A Thesis: Presented in Partial Fulfillment of the Requirements for the Degree Master of Arts

DETAILED ANALYSIS OF THE FIRST MOVEMENT OF BARTOK' S MUSIC FOR STRING INSTRUMENTS PERCUSSION AND CELESTA

by Richard Adrian Simons, B.S.: B.M. •I The Ohio State University 1962:

Approved by

·"''""~..... -~· ... M .....• dviser Department of Music TABLE OF CONTENTS

Chapter Page I. INTRODUCTION • • • • • • • • ...... 1 Purpose of the Thesis Types of Analyses Involved Special Terms and Definitions Organization of the Thesis II. FORM ••••• ...... 10 The Larger Structure of the First Movement Structural Elements 1. Tonal considerations 2. Dynamics 3. Tension degrees

III. COMPOSITIONAL MATERIALS • • • • • • • • • • • Melodic Materials 1. The Subject 2. Associated Melodic Materials 3. Additional Melodic Materials Rhythmic Materials 1 • Rhythmic Fl ow 2. Meter and Tempo

IV. COMPOSITIONAL TECHNIQUES • • • • • • • • • • 57 Combining of Melodic Materials 1. Strettos 2. Imitation 3. Melodic Mirroring 4. Free Counterpoint 5. Vertical Sonorities Compositional Devices 1. Melodic Inversion 2. Retrograde 3. Augmentation and diminution Orchestrational Technique

ii Page v. SUMMARY • • • • • • • • • • • • 111

BI BLI 0 GRAPHY. • • • • • 116

iii an antiphonal string orchestra, it is scored for the following instruments to be arranged in the approximate position of the following diagram.

C.B. I C.B. II Vel.I Timpani Bass Drum Vcl.II Vla.I Side Drums Cymbals Vla.II Vln.II Celesta Xylophone Vln.IV Vln.I Pianoforte Harp Vln.III

Conductor

Throughout the first movement, with very few exceptions, only the string instruments are used. There is no attempt in this movement to exploit the possibil ities of antiphonal writing. The strings usually play together in the following combinations: first and second violas, first and second violoncellos, first and second contrabasses, third and fourth violins, second violins, and first violins. The most notable exception to this grouping is in measures seventy-three through eighty-one where the first and second violas and third and fourth violins each have individual lines. On several occassions the first and second violins are combined. The first movement is an intricately organized fugue. It is a movement of almost unparalled concentration; its six and a half minutes represent a single cres-

2 cendo to a climax and a subsequent falling away to silence. It displays a unanimity which is equaled in the work of no other composer; And which Bartok himself achieved only in the Fourth String Quartet.1

Types of &nalysis Involved

An analysis is the resolution of a complex struc ture into its elements. In artistic products (liter ature, painting, music) analysis is the critical exami nation of the product so as to exhibit its elements in simple form. So the analysis of the complex musical work undertaken here must be a compilation and evaluation of smaller musical units each dealing with a single facet of the total composition. Each of these smaller units are necessary and indispensable in themselves for it is the comprehension of these smaller units that provides the basis for a fuller understanding of the composition. The reader should be reminded that the formal analysis of this thesis can impart only a limited number of the factors necessary for a thorough. understanding. The analytical discussion in this thesis may appear .to neglect aural analysis, which in all musical analysis must be the final arbiter. The data included in this paper is intend ed as an outline and a detailing of particular composit-

lffalsey Stev~ns, The Life and Music of Bela Bartok (New York: Oxford Uiiiversity Press, 1953), p .. 273 .. ional units. The reader is therefore advised to use this thesis as a guide to aid the ear in the abstraction of significant structural events in the composition. The reader's understanding of this composition will be en hanced by the employment of the two procedures discussed above, that is the comprehension of the compositional units (formal analysis) and the experience of these elements in tonal context (aural analysis). The analytical devices employed in thiE thesis may be divided into two categories~that of description, a detailing of what happens without arty endeavor to explain why; and prescription, which endeavors to offer an explanation of why the music was composed as it was. Both of these processes are vital in their own way. Description need not be as superficial as it may some times appear to be, it involves a det~iled understanding of both the large and the small structural and composit ional units. It is through these descriptive processes that the analyst becomes aware of prescription; the reasons why certain events occur. Descriptive analysis is primarily concerned with the examination of the physical aspects of the music such as tonal centers and tonal development, structural units, (both large and small), dynamics, tensions, com positional devices, methods of combining the parts, and often employs tables, charts and graphs. As the examin- 4 ation becomes more detailed many of these items begin to overlap the prescriptive properties of analysis.

Definitions of Special Terms

In an analysis of a twentieth century composition it occasionally becomes necessary to find new terms to deal with the specialized problems involved in accurately describing specific structural or compositional techniques. Such terms as stretto, fugue, episode, subject, countersubject, and coda retain the same structural implications they have in classical terminology. The adopting of new terminology has, as much as possible, been kept to a min- _ imum in this thesis. Several terms used throughout this analysis may not be immediately familiar or clear in their application. In order to avoide any possible confusion they are defined in the following list. Arch-form: A symmetrical architectonic device which balances structurally related sections or movements symmetrically around a contrasting center section. The following diagrams and discussions are examples of Bartok's application of this device. The Fourth String Quartet: The quartet consists of five movements which are organized in a pattern one could conveniently des cribe as an "arch". The first and fifth movements are thematically connected and so are the second 5 and fourth, while the third, a slow movement, stands in the center of the scheme. Symmetry also exists in key-relationship between movements: the fi~t and last movements lfnd also the third movemen~ are in the central key of C, the second is a major third lower, in A-flat. The two fast movements flanking the central Lento are effective virtuoso piecea.

Ii 111 iii ivI v Allegro Prestissimo Non Troppo Allegretto A'.llegro con sordino lento pizzicato molto The symmetrical planning, the constructional de vices of the Fourth String guartet are even further developed in the fifth. The disposition of the five movements here follows the same n:arch": pattern, only with reversed characters: the central movement here is a Scherzo, flanked by two slow movements:

Ii iii v Allegro Adagio molto Scherzo .&ndante Finale

Architectonic ideas, symmetrical patt~rns are conspicuous throughout the whole work.

Item: This term is applied to the various motives or phrases of the subject. There are four 'Items' in the complete subject.

2~1a Bart6k, A Memorial Review (New York: Boosey & Hawkes, 1956), pp.30-31.

6 Item I -Item II Item III

Item IV

Mirroring: Mirroring may be of two types, ver tical or horizontal. It is a device by which a composer may reverse an idea against itself. Vertical mirroring of a unit will result in its intervallic inversion. Horizontal mirroring of a unit will result in its retro grade form. .Although. material resulting from either form of mirroring may be used compositionally at any time, the term will be applied particularly where the mirrored part is simultaneously sounded against its original form.

Meas. 86-88 Vlns.1&2

7 Original: The original, or basically unaltered version of an idea is used when referring to a non-inverted statement. Prime interval generator: a series of four notes common to all of the four subject items. This grouping of notes is the "germinal" element of the movement.

'13

(This is discussed in detail on p.!µ.)

Octave indications: The following system will be employed throughout this paper. All chromatic tones within the octave above the indicated C will use the same characters but will be given their letter names.

i(VtL. ·------~

cc c c c ' c. ' ' c ' ' ' contra great 'small first second octave third octave octave octave octave octave

8 Spread:: Spread is the vertical distance between two parts, usually used when referring to the outer most parts. Tritone: The interval of either a diminished fifth or an augmented fourth.

Organization of the Thesis

The first chapter of the thesis surveys the architectural design of the movement. It extracts the form of a fugue from the music, then proceeds to discuss the form and its component elements. The second chapter deals with an examination of the compositional units employed. The primary concern of this chapter is an in vestigation of the melodic and rhythmic materials, and the vertical sonorities of the music. This examination involves the dissection of these compositional materials into their smallest integral units. The following chapter probes the composer's methods of combining these materials to create an integrated art-form. It also considers the use of "mechanical" compositional devices, such as diminution, augmentation, mirroring, and other contrapuntal techniques in the manipulation of the musical elements.

9 CHAPTER II

FORM

The Larger Structure of the First Movement

The first movement, marked Andante tranquillo, i':ca.116-112, is cast in the form of an ingeniously organized fugue. The term fugue is used, not in the sense of a specific stylized formal structure but rath er, as a general term which may be applied to a composi tion possessing the basic characteristics of a fugal texture. "The question may well be raised whether there really exists such a thing as the 'form of the fugue,' and whether it would not be more proper to speak of n3 'fugal procedure' rather than 'fugal form'. To be sure, Bartok'sI treatment of the fugue differs from Cherubini's or Bach's but essentially the same structural features apparent in the fugues of earlier composers are present in Bartok'sI work. It is written in a contrapuntal style, i.e. in a texture con sisting of a given number of individual melodic lines. It is constructed from a short melody called the subject

3w111i Apel, Harvard Dictionary of Music (Cambridge, Massachusetts: Harvard Univers!ty Press, 1953), p.286. 10 which is stated as a solo at the beginning of the com position. The subject statement is then taken up in the entries of subsequent voices until each of the voices has stated the subject one time. The section where the theme appears once in each part is called the exposition. In the Music for String Instruments Percussion and Celesta there are five statements of the theme at vary ing pitch levels during the exposition. Because of these five subject entries and because of the texture of the rest of the movement, this work will be regarded as a five-voice fugue. Although much of the fugue is a four, three, or even two-voice texture, the mere fact that all five voices are not present at all times, in no way refutes the allegation that it is essentially a five-voice fugue. _The exposition is followed by a section that contains no subject statement and is called an episode. There are also several stretti (overlapping of subject statements). All of the above factors, essential to fugal writing, are present in the first movement. Bartok," like Bach, treated the fugue with considerable freedom, more as a manner of conposing than as a formal mold. The first movement is eighty-eight measures in length, requiring approximately six and one-half minutes for its performance. Throughout the movement the eighth 11 note provides the basic pulse unit with the phrasing of the subject material determining the meters of the individual measures. Architecturally the fugue contains many of the symmetrical elements of the arch-form frequently found in Ba.rtok'sI compositions. This symmetrical balance is the basis of the entire structural framework of the Music for String Instruments Percussion and Celesta. Some of the applications of this structural form in the fugue may be seen in the diagram on the following page.

12 dynamics: pp p mp f ff f ff f mf p p pp PPP ------l a r#-c eH t#-c a

Subject Stretto Climax Stretto Subject statements complete incomplete incomplete complete statments subject subject subject subject I-' w I I

con sordino senza sordino con sordino The melodic organization of the fugue is based on a subject constructed predominatly from minor seconds and augmented seconds. The subject contains four re lated motivic Items and a tonal structure that progresses concurrently through two series of perfect fifths. Both series of fifths begin with an initial statement of the subject on~· This seatement is scored for muted violas. The initial subject statement is followed immediately by a repetition of the subject a perfect fifth higher on ~'1 This second statement is scored for muted third and fourth violins. Four bars later at the same relative point to the second entry as the second entry was to the initial statement, the subject makes its third appearance on ~ a perfect fifth below the first statement. The fourth entry, by the muted second violins on £ ' (a perfect fifth above the second entry) and the fifth entry by the contrabass on ~ (a perfect fifth below the third entry) follow the same rhythmic relationships as did the first three statements. These first five entries complete the exposition and set the pattern of tonal expansion by two parts moving simultaneously in opposite directions around the circle of fifths from ~· This pattern establishes the tonal framework of the movement. The following diagram represents the organization of this tonal structure.

14 0

~ ~ H Hm m A A H H ~ ~ A ~ 0 ~ ~ <

4Hurnphrey Searle, Twentieth Century Counterpoint (London: Williams and Norgate, ll954] J, p.48. In the following diagram the outside ring repre sents the tonal progression of the lower part while the inner ring represents the tonal progression of the upper part. Both the upper and lower series begin on a and progress in opposite directions around the circle of fifths. The exposition employs the tonal centers of ~,

~·,and b 1 in the upper part, and~'~' and Gin the lower part. The next key-centers in the sequence are f#, and c. These keys occur at the one-fourth and three fourths points in the progression through the circle of fifths. They also represent the half way points from the beginning to the climax and from the climax to the ends fl and c are the tonal centers of the two principle stretto sections. These tonal centers of the two sections form the interval relationship of a tritone to one another. Both parts continue in their respective di rections until they reach the tonal center of eb, or its enharmonic equivalent d#• The eb-~ section is the climax of the movement. It lies half way around the circle of fifths from its beginning point on~· The relationship of the eb climax section with the ~ tonal ity of the movement is that of a tritone.

16 Ou~e.F ring = lower part Inner ring = upper part

Finish

Start

Important. stretto tonal centers

Climax

17 These diagrams appear to be mechanical, but var iation in the treatment of subject entries eliminates any possibility of monotony, or immediate awareness of this obvious structure. Some of the entries may be found in augmentation, fragmentation or some other alteration effected by the use of compositional devices. The exposition develops not only by the tonal pattern of ascending and descending perfect fifths and an expansion between the parts, but also by an increase in the density of the vertical texture and an amplifi cation of the dynamics effected by louder dynamic indications and the addition of more instruments. The first movement is constructed almost entirely from material directly derived from the subject. The subject itself may be found, in some form, in all except six measures of the fugue. The only time the listener is afforded any relief from the subject is between bars 21-27 where the predominant melodic motion is in fourths. This section serves as an episode between the fifth state ment of the subject by the muted contrabasses (on G) and the subsequent stretto section. This six measure episode is placed half-way between the first statement and the climax. Only here does Bartok/. permit the auditor relief from the driving, climbing impetus of a fugue whose subject is, except for these six measures, omni- present. For the duration of the movement, with its 18 relentless climb to the climax in measure 56 and the sub sequent descent to a tranquil piano-pianissimo ending,

the subjec.t is always v~i th us; too dynamic to re st un til it returns to the place of its origin, a simple piano-pianissimo, on a. The episode is followed by the first stretto. Here the subject continues to expand outward with an t# statement, un the first and second violins in octaves, in stretto with a _£ statement played by the v:toloncellos and contrabasses, also in octaves. Both this stretto and a later one at bar 65 are at the interval of a tri tone; an interval which proves to be very important both in the structure of the fugue and in the subse quent movements of the work. (See diagr&m on p.17 and discussion on p.31.) Evidence of the arch-form discussed earlier in this chapter may be found in the two stretto sections of the fugue. These strettos, which prepare and re lieve the climax of the movement, have marked structur al and tonal similarities. After the first stretto section there is a slight ly altered statement of the subject on eb by the violon cellos and contrabasses. Items I and II are altered by the substitution of a tritone in place of the initial minor second. The subject is also extended by repeti tion of each Item before the next Item is introduced.

. t\.J. C\l --' I '° ~.. "' >- >--- \ >-

----- ~------·~------

21 In measure 52, the sequential bass pattern reaches a' with a dynamic level of fortissimo. This a ' is present in all parts and is sustained throughout most of the measure. It is reenforced in measure 53 by a crescendo roll on A in the tympani. This strong ! sound is combined with a sustained d in the third and fourth 1violins and violas, and a descending chromatic line in which the violoncellos and contrabasses are moving in parallel tritones with the descending double-stopped notes of the third and fourth violins. The two pedal tones of

!. and ~ serve respectively as the quasi-dominant and the leading-tone of the fortissimo eb chord in measure 56 which is the climax of the movement.

The climax is reached at bar 56. It is achieved in part by the tonal relationship of eb to ~, and is prepared and supported by an increase in tempo from J'. 116-112 toJ': ca.120-116 and by an increase in dy namics (measure 53). In measure 56, the music reaches its highest dynamic level of forte-fortissimo as well as a vertical spread of almost five octaves. The dynamic level has increased from a muted pianissimo beginning, that gradually increased in intensity to this peak at measures 56 and 57 after which it constantly decreases until it closes on a unison ~', muted piano-pianissimo. The vertical spread develops in a similar manner begin ning on ~ and increasing until at measure 56 we find the greatest spread in the movement encompassing fifty-eight semitones (four octaves and a major seventh). After this peak, the spread, like the dynamics, reverses its course and diminishes until the final cadence on a un ison a'. Measure 56 contains a very strong syncopated figure which emphasizes and elongates the eb. On the last eighth note of this measure, and in measure 57, we find an inverted statement of Item I in the third and fourth violins, violoncellos, and contrabasses against the syncopated eb pedal. In the next measure, the syncopated pedal-point shifts to bb and on the last eighth note, the same instruments state Item II in inversion on ab. By measure 61, the rhythmic pulse has slowed and the dynamics have returned to mezzo-forte; at this point, the tonality changes to f. This is followed by a db inverted statement of Item IV:: in the rhythm of Item III. This statement may be considered to serve a dual function both as Item III (rhythmically) and Item IV (tonally). At measure 65, the tempo returns to J\ ca.116- 112, the dynamic level is piano, and the vertical texture has been reduced to a two-voice texture (end of measure 67 and beginning of measure 68 one-voice). This is the beginning of the second stretto section in which the inverted Item I is stated on fl and £~ start ing in the first violins with each subsequent entry a tritone below the preceeding entry. From measure 68 to the end of the movement, all of the parts are marked con sordino. Measure 68 begins with a two-voice stretto played by the third and fourth violins on s_, and the first and second violas on b, accompanied by a free contrapuntal line in the violon cellos. This is followed by another complete stretto of the inverted subject played by the second violin on d and the violoncellos on~' (measure 73). Before the completion of this stretto, the first violins begin a tn statement of the inverted subject on ~ simultaneous with an original statement of the subject by the fourth 25 violins on a (measure 78). This mirrored statement is accompanied-by a further slowing of the tempo to.J'-= ca. 108, and the entry of an arpeggio figure in the celesta. The return to !. by the upper and lower parts marks the completion of their journey through the circle of fifths and establishes this section as the beginning of the coda section. The remainder of the movement does not leave the tonal center of !.• In measures 88-85, there is a small stretto sec tion which uses both the inverted and original forms of Item I (the dynamics have dropped to piano-pianissimo at this point}. Measures 86-88 present Item II on~', mirrored by the first and second violins. These three measures provide a condensation of the structure of the entire movement. They begin on !.', e.xpand in opposite directions to eb, and then return to a unison~'· This kind of cadential figure, i.e. the symmetrical approach from above and below to a final tone, may be frequently found in Bartok's later compositions. Some other compositions using this device are the Fifth String Quartet, the Concerto for Orchestra and the Third Piano Concerto.

STRUCTURAL ELEMENTS

Tonal Considerations

The primary problem in a discussion of tonal considerations is the method which the analyst uses to determine what constitutes a tonality or tonal center. This problem cannot be resolved for some twentieth century works as readily as it has been resolved for the music of earlier periods. The fact that this work is contrapuntal and that the main emphasis is on the move ment of the melodic lines with an apparent avoidance of academic triadic functional harmony makes any attempt to discern the tonality by reference to such vertical or harmonic structures impractical. The tonality must be determined by the relationship of a tone to the other tones of the melodic line. By studying the relation ships of these tones to one another it may be possible to discern which tones, if any, are of primary importance in establishing the tonality and which are less essential.

27 The melodic material of the subject is the determining factor in the establishment of a tonal center in the first movement. This is particularly true since practi cally all of the melodic material of the fugue is derived from the subject. Eight tones are used in the statement· of the subject. The range of these eight tones encompasses all of the chromatic notes between a and e I • There are several methods which could be used to determine which of these eight tones are the most significant. One method is to determine the frequency of occurrence of a given pitch, maintaining that the number of times a pitch is sounded will determine, to a great extent, its rela tive importance in the melodic line. Another approach would use the duration or time element in evaluating the relative importance of different tones, e.g. there are more eighth-note time units of £ 1 than any other tones in the initial statement of the subject therefore £' is the most important sound thereby establishing the tonality as c ' • The following table illustrates, on line one, the eight pitch levels of the subject; on line two, the number of times each tone is sounded; and on the third line, the duration of each note measured in eighth note units. The numbers in parentheses apply if the resolution tone immediately following the subject is included.

28 Although. this note is not actually part of the subject and is not used by subsequent subject statements it aurally completes the resolution of subject Item IV and constitutes an essential element of the tonality. pitch level a bb b c ' ell' d' d#' e b' e I number of notes 2(3) 4 4 5 5 3 3 1 duration in 2(4) 5 5 7 6 4 3 1 eighth,..notes

A third means of establishing the tonal center could be based upon the position of the tones in the subject or subject Items. This method would maintain that the first, and possibly the last notes of the sub ject Items are of special significance in the tonal scheme. Considering the first notes of each of the four subject Items; the first two begin on !., the third begins on c1' and the last Item begins on ~· • Also to be considered is the melodic contour. All four Items following an ascending and descending melodic line.

The first Item begins on !,, ascends to c#' and descends back toward a. The sec.ond !!!!, also begins on !_, ascends this time to eb ' before descending back to bb. The third ~ is the high point beginning on c#, rising to

~ ' , then falling to £• Item IV is intervalically a repetition of Item III a semitone lower in pitch.

29 The final tone of Item IV (bb) has a strong resolution tendency to the a which follows it. The melodic lines of the four Items are all related tonally to a center on a. The subject begins here, it expands by four rising and falling subject fragments and then it returns to a. In the case of the subject of this fugue, the tonality is determined primarily by the melodic contour and the relationship of the various pitch levels to certain key tones. These key tones are the first tones of the first two subject Items and the resolution tone of the final ~b of the subject. The proof of the as sertion that ~ is the tonal center of the subject lies in listening to the subject. An aural analysis of the subject unquestionably establishes the first note of the subject as the most important tone. When discussing tonal centers reference will be that the tonality is "on'' a given pitch rather than "in" a tonal center, e.g. the second subject entry is "on" e' rather than "in" e'. The word "in" tends to imply a harmonic rather than a contrapuntal concept. Several facets of the discussion of tonal con sideration have already been mentioned in the preceding section on form (Chapter II, pp.13-17). The interval of a tritone, or "twentieth-century dominant" as it is sometimes called, is of particular 30 importance in this movement. It is the relationship of the tonal center of the beginning and ending of the fugue, on ~, to the tonality of the climax of the move ment on eb. It is also the interval relationship used in the two stretto sections, i.e. f#-£• The tritone is also an important factor in the tonal plan of the com plete Music for String Instruments Percussion and Celesta for the first movement centers on ~' the second movement a minor third higher on £ ' , the third movement is a tritone below the second, or a minor third below the first on r#, and the fourth movement, like the first, centers on a. In this plan, ~ is the tonal center of the entire composition, while the second and third movements, a minor third above and below respectively, form a tritone around the central tonality. In addition to its importance as an element of tonal organization, the tritone is also important as a vertical sound, i.e. as an harmonic interval. In a tabulation of all of the vertical sounds in two and three part textures in the first movement 12.35% of the inter vals were tritones. This figure represents the greatest percentage of any of the dissonant intervals. The next most common dissonance was the major seventh which rep resented 9.1%. The only intervals to exceed the tritone in frequency were the major third and major sixth.

31 Dynamics

The dynamics of the.first movement consist of a fifty-six measure crescendo from a pianissimo, ..££!! sordino statement by two violas in unison in the first measure, to a forte-fortissimo with full ensemble. This is followed by a thirty-two measure decrescendo which ends on a con sordino, piano-pianissimo unison. In the , course of ~his movement Bartok employs all written dynamic levels from piano-pianissimo to forte-fortissimo. In addition to the written dynamic marks, used to indicate relative levels of loudness and softness, there are also changes in the dynamic level which are effected by the addition or subtraction of instruments. Although the first twenty-seven measures of the movement are all marked to be played pianissimo, there is a crescendo during this section created by the gradual addition of more voices to the texture. Beginning with a solo part an additional instrument is added every four measures until in measure 18 there are five voices all playing pianissimo. This kind of dynamic increase may be con sidered as an implied dynamic change or an increase in density. The density and the number of different in strumental parts at a given point do not necessarily coincide since it is possible for string instruments to sound several notes simultaneously. 3Z Another factor in a discussion of dynamics is the vertical spread or the distance between the highest and lowest parts. As the spread increases, it creates a feeling of expansion and an increase in volume. The graph on the following page illustrates the vertical spread. It indicates the average spread in each measure and is calibrated in semitones. The greatest vertical spread in the movement is fifty-nine semitones. This occurs during the first three eighth-notes of measure fifty-six and coincides with the point of greatest am plitude and density. The average spread for measure 56 however, is not as great as it is elsewhere in the move ment. Vertical spread of one to three octaves is em ployed in 64.8% of the movement; 23.86% of this move ment has a vertical spread of less than an octave, and only 11.36% exceeds a three octave spread. The graph on page 34 illustrates the written dynamic level, and the graph on page 36 illustrates the density, or number of written notes including unisons. The density, like the vertical spread, is a computed average for each measure.

33 T - , - ~ ---1- -t- - ! T ~+-~~--l-+--'--~c-+-~--i---+--+--t--1-+-~~-+-r--'-'-+--t-+-1-+ff'"C!! mi-+----+-+ 'i ~--~~ -;- -t ~ -+ ·-~- ----~-~h~ I- :~~---+-+-+- -J ,_: t --~

I 1 r- t l ~

I- - \- -r-- ·-·r- --1> \- - i----t·-.-+-+-+-+--~-+-+-+-+-t--t--1---+-l - --'- r- " . -r--r-- ·--t--T--1--+---t--t-t---J t- --- _,__ --,-+--1...,._--t--t--~~ --L- -1--\ -+--t--+--+---t---+--+--+-t-+--+--l t-+-+-+-1-t--t-t--t~f-1-+,-+-t--t-+-+-1-+-+-t--t-+--t-1-t--t-t--t-+--t-1---\"-t-t-t-+-+-1-t--t-t--t--t-1~ +-+-++-il'J'~l--i--H,-f--r-- - --t-.-- ~-- -+--+-+-+--+--l--+- - -~+- - G +-t-+--&l---1-+-+-t-t-+--+- +--+---+--+-- ,_- --+1-+--+--t---+--+--+-t- -t-t---tl\-\-+--t-ti' --t--t-+-t--+-+--J i;::; , --i--+--i--t +-1--+-+-+-+--+--+--1---+-+-+-t-+-+--~-+-tl\ - I I ~ ; --r-~ ~ -+-t - -I_-i--+-l +-4 I\ +-+--~ ---+--~~, --r, ~ - -r--+, , ---+---~.- , f-r---i------i-----r-- --f--r--r-- j-f- - '-~ -i-- -- -+-I-- .1-. '----'------+-,~-- --t---·- --i-----r-- - ~+- -~+-- +--~+-- (_L[-i-+-~ ' ;-~t ,- ~ +- + H--t-- j ~L- - I\ '->

/ ,_ f- -- - -r- -- -~ W-~ -i- +--~ - -L~- - ~+--~ - -+-+-+l\+t-T--J-+--+---+-- t-~-+--+-!--+--"--j-+-----t---+---t--+-+--+--l-t---:-_,-i-_--:_-_,_-r-_-:-:._~,_:_: H I i -H- ~ ~ 'ii\

~:::0:$.~CI0>~-111.c)>t-~~- .... 36 As one might expect, the density and spread factors usually support the written dynamics. There is only one decrescendo marking in the last measure of the movement. There are three occurrences of the term crescendo in the movement. There is one other dynamic indication: a piu-piano in measure 73.

Tension Degrees

The various degrees of tension encountered in this composition are achieved by a variety of compos itional devices. The use of dissonant vertical combin ations, the dynamic level or amplitude, tempo, spread, timbre, density, rhythmic activity and even the melodic contour are all factors which may be used either singely or in combination to create greater or lesser tension. Three of these elements; dynamics, spread and density, have been discussed in the preceding section and their. relationship to the creation of musical tension requires no further discussion. Rhythmic activity and changes of tempo have always been an important factor in creating tension in music. An increase in either rhythmic activity or tempo creates an impression of drive, agitation and excitement. Con versely, a slowing of tempo or rhythmic activity generally produces an atmosphere of relaxation, calm, lethargy or some similar emotional reaction. In the first movement, 37 there is very little contrast or change in either the rhythmic activity or the tempo. The changes that do occur are subtle and slight. The movement is marked Andante tranquillo and the five metronome markings in the move ment range from (.fl: ca.108) to c.J'= 120-126) and fall within the general limits of this term. The ca. indicates that these are approximate tempos, and are variable de pending upon the acoustics of the auditorium where performance takes place or other external factors. On two ocassions, first following the climax and second at the end of the movement, there are minor fluctuations of tempo indicated by the term poco rallentando. Obviously, in this movement, Bartok/ did not depend upon contrast of tempo for the creation of tension. The tempo-pattern employs a slight increase after the first stretto section followed by a broadening before the climax. After the climax:, there is a poco rallentando preceding an a tempo. This is followed by a subsequent slightly slower tempo throughout the last eleven measures. The rhythmic activity shows almost as little variation as do the tempos. The rhythmic motion through. out the entire movement is almost entirely in eighth note units, except in the four measures that the celeste is playing a repeated arpeggio. There are a few isolated

38 examples of pairs of sixteenth notes which help to drive the music forward but at only one point (a sixteenth note triplet in measure 14) are there more than two six teenth notes in succession. The rhythm does become slightly more insistent and forceful during the section where the fastest tempo indication occurs. This is the section leading to the climax. Equally as rare as any rhythmic motion more rapid than the eighth-note, is any motion that is slower. Only during the climax (measure 56 and the measure immediately following, where there are syncopations and rhythms) and at the end of the move ment (which is also the place of the slowest tempo mark ings and there is a gradual augmentation of rhythm from J, J , J., J ,CLJ accompanied by a po co rallentando), is the rhythmic motion slower than an eighth-note. One of the most commonly applied devices in the

creating of musical tension is the use of dissonance~ It is particularly interesting to note that at the climax of the movement, in measure 56, where the dynamics, spread and density are greatest, the vertical sonorities are almost entirely consonant. This measure is composed primarily of octaves, unisons, and a few perfect fourths. There are also three diminished fifths or augmented fourths between the timpani, violoncellos and contrabass which are probably a result of the tuning of the contra bass's low E string. After the third eighth-note, the rest 39 of the measure is in unison or octaves. A similar use of consonant sounds may be seen in measures 58-64. Another interesting section occurs between meas ures 69 and 72 where almost everything is in a state of relaxation. The dynamics are piano (con sordino), the density and spread are correspondingly small, and the melodic line has been inverted. Yet in these four meas ures there is a marked increase in the amount of dissonance. Orchestrational technique and timbre are other effects which may impart an element of tension or of relaxation. The most outstanding application of these devices in the first movement are the four measures of bars 78-81. At this point, the strings are playing a tremolo accompaniment to the mirrored statement of the subject between the first and fourth violins. The effect of this tremolo is further heightened by a series of very rapid arpeggios on the celesta. When this is coupled with a muted string tremolo and contrabass harmonics, the result is quite dramatic. Possibly, one of the most subtle but certainly one of the most efficient mechanisms for producing ten sions lies within the subject or the basic motif from which the subject originated. The melodic contour of the subject of the fugue is one of rising and falling even as is the contour of each of its Items. These germinal 40 elements support the rising and falling structure of the entire movement as evidenced in the dynamics, density, and the spread. Does it not follow then, that their inver sion will produce an impression opposite to that of the original? The proof of this is in listening to the move ment. In the measures immediately following the climax and the subsequent inverted stretto section (measures 65-72) the melodic inversion supplements the decrease of spread, density and amplitude in producing a feeling of relaxing tension. Without this melodic inversion, much of the feeling of relaxation of this section would have been greatly impeded. It is the synthesis of all of the elements discussed in this section that produces the sensations of tension, relaxation, and unity which are so successfully fused into this composition by Bela/ Bartok./ CHAPTER III

COMPOSITIONAL MATERIALS

Melodic Materials

All the melodic materials of the movement have been separated according to their compositional purpose. Three uses or categories of material were found to be su!'ficient. The first category includes subject material; the second, melodic materials used in conjunction with the subject; the third includes non-subject materials which are used when the subject is not present.

The Subject

The analysis of the melodic materials will begin with an examination of the subject. The initial state ment of the subject is made by the first and second violas, con sordino. It is four measures in length and covers a vertical span of a perfect fifth, from ~ to e ' • Intervallically the subject contains fourteen minor seconds, four major seconds, three minor thirds and two augmented seconds. The melodic motion of the subject is predominantly chromatic with the major seconds, aug mented seconds, and minor thirds interspersed throughout the statement. These larger intervals never occur in

42 succession and there are no more than two minor seconds used in succession at one time. The subject is composed of four small melodic elements which will be referred to as Items I,II,III, and IV. These melodic Items are each separated by single eighth rests and are further by phrase markings. A comparative analysis of the four melodic Items of the subject reveals that each Item of the subject reveals that each Item observes a similar rise and fall in the ~ melodic contour. In like manner to the melodic contour of the Items, the entire subject also follows a rising and falling line. Item I begins on ~' ascends to c#' and then descends to b. It has a time span of seven eighth notes. Item II also begins on a but it is expanded by the insertion of a ~· and ~b' (the fourth and fifth notes) and the addition of a bb at the end. Item II has the longest time span of any of the melodic Items, ten eighth-notes, as well as the greatest vertical range.

It encompasses a tritone (diminished fifth) from ~ to eb'. The third ~ starts on a c#', the highest pitch level of any of the four Items. It then ascends a minor third to -e' , the highest tone of the subject. It then descends by using major and minor seconds to b. Like Item I, it has a time span of seven eighth-notes. Item IV begins a semitone lower than Item III and foilows an identical interval sequence to that of Item III, although 43 there are variations in the rhythmic pattern. The final resolution of Item IV to an ~' the same note on which the subject began, comes immediately after the second voice (violins three and four) begins its statement of the subject a perfect fifth higher on e ' •

Melodic Contour Graph of Subject

- ll ... LI I

Each vertical square equals one semitone. Each horizontal square equals one eighth-note.

44 Further examination of the subject reveals certain interval relationships common to all of the subject Items. In each Item we find a minor third or its enharmonic equivalent, an augmented second followed by two minor seconds. In Item II, it occurs two times in suc cession, first in an ascending pattern, the second time in a descending pattern. The following diagram helps to illustrate the use of this melodic interval sequence. The numbers above zero represent art ascending melodic interval in semitones; the numbers below zero represent a descending melodic interval in semitones. One semitone equals a minor second, two semitones equal a major second and three semitones equal an augmented second or minor third. The sequence of an augmented second (minor third) followed by two minor seconds, is indicated by the use of brackets.

-- I ' I - : r 1 • -- ' - --t-1 I • h \ I H ' . . I .3 ~ _ ------1 - r.r- - -rt' : ' : i a.•- +__; ,. I l ' ;- f t~" •-. . /;~ ' . I . A A -- ~ ~-+ti'-- - __ l~4 ; _--- l...~1 "'I": I ~- -~ ,n -- y~ -+ ! ! j .. -~~-YN~ ·-· , v v n _; · :I/NJ fP 71j ---- ~- H- . -·. · ~ · 1 ~~- t- ; i a ~ • , I , I -'t- t ' - -j ! - -.--~·---+ ,3• 1-H .+ [j-+- L.; ~---- , - ' -'- t- - . i

------_-J -_t__ L::L~-~ ~ : ~- ~ l_-~ : ~ ~ ,__ ; This motif of a minor third and two minor seconds constitutes 65% of the melodic intervals of the subject and may be considered to be the prime, or principle in terval generator. It is the primary unifying factor of 45 the subject and consequently of the entire fugue. The technique of constructing an entire composition from a very limited amount of motivic material, is frequently in evidence in Bartok'sI compositions. This ability to synthesize and develop a germinal idea into a complete composition imparts an impression of logical order and provides a sound structural framework for his works. So imaginative and varied are Bartok'sI applications of this melodic material in the fugue, that one may find it difficult to believe that this fugue is constructed from a motif including only two melodic intervals, one of which is used twice and the complete unit having but four notes. Certainly this great economy of means was not a hindrance to Bartok/ but it rather served to streng- then the work by providing it with a unified atomistic structure. Many of the subject statements are fragmentary. Sometimes only one Item is present and even this may not be complete. These fragmentary statements are often distorted in rhythm, inverted or altered by other com positional devices but there are seldom any changes of the composite melodic intervals of the subject. Only in measures 37-40 is there a significant alteration of melodic interval. Here Bartok/ substitutes a tritone for the customary minor second as the first interval of Item I.

46 Associated Melodic Materials

An important melodic consideration in the study of fugue is the nature of the counter-subject or counter point which is to be used in conjunction with the answer or later subject statements. Some fugues use a countersubject which is present at each entry of the theme while others depend upon a free type of counterpoint which may vary with each presentation of the subject. In the Music for String Instruments Percussion and Celesta, Bartok~ ~ uses the latter technique. At only two points is a subject entry accompanied by a similar counterpoint. In measures five - eight, the third and fourth violins on e' are imitated on the fourth eighth note later and a perfect fourth lower by the first and second violas. In a similar manner in measures 13-16, the second violin on b' is imitated four eighth-notes later and a perfect eleventh lower by the first and second violoncellos. Actually the imitation of the subject in these two pas sages continues for only five notes and is followed both times by a leap of an ascending perfect fourth and a subsequent descending chromatic line.

47 Vt··~ -1--;.,....._*4M-~-+-~+-~~-=----++r'-F--+-if.:ir---+---''--t~___,.,:a:::---tr:-:H"t"T r"f 11-U:1;~-1-=-+M--z1-..J.e1.--:...,...-+.d--:-L-t+l""rk'311~..z.:.:-+.1.__---;;!f": __-nt-:--t~"""'--t'O"'

\/la16=:;::t:::k:::£:~~2~=b:;;:;:::::~:+=:;;=::~~~~~ liUL~-'-...a..L~~.!-!4'£.-+---=-+--'-"~~~~--~~-r-~-t--;o~

48 Examination of the preceding example as well as other associated melodies reveals a close intervallic relationship between these counterpoints or counter melodies and the subject. The counterpoints, like the subject, are constructed primarily from major and minor seconds. In the subject, 57.7% of the melodic intervals are minor seconds and 19.2% are major seconds. In the melodic materials used as counterpoints to the subject, 54.1% of the melodic intervals were minor seconds and 18.4% were major seconds. The similarity in the pro portions and percentages of these intervals supports the statement that the added counterpoints, or associated melodic materials, consist of essentially the same melodic interval units as the subject. The only melodic interval of the subject other than the major or minor second was the minor third or its enharmonic equivalent the augmented second. In the associated counter-melodies, the remaining portion is divided approximately between the perfect fourth (8%), minor third (7.5%), and the major third or diminished fourth (5.5%). Melodic leaps ex ceeding a perfect fifth are rarely used.

Additional Melodic Materials

There are only two places in the fugue where the subject is not present. The first is the episode (measur es 21-27) and the second is at the climax of the movement. 49 In the episode there is a change in the texture of the melodic line affording the listener some relief from the diatonic and chromatic motion that otherwise domi nates the movement. Here the interval of primary im portance is the descending perfect fourth which is pre sented by all voices. There is also an increase in the use of major and minor thirds. It is interesting to note that the number of major and minor seconds is almost exactly equal to the number of major and minor thirds and perfect fourths. This represents a considerable change in melodic texture. Throughout this section, major sixth and diminished fourth intervals are also more com mon. If it were not for the major and minor seconds written in the viola parts and imitated in the contra- J bass part, there would be very little chromatic or dia tonic motion in this section. The violas and the contra baa sea bind the melodic motion of the episode to what preceds and follows it by their retention of melodic characteristics which, although only remotely related, are nevertheless reminiscent of the subject.

50 The melodic material used at the climax (measure 56) is not of any real significance as far as its melodic content is concerned. Its real importance is as a rhythmic figure and to emphasize certain vital tonal relationships in the structure of the fugue. The fact of the matter is, if we are to consider variation in pitch level as a necessary element of melody, measures 56, 61, and all but the last note of measure 58 and part of meas ures 62 and 64 do not possess the essential character istics of a melody. Therefore the melodic materials of measures 56-64 may be considered as either fragments of the inverted subject or non-melodic rhythmic figures.

Rhythmic Materials

Rhythmic Fl OW

The melodic materials used in the first movement do not have strong rhythmic characteristics. It may be an exageration to say that the rhythms of this fugue are essentially nonaccentual but a statement of this nature would be very close to the truth. The fundamental metric unit is the eighth-note and only on rare occassions is there an absence of motion using this unit. The sub ject itself contains twenty-four eighth-note units, six quarter-note units, and no note values greater than a quarter note. There are no strong rhythmic accents in the subject. For that matter, nowhere in the entire movement is there any accent mark, sfz. or other indication of a strong rhythmic stress. Whenever there is a sustained note in one part there is almost sure to be eighth-note motion in another voice. The first time in the fugue that rhythm becomes really evident is the section leading to the climax (measures 45-55), where almost all of the parts are frequently moving in an eighth-note rhythm. The place where rhythm makes its greatest impression is between measures 56 and 62, the climax of the movement. Through out these measures limited melodic activity and strong quarter note syncopations become a very powerful element. The impact of the rhythm during this section is made even more dramatic not only because of the syncopation but also due to the fact that until this time, Bartok/ has avoided the extensive use of any other rhythmic unit than that of the eighth-note. This change in rhythm heightened by the comparative absence of melodic motion, enhances the effectiveness of the climax as much as any of the other climactic elements; the forte-fortissimo dynamic level, the vertical spread, the tonality, and the addition - al resonance resulting from scoring almost all of the instruments in octaves or unisons. The rhythm of the rest of the movement is basically in eighth-notes. Only during the last five measures is there a significant 52 change in the rhythmic flow.

Meter and Tempo

The meters used in the first movement are irregular or changing, and they all use the eighth-note as the unit. During the exposition of the fugue, it appears as if the meters are falling into an asymmetric pattern that repeats every four measures as follows: a,8 a,12 a.8 s 7 etc •• This sequence is repeated four times. In the fifth entry, the series is altered by the addition of one eighth-note in its first measure, changing it to t• The following six measures are the episode. Here the subject is not present. The four measure metrical sequence of the exposition is abandoned and the meters follow no set pattern. In measure 27, the subject returns and begins the statement of a two part stretto. The return of the subject is accompanied by the return of the original four measure metrical sequence which is followed for only four.measures. After its appearance in measures 27-30, the four measure metrical sequence does not appear again until measure 69 where it is used twice in succession. This is the last time the sequence is used. The meters of the first movement, with the except ion of the use of the four measure sequence discussed 53 above, change freely from measure to measure and do not fall into any definite pattern. Only rarely are successive measures in the same meter and at only two places do successive measures with the same time signature exceed three. The longest group of measures in the same meter is from measures 58-67 where nine of these ten 6 measures are in g time (the first six measures are in 6 ~, the seventh measure in ~, and the last three in a>. The greatest number of eighth-notes in any measure is twelve and the least number is five. The following graph illustrates the number of eighth-note units in each measure. The measures in 8 12· 8 7 brackets are the metrical sequence of ~' tr' 8 and ~ •

] -! I r I l - T - 1----t-

I l I l I 1 I I I I ,, .JI"\ - - , -!------1-- - ~- --C-+--+-+-+-+-+----'---l---1----l---l----!-.-l--"""'---' 1----+-+-+-+--+-+--+-+-+--+---t--+-1----+-~+--+--+- - --+---'--'-"·--l---l----+--+---+-l--'-'--+-l--l-----l----1--+-•-'--'--'---'------++---!->..+-+-I.-" -

/() IS-

1-;-- i i

S I : I i--- ~-~1--- -~ -·-~~~- ',_,___ l~J 1----+-+-+--+-T---r-t---r-t---r- - I : +-•-d- ~ _::- ~-r- ~~ -~~ :::- ,_ i l--l-+-1--l---l---l----i---+-l---l--+-+++1-H-~,-1f-t--T-;-~~+- -- ~1---1--;1---~--~+-"

54 When a complete statement of the subject is used, it is accompanied by a division of the eighth-note units into smaller groups by the use of dotted bar lines. The ~ measures are always subdivided into 3+3+2, the ¥ measures into 3i3+3+3, and the ~ measures into 4+3. Dotted bar lines are used in the score only with the complete subject and are not present in the accompanying parts or in fragmentized subject statements. In the strettos, where there are two overlapping subject state ments at the same time, the dotted bar lines are used in both voices. The dotted bar lines are used as a division of the measure into smaller rhythmic units and also to indicate those notes of the measure that should receive slightly more weight. Finally these dotted subdivisions should be an aid to the conductor in determining the pattern of his beat. There is, in the subject, what may be a germinal application of rhythm to the principle of symmetrical form that is so important in the structure of this fugue. It occurs in the first two melodic Items and is illustrated by brackets in the following rhythmic diagram.

55 There is very little variation in the tempo of the first movement with all of the metronome indications falling betweenJ'=108 and.J'=ca 120-126. The movement is marked Andante Tranquillo and the character of this marking, at least the Andante part of it, is preserved throughout. There are two occurrences of the term poco rallentando; the first in measures 63 and the last during the final two measures of the movement. Outside of the poco rallentando, the only other means employed to denote a change of tempo are metronome indications. At the conclusion of the movement, there is a notation that the entire first movement should require approximately six minutes and thirty seconds for its performance.

56 ~RAPT.ER IV

COMPOSITIONAL TECHNIQUES

Combining of Melodic Materials

Strettos

There are two large strettos and one shorter one in the fugue. The first large stretto occurs in measures 27-37; the second in measures 65-76; the third and shorter one in meaaures.82-85. In each of the large stretto sections there is a complete statement of the subject in two-part stretto as well as a fragmentary presentation of the subject in which the four subject Items are stated by various instruments. The following diagram is an outline of the form of the two large strettos illustrating the relative positions of their ,complete and their fragmentary sub sections. A further evidence of the symmetrical or arch form discussed in chapter II will be noticed in this diagram.

57 STRETTO SECTION I STRETTO SECTION II 27-37 65-77

subsection A exten. subsection B subsection C subsection D 27-30 31-33 34-37 65-68 69-77 (complete (subj. fragments (subj. fragments (complete subj. subj. in in stretto) in stretto) in stretto) stretto) 'gl ~l ______I [----~------~----] I _ Both sections begin with strettos having tonal centers on f# and c with the subject entries three eighth-notes apart.

Stretto Section I: (Complete to Fragmentary)

Subsection A begins with a two part stretto in which the presentation of the entire subject, on r# by the first and second violins in octaves, (f# " and r#' respectively) is followed three eighth-notes later by the violoncellos and contrabasses. This entrance is in octaves on£ and c. It is followed by an extension in bar 31 where Item IV is reiterated by the first viol ins,. now on c# and the violoncellos on Ei• This is further extended in bar 33 by the restatement of Item IV, this time on~, by the violoncellos and contrabasses. These subject statements in stretto and their ex tensions are supported by the third and fourth violins and the violas which add a free contrapuntal support by enriching the vertical sonorities and rhythmic movement. Subsection B (measures 34-37) of the first stretto consists of statements of the four subject Items by various voices on different tonal centers. This subsection commences on the last eighth-note of measure 33 when the violas begin their statement of Item I on f. Three eighths later, Item I appears in the second violin, this time on c#'. Both of these statements are repeated 59 in measure 35, by the second violin of f' and the first violin on c#". Concurrent with the C# " statement of Item I, Item II appears in the violoncellos on bb.In measure 36, Item II occurs on E# " in the violas, followed two eighth-notes later by the third and fourth violins statement of Item III on bb'. The last entry, in which the second violins present Item IV on bb', be gins on the last two eighth-notes of measure 36, three eighths after Item III was begun by violins three and four. The relatively rapid utilization of the tonal centers of f, bb, c#, and if; the increase of stridency in the string timbre effected by the removal of mutes, the £b pedal of the tympani and the increase of dis sonance in the resultant vertical structures all contri- bute to a feeling of mounting tension, agitation and greater complexity in this section.

60 '' I ., pp

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Subsection B, unlike subsection A (which has added counter-melodies), is constructed almost exclusively from an interweaving of subject material. Although there are some rhythmic variations, the only part which is not subject material is the bb pedal in the tympani and contra- 61 bass which anticipates the next statement of the subject on eb (measure 38) by the violoncellos and contrabasses. Stretto Section II: (Fragmentary to Complete} The second major stretto section (measures 65-76) opens with an inverted statement of Item I. This sec tion may be divided conveniently into two subsections; subsection C, for the fragmentary part, and subsection D, for the complete statements. Subsection C is four measures in length and like subsection B, it is constructed from unmuted statements of subject Items presented by various instruments on different pitch levels. However, subsection C is also similar to subsection A in as much as both of these subsec tions ~se Fl and c as their tonal centers. In other respects this subsection differs from the two preceding subse ctions in that it uses only Item I of the subject. The climax has passed, the fugue, now gravitating toward its conclusion, has reversed its building tendency and is, at this point, in a process of relaxation. The tempo has slowed to its earlier rate ofJ'-=116-112, the dynamic intensity has dropped from forte-fortissimo to pia!!£ in only nine measures, the number of parts has diminished to two, or momentarily one, and the vertical intervals have very little tension. In addition to this general

62 relaxation, the subject itself has been reversed. No longer does its contour rise and expand but it now con veys a feeling of gradual descent. This impression is further enhanced by the fact that each entry of Item I is a tritone below its preceding entry. There is also a diminution within the successive statements of Item I. The first four entries present the.motive in its entirety, but in the last two, the motive becomes fragmentary and incomplete. The initial statement of the inverted Item I is made by the first violin beginning on the last eighth

11 note of' measure 64 on £ .. Four eighth-notes later, i.e. beginning on the fourth eighth-note, it is followed by the second violin on 'f!'. These two entries set the pattern which the next four entries will follow. All of the entries in subsection C are imitated four eighth notea later and a tritone lower in pitch ..

63 ,.. :. " ,,., ~ I ~ ,.. f'J - I t .__ J Vl. • , i- ~- r ' ., II ""' 1: .. J I I • I .;/!. r' I I r

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. ~-·~--~------

Subsection D is composed of a two part stretto of the entire subject in inversion, by violins three and four and violas one and two, accompanied by a free counter-melody in the violoncellos. All parts are once again con sordino. The strings remain muted for the duration of the first movement. In measures 73-77, this subsec tion is extended by a second stretto treatment of the

64 entire subject in the outer parts. Tonally subsection D is a continuation of progres sion around the circle of fifths following the fragmentary subject statements of subsection C. It begins with a complete statement of the inverted subject on £ by the third and fourth violins thus completing the £ to E portion of the tonal scheme of the upper part as it progresses through the circle of fifths. In similar manner, the stretto voice, also in inversion, enters on b 1 and completes the r# to b portion of the tonal cycle - . in the lower voices. This statement instead of being at the usual four-eighth time interval, as was the case in all of the previous entries, now follows on the third eighth-note after the first entry. In measure 73, the stretto entries are once again four-eighths apart but due to an extension in the rhythm of the second entry the time interval between the statements of the ensuing entries becomes even greater. The stretto of Items II and III is six eighths later than the first statement and the stretto of Item IV, in measures 76-77, is eight eighth-notes later. This lengthening of the time interval between the entries, the increased spread separating the stretto parts and the decrease in dynamics combine to ritard the motion and reduce the tension of the music. In measure 78, the tempo is slowed to .!':ca: 108, the 65 slowest tempo yet encountered in the first movement. The tempo remains at.1':108 until the last two measures if the movement where we find a poco rallentando. In measure 73, the second violin begins on d "' ; this is strettoed by the violoncellos on e ' • The d "' violin statement is tonally subsequent to the previous E state ment of the third and fourth violins and the e' violoncello statement is subsequent to the b statement of the violas. At this point, the second stretto section has brought the tonal centers to the last step of their journey through the circle of fifths. The tonal centers are now a per~ect fifth above and below the central tonal of the movement. At this point, the composer presents the last complete statement of the subject. It begins on the eighth-note preceding bar 78. The final resolution of Item IV in the second violins is delayed one eighth note. Item IV in the violoncellos is altered rhythmically and its final resolution is delayed until it reaches e' on the last eighth of measure 79. The last stretto section is in the coda between measures 82-85. It is entirely fragmentary in structure and employs only Item I. Tonally it centers on~ and it utilizes a combination of both the inverted and original forms. The entries are at varying time intervals and

ject material. After this has been discussed a third use of imitation employing imitative figures which are composed from non-subject material will be described. Omitting the three stretto sections there is only a very limited amount of imitative counterpoint which uses subject material. The first example of imitation may be found at the beginning of the two part texture in the fifth measure between the third and fourth violins and the violas. The violins statement of the fugue subject on e' is imitated four eighth-notes later and a perfect fourth lower in pitch by the violas on b. The imitation lasts for only five notes where it becomes a free counterpoint. In measure six, an imitation may be found between the descending chromatic line of Item II of the subject and the following descending chromatic line in the violas, fifth, sixth, and seventh notes of both voices. In measure seven, we find that the violins, now stating Item III, are imitated by the violas as in measure five. Again the imitation is four eighth-notes later and a perfect fourth lower. This same pattern of imitation appears again in measures 13-15 between the subject statement by violin two on b 1 and the violoncel los a perfect fourth lower. It may be interesting to note that these two imitative passages accompany the second and fourth statements of the subject on e' and b'

68 respectively. These are the second and third subject entries progressing through the circle of fifths by en tries a perfect fifth above the preceding entry. No comparable imitative figures may be found for the second and third subject entries progressing by fifths below the initial statement. The next imitation encountered is in the episode (measures 21-26). It begins in measure 21 with an irre gularly broken chordal pattern in the second violins. It is constructed primarily from descending intervals of a perfect fourth. This tonal pattern in the violoncellos one and two and violas one and two which are moving in parallel minor thirds. This imitation becomes more frag mentary and is freely dispersed among all voices. The unit of imitation now consists of only the two notes outlining the descending perfect fourth. It is this interval of the descending perfect fourth which up to the episode has been practically non-existent (only three occurences), which forms the main structural unit of the episode section. The perfect fourth is doubly effective as episodic material because of its previous absence as primary melodic material. In measures 22 and 23, the descending perfect fourth occurs in a sequence beginning in the countrabasses and following through the violon cellos, violas, third and fourth violins and second

69 violins at varying rhythmic intervals. In measure 24, a short sixteenth note figure in the violas is imitated by the countrabasses. This short reiterated figure increases the rhythmic motion to the following stretto section by a quickening of the melodic movement. Following the first stretto section, in measure 38, there is an altered statement of the subject on eb (a diminished fifth is substituted for the original minor second between the first notes). This ascending diminish ed fifth in the violoncellos and contrabasses, is imitat ed in inversion, by a descending diminished fifth in the third and fourth violins and the violas. This type of inverted imitation continues through measure 40. At measure 45, there is an unaltered statement of Item I on eb'" by violins one and two, this is imitated by the violoncellos and contrabasses statement of a rising melodic pattern constructed primarily of minor seconds and perfect fourths. This ascending passage is repeated six times, each time at a higher pitch level, against repeated agitated statements of Item I in the violins. The effect of this passage is the creation of greater tension which builds to the climax that is achieved in bar 56. The ascending passage culminates with a chromatic ascension to ~· in measure 52. This is followed by a four measure section ending on bar 56 in which the lower voices descend chromatically to ~' while the upper voices 70 b ti' ascend to e •

Melodic Mirroring

The first of three passages in which melodic mirroring may be found begins on the eighth-note preced ing measure seventy-eight. It follows the inverted subject statement (in stretto) and is presented by the first and fourth violins. The fourth violin states the subject on -a. This statement retains the original melodic contour but there are several alterations in the rhythm. Concurrent with the entry of the fourth violin on a the first violin enters on a "' with a strict melodic inversion of the subject. The inverted statement of the first violins, like the original statement of the fourth violins, also has rhythmic alterations. The rhythmic changes in this section prevent the mirroring from being perfectly strict but at no time are the two mirrored parts more than one eighth-note apart rhythmically. The rhythmic alterations serve primarily to sustain the contrapuntal flow which would be impaired if both parts moved together in identical rhythm. This technical device complies with the elemental contrapuntal precept that when one part remains static, some other part should be in motion. This manner of maintaining rhythmic pulse is particularly important at this point since there is

71 virtually no other melodic or rhythmic motion (the other strings are playing long sustained tremolos while the celesta is playing a rapid arpeggio). During this passage there is a mirroring of the entire subject. Immediately following the completion of the mirrored subject statement there is a four measure section in which Item I is presented eight times on a. The first four times Item I is complete, the last four times it is fragmentary. The first four statements begin on the following notes ~ ", ~ ' ~ ~ and &; the last four are on

~ "' , ~," ~ ' and~· The first, third, fifth and seventh statements are inverted. Compositionally these four measures constitute a mirrored stretto of Item I. The remaining three bars of the first movement are an exact mirroring of Item II beginning on ~ ' with a gradual rhythmic augmentation and a poco rallentando to relax the rhythmic drive and bring the movement to its conclusion. This final mirrored statement reflects the overall structure of the entire fugue. It begins on a unison~', expands in opposite directions until it reaches the tritone eb and then returns to a unison piano-pianis simo !.'•

Free Counterpoint

Free counterpoint is free from those restrictions

72 or limitations imposed by stretto, imitation, mirroring or other contrapuntal devices. It is the result of the technical procedure employed when adding a third voice to a two-voice imitation or stretto or when adding a counterpoint to any number of voices. Free counterpoint usually fills out the vertical texture of a contra puntal composition. In the Music for String Instruments Percussion and Celesta, the melodic material of the free counterpoint is constructed from melodic intervals similar to those of the subject. That is, there is a predomi nance of minor seconds, major seconds, and minor thirds. Over one half of all melodic intervals in the first movement are minor seconds. Eighty-five percent of the melodic intervals in the first movement are either major or minor seconds or minor thirds. Therefore, as is frequently the case in the works of many composers of counterpoint, even the free counterpoint is not completely free in its melodic interval considerations. It is consciously constructed from the intervallic material of the subject. Rhythmic units of the counterpoint are also derived from the subject. It moves principally in eighth and quarter notes with occassional use of longer note values when three or more parts are employed. It is not merely an added contrapuntal line to accompany the subject but is, in itself, a carefully conceived 73 melodic line which interweaves with the subject to perform a vital supporting role in the composition. The counter point almost always provides an eighth-note motion in the fugue. Whenever the subject has a rest, a quarter-note, or is not present as during the episode, the eighth- note rhythmic unit is still present in one of the other voices. There are only nine measures in the entire movement where there is not motion on every eighth-note. (Five of these measures are between bars 56 and 65, and the remaining four are found in the last five measures of the movement.)

Vertical Sonorities

Thus far the discussion concerning the combining of melodic materials has been limited to the description of melodic (or contrapuntal) techniques. An analysis of the manner in which Bart~k combines melodic materials will now be presented. The difficulties encountered in attempting to prescribe how and why the composer combines the various melodic lines in a particular manner in this composition have proved to be extremely complicated. To use one of the simplest examples from the first movement, let us consider Bartok"" 1 s choice of the counter- melody during the second statement of the subject in measures five through eight. In order to fully under- 74 stand the re&sons .,~hy the composer used the particular counterpoint he did it would be necessary to know his personal concepts of consonance or dissonance, suspensions, passing tones, rhythmic flow as v,ell as innumer- sble other factors. Obviously many of these quest1one cannot be answer"d b:'l the analysis of a single composition. It would undoubtedly be possible to prescribe in

/ greater detail the reasons for Bartok 1 s choice of his counterpoints if one were to an~lyze the entire creative output of the composer. Even then meny of these ~ues- tions would remain unans»t•ered and would have to ~ considered as pro~1cts of the creative process with its seemingly infinite variable possibilities. Obviously it is not possible to consider all of these factors in the scope of this thesis. It seems probsble that

/. Bartok 1 s primary consideration in this particular composition was the melodic line and that the vertic8l combinations were of seconda.ry concern being the result of the interweaving of the melodic lines. This does not imply, however, that any given vertical combination of sounds is a completely coincidental occurence. With- out a doubt, considerable thought was given to the vertical sonorities. Problems presented in the analysis of two part counterpoint become considerably more complex when

75 the texture increases to three, four or five voices. A two-voice counterpoint requires analysis of single harmonic intervals. The addition of a third voice increases the number of vertical interval combinations at any rhythmic point to three; four voices present six different harmonic intervals; and five voices have ten possible combinations of harmonic intervals. This progressive increase of combinations is outlined below:

Texture Intervallic Combinations 2 voice 1:2 - 1 3 voice 1:2 2:.3 - 3 1:3 4 voice 1:2 2:3 3:4 1:3 6 2:4 1:4 5 voice 1:2 2:3 3:4 4:5 1:3 - 10 2:4 - 3:5 1:4 2:5 1:5

76 A further difficulty in four and five part text ures is to determine the comparative importance of the parts. A method of evaluating the relative importance of the various voices would provide an invaluable aid in the analysis of a fugal composition. Variables such as amplitude, voice doublings, pitch level or tessitura, and timbre must be considered. Establishing the relative importance of the voices has been one of the most diffi cult phases of this analysis. It would be very helpful to know the order in which the various melodic lines were composed but there is no method for determining this. One may speculate that the subject, when present, was the first part written in the score. If we are to accept this assumption, we will then need to determine which part the first counterpoint composed against this melodic line was. Setting aside the problem of which counter-melody is most important, the analysis of vertical combinations of sounds was begun with an examination of the two-voice textures used in the fugue.

Two-Voice Textures

There are only nineteen measures in the fugue where two part texture is used. Fourteen of these meas ures are found in three separate sections. They are:

77 measures five through eight, 65-67, and 82-88. The remaining five measures occur between bars 57-64 where there are statements of inverted subject Items accom panied by a pedal point in the other voices. These pedal points are important elements in establishing the tonal centers of this section but they are not significant as a contrapuntal line. In the first section, the violas have just con cluded the initial statement of the subject and are continuing with a free counter-melody while the third and fourth violins play the second statement of the subject. Although this counterpoint occupies the position of the countersubject in the classic fugue, it is not a countersubject, in the usual sense of the term, because it is used with only one subsequent statement of the subject and does not occur at any other point in the movement.

78 where the two voices move in chromatically descending parallel minor sevenths. (The only other example of parallel motion is found in measures 82 and 83 where there are two consecutive major tenths.) The longest series of consonant intervals in any two part texture is six. This series occurs in measures seven and eight where there are two major thirds, two major sixths, and two minor sixths. The longest series of consecutive dissonances in a two part texture is two minor sevenths and an augmented fourth in measures six and seven. The general tendency to intersperse dissonant intervals between consonances and not to group either consonances or dissonances together in succession results in a practice not unlike that of 16th through 18th century contrapuntal compositions. A dissonance is almost always preceded and followed by a consonance. This treatment of dissonances is similar in some respects to sixteenth century counterpoint where dissonances, such as suspensions, or passing tones, were preceded and followed by a consonance. The rhythmic freedom of the fugue frees us, at least in part, from concern with the problem of on what beat in a measure a suspension or passing tone may be used. Dissonant intervals are usually approached and left by step but this is not always the case, e.g. in

8C; measure seven, a minor seventh is followed by a major

third.

The following example is a detailing of the ver

tical intervals in measures five through eight. A plus

sign ( ) indicates a major interval, a minus ( ) indi

cates a minor interval, no mark indicates a perfect in

terval and a virgule (/) is used to indicate an augmented

interval and a lower case u (u) stands for unison. In

the case of a few intervals, I have substituted the

enharmonic equivalent for the original. The numbers in

parentheses are used where there is a rest. They in

dicate the interval formed between the continuing voice

and the tone last sounded by the resting part since this

sound, being the last one heard, tends to be retained in

the mind. There is an interval indicated for every

eighth-note.

5 6 4 -6 7 6 u 3 -3 ( 3) 2 3 5 6 7 -6 -3 2 -3 2 (-3) u -7 7 8 -7 3 2 -3 2 ( 3) 3 6 -6 6 -6 3 u 3

The next occurence of two part writing is in measure 59-67. This is the section immediately after the climax of the movement in measure 56. The first five 81 measures of this section are basically in a two-voice texture, with numerous unison and octave doublings. A few spots in this section are in unison (measure 61) or in three parts (part of measure 60). Beginning at measure 65 and continuing through measure 67, we find a two- voice stretto of tbe inversion of Item I of the subject. Item I is stated six times in descending order beginning in the first violin. Each entry follows its predecessor after a three-eights time interval and is a tritone - f#' lower in pitch, i.e. .£. " , - ' - .£. ' , - f #, - .£., - Fil. The third section in two parts consists of the final seven measures of the movement. A detailed examination of every vertical interval in these last two sections revealed contrapuntal practices consistent with those of the two part texture in measures five through nine. The following chart is a tabulation of the number of occurrances of vertical intervals in all of the two part textures of the first movement. interval u -2 + 2 -3 +3 4 I( 5 +6 +6 -7 no. of times 0 0 13 5 13 1 7 7 12 7 4 used +7 8 -9 +9 -10 +10 11 :J/.I_ 12 -13 2 1 1 1 0 5 0 2 2 1

Three-Voice Textures

The analysis of vertical intervals in three part

82 writing presents several additional complications. Instead of the problem of a single interval between two voices there are instead three intervals between the three voices. (The interval between voices one and two, voices one and three and voices two and three.) There is also the probability that the intervals produced between the various parts are not of equal importance thus presenting the additional problem of determining which intervals are most essential. There are approxi mately sixteen measures which are in a three part texture. These sixteen measures occur in three sections, the first is in measures nine through twelve with the entry of the third statement of the subject; the second is in measures 38-45, following the stretto section before the climax; and the third is in measures 69-72, during the stretto of the inverted subject following the climax. In the first section (measures nine through twelve) the third voice enters with a statement of the subject on d by the violoncellos. At this point the third and fourth violins, which have just completed their subject statement on~·, continue in free counter point with the subject while the first and second violas add a second free counterpoint. During these four meas ures the intervals created between the subject statement and the voice which last stated the subject (third and

83 fourth violins) are only 30.7% consonant in quality. The intervals between the subject and the free counterpoint of the violas is, by contrast, quantitatively more consonant with 65.4% of the intervals being consonances. The intervals between the two counterpoints are 61% consonant. The percentages of consonances in the last two combinations approximates the percentages present in the two-voice texture. It appears, at this point, that Bartok's~ primary concern may have been with the intervals created between adjacent voices since the percentage of consonance and dissonance occuring between adjacent voices agrees substantially with the two-voice practice. The intervals which occur between the outside parts contain a markedly greater proportion of dissonant sounds and are probably of secondary concern. The first six intervals between the outside parts are either major ninths or major sevenths. Also, in contrast to the two part practice of limited usage of consecutive consonant or dissonant intervals, the consonances and dissonances between the outer parts in these four measures are frequently found in groups numbering from two through six. On the other hand, the intervals between adjacent voices tend to follow more closely the principles observed in two part writing.

The second three part section, measures 38~5,

84 observes the same tendencies as the first section al though there is somewhat less contrast between the per centages of consonance and dissonance between the parts. The three voices present during this section are violon cellos one and two and the countrabasses one and two in unison on the lowest part; violas one and two and vio lins three and four in unison on the middle part; and violins two on the upper part. The lowest part presents fragmentized statements of the subject while the middle and upper voices are in free counterpoint. Here, as in the first three-voice section, the adjacent voices are relatively more consonant than the outer voices. The interval between the lower and middle parts are 53.5% consonant; the intervals between the middle and upper part are 52% consonant while the intervals between the outside parts are only 41.3% consonant. There is an increase in the incidence of consecutive consonant and dissonant intervals in this section although the general practices remain consistent with the first section. In measures 42 and 43, there are six consecutive disso nances between the lower and middle parts and in measure 45 there is a hitherto unprecedented series of five consecutive major sixths in parallel motion. The third three-voice section is in measures 69- 72. This section presents the greatest problem of the three-voice sections primarily because of its incon- 85 sistence with the practices of both the two and three part sections which have preceded it. The three voices are performed by violoncellos one and two, violas one and two, and violins three and four. The violas and the violins present a two part stretto of the inversion of the complete subject while the violoncellos add a free counterpoint below. The following table illustrates the frequency of various vertical intervals in all of the three part textures of the fugue. The numbers are based on eighth note units. Half numbers are created by occurrences of sixteenth-notes. The figures in column I represent all of the intervals between all three voices. Column II does not include the intervals between the outside parts. Column III reduces the compound intervals, (i.e. intervals exceeding an octave) of column I to simple intervals. Column IV reduces the compound intervals of column II to simple intervals.

86 Interval I II III IV u 3 3 6 6 -2 5.5 5.5 21.5 8 4-2 6.5 6.5 27.5 16.5 -3 13.5 13.5 36.5 19 +3 30 30 45 33 9 9 20.5 13.5 ~ 23.5 23.5 42 27 5 9 9 16.5 11 -6 31 25 34 25 46 34.5 33 43.5 35 -7 18.5 13 20.5 13 +7 26 18 31 18 8 3 3 -9 16 2.5 +9 21 10 -10 23 6.5 +10 15 3 11 11.5 4.5 J/l 18.5 3.5 12 7.5 2 -13 3 0 +13 9 2 -14 2 0 +14 5 0

If the intervals between the outside parts are included, 47.8% of all intervals are consonant. If only the intervals between adjacent voices are considered, 54.2% of all intervals are consonant. The difference in proportion of consonant and dissonant sounds in columns III and IV of the chart is not sufficient to support any proposition regarding whether or not the intervals only between adjacent voices are of significance or if the intervals which are produced between the outer parts must also be considered. It is interesting to note that 87 there is a relatively small percentage of harsh or in tensely dissonant sounds such as seconds or sevenths. Perfect fourths or fifths are also relatively scarce and the most frequent of all dissonant intervals is the augmented fourth.

Four Voice Textures

The addition of a fourth voice to the texture increases the number of resultant vertical combinations to six. The problem becomes not the addition of a single voice but the relationship of the added part to all of the voices already present. In the analysis of four voice textures, unisons, octaves, major or minor thirds, major or minor sixths, perfect fourths, perfect fifths and all of their compound intervals will be considered as consonances. Parallel octaves or unisons will be considered as a single sound. Fourths and fifths are added to the list of consonances because of their function in the vertical sound of a four or five voice texture, i.e. when a perfect fourth ·or perfect fifth is considered as an interval by itself, it is often classified as a dissonance or "imperfect con sonance" but when it is combined with other tones such as thirds or sixths, in a vertical texture, it is often classified as a consonance.

88 Whether fourths or fifths are accepted as consonances or not the fact remains that there is a greater percentage of consonant sounds between adjacent voices than between non-adjacent voices. Parallel motion between various voices, and notes of longer duration than an eighth-note, are common in the four voice texture than in either the two or three part textures. In two and three part textures there is a pitch change in one of the parts on practically every eighth-note unit. Notes of longer time values such as quarter-notes, dotted quarters and half-notes or longer are more common in four voice textures. In the analytical techniques employed in this discussion, two quarter-notes a perfect fifth apart constitutes two eighth-note time units of a perfect fifth, i.e. the ver tical interval e' - b 1 notated in dotted quarter notes would be written as 5, 5, 5 indicating three eighth note units of a perfect fifth. This system of analysis makes no attempt to differentiate between parallel mo tion and intervals of a longer time span. It is concerned only with the composite interval or intervals of every vertical sound as a unit. The first of four sections involving a four voice

89 texture begins on the last eighth-note of measure twelve and continues through all but the last eighth-note of measure sixteen. This passage consists of the fourth statement of the subject. The statement is made by the muted second violins on b ' • The violas, violins three and four, and violoncellos (the first, second, and third sub ject statements respectively) are continuing in free counterpoint. The second four part section begins on the last eighth-note of measure twenty-six and extends through the first part of measure 31 (the analysis involves only measures 27-31). The four measures encompass the complete statement of the subject in a two part stretto with tonal centers on r# and c. The stretto occurs between the first and second violins (on the octaves f# and f#' respective ly) and the violincello and contrabasses on c. The octave doublings in the first and second violins and the octave doublings between the violoncellos and contrabasse~ (resulting from the transposition of the contrabasses) are not considered as separate parts. The pitches used in the analysis are those of the second violin and the violoncello. The outer voices are engaged in a two part stretto three eighth-notes apart and at the interval of a tritone. In contrast to every contrapuntal section up to this point, the intervals between the outside or non-adjacent

90 voices have a very large percentage (72.4%) of consonant sounds. The two inner voices, the third and fourth vio lins and the violas, have the greatest percentage of consonant sounds to be found at any point in the first movement. There are only three dissonant interval units in the entire four measures. The two upper voices, i.e. the second violins and violins three and four, move primarily in oblique or parallel motion. The most im portant interval in this section is the tritone. 59.4% of all of the intervals between the upper two voices are tritones and there are examples of as many as five par allel tritones in succession. The two lower voices have essentially the same relationship to each other as the top two parts have. There is a great deal of parallel motion and the tritone is the predominating interval comprising 53.1% of all of the intervals. The percentage of intervals represented by the tritone in these four measures is considerably greater than the percentage of any other single interval in any section in the movement. The third four-part section extends from measure 46 through measure 51. This is the section immediately preceding the climax of the fugue in bar 56. The four voices are represented by the first and second violins on the top part; the third and fourth violins, on the second voice from the top; the violas, on the third

91 part; and the violoncellos and contrabasses on the low est part. The fundamental melodic material of these six measures is derived from repeated statements of Item I in the highest voice accompanied by a rising sequential figure in the lowest part. The two inner voices fill in with free contrapuntal lines. The fourth and last four part passage is only two and one-half measures in length. It begins on the last eighth-note of bar 72 and continues through the third eighth-note of bar 75. It comes at the beginning of the inverted stretto statements of the subject on d "' , by the muted second violin,. and on ~ ' , by muted violoncellos. The two inner voices are played by the second viola and the fourth violin. The following table presents a tabulation of all of the intervals between all voices in a four part texture. Fractions of intervals such as one-half or one- third arise when the basic eighth-note unit is subdivided by a smaller time unit such as sixteenth notes (.5) or sixteenth-note triplets (.33). The column on the left represents the various intervals. The small numerals at the upper right of some of the larger numbers used to indicate the intervals designate the actual size of the interval, i.e. a +91. equals a major ninth plus one octave; a +10~ equals a major tenth plus two octaves. 92 The next six columns from left to right, present the number of occurrences of each interval between the voices indicated at the top of each column. The last column gives the total number of times each individual interval is used. The columns containing the intervals between adjacent voices are marked with asterisks. The subsequent table reduces the compound inter vals. The right hand column where totals are given indicates that the most frequently used interval in four part texture is the tritone. This is, to a large extent, due to the extensive use of this interval in measures 27-31. The figures at the bottom of each column repre sent the percentage of consonant sounds. Unisons, major and minor thirds and sixths, perfect fourths and fifths are included as consonances. Asterisks are again used to indicate the columns containing the intervals between adjacent voices, however, because of voice cross ings in measures 14-16, 46, 48, 50, and 51 the columns markedl by the asterisks do not represent the intervals between adjacent voices at all times.

93 Vl.2 Vl.2 Vl.2 Vcls. Vcls. Vlas. Interval Vcls. Vlss. Vl.3&4 Vlas. Vl.3&4 Vl.3&4 Total u 4 2 2 8 -2 1 1 1 2.33 5.33 +2 1 5 7 5.5 18.5 -3 2 2 11 2 9.JJ 26.33 -+3 3 6 10 8 13.33 40.33 2 9.33 15 17.5 26.5 79.33 ~ 3 26.33 22 7.33 17 75.67 5 2 3 13 3.5 7.5 29 -6 2 15 18.33 13 2.83 18 69.33 f 6 10 11 4 6.33 14.5 45.83 -7 L 6 7 12 13-5 11 51.5 +7 1 19 5 5 20.5 6 56.5 8 2 5 1 1 3 12 -9 1 8 3 2 6 20 +9 12 11 4 3 9 1 40 -10 9 9 6 1 13 38 +10 17 11 10 1 4 43 11 6 11 4 1 1.5 23.5 )/.1 14 12 5 2 33 12 5 2 7 -13 16 1 1 1 19 +13 9 9 -14 5 1 6 +1~2. 8 1 9 1 1 -92. 3 1 4 +9i. 3 3 -101 +10~ 2 2 lP J;it. 1 1 122. 1 1 -131 +13'" 1 1

94 Vl.2 Vl.2 Vl.2 Vela. Vcls. Vlas. Interval Vela. Vlas. v~.3&4 Vlas. Vl.3&4 Vl.3&4 Total u 1 2 5 5 3 5 21 -2 4 8 4 7 2.33 29.33 +2 15 11 5 i 16 6.5 61.5 -3 9 11 8 12 15 9.33 64.33 +3 19 14 16 11 12 13.33 85.33 6 13 13.33 16 19 26.5 93.83 ~ 15 15 31.33 24 7.33 17 109.67 5 6 4 3 13 3.5 7.5 37 -6 18 15 19.33 14 3.83 18 88.17 +6 10 10 11 4 6.33 14.5 55.83 -7 7 6 7 12 14.5 11 57 .5 +7 9 19 5 6 20.5 6 65.5 58% 53.9% 59.1% 58.1% 49.% 68.9% 57.9%

A comparison of the intervals between adjacent and non-adjacent voices reveals that between adjacent voices 61.98% are consonant while the intervals between non adjacent voices are 53.33% consonant. The difference between these percentages would have been greater had it not been for the very large number of tritones, many of which occurred during the four measures from bar 27-31. The difference in the distribution of intervals and percentage of consonance in these four measures is sufficiently interesting to merit special attention.

95 ooj} ~'" {~ Vl.2 Vl.2 Vl.2 Vcls. Vcls. Vlas. Interval Vcls. Vlas. Vl.3&4 Vlas. Vl.3&4 Vl.3&4 Total u 0 0 0 0 0 0 0 -2 0 2 0 0 3 0 5 t2 2 3 0 0 6 0 11 -3 4 1 0 5 1 5 16 +3 7 1 5 1 0 4 18 6 3 3 2 2 11 27 ~ 0 1 19 17 0 0 37 5 1 0 0 2 0 4 7 -6 3 1 3 3 1 4 15 -+6 0 5 2 1 0 3 11 -7 2 5 0 0 5 0 12 +7 4 9 0 1 14 3 31 72.4% 35.5% 40.6% 43.8% 12.5% 91.2% 49.5%

Here again there is a greater percentage of consonance between adjacent voices (59.2% consonant) than non-adjacent voices (39.1% consonant). It is interesting to notice that the intervals between the third and fourth violins and the violas is almost entirely con sonant (91.2%) and by contrast the intervals between the violoncellos and the third and fourth violins are extremely dissonant (12.5% consonant). These percentages are the greatest extremes of consonance and dissonance between any two voices in the entire movement.

Five Voice Textures

Approximately fifteen measures of the first movement are in a five voice texture. Ten of these measures are from bar seventeen through bar twenty-six. The remaining five measures occur in two short sections; 96 measures 31 and 32, and measures 75-77. The analysis of five part textures will be confined to an examination of the ten measure section beginning with the anacrusis to bar seventeen and continuing through bar 26. Included in these ten measures are the fifth and final subject statement of the exposition by the contrabasses on G, and the episode section that follows this subject state ment. The episode section included in these measures is the only section of the fugue that uses melodic material which is not derived primarily from the subject. This ten measure section ends with the beginning of the first stretto section on the last eighth-note of measure 26. In the five voice textures there is an increase in the incidence of notes of a longer time span. There are frequent occurrences of notes with a duration of six to eleven eighth-notes in length. The greatest time

span of any single tone in this section is an ~', in the second violin, that begins in the middle of bar twenty-one and continues through the first eighth-note of bar twenty-three (a time span equivalent to fourteen eighth-notes).

Parallel motio~ if defined as the simultaneous movement of two or more melodic lines that maintain a constant vertical interval spread while progressing melodically, is practically non-existant in the five

97 voice sections. There are numerous places where two, or infrequently three, voices maintain the same vertical interval for from four to seven eighth-note units but in none of these places are the parts moving melodically;

t i.e. one voice may be playing a dotted half-note b while simultaneously another part may be holding a dotted

1 half-note f • In this case there are six consecutive eighth-note units of an augmented fourth. This should not be considered to be parallel motion because the word motion indicates movement or change whereas in this case, both of the voices are melodically static. It is simply a single interval of greater duration. Despite the fact that at several points two, or even three voices are maintaining the same interval relationship over a period of more than one eighth-note unit, there is at all times melodic motion in one of the parts on every eighth-note. There is a considerable increase in the number of consecutive consonant or dissonant intervals in the five voice counterpoint. It is not uncommon to find from four to eight consecutive dissonant intervals between the different voices. This is somewhat to be expected in a five voice texture. When the relationship of each part to every other part is being considered some of these re lationships are necessarily of secondary importance. Series of consecutive consonant sounds are common and

98 frequently quite long. There are examples of eleven, thirteen, fifteen and twenty consecutive consonances. These all occur in the intervals between the second violins and the third and fourth violins. The intervals formed by these voices have a higher percentage of

consonant intervals than the intervals formed by any other two parts (68.4% consonant). The tables on the following pages are essentially the same as those employed in the analysis of four-voice textures and should require no further explanation.

99 ~ ~ :'(. C .B. C .B. C. B. C.* B. Vl.2 Vl.2 Vl.2 Vlas. Vlas. Vl.3&4 Interval Vl.2 Vlas. Vl.3&4 Vela. Vela. Vl .3&4 Vla.s. Vl. 3&4 Vela. Vela. Total

u 1 1 -2 1 1 2 4 8 +2 2 5 5 2 14 -3 1 12 1 21 6 41 +3 3 4 2 14 23 4 9 2 8 3 3 29 ~ 7 4 3 13 6 3 36 5 7 5 4 7.5 13.5 4 41 -6 7 1 21 15 4.5 4 1 53.5 +6 1 5 1 6 9 9.5 6 37.5 -7 2 12 3 4 3 3 .. 5 10 13 50.5 +7 1 4 3 2 10 2 .5 2 3 27.5 8 -9 4 2 1 4 7.5 1 3 22.5 I-' f9 7 3 4 2 7 1 1 9 34.5 0 -10 11 1 2 5 1 2.5 1 7 30.5 0 410 6.5 2 1 1 9 4 23.5 11 15 2 1 6 2 3 5 34 J/L 6.5 6 9 8 3 36 .. 5 12 5.5 ~ 4 1 3 18.5 -13 2 4 13 3 7 1 5 14.5 +13 2 4 7.5 1 3 1 21 -14 6 2.5 3 3 1 +14 1 1 10 8 1 20 81 1 17 -9'" 8 11 1 12 +9'" 7 5 5 21 -10~ 3 4 5 11 • .5 +10'" 12 3 6 2.5 11,. 8.5 3 :vi,. 1.5 1 * C .B. C.B. C.B. C.B. Vl.2 Vl.2* Vl.2 Vlas.* Vlas.* vl.3&4 Interval Vl.2 Vlas. Vl.3&4 Vels. Vela. Vl.3&4 Vlas. Vl.3&4 Vela. Vela. Total 12'1- 3 3 -13~ 3 3 +131. 12 12 -141. 2 2 -ti~; 6 6 -9~ 3 3 +9~ 1 1

...... 0 ...... The next table presents a condensation of the compound intervals of the preceding table to simple intervals. Asterisks indicate adjacent voices. The row across the bottom gives the percentage of consonant sounds when unisons, major and minor thirds or sixths, perfect fourths, and perfect fifths are considered as consonances.

102 -Jt .. C. B. C.B. C.B. C* .B. Vl.2 Vl .2 Vl.2 Vlas. Vlas.* Vl.J&4 Interval Vl.2 Vlas. Vl.3&4 Vela. Vela. Vl.3&4 Vlaa. Vl.3&4 Vela. Vels. Total u 1 1 2 -2 11 4 11 2 2 5 7.5 2 2 7 53.5 +2 8 7.5 5 3 9 4 7 6 6 11 66.6 -3 3 11 5 3 10 13 3.5 2ll. 7 7 83.5 -+ 3 12 6.5 5 4 7 4 9 2 14 67.5 8.5 15 5 5 6 11 5 8 3 i 74.5 ~ 1.5 6.5 5 13 13 3 8 13 6 6 75 5 3 5.5 5 11 1 5 7 7.5 13.5 4 62.5 I-' -6 5 13 10 8 21 16 4.5 4 6 91.5 w0 t6 14 ~ 7.5 6 4 6 0 9 9.5 7 68 -7 2 8 2.5 12 6 4 6 3.5 10 13 67 f 7 7 2 10 4 11 2 10 2.5 2 4 54.5 5 4 6 7 (9) 1 8 3 2 (9) I 59.3% 62.7% 55.3% 53.4% 46.81~ 68.4% .51.3% 65.8% 66.2% 46.8% 58.7% In five voice textures, as was the case in three and four voice textures, the intervals between the adja cent voices have a higher percentage of consonance (65.9%) than the intervals between non adjacent voices (53.8%). Parallel motion between voices is very rare (one of the few exceptions was in a four part texture in measures 27-30 where there are numerous parallel tritones). The tritone is the most common of all of the intervals con sidered to be dissonances. The minor second, generally considered as harshest or most active dissonance, is the least common of all dissonant intervals.

104 Compositional Devices

Melodic Inversion

~elodic inversion, that results from changing each ascending melodic interval of the original into the corresponding descending interval and vice versa, is first found beginning on the last eighth-note of bar 56 in the violoncellos and countrabasses. This inversion consists of a statement of Item I on eb. The fugue subject, up to this point, has been constantly building toward its climax (acheived at the beginning of measure 56). After the climax has been reached, BartokI inverts the subject in order to relieve the tensions of the subject contour. The effect of this inversion changes the restless, driving character of the original melodic line to one of relaxed calm. The appearance of the inverted subject is the turning point of the movement. All of the compositional devices leading up to this point have been of a forward surging, expanding nature. The dynamics have increased from piano-pianissimo to forte-fortissimo, the number of voices has increased from one to five (all but one of these five voices are here playing double stops), the vertical spread between the highest and lowest voices is greatest at this point, and the tonal centers of eb and d# are at their farthest

105 distances from the initial tonal center of the movement in their journeys around the circle of fifths. The appear ance of the invert~ct is the beginning of the movements return to its place of origin. The climax is passed, and like a mountain that has been conquered, all

that remains is the descent. From its appearance in bar 5~

"'·..._...... , to the end of the movement, some fragment of the in~rted subject is always present. The stretto sub-sections C and Dare constructed from inverted subject statements. In measure 78, the beginning of the coda, the inversion is mirrored vertically against the original statement. In measures 82-85, the inverted melodic Items are frag mentary. And finally, in measures 86-88, we find a perfect mirroring of the original subject against its melodic inversion. The melodic inversions of the first movement are as important and necessary to its conclusion as the subject itself was vital to its growth.

Retrograde

This term denotes the reverse reading of a melody; beginning with the last note and ending with the first. This device is not in evidence in the first movement of the Music for String Instruments Percussion and Celesta. There is also no retrograde treatment of any of the rhythmic Items of the subject.

106 Augmentation and Dimunition

Augmentation, or diminution, in the sense of the presentation of the subject or melodic Items in doubled or halved note values, is not used in the first movement. The only places where there is any alteration in the length of the note values of the subject are in measures 47-55, where there is an irregular shortening of some of the notes of the subject in order to increase the rhythmic motion and in measures 76-79, where the eb ' in the violoncello statement of Item IV is extended one and one-half measures to its e' resolution in bar 79. Neither of these sections may be considered to be either augmentation or diminution in the usual sense. They appear to be merely irregular extensions or condensations of isolated note values permitting rhythmic flexibility and slight melodic variation. Vertical melodic interval augmentation or diminution, i.e. the expansion of a small interval to a larger interval, such as a minor second to a major second or a minor third; or the shortening of a perfect fourth to a smaller interval such as a minor third or major second is not employed as a compositional device with the exception of a few isolated instances where the vertical sonorities of the counterpoint necessitate an intervallic

107 alteration. In the few places where the characteristic intervals comprising the subject are intervalically altered they usually fail to retain their aural identi fication as subject material.

Orchestrational Technique

The reader should recall that the stringed instru ments are seated on opposing sides of the ensemble so as to form two antiphonal string choirs. The first choir consists of violin I and II, viola I, violoncello I and contrabass I, the second choir of violins III and IV, viola II, violoncello II and countrabass II. The per cussion, harp, celesta, and piano are grouped in the center. The celesta and piano are placed side by side to enable the celesta player to take over the second part of the piano in several places. The timpani are to be the chromatic pedal type in order to perform the glissandos in the third movement. There are to be two side drums, one with snares and one without snares, there should also be two pairs of cymbals, one large pair and one smaller pair. The cymbals, side drum, bass drum and tam-tam are all to be played by one performer. The orchestration of the composition is very imaginative and exploits the techniques of the performers in many ways. The stringed instruments are required to

108 play col legno, sul ponticello, flautando, multiple

stops, (both ~and pizzicato) tremolo, harmonics, glissandi, and con sordino, as well as four different types of pizzicato effects. The timpanists must play glissando passages and the percussionist must execute several special effects. The orchestration of the first movement alone did not exploit many of the above mentioned effects. There is very little activity in any of the parts except the strings. The celesta plays for only four measures. The bass drum plays one note in measure 56 to punctuate the climax. The tympani plays two sustained rolls, which serve the function of pedal points and there is the metallic rustling sound of a pianissimo roll of two meas ures duration to be played on the cymbal in measures 51 and 52. The rest of the movement is performed by the strings alone. The strings are col arco throughout this movement. They begin con sordino; near the middle of the movement they are senza sordino, and from measure 69 to the end, they are again con sordino. Concerning other special effects, there are three very short glis sandi following the climax, and very few harmonics, tremolos or double stops. The treatment of the string family, in the first movement is, with the exception of the seating arangement, generally traditional. There

109 is no attempt to exploit the possibilities of the an tiphonal seating order to create any sense of dialogue until the second movement, where this device becomes very important.

110 CHAPTER V

SUMMARY

, / The first movement of Bela Bartok's Music for String Instruments Percussion and Celesta is. in the form of a five voice fugue. It is 88 measures in length and in performance it requires approximately six and one-half minutes playing time. In the first movement there is very little use of either the percussion or the celesta. The subject of the fugue is constructed from four short phrases or Items all of which have certain basic similarities which tend to unify both their melodic contour and their composite intervals. Throughout the movement the subject provides practically all of the melodic material used and the subject itself is present in some part at almost any point. The melodic material of the first movement that is not actually part of the subject is usually derived from it. In addition, this subject provides much of the melodic material for the three remaining movements of the composition. "Arch form" or symmetrical structural balance is frequently used in the formal framework of the first movement. Some of Bartok'sI applications of this structural device are illustrated by the diagrams on pages twelve, (the larger structural framework); thirty-one, (the

111 dynamics and use of mutes); fifty (a graph of the meters used); and fifty-four (a detailing of the major stretto sections). The tonal structures of the fugue is based on two series of tonal centers that progress in opposite dir ections through the circle of fifths. One series modu lates through a succession of ascending perfect fifths while the other series progresses through a succession of descending perfect fifths (see the diagram on page 14).

The most important tonal centers are on ~, the tonality of the beginning and end of the movement; and eb, the tonality of the climax of the movement, half-way through I. both the ascending and descending series of fifths. Other important tonal centers are f#, and £, which are used in both stretto sections. These strettos occur at the half-way points between the beginning and the climax and the climax and the ending (see diagram on page 16). It will be noted that the relationship of ~ to eb and of t:# to £are tritonic. In addition to their position as important tonal centers, tritones are in this work, most frequently used among those classified as dissonances.. The dynamica, spread (vertical distance from the highest to the lowest tone) and density (number of dif ferent notes being sounded at any given point) all follow a pattern of expansion and contraction. Each of these elements from a very small beginning expand to a powerful climax, and then contract to a very small finish (see graphs on pages 31, 32, and 33). It is important to note that at the climax, when the devices that are employed in the creation of tension, dynamics, spread, and density are greatest, there is practically no use of dissonance in the vertical texture. The fundamental unit of rhythm is the eighth-note. There are very few places in the fugue where there is not movement on each eighth-note unit of the measure in at least one of the voices. The rhythm, which include strong- er rhythmic elements than those used elsewhere in the movement, is essentially non-accentual ( with the possible exception of measures 56-62). Metrical indications for each measure all use the eighth-note as the unit but the number of eighth-notes in each measure is irregular varying from five through twelve. Changes in the tempo are effected gradually and the variations in the tempo indications are small with the slowest markingJl= c.108; and the most rapid,J'"= c.126. Analysis of two voice vertical sonorities revealed a contrapuntal practice in which (a) there was almost no parallel motion (other than octaves or unisons), (b) the dissonant intervals were almost always interspersed between consonant intervals (c) approximately 60% of the

113 vertical intervals were consonant, (d) there is contra puntal motion on every eighth-note, (e) the melodic material of the counterpoint is derived from the subject. In the analysis of three, four, and five voice textures there was an attempt to formulate a basic theory of the relationship of a given part to any other part. The principle purpose of this theory was to establish that the intervals between some voices were more contrapuntal ly important than the intervals between some other voices. Although the data obtained from the analysis of these textures did not yield a sufficient amount of evidence to be termed conclusive, it indicates that the intervals between adjacent voices had a greater percentage of con sonant sounds than did the intervals between nonadjacent voices. This seems to imply that the primary contra puntal consideration was with the adjacent voices while the non-adjacent voices are merely the products of the contrapuntal interweavings of the adjacent voices. The use of dissonant intervals in the counterpoints between adjacent voices was more consistent with the two part practice of interspersing dissonances between consonances than it was between nonadjacent voices where there are frequent occurrences of extensive consecutive dissonant sounds. A more comprehensive survey of Bartoks contra puntal compositions, such as the forty-four violin duets,

114 would undoubtedly yield additional information concern- , ing Bartok's contrapuntal technique. Of the mechanical compositional devices, such as (a) melodic inversion, (b) augmentation, (c) diminution, (d) retrograde, and (e) mirroring, only melodic inversion and melodic mirroring are used to any extent. The orchestration of the fugue is almost entirely for the strings with the percussion and celesta being used for only a few measures of the movement. There is no attempt to exploit the antiphonal possibilities of the seating arrangement illustrated on page two, although this seating does produce some differences in the auditor's experience when compared with the normal orchestrial disposition of instruments. The only orchestrational string devices used are mutes, tremolo, a few glissandos, and one harmonic note in the contra bass part.

115 BIBLIOGRAPHY

Books Apel, Willi. Harvard Dictionary of Music. Cambridge, Massachusetts: Harvard University Press, 1953.

B~la Bart6k, A Memorial Review. New York: Boosey and Hawkes Inc., (1950). Dallin, Leon. Techni ues of Twentieth Centur osition. Dubuque, Iowa: Wm.C.Brown Company, 19 Forte, Allen. Contemporary Tone-Structures. New York: Bureau of Publications, Teachers College, Columbia University, 1955. Searle, Humphrey. Twentieth Centurl Counterpoint. London: Williams and Norgate, (19$4 • Stevens, Halsey. The Life and Music of Bela Bartek. New. York: Oxford University Press, 1953. Periodicals Cone, Edward T. "Analysis Today'', The Musical Quarterly, XLVL, No.2 (April, 1960), 172-188.

Forte, Allen. "Bart6k' s 'Serial' Composi tion11 , The Musical Quarterly, XLVI, No.2 (April, 1960), 233-245· Hawthorne, R. "The Fugal Technique of Bela Bartbk", Music Review, (Nov.,1949), 277-285. Musical Score Bartok, Bela. Music for String Instruments Percussion and Celesta. (New York): Boosey and Hawkes Inc. Pocket Score No. 16155, (1938). Unpublished Material Biales, Albert. "The Orchestrational Technique of Bela Bart6k". Unpublished Master's thesis, School of

116 Music, Ohio State University, 1954.

Green, Burdette L. 0 A Comprehensive, Analytical Study of Bela, Bartok's, Fifth String Quartet ft • Unpublished Master's thesis, School of Music, Ohio State University, 1953. Taylor, Vernon Husson. "Contrapuntal Techniques in the Music of' Bela Bart6k". Masters Thesis, School of' Music, Northwestern University, 1950. (University Microf'ilms, Ann Arbor, Michigan). Walker, Mark Fesler. "Thematic, Formal, and Tonal Structure of' the Bartok String (iuartets". Doctoral Dissertation, School of' Music, Indiana University, 1955. (University Microf'ilms, Ann Arbor, Michigan).

117