

In this example, preceding the recapitulation found

after Fig. 20, the lower striDES repeat the procedure of Ex.

48; they are found here enclosing the third (Q) of the new

E-flat major scale. 1;11 of the other line have resolved to

!!-flat, the fifth of the sce11e, prior to this.

Example 52. (I - 1 measure Fig. 25)

----""-------- ~- -------- .


b .. b~~: --4-,~__IIL-:J.-11!.-~-,1-~+-------I'"f-------11--i' G-----


In this example, the E-flat major scale is used in

contrary motion. The final resolution of the sco:.ile lines

is suspended during the rest for dramatic effect. All lines

then resolve to chord tones of the E-flat major tonic chord,

with the exception of Q-flat1 which resolves to £2, an ndded

chord tone.


Page 68: Analisi Dumburton Oaks


Example 53. (I - 5 measures before Fig. 29)

The cadence of the linking material is bosicC\ll.f

plagal. In the first two measure$of the example three chro­

matic lines are employed which lead to important chord tones

in the third measure. These are as follows: ~-fl,,tl in the

first chord of the example to ~-natural in the second chord

with its resolution, E, already present in the lower strines;

g-naturall in the first chord to g-flatl in the second chord,

resolving in the third measure to the added tone, £,-naturall;

and, finally, the bass line itself, ~flat to ;E. The third,

a-nc:ttural, of the tonic E major chord in the third rne:.:<.sure is

found enclosed in the previous beat by g and Q-flct. This

chord is reduced to an ! which is used as the first tone of

the second movement.

Page 69: Analisi Dumburton Oaks

Example 54. (II - 2 measures before Fig. 32)

m~~~--~~~w ----~· nJz

The final tone of the ascending ~-flat ~~jor chord

line, gl, is emphasized by the violin figure, and becomes

the tonic note of the new D scale found after Fig. 32. This

scale is not D major, however, for the !-naturall of the

clarinet in the third measure changes it to D minor.

Example 55. (II - Fig. 3. 8) 'f-.~.~

[su• .. u) ~~f'~: ) .... ,

---- ~

f /'L Tofll£ S'A&.f. _, The material

third measure of the example is the broken chromatic line

g-flat3, £3, £•flat3, ~-flat2; this final Q-flat2 is adop­

ted as the fifth of the scale of the linking section. The

B-flat in the bass is the actual governing harmonic note of

the three measures of bridge material. The next section


Page 70: Analisi Dumburton Oaks

is announced by the dissonant .§-n:.:.tura11 which leads toward

the third, !!-flat, of the next scale (basicdlly G minor).

This s.-naturol1 definitely establishes the polarity of the

,12-flat as the tonic note of the series.

Example 56. (II - 3 measures before ~'ig. 51) [.Sc H ~ ""ej


~E~:::::E~~~~3 ~ o_'~- I ~ lro:-1.

cqt I(T!~ "" In this example the relation of the first me:;;;:mre

to the second is that of le~ding tone to its tonic. lt re­

sembles to this extent the contrasting section in the first

movement based on a D major SC3.le, which resolved in tLe

next section to E-flat major. It is interesting to note

that there are no common tones found in the two chords;

threfore, the stepwise motion of the bass pt:trt must be con­

sidered c:s the most important single factor in this C<i.­

dence. The final portion of this linking section will be

considered in the chapter on Harmony and 3cales.


Page 71: Analisi Dumburton Oaks

Example 57.

This c:~dence occurs in the first section of tLe

third movement, and contains a high concentration of' dis-

sonant intervals. The scale employed in the first me,, sure

of the example is a complex scale in which the polarity of

Q has already been eatablished. The emphasis given £:-sharp

by association with £:-natural and .Q creates the irnpres;:don

that this tone is of more than ordinary import: .. mce. '::.'he .Q­

flat found in the following serlies is the enh.:~rmonic equi­

valent of this tone, and its polarity ~1s the new tonic cen­

ter is quickly established.


Page 72: Analisi Dumburton Oaks

Example 58. (III - 2 mensures befor·e .::•'ig. 63)


J) .. P, f~f~F," 1'.~ 4,A~ ri\~,~,C,ap I E'~ F, Q.

D•, ~ F; ",j-, A•, 8~, c.. Two elements hold the key to this c,:.-:dence, anc1 these

Lre found in the first two meesures of the example. doth

nre SC<.1le lines, the first from :Q-flat2 down to ,t:-fl~Jt~' in

the upper strings, and the second one from Q-flat up to s., found in the lower strings. The first one leaa...; to g,-flut2

in the clarinet line which starts in the third measure.

1'he second one le,_;.ds from .£ to the g-:flat o:f the bassoon



Page 73: Analisi Dumburton Oaks

Example 59. (III - 3 meosurES before It,ie. 68)

[.5c:KfHq~---~···® ___ r-,b ~~ f t. ,. ·~- . ..~

1 I l ;J:. + 1- J- ~ ' ~ ~-., I

·~ --- tLtL ··-_. _L I r

• '2 ...&:::1~ - ... ~----"""""-- ..... ~ 1f ~ ~---------- I

This cetdence has one active element, ,_tnd that 1.s

the descending scale line. rrhe sustcdned chord i3 lleld o-

ver froo the harmonies of the previous section; the sc~le

is the melodic form of C minor, and descends from tl1e i.igh

point found in the L~st three me:sures of Ex. 42. 'l'his

high point wa.s attained by an ascending scule of C m:..~j or.

The end of the scale line in this exemple emphasize;.;, i in

association with its lower neighbor, ,!i•flat. This f is in

leadin,g-tone relation to ,W- flat, found in the next s£~c­

tion. The polarity of this tone as the center of the series

is estoblished in the l8st measure of the example.


Page 74: Analisi Dumburton Oaks

In this cadence all elements of the la.st cr.orc in

t.he first measure, except £. and £1, are in hRlf-ct,er rel.::;-

tion to some element in the first chord in the second :18:~!­

sure. The g is held over as a common tone; the £1 is

cropped from the texture.


Page 75: Analisi Dumburton Oaks

LXumple 61. 3 measures o.fter Fig. 90)


The final cadence of the third movement is si.:~1ply a

repetition of the !Q•flat major chord with the adGed tune,

g,l. It has already been indicated that this g1 is a ~·:,rt

of the motive series 12-flat - 12 - E-flat. There is one o­

ther application, however; this could be an example of e

compressed cadence, the ];!-f'l1.:1t and g1serving as a partial

V chord to the I chord of E-flat major.


Page 76: Analisi Dumburton Oaks


Throughout the Dumbarton Oaks Concerto, harmons· is

of second.:::ry importance and the line becomes ell import~mt.

'l'his is shown in the soloistic style of writing which is so

characteristic of this composition. The harmonies he:.rd

are nl· .. 'IJc::ys found as the result of the interweaving of lines

of equal interest. The purpose of this chapter is to uis­

cover wh:;t meterials are employed in the construction uf

these lines.

The most lo,sical approach to an understandir.g of

the contrapunt21l style of writine is in .:.~ study of the scale

or series of tones employed in each import:::mt section.

This will include a study of .3travinsky 's method for '..:re­

ating a more complex scale series, and, conversely, n..: .. _,

method of' simplification of the comrlex scales. In L. .. "is

study1 the relation of tJ.1e growtL of co;nplexity in :.~ p;..;t-

tern of scales to the development of tension tow,.rd c ud-

j or cadence will be noted when it occurs. 'I'his is one of

the composer's favored methods for moving from one plane,

or compositional block, to the next.

The important developments in the scale serie3 ';Jill

be considered here, in addition to certain relationsh:~;'s of

the tonic center or tone in one series to the tonic center


Page 77: Analisi Dumburton Oaks

of one or more other scales found in the vicinity. The se­

cond movement sho'.'IS a surprising <:lmount of relation in this

L::st respect. 'I'he examples included in this section ·,dll

contcdn a list of scale tones used in a section; the first

tone indic;:,ted is to be considered the tonic, unless it is

st<.ted otherwise in the discussion.

The bosic tonality of the first movement is found

in a seven-tone series composed of the tones of the E-flat

major scale; the polarity of ~-flat is established :.::t the

very beginning of the movement. The first import:·nt change

in the scale is found in the section after Fig. 2; thiL

section is a bridge between the E·flat series and the C

minor tonality found after Fig. 3. In the first measure

of Ex. 62 the ~-sharp and s.-naturall found in the fir:;t

beat are the first two tones which are not a part of tJ:Le

E-flat major series. On the second be <:it of this meL. sure,

the Q•naturc:•ll is found with .s,-f'lat2; this method of em­

phasizine the new tones added to a series by includin~; its

relative tone a half-step distant is used throughout the

entire Concerto. The tones found in this series in the:

first measure of the example ure nine in number, and L,re

based on the root of this dominant chord structure. In

the second men_sure of the example the SC3le is simplified

and only seven tones are used, still based on Q; however,

this series employs the tones of the ascending melodic rni­

nor on c, which is the tonality of the third measure of the


Page 78: Analisi Dumburton Oaks


exa:nple. In the third measure, £ is estr.blished us the new

tonic center, and the sce:;le becomes C harmonic minor. In the

following mee1sure the Q•natural1 becomes 12-f'latl, ;::;nd the

scale once ng .. ,in becomes an E-f'lat major series. This atonol

passage is best explained in :.3trvinsky's own words in his

discussion of this term:

The negating prefix ~ indicates a state of in­difference in regard to the term negating without en­tirell renouncing it. Understoo! in this way, the word 9tQna ity hardly corresponds to what those who use it have in mind. If it were said that my music is atonal, that would be tantomount to saying that I had become deaf' to tonality. Now it may well be that I remain for a considerable time within the bounds of the strict order of tonality, even though I may quite consciously break up this order for the purposes of' establishin~; a new one. In that case I am not ~tonal b~t ~tonal. I am not trying to argue pointlessly over words; ir is essential to know what we deny and what we affirm.

~:ample 62. (I- 3 measurmafter Fig. 2)

...,_~~.__ _________ __.L-fill,___ ___ ..__.--::--· --- -- .

G,A~,A,B~ B,C,-E~, E, F.# (;,~,~C,P,f4 F Hjf4oN• c (S, ~SC.. MEL.MINtl) ~&HDIZ-

lst.ravinsky, Igo~. Poetic§ .2.f. 11yaic1 (Cambridge, J\!ass.: Harvard ~niversity Press, 1947), P• ~8.

Page 79: Analisi Dumburton Oaks

The E-fl:1t major serie!3 continues until the :7Jodula­

tion to em F minor series indicoted in Ex. 2. In the beat

preceding the first measure of Ex. 63, the new tones, f­

sharp and 2-natural, which are derived chromatically from

their own lines, introduce the twelve-tone chromatic series

which follows; the §-flat major triad outlined in the first

bent determines the tonic harmony of this section.

Example 63. (I - 6 measures after

(IZ To~£ Sc:A&.E)

The same cr.LI'omatic series is continued in the section which

follows after Fig. s, but here two notes are missing, i.e.,

£ and £-sharp. ;\fter two measures of this scale a still

shorter series (eight tones) is found: Eb ,F ,F#,G,f,b ,Bb ,c ,D.

In the fifth measure after Fig. 5 a seven-tone B-flat major

scale series is found; however, the tonic element of this


Page 80: Analisi Dumburton Oaks

series is determined by the ~-flat major chord given in

the bass line. See Ex. 38. This B-flat major series hes

four additions in the three me<:lsures after Fig. 6; the

scale lacks only one tone, 12,, to be a complete chromatic

series (This tone is not used until the contrasting sec­

tion after Fig. 7). In the final three measures of tllis

section before I~ig. 7, the only scale members employed in

the texture constitute a chromatic line; E,~,.Q,jb,.£\,ah·

~flat continues as the tonic of the series. See Ex. 48.

The two important series employed in the contr·as­

ting section of the first movement are quite similar to one

another. The.relation of these scales is shown in the fol-

lowing insert:

D, Bb, B, C#

G, G#, A, A#, B, C, C#, D, 1' t

E, F#

variable fourths

The variable fourths of the two scales is an import:.~nt ele­

ment of similarity. 1$ch sc.9.le is equally import<::nt in the

f'orm of the contrasting section.

These two scales are identical if the ~-flat of the

D scale and the Q-sharp of the G scale are eliminated from

the two series. These tones occur only in the last me .. sure

of each of the two sections which employ these scales (The

D scale is found from Fig. 7 through the first measure after

Fig. 8; the G scale begins in the third measure after· .i?ig.

8 and continues to Fig. 9). In these final measures of the


Page 81: Analisi Dumburton Oaks

two sections the new tones Dre introduced with their rela­

tive half-steps pre;:Jent (the li-flet with ~-natural, ;:md the

.Q•sharp with g-natural); these new tones serve in the mo­

clulntions to the following sections.


In an earlier section, mention was ~~de of the f~ct

that the modulation from one scale to the other at tLi;:. point

was through the enclosed third of the two scales. ':I'LL- is

another exnmple of ant~ton§l use. The ~major-minor ncventh

chord is employed in the second me<J.sure after· F'it;. 8 to

break up the :U major harmony, and to pass the tonic center

from a D scale to a G scale.

In the eleven-tone series found in the five mec:.sures

before Fig. 1:3, the single tone, !1-flat, is avoided; +i- • v~llS

section is part of the extended dominant v-1hich lend.J to the

fugue of the first movement. The Ja-flat is used in tLc sec-

tion v1hich follows after F'ig. 13 in the fugue subject .. ad

the ostinato accompaniment. ..::ee. Ex. 10.

The next important development is found in the ca­

dence shown in Ex. 50. In this example a ten-tone series

b.:~sed on the F major scale moves to two separate scc:le.s;

i.e., a new ten-tone F major series, and an eleven-tone

series based on C major. The C major series is the s::t;ne

one found in Ex. 10 plus one new tone, 12· In the fourth

measure after Fig. 16 a modulation to an A-flat major se­

ries occurs; this is the enclowed third between the two

previous scale. The scale consists of all but one of the

tones (an .£) found in the previous F scale.

Page 82: Analisi Dumburton Oaks

. i

1'his ,'-flr,t sco.le is used t.hrough the fourth mec.sure

after I;'ig. 17; in the fifth me.·:tsure .-:::fter Fig. 17 two new

scales are ini ti&ted. The fugal material employs a sj_x-tone

gap scale with ~-flat as its center; the ecole of tLe <:'.C-

comp:_:niment is a ten-tone series based on /:.-flat. The six-

tone scale continues until the end of the first mec:::n.1re J.n

Ex. 64. :I'be 1~-fl.at scale continues through the first beot

in the tltdrd me.:.sure of this example. The new ele.:T~.t :.s

found in the horns which employ a different A-flat .':.ica:.e

for their· re-statement of the fu£;ue subject. :i:I:FtCh of t.Le

two l1•flat scales employs a totc:'l of ten tones, with two

tones differing in each sce.le. In comparing the scco~1a ·Nitr1

the first, the second adds r-tle.t and ~flat (both tones

necessary to a st£;tement of the fugue subject in J,-fl t),

and drops .. and Q• All lines adopt this new A-flc.it t;c.,le

in the last measure of the example •


Page 83: Analisi Dumburton Oaks

:xample 64. (I- 4 mec:sures 3ft.er Fig.

A"·. A~ A,t3~ c.~ c, ~ D, e'IJ, F, G- L

Nrw "~'b · 4 b- "'"" C OIJ- f~ F~, F, G-v, Go •.C:•nl 1 1 1 I

The polnrity of ,6-flat in this section shown in ·'-'X•

64 is broken in the second meDsure after Fig. 19 by the en­

try of fugue materinl in a series in which !a-flat is the

center. ;.Jee Ex. 15. These two scales are quite sir1.ilar as

the insert below indicGtes:

original A-f'lc.t: l}b, .§b, .Qb, c, ]2b, ];lb, Eb, ,E, Qb, g

New B•flat:

It is apparent that the B-flat scale is extracted

from the previous l\-flat scale, since only one new tone is

added; i.e., the leading tone, !t necessary to a st;.~t·a:11ent

of the fugue subject based on _&.flat.


Page 84: Analisi Dumburton Oaks

The scale on ~-flc:t used in the final section of

the fugue (shown in Ex. 15) is the last scc\le found before

the entrance after Fig. 20 of the seven-tone E-flat major

series which is used until the end of the Coda at Fig. 28.

The scales are in obvious V - I relation, but the two

scales are not similar (the B•flat scale is minor). It


does contain two elements, found in a statement of the fugue

subject in B-flat minor, that have relation to an element in

the E•flnt major scDle; these are the tones £1-flat and Q-flat

which enclose the third, ~~ of the E-flat seal·-. See Ex. 51.

The first movement is based on the scale of E-flat

major; this is shown in the amount of material which occurs

in this sC<J.le, Qnci in the relation of the other scales to

this bDsic tonality. The pc:.ttern of the scales used in the

major portions of the movement is given in the insert be­

low. Every member of the E·flat major scale ho.s at len.st

one appearance in this series.

I .. v - VII(III) - I • VI&II - IV - v I

.Eb ' llb ' (;Q, .£, 12) , §b ' .Q, Q,

~b, ~b, §b £:,

The movement of tonalities in the last portion (I, VI~ II

or IV, v, I) has the appe.s.r.:;mce of a standard phrase har.,.


The linking section :.:::.fter Fig. ~?8 can not be iden­

tified with any one scale; it is simpl~ a bridging acent

Page 85: Analisi Dumburton Oaks

between the old scc .• le of E·flat major and the ne·:.~ one on B­

flat in the second movement. In relation to the old seven­

tone scale of E-flat major, the new tones introduced in this

eight-measure passage are lh J2':'flat, ~, and Q-flat.

The violins and violas seem to be preparing to the

more natural scale of F major with the introduction of the

§.•naturall (third measure after Fig. 28) and §.-naturz_,l (in

the fifth measure). The lower strings lead towara the flat­

ter key of B-flat minor with the introduction of Q-fL1t in

the fourth measure after Fig. 28. Immediately after this g.­

flat the upper strings turn back toward the flat keys with

a new tone, g-flatl. See second measure of Ex. 53. Both

lines then converge on ft at first with its third and then

alone; it is the dominant scale step of the key of B-flat,

and is the first tone used in the next movement.

The basic scale of the second movement is expressed

in the theme and accompaniment from Fig. 29 to one me .. .:mre

before Fig. 32; it is a nine-tone B•flat series which is

clearly .!Illijor in character. The series as found in this

section is as follows; ~b,~,~#,~,~,§,E,~,~.

The one measure in D major before Fig. 32 is not

intended to express the mode of the next section. The D

major measure simply calls attention to the fact that the

polarity of ~ is to be established; the section after

Fig. 32 is in D minor. See Ex. 54.


Page 86: Analisi Dumburton Oaks

The scale of the D minor section ~fter Fig, 32 (see

Ex. 18) is a gap scale consisting of the following tones;

~,-,l,~'~'~b'~'~#. Its relative major scale on E i2 used

in the next section after Fig. 33; this is a doubtful major,

however, since both the major and minor thirds are present;

E,£l,.db,.Ll,Jab,.§,.Q,~,;Q,~. The section in D was the link be­

tween the B•flat major scale of the first section and the

F scale of this section; i.e., a link by the enclosed third

of the two scales (Bb- D- F). - - -The section after Fig. 34 employs a complete twelve•

tone chromatic series based on l• See Ex. 19. The ~-flat t

of this scnle is dressed to such an extent thct the scale

becomes definitely minor in character. In the next two sec­

tions after Fig.36 and 37 the two F scales found after Fig.

33 and 34 are repeated in the same order with similar m:Jte­

rial, which leads to the linking materiel between setion h

and section ~ of the movement.

The scale of the linking material found in the third

measure <=1fter Fig. 38 (see Ex. 55) is a series with £1-flo.t

as its center. It consists of the B-flat major sctlle tones

with an added seventh, ~-flat. This ,6-flat is hear6. first

at the beginning of the third measure of Ex. 55, and it is

still heard when the A-natural is introduced to the series

in the fifth me<)sure; it is, then, another example of the

introduction of a new tone to a series in association with


Page 87: Analisi Dumburton Oaks

its relative half-step. 'rhe A-n::.tural is also the link to -the scale of the section which follows in the sixth mea-

sure; it is found in the new scale as the second step of a

series in which the note g is established as the tonic.

In this movement there are no instances of two dif-

ferent scales, or series of tones, being employed ct the

same time; however, an approximation of this idee:;, when on­

ly one scale is avo.ilable, is found in the section follow­

ing Fig. 39. In this case the melody line uses one portion

of the scale, and accompanying elements use another portion.

Examf'le 20 shows that the ostinato accompaniment employs the

tones a,a,~b,~,and.~J the first statement of the clarinet

in the second and third measures of this example cont::ins

all of the tones found in the basic melodic element fron1

this point to Fig. 41. These tones constitute 'the upper

portion of the G minor scale plus one tone (~-flat) which

is found only in the first statement; the other four state­

ments which follow span the perfect fourth from £ to g.

After a short section in G major after Fig. 4?, the

scale returns (after Fig. 43) to a series quite similar to

that found in the first measure of Ex. ~>,(). The scule used

in this section (see Ex. 23) lacks only the fourth step,£,

of the scale found after Fig. 39.

The scale of the following section (theme ~ in

Graph I) is shown in Ex. 24. This scale centers on the

third step (~-flat) of the previous scale, and lacks its


Page 88: Analisi Dumburton Oaks

fourth step, :.is does its predecessor in Ex. 23; the ne\:

scale is clearly a B-flat minor series.

A good example of polytona*i~~ (simultaneous use

of two or more tonalities) is found in Ex. 25. The outer

parts (bass and melody) imply the scale of B·flat ffi.i:l ior ..,

found at the beginning of the movement; the inner p~rts

move in the key of F major, emphasizing the tonic chord

of ·that key.

'rhe next scale alteration eccurs in the fourth

mensure after Fig. 45; the compositional technique here is

quite similnr to the procedure found after Fig. 39. :>ee

Ex. 20. This particular usage is shown in Ex. 26. The

melody employs tones in the perfect fifth from ~-flat to

[; the accompaniment, a series with ~-flat as its tonic

center, uses all twelve tones of the chromatic scale.

This combination of scale patters is used until the return

of section~ material in the measure following Fig. 47.

The major climax of the movement, which occurs in

this section from Fig. 46 to 47, makes use of the most com­

plex scale possibile, a complete chromatic series. SLe in-

traduction of the two tones which complete the series oc­

curs in the fifth mensure of Ex. 26. These two tones occur

with their relative half'-steps present at the same time.

(Q with ,!2-flat, ~ with ~-fl.:.:t) This is the focal point of

the climax which has been developing from the begifnning of

section .12•


Page 89: Analisi Dumburton Oaks


In the section from Fig. 47 to 50 the scale used by

the melody and its accompaniment is the same as the sc~lle

found at the beginning of the movement. In this section ~­

flat is substituted for £-sharp in every case, but it does

not alter the sound of any of the lines. The new ele::-.ent,

the flute counterpoint, employs c-::11 twelve tones of the chro­

matic scale based on the tonic (.!}-flat) of the primarJ scale.

See Ex. 27.

The scales found in the linking section are clearly

related. The series based on the D major scale, found ,_~fter

Fig. 50 for three measures, is a repetition and development

of the ll major triad found at the end of the first phrase

group of section !J.• See Ex. 54. This D major aerie;:; .noves

to a similar scale one-half step higher with a tonic center

on ~flat. The insert below shows a comparison of the two

scales, both of which contain eight tones. See Ex. b6.

Eb, F, G.Ab, Bb, c,Db.zD :r ,- /"_,_ - !' .. /'-D, E, Fti,G)', /,;~:f,E, C# ---- ...... --

Except f~the two tones <a-sharp and ~-flat) foreign to the * * basic major pattern, each step of the D scale moves to its

parallel member in the E-flat scale by half step.

The first measure in the new E-flat sco.le occurs

two measures before Fig. 51; the winds continue in the mea-

sure before Fig. 51 in a re-statement of the material found

in the linking section at the end of the first movement.

Page 90: Analisi Dumburton Oaks

The rhythm is altered only slightly in the measure before

Fig. 51; this re-statement occurs on tones a perfect fifth

below the first example, in order to place it in V-I rela­

tion to the last movement in E-flat. In this re-statement

the final chord is supplied with its third; in the earlier

case only the tonic member was present. See Ex. 53.

Again in the second movement the pattern of the

principal notes of the important sections provides an inter­

esting conmination of tones. See insert below:

A B A' la),a~lacac 11.-i~el ,_c(_e,_l ... a~)O-a_'»_tw_icl-9e ... l m ]b-P-F--Ab- · G-- 6b--O· EJ,-P-EJ, - J- J_


The pattern of principal notes from the beginning to section

12 gives a complete }a-flat major-minor seventh chord; the

combination of notes found from section I} through tbe first

portion of the linking material to the third movement gives

a g minor triad; and, finally, the tonic notes founo at the

end of the linking material and the beginning of the third

movement give an empty fifth, §-flat - ]a-flat. This is ano­

ther example of modulation through the enclosed t.hird; the

first tones of these chord series are !a-flat, .Q, and §-flnt.

The beginning of the third movement employs the same

seven-tone E-flat major series which was found at the begin­

ning of the first movement; this series, however, does


Page 91: Analisi Dumburton Oaks

not stress the tonic chord, but the polarity of ~-flut as

the center is established in the b:_iss line. i\s shown in

Ex. 28, a new sc.::::.le on the third (.Q) of the E-flat sc<.:ile

enters in the seventh measure; this sc[de employs tvJO

thirds, two fourths, and two sevenths. In the repetition

of this portion which follows after Fig. 55, this scnle on

~ makes use of two seconds, two thirds, two sixths, :no two

seventh steps of the scale. The doubled fourth of the eCJ.r­

lier section is dropped, and the doubled second and seventh

steps of the scale are added.

In the next scale shift the tonic note of tni3 g

scale is dropped a half-step for the new scale; this new

scale, found in the section after Fig. 56, is the scule

found at the beginning of the movement (E-flat major se­

ries) transposed up a minor third to a G-flat major series.

The melodic and textural content of the G-flat section is

a re-statement of the content of the first seven measures

of Ex. 28, which shows the E·flat section. The scale on

B-flat which follows in the section after Fig. 57 resembles

the scale used in the second portion of Ex. 28.; it con­

tains only two of the variable, or doubled, steps (second

and seventh steps of the B-flat scale after Fig. 57).

The fugal material which follows, as shown in ~x.

29 employs a normal B·flat minor scale with two leading

tones (~-flat, !); this scale continues until the fourth

measure after Fig. 58 where a twelve tone chromatic series


Page 92: Analisi Dumburton Oaks

is employed for two measures~ This chromatic series is en-

ded b.Y the next entrance of' the subject at the end of the

fifth measure after Fig. 58; here the B-:f'lat minor scnle

returns, now employing doubled sixth and seventh steps of

the scale.

In the third measure before Fig. 60 a statement of

the primary motive of the movement occurs which adds .Q-flat

to the B-flat{minor series which has been in use since the

sixth measure after Fig. 58. This new series continues

through the third bar after .r'ig. 60 In the fourth b<:r af­

ter Fig. 60 an eight-tone D-flat major series with doubled

fourths enters after a rest in all parts at the beginning

of the measure; this series was extracted from the ten-tone

B-flat minor series which began three bars before Fig. 60.

It serves as introductory material to the double-scsle usage

found in the section after Fig. 61. See Ex. 31. 1'hese

scales are two different series with the comnon tonic note

of R-flat. The one which presents the fugue subject in aug­

mentation is a IJ-flat major scale with variable fifths;

the accompaniment to this employs a D-flat major scale with

variable second and fourth steps of the scale. These two

scales continue until the second n.~~~sure before Fig. 63.

See Ex. 58. 1\t this point the scales combine, and the two

tones which were missing from both scales (~ and ~) are

added to cre: .. te a complete twelve tone series. In this

case the concentration of scale tones has been built up to


Page 93: Analisi Dumburton Oaks

its highest point; after this the scale series can only be­

come simpler, <:tnd this occurs in the third measure of the

example. A D-flat major series with variable fourths is

established in the lower voices; in the higher voices a pa­

rallel series is found based on A-flat major. These two

scales are so employed in the section after Fig. 63 that a

definite feeling of polytonality results. This movement

from a complete chromatic scale to two scales in a new block

of the form is another example of the connection of scales

with the form of the composition. This change serves here

to break off any further development of the fugue; com­

pletely new material has entered.

In the section which follows this after Fig. 64

the D·flat scale moves to a new scale based on E, and the

A-flat scale moves to a new combination of tones based on

the same tonic note, [1-flat. See Ex. 33. A comparison of

these two scales is given in the insert below:

8 tones

9 tones

The combined scales lack only ~ to be a complete twelve tone

series; this ~ is supplied in the section after Fig. 65.

From Fig. 65 to the fourth measure after Fig. 66

the only elements employed in the texture are two chords:

one is a ~ major triad, and supplies the missing tone in

the previous series; the other is a ~ major triad. Jee Ex.

42. This is the best example of polychord treatment found


Page 94: Analisi Dumburton Oaks

in the composition. The monopoly of .Ufte the triads i.s bro­

ken in the eighth measure of the example by the risin," line

employing the C :naj or scale. , t the end of thd s line the


12 m2j or triad is dropped, and a new chord series <~ppe:::trs,

based on the following tones: ~b, .Qb, !!b, Jab, basicallJ E­

flat minor; the £ major triad continues through this section.

In Ex. 58 the close of this section is shown; n de­

scending scale line leads to the final statement of th~:; theme

in the first setion of the movement. The scales used in this

appearance are the scales of the first section (Ex. 23) trans­

posed up a minor third. "'~t the end of this section (one mea­

sure before Fig. 70) a D-natural is introduced to the 'texture

with its half-step associate, !1-flat, also present; this B·~

leads to the scale of C minor used in section 12·

The members of the C minor series after Fig. 70 are

shown in Ex. 34. The scale of the next section found after

Fig. 7~? hBs the same scale Ds the first transposed dovm to

B-flat. The second section contains the same melodic ele­

ments found in the first, here developed and extended. /,t

the end of this second section the B-flat minor series be­

comes B-flat major. See Ex. 43; the series shown here em­

ploys only five tones: ~b) Q, Q, ~b, E• In the last t'NO

measures of the example there is a shift to two scele pat­

terns in a polytonal relation; one is based on the G m.=-,.ior

scale, <.:.nci the other is based on the & major chord. In

combinat,ion, these two tonalities produce a complete seven-

Page 95: Analisi Dumburton Oaks

tone scale of C major. The third, §, of the C major chord

line moves to ~-flat in the next section after Fig. 74;

this ~-flat is the tonic note of the section which con­

tinues to Fig. 75.

'I'he section after Fig. 75 employs a complete

twelve-tone series based on £i-f'lat. See Ex. 44. The five

measures rerr~ining in the section which continues after

this example employ a twelve-tone series based on !2-fldt,

a fourth higher; the A-flat scale continues in this sec­

tion in a less complex form, as follows: ~b,~9,~b,~,~b,~b,

.[,Qb. The close of this section is shown in Ex. 60; the

modulation over the cadence is to a remote scale;i.e.,

from ~-flat to ~-natural.

Both scales in the section after Fig. 77 are based

on !• There is no apparent relation to anything in previous

portions of the movement, either in a melodic or scalevdse

sense. These scales based on ~ introduce the basic scale of

the section after Fig. 79 which is aD minor series.(see Ex.

60 for .!::. scales.) Here is another case of the melody making

use of one scalt, and ahe accompaniment another scale with

the same tonic in the section after Fig. 79. If the t;Jo

scales are combined the one tone lacking in the eleven-tone

accompaniment &cale (a ~flat) is supplied from the scale

used by the melody. This section ends with an [•shar-p in

the melody line leading to ~ in the next section after Fig.


Page 96: Analisi Dumburton Oaks

81. This g is the third of the scale of ~-flat nwj or which

js used in the next section.

The scale of the section after Fig. 81 employs dou­

bled third scale step in a basic E-flat major series. This

is necessary because of the melodic elements emploJed; the

entire melodic element of Ex. 28, which occurs at the be­

ginning of the movement, is found here. The accompc:;ni:;.ent

is altered in this example, and the scale remains the :Jame

in both of the phrases presented, instead of modulating up

a major third, as in the seventh measure of Ex. 28.

In the measure before Fig. 83 the introduction of

E-flat in association with i-flat a half-step b~low indi­

cates the next scale shift. In the form of the composition

a new development and extension of the previous theme occurs

in this section. See Ex. 45. The introduction of the new

tones (1}-flat and ~) is accomplished by the usual associa­

tion with a relative half-step. The E•flat--~-flat combi­

nation preceding Fig. 83 was actually the first appee:•rance

of ~ in its enharmonic equivalent.

This scale continues in this development of the

theme until Fig. 85; from t.his point on to the end of' the

movement the scale is E-flat major with two seventh steps

of the scale, Q-flat and ll• The final development anct

extension of the primary theme is found in the section from

Jl-.ig. 85 to Fig. 90. /.;fter a brief plagal cadence in ti1e

measure after Fig. 90 (see Ex. 46), this final cadence


Page 97: Analisi Dumburton Oaks

chord is emphasized by repetition <md the composition is

completed. 'I'he V - I relationship of the chord members in

these last two measures hns ::dreo.dy been explained in t.he

cllapted devoted to Cadences.

The ht:::rmonic and scale rel;',tion in the third :nove­

ffit~nt is not of vi tal importance; the element which 'IJvelJs

the movement into a whole is the rhythmic drive founct ir,.

the develol)ment of material from section fl· ':'his is .:ds­

cus,ed in the section concerned. with meter and rhyth.m.


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The melodies found in the Concerto will be considered

from three general classifications: 1. the method of line

construction; 2. type of intervallic motion, that is, either

conjunct or disjunct; and 3. the general tendency of the line

to remein neutral, or to move upward or downward. Cnder the

first of these, method of line construction, five types of

melodies will be considered, as follows:

1. melodies built on the repetition of a figure

2. melodies built on the repetition of un interv:..tl

3. melodies built on a chord.:.,l outline

4. r.hythmic melodies (monotonal, chant-like)

5. melodies that are not built on any specific in­

tervals, figures, etc., but may be developed from figures,

or motives.

The closing portion of this section on ::lelody will

consist of a discussion of Stravinsky's method of achieving

a musical climax.

,Melodies built .sm ~ J,iter~J. r.,e.Qe~ition .2t, 1a ;(ig\are

The melody in the violins shown in Ex. 2 is composed

of three repetitions of the primDry motive t in a combincltion


Page 99: Analisi Dumburton Oaks

of conjunct and disjunct motion. The line direction is


The melody in the violas in Ex. 17 is bused on a

repetition of the first two measures, and also the repeti­

tion within these two measures of the minor second figure,

fl-~l-t1 • The first four measures are disjunct in motion

and the line direction is neutral. In the last three mea-

sures the line is disjunct: the line tends to rise in the

fifth meusure, but returns to its original center; in the

sixth measure the line tends downward, but reverses itself

in the seventh measure in a leap of a tenth upwdrd, and once

again returns to its original center.

In Ex. 28 the melody of the first phrase (lst meG­

sure through the 7th measure) is based on the repetition of

a figure which revolves around !!-flat. The pattern of the

upper neighboring tone, followed by the lower neighboring

tone (after the return to ~-flat) is repeated twice in this

phrase. The motion of the line is conjunct, and the line

direction is neutral.

The fugue subject shown in Ex. 29 is derived from

two repetitions of the first part of the main theme. It is

conjunct in its motion, and the line direction is basically

neutral in the first portion; in the second portion the

leap of a seventh is to be considered a conjunct inversion

o:f the scalewise minor second (Therefore, the second rortion

is also conjunct in its motion, with the line having a


Page 100: Analisi Dumburton Oaks

downward tendency at its close).

In Ex, 32 the melody is built on the repetition of

E,n altered form of the main subject of the movement. The

1notion is disjunct; in one statement the motion is upward

a r~jor second, then down a major third, down a minor se­

cond, and returning upward a minor third. The tendency is

to return to the ~-flat.

In the first and second measures of Ex. 44, the me­

lody is built on the repetition of a stepwise movement down­

ward on scale tones. In the fourth and fifth measures the

same thing occurs in an upward direction. If the repeated

notes are disregarded, the line is conjunct in itL; motion

in both of its sections.

Melodies built 2n ~ ~~teral repetition 2i ~ interval

The flute line in Ex, 6 is a repetition of the in­

terval of the minor second from sl to ~-flatl, At the end

of the first measure the line makes its only leap, up a

perfect fifth. It drops back a minor sixth to repeat the

figure from the beginning. The minor second is spre<-1d to a

ro~jor second at the end of the second measure, and continues

in a similar manner. The line tendency is neutral.

The clarinet line in Ex. 20 is based on the repe­

tition of the interval of a minor second, specifically

in a rising chromatic line. The motion is conjunct.


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iLelodies bQil!t .Q.!l _s cbord

Ex. 1 includes numerous melodic elements b8sed on

chords. The flute line of th~ second measure outlines the

~-flat major chord, in a combination of conJunct and dis­

junct motion with neutral direction until the close, which

moves downward from ~-flat3 to t2• The viola line in the

first measure emphasizes the ~flat major chord by the use

of each chord tone in combination with its lower· neighbor.

The motion is conjunct and disjunct, and the liae direction

is downward.

In Ex. 40 the chordal ostinato descends on tones of

the ~-flat major chord. The line is a combination of con­

junct and disjunct motion.

In Ex. 18 the melody is built on a 12 minor chord

with the added tones ~flat and ~·· The motion is disjunct,

and the line direction is generc:,lly downwctrd.


In Ex. 21 the flute outlines two chords in two ranges

at the same time; one is ~b, ~, .§b in a series ana the other

is a Q, !!, Q, Q series. The motion is disjunct, und the line

direction is upward at first, and then down.

;\ll of the ostinato melodies shown in Ex. 42 are

built on chords. f.1otion in the & major triads is con,_iunct

and disjunct;ynotion in the ~ major triad is conjunct .:.md

disjunct, also. The £ major triad material tends to rise,

and the~ major triad remains in the same range.

Page 102: Analisi Dumburton Oaks

Rhythmic melogiee

In Ex. 33 both outer parts (on § and £2) are static

melodies. The motion of the line exists only in the dif­

fering lengths given to the melody tones.

r.lelqgies geriveg ~ figure§. .Qr. motiv~s

The melody of Ex. 6 is actually two forms of the

primary motive used in succession. The motion is disjunct,

and the line moves upward.

The fugue subject from the first movement, shown

in Ex. 10, is derived from two forms of the primary motive.

Ihe motion is disjunct, and the tendency of the line is

neutral in the first two measures; the line moves downward

in the last two measures.

The subject of section ~ in the third movement is

derived from the £ minor scale line. See Ex. 34. The line

is conjunct in the first two measures, and disjunct in the

third and fourth. The tendency of the line is upward in

the first portion, and downward in the second part.

'I'he melody found in Ex. 36, from the theme of sec­

tion Q in the third movement, is derived from thematic ele­

ments found in the section immediately preceding it. The

motion is disjunct, and the line direction is neutral.

The melody found in Ex. 45 is the final development

of the basic thematic material of the third movement. The

motion is conjunct for eight measures, and the tendency of

the line is to move upward.


Page 103: Analisi Dumburton Oaks


t!:ethods .2! achieving .sa <climax

In achieving a musical climnx, Stravinsky seldom

makes use of his melodic line; the climaxes are achieved

by use of the following special effects:

1. Repetition of the final measures of a melody;

repetition of a motive or chord. (End of the third move­

ment. Ex. 61)

2. Use of an ascending scale line independent of

the melodic line. (Ex. 58, 2 before Fig. 63, bottom line

scale; also Ex. 42, ostina.to section)

3. By sequential use of an idea. (Ex. 42)

4. By deliberate dynamic contrast. (Two examples

continuous, cr~scen4o to piano subito: Exs. ll and 12)

Meter swg RhVtbm

In the Concerto numerous changes of the metric in­

dication occur. These changes are usually in relation to

the large sections in the first and third movements. In

the second movement, the only metric changes are found in

the linking sections before section ~ and at the close of

the movement. In all three movements the time vulue 2llot­

ted to a note remains constant as long as the particular

metronome indication for thDt section is in effect.

In the first section of the first movement (Begin­

ning to Fig. 7) the meter indication is changed twenty­

eight times, and involves seven different signatures, as


Page 104: Analisi Dumburton Oaks

follows: 4/4, 3/4, 2/4, 3/8, 2/8 1 7/164 5/16. The section

consists of forty measures.


From Fig. 7 to Fig. 11, the contrasting section of

the first movement, only two signatures are used and these

are 3/4 and 2/4. In the twenty-five measures which comprise

this section, the signature is changed four times.

From Fig. 11 to Fig. 20, the section containing the

fugue of the first movement, the meter indication is cho.nged

forty times in this passage consisting of sixty-two measures.

Jix different time signatures are used, and these are 4/4,

3/4, 2/4, 5/8, 4/8, and 3/8.

The return of material from the first section, found

from Fig. 20 to Fig. 25, also employs seven different time

signatures, as follows: 3/4, 2/4, 3/8, 2/8, 11/16 1 9/16,

7/16. This is no1the same series of signatures found in the

first section, however; the 4/4 and 5/16 signatures ure

dropped, and 11/16 and 9/16 are added. In the twenty-three

measures comprising this section, the metric indication is

clwnged sixteen times.

In the Coda from. Fig. 25 to Fig. 28, two time signa­

tures are used, 4/8 and 3/8. /:.ctually, the two 4/8 bars

are found to consist of a 3/8 bur plus an eighth rest, the

only two rests found in the section. In the 19 measures of

this section, there are threetime changes involving these

two signatures.

The linking material at the end of the first !aove­

rnent is in 6/8 time throughout its eight measures from Fig.

Page 105: Analisi Dumburton Oaks

28 to Fig. 29. 'I'he relation of this passage to the previ­

ous one will be discussed later in the section devoted to

note values.


The second movement uses onl.J one signature in the

main portions of the movement, and this signature is 3/8.

The only changes of signature occur in the linki!l£ sections.

See Ex, 55 and Ex. 56. In these examples, the sign .tures

6/8 and 9/8 are employed, and contain, the same factors

found in the linking section at the end of the first Elove­

ment wlich will be discussed later.

In the third movement once ag.;;in\there is a compli­

cated series of signatures used, ~~nd a~:c.·in no more thc:m

seven different indications are found in any one section.

The first section from Fig. 52 to Fig. 70 contains the 011-

ly series of seven signatures four:;.d; these are 3/2, 2/~:',

7/4, 5/4,4/4,3/4, and 2/4. In the 102 mea~ures which m:;ke

up the first section ~ in Graph II, sixty-four changes of

time signatures accur.

In the slower tempo of section~ (Fig. 70-74),

there are only two different time signatures used (5/4 and

4/4). The basic signature of this section of twenty-four

measures is 4/4. In the second measure from the last in

the section the only appearance of the 5/4 signature occurs;

the last measure is ag:.5n in 4/4 time.

The next return of section~ (Fig. 74-77) employs

three different signatures; 5/4, 4/4, and 3/4. 'Ihe section

Page 106: Analisi Dumburton Oaks

consists of twenty-six measures if the repeated section is

included twice. 'Ihere are fifteen changes of signature, if

this repeat is counted.


In section £ of Graph II (Fig. 77-81) two different

time signatures are used (5/4 and 4/4). The only occurrence

of 5/4 is in the first measure, which is actually a 4/4 bar

plus the one beat rest which separates it from the previous

section !;;; material, This section is eighteen measures in


The final return of section ! in the movement is

from J?ig. 81 to Fig. 83; in this section only two signatur·es

are found (4/4 and 2/4); however, the ten measures of the

section contain six changes of time signature.

The Coda of Graph II is actually an extension nnd

development of section ~ material; its time signatures con­

sist in a new series, five in number: 3/2,5/4,4/4,3/4,2/4.

The one measure emp~ing the first signature, 3/2, is con­

ducted in six, giving a signature of 6/4; therefore, every

type of conductor's beat from two to six per measure is em­

ployed in this section. The fifty-eight measures of the

Coda, with the repeated section counted twice, include

thirty-seven changes of time signatures.

In this work there is no indication in the score

for any use of free rhythml; however, Stravinsky makes G

lJ\ccording to Willi Apel, two types of free rhythm exist. "Free rhythm, i.e., the use of temporary values which have no co~Tion metrical unit (beat) •••• Free rhythm is also 3Ctu­ally present whenever a striking deviation from strict rhythm is demanded, e.g., by rallentando 1 accelerando, rube:• to." Cf. article "Rhythm," II, c, Harvard Dictionarv £1. Music, ed Willi ilpel, (C8mbridge 1 Mass.: Harvard University ~'ress, 1945).

Page 107: Analisi Dumburton Oaks

definite tempo change in the third movement in his recor-

ding of the work. This tempo change occurs in the six-mea­

sure section after Fig. 60 which leads to the final section

of the fugue after Fig. 61. The beat employed in this sec­

tion is slower than that of both the section preceding and


the section which follows; this is done, apparently, to give

added emphasis to the last section of the ft~ue, which follows

immediately in the original tempo (after Fig. 61).

The division of the basic unit ( J) in the first

movement is by multiples of two, the smallest note vulue

being a sixteenth note. There is but one exception, the

thirty-second-note triplet figure which is confined to the

closing portion of the first section of the movement. See

Ex. 5. The general rhythmic effect of the first movement

is one of flexibility; many sections employ combinations of

tied notes which emphasize the off-beats of the measure.

The linking section at the end of the first move­

ment (Fig. 28) is also typical of the linking material found

in the second movement; the 6/8 tempo indication used has

the effect of slowing the tempo of the previous section by

exactly one-half. In the section preceding Fig. 28, the

beat is subdivided, but the basic unit is felt to be u J ; in the section following Fig. 28, three subdivisions of

the previous beat, the unit (J·), become the main beat.

In the third measure of this linking section, a figure which

is described as a dyplet occurs. (The duplet is a group of

two notes to be played in the time of three). By use of

Page 108: Analisi Dumburton Oaks

this figure in a 6/8 section, Stravinsky avoids the trip­

let subdivision of the main beat, and also achieves o slow­

ing of the tempo in an exact relation to the preceding sec­

tion. See Ex. 56, first measure, for an example of the use

of this duplet figure in tl!e linking material of the second



In the second movement the basic unit (.r) is again

divided by multiples of two, the smallest division being

thirty-second notes; there are two exceptions to this, how­

ever. Ex. 54 shows a thirty-second-note triplet figure in

the time allotted to one sixteenth; this is similar to the

rapid triplet of the first movement shown in Ex. 5. 'I'he o­

ther use is found in the applicntion of the quintolet in the

ascending line shown in Ex. 24; this is the use of a five­

note figure in a beat which normally includes only tvvo six­

teenths. 'This five-note figure first Bppears as the repe­

tition of a single tone in theme s of section ~. This is

found in the sections after Figs. 34 and 37. See Ex. 19.

It is found again in the flute line (Examples 21 end ~~2)

in theme g of section ~·

This movement has very little emphasis on the off­

beats; the main beat is usually stressed by an upbeDt figure.

An example of this is found in the first measure of the move­

ment. See Ex. 17. The off-beat is stressed by accents in

two places; i.e., the clarinet line in the sections follow­

ing Figs. 34 and 37. See Ex. 19. The general effect of the

Page 109: Analisi Dumburton Oaks

:ovement is one of flexibility with the use of a minimum

of rhythmic figures; the sixteenth followed by tv-Jo thirty­

seconds, · 'nd the reverse of this; the dotted sixteenth nnd

a thirty-second note; two sixteenths; and four thirty- se­

cond notes are the patterns used throughout the movement.

The basic unit (J) of the third movement is found

subdivided by multiples of two. The section from Fig. 52

to Fig. 66 employs, as its smallest subdivision, onl~" eighth

notes. 3ee ostinato Ex. 42. In the fourth measure of the

example, sixteenth notes in an even pattern are introduced

for the first time; the sixteenths are discontinued in the

texture aftGr the descending scale shown in Ex. 59.


'I'he slower section (,!2J makes use of sixteent)ls in

both the melody and accompaniment. The patterns are not

obtrusivef they occur either as a group of four, or an eighth

followed by tv1o sixteenths. See Ex. 34. The onl.'/ apr.-earance

of the quintolet in this movement occurs in this section in

the two meCtsures before Fig. 72; this figure taken part in

the modulcttion from C minor to B-flat minor, the scdle used

in the section after Fig. 72.

The return of section h. after Fig. 74 doe.s not u1, .ke

any use of sixteenths; the eigl:lth note once ag<::in is the

snudlest subdivision of the be~;t.

'I'he final use of sixteenths in the third mov::cment

is in the rising scole line which is found at the end of

section £ (one mec:1sure before Fig. 81).

Page 110: Analisi Dumburton Oaks


The general effect of this movement is one of motion

toward the fin<:>.l cc:~dence; it is slowed somewrwt by the Pogo

~ (section 12,), but it returns quickly to its oricinal

style. 'I'he section £ materiC~l, which is be., sed on a ~iffer-

ent scale, tends to stem the forward motion for ::~ sbort

while, but the return of section A materi<.::.l etfter· I-'ig. 81

marks the beginning of a direct rhythmic treatment le.otding

to the final c~dence.

::>travinsky uses many rhythmic devices to o.voi~ .~~unre

phrc::.se construction (two or four me,,surej. One of u~ese is

the use of' extension, as shown in the first movement in the

long dominant from Fig. 11 to 13. In another case he will

shift I-~is accent from a strong to a weak be<:'it, as found in

the clarinet line after :i;'igs. 34 and 37. See Ex. 19. This

is also found in the two measure.Sbefore l',ig. 11. .~·ee Ex. 49.

These metLods tend to throw the rhytr..m off center for "-' short

_;)eriod of time.

In certain places in the Concerto, .Jtravinsk..,· 1mkes

use of polyrhyth.mt In speaking of this term, "'pel inuic;.:.tes

that n. • • • a distinction can be .;..1cde between two types of

polyrhyth.m; contrasting rhythms within the same scheme of

1Polyrhytrun may be defined as "the simultaneous use of stri­kingly contrasting rhytr.uns in different parts of the musicc:tl fabric, e1lso known as cross-rhythm." C11. Harvard .;Qi9tionary, P• 593.

Page 111: Analisi Dumburton Oaks

3Ccents (meter); contrasting rr~thms involving a conflict

of meter or accents. The latter type is sometimes tE:;rmed

t pOlymetriC I ul

Stravinsky's use of polyrhythm is mainly of the

polymetric type. Two examples of polyrhyth:n of this tJpe

deserve to be mentioned here. :::>ee Examples 40 and 4".

1------· Ila;ryard Dictionarv, P• 593.


Page 112: Analisi Dumburton Oaks



The outstnnding element of the Dumbarton Oaks Con­

certo is the economy of materials used in the develor::-aent

of the work. The first movement was based on one pri;:;ar J

motive which was found in all sections of the movement in

one form or another. This motive was also discovered as

an additional element in the last. two movements and cerves

to tie all three more closely together. The second J~lOve­

ment, of strikingly different character, also had one the­

matic element of importance; this wus found in the tv,o out­

er sections (i;!). Its middle section (Ja) contained tLe only

references in this movement to the primary motive of the

first movement. In the third movement section f:: returns

after each of the two digressions; the movement depends on

the rhythlnic impetus found in the ::~e 11 sections to cc1r·r J the

feeling of continual movement towara a cadence through

its contr~isting sections (Ja and ~).

The progression. from one idea to the next is accom-

plished in the cadential movement by the discovery of 3ome

tonul rel&tionship between the two ideas. ;·m enharr::1onic

equi v&lent or the extension of a scale line into the next


Page 113: Analisi Dumburton Oaks


idea, for example, provide smooth links and good continuity

of material. The cadences between the movements are con­

structed to connect one with the other in an harmonic relc:­

tion. 'l'he fine1l cadence is the only one which is conclusive;

however, this cadence includes the only reference in the

third movement to the motive of the first movement. l.'his

could be an indication that the piece was constructed in a

full circle with the final chord as the introduction to the

first part in a re-hearing of the work.

The rhythmic and literal ostinati are found in the

first and third movements; the second movement makes conti­

nuous use of literal and pedsl ostinati, with only one use

of rhythmic ostinato, in only the ~ section of the movement.

The tempo changes in this work are few, but the me­

tric change is an integral part of the composition in the

first and third movements. The only use of' a tempo wLich

is not in relation to anything else is heard in the rer0on­

al recording by Stravinsky. There is no indication for

this in the score.

Rhythmically, the work is quite clear for this rerl­

son; the infrequent use of polyrhythm stands out all tl1e

more plainly in relation to the other sections.

The derivation of the melodies in this work is from

simple motives or fragments; however, the melodies found

often betr::1y a richness wb.ich is surprising in viev: of the

economy of materials used.

Page 114: Analisi Dumburton Oaks

Since the harmony of the composition is secondary

to the linear development of material, the series or scale

becomes the most important harmonic element. All lines

seem to have some melodic importance; even obvious ~ccompa-

niments have their own direction and melodic interest.

The analysis of the style of this work in relation

to the music of the present day is given by Ingolf Dahl in

these words:

The affinity of contemporary music to the es­thetics and techniques of the baroque period in music has often been noted. The baroque orchestra (Concer­to Grosso) in particular, with its flexibility of in­strumentation, its chamber music texture! its cleun divisions into passages for "tutti" {f'ul ensemble) and "solo" (individual instrumental groups), its ob­jectivity of expression and unified dynamic levels are reflected by our jazz bands and our radio orche­stras as well as by a large number of' contemporary concert works. "Dumbarton Oaks," differing in sever­al ways from the 18th century prototype, could best be called a oor\raii ~ ~ Concerto Qrosso, painted by a modern artist.

lNotes on the recording of the Concerto.


Page 115: Analisi Dumburton Oaks


Books ~ Stravinskx

[:itravinsky 1 Igor. Chronicles. ,g! ~ ~. Go~1ancz, Ltd., 1936

London: Victor

3travinsk.y, Igor, Poetf{~ ~ Musig. Trans, by .Arthur Xhodel, Ingolf' a 1. Cambridge, Iifass.: Harvard University Press, 1947.

Books about Strayinsty

Tansman, Alexandre • ~ l3:ttrayin§k,y : Ill!i. Msn and £!.1& ~. Trans. Therese and Charles B1eefield. ~ork: G. P. Putnam's Sons, 1949.

White, Eric Walter. Strayinak;y: £!i.a ~ JiW-9. Work. New York: Philosophical Library, 1948.

Gengra;L Sources

J.pel, Willi. Harvard Dict!gnary .Q! Music. Cambridge, IV'.tass.: Harvard University Press, 1948.

Hull, 11., Eaglefield. Mpde;:n ijarmonv• London: Augener, Ltd,, 1915.

McHose, Allen Irvine. ~ Contrapuntal Harmonic Teghnique 2! lbi la1h ~entutY• New York: F. s. Crofts and Co., 1947

Prout, Ebenezer. Fugal Ana;J,ysia. London: Augener Ltd., 1892

Slonimsky, Nicolas. Music Siooe le.QQ.. New York: Norton, 1937.