As far as concentration and closeness of form are concerned, none of Bartók’s works surpasses the opening movement of the Music: the famous ’pyramid-fugue’. Its closeness, resembling a circle, is already manifest in the key structure. The entrances of the fugue-theme are based on the circle of fifths. Starting from the central A note and the ’middle’ viola part, the entrances progress in two directions – up and down – round the circumference of the fifth-circle, till they meet at the centre of the movement on the opposite side (the ’counterpole’ Eb):

Fig. 94

then continuing their progress, they find their way back to the starting-point: from Eb to A.

The dynamic line also follows this arc-form: the movement is based on a single-sweep crescendo-decrescendo: starting from pianissimo, it rises steadily to attain the climax, the fortefortissimo – and then step by step sinks back to pianopianissimo (this is why the movement is also known as the ’scissor-fugue’ or ’fan-fugue’). In addition, the entrances become more and more frequent up to the culmination, and from there they become rarer and rarer: the first five theme-entrances are presented one by one, entrances 6-7 appear in canon, and entrances 8-11 simultaneously (in a narrow sequence); while after the culmination the same process is reversed. This means that the pyramid form is also effected in the condensation and thinning-out of the material. In fact, the fugue-theme itself is inverted from the peak of the pyramid, and proceeds in mirror fashion:

Fig. 95

Faced with such a degree of concentration, we can be justified in asking whether this is merely a technical stunt or whether, on the other hand, the visible form itself represents the projection of the poetic conception.

As far as my own impressions are concerned, I would define the place of the fugue in the work as follows. The opening movement is born in the spirit of the Bartókean ’creation’ idea. Bartók evokes the elementary explosions at the movement’s central point in order to create the transition from chaos into a dialectically articulated world. At the moment of culmination, the swirling, shapeless material – a resound-ing chaos – is organized into ’intelligible’ pairs of antitheses (questions and answers): the material separates into mutually complementary elements; set against the homogeneous, impersonal whirling of the first part, it is precisely this dialectical separation of light and shade that signifies the appearance of personal elements and individuality in the work:

Fig. 96

In the qualitative transformation of the material, a significant role is played by the double sound stage: the double orchestra. The piece engages two string orchestras, between which the piano-celesta-harp group and the percussion are placed. Thus the arrangement of instruments not only polarizes the tonality (as the title vividly expresses, from the resounding drum to the ethereal celesta), but through the stereophonic effect of the strings on the right and left polarizes the musical ’stage’ as well.

The introductory part (the exposition) of the fugue takes place in the acoustical area to the right of the centre; the movement, however, comes to an end on the opposite, left-hand side of the stage. The concepts of left and right even in ancient philosophy were identified with the ’inner’ and ’outer’ worlds. On modern stereo stages (’sonic stages’) this identification has actually become the rule! The special content of ’right’ and ’left’ may be connected with the asymmetrical construction of our body – in particular with the fact that our heart is on the left side.

A stereo record-player easily persuades us how completely the character of the movement would change if the orchestras on the left and right were exchanged. (My art history teacher once put slides of Giotto’s fresco, The Mourning of Christ, and one of Rembrandt’s landscapes became in the projector in ’mirror-view’, reversing the left and right sides – in order to illustrate how the change radically altered the effect, mood and message of the picture; for example, the landscape impressionistically open or intimately personal in character, depending on whether the tree came to the right or left of the picture.) All this coincides with our previous observation that the shapeless swirl in the first half of the movement contains impersonal, while the clarification in the second half, personal elements.

This is how the fugue-theme rises from the depths to the heights: to the dream-like swaying of the final part – and from the ’outer’ (right-hand) stage to the ’inner’ (left-hand) stage. (The progression from the right to the left corresponds to the Eastern way of thinking – similarly to the pentatonic system of the movement.)

The foregoing reveals that the severity of the composition reflects not the laws of formal logic but those of organic development. This is all the more evident in the formation of the proportions, for these follow not the principles of classical symmetry but the laws of natural growth. For example, if each branch of a tree grows a new branch every year, but the fresh branches grow their first young branch two years later, the number of branches shows an annual progression as follows:

2, 3, 5, 8, 13, 21, 34, 55, 89 

The 89 bars of the fugue are divided by the climax into 55 + 34 sections. The removal of the sordino divides the first part of the movement in a 34 + 21 ratio, while the second part of the movement is chopped by the renewed con sordino effect into 13 + 21 bars – with sharp contours. The exposition ends in b. 21, and even the final 21 bars of the movement show a 13 + 8 proportion. The section–points – like the nodes of a longitudinal wave – are attracted towards the centre (in keeping with Bülow’s Beethoven analyses, the movement must be completed by a rest bar):

Fig. 97

The form of the movement thus creates one single wave-arc.

The centre of the movement has the task of bringing about the metamorphosis – that transformation which is the basis of every real dramatic action. The form constitutes one single ’magnetic field’: crossing the centre the poles of attraction are exchanged! So the appearance of the ’counterpole’ – at the climax – also has a fairly essential function of content.

The transformation of the material is also indicated in the other movements by the appearance of the counterpole – by this means the four movements, collectively as well as individually, are enclosed in a polar circle:

Fig. 98

beginning and end: A,
middle point: Eb (56). 
beginning and end: C,
middle point: F# (263). 
beginning and end: F#,
middle point: C (46). 
beginning and end: A,
middle point: Eb (83). 

In order to illustrate the dual plan of the Second movement, let us place the themes of the exposition and recapitulation side by side. The movement springs to its feet with an irritated reflex. Observe how (with a tigre-like gesture) the second orchestra cuts into the theme-entrance of the first!

Fig. 99

(And vice versa, from b. 10 the first orchestra into the second.) It would scarcely be possible to bring about this effect with mono sound! The parts ’bite into one another’ savagely. (The collisions and sharp clashes of the parts also determine the character of the exposition in what follows.)

On the other hand, in the principal theme of the recapitulation the instrumental groups of the two orchestras unite. The rapid, tearing motions of the exposition pass into a balanced ’rocking’:

Fig. 100

this is why the role of the timpani alters (see: Fig. above).

The sharpest contrast is nevertheless produced by the closing theme. Its entry in the exposition is equivalent to ’conflict’: the broad flashing lines and flashes of lightning (accompanied by side-drum crescendos and crackings of the bass) lead to a ’wrestling’ of the parts: the various instrumental groups struggle resolutely with one another – without arriving at a result (b. 141). The essence of the exposition is that its plot remains unsolved. Not so in the recapitulation! The closing theme of the reprise is meant to bring about fulfilment: Un poco largamente (b. 466, taking the place of the previous wrestling!).

After the unresolved, unaccomplished exposition, the secco clatter and high tension ’spark-discharges’ of the development ensue with the certainty of a physical reaction. Behind the string-rending staccatissimos and murderous excitement of the rhythmic flashes, there once more stands the fugue-theme – note for note:

Fig. 101

At its every step, the score of Music for Strings, Percussion and Celesta betrays that the composer’s inner hearing was stereo. What is more, Bartók was acquainted with principles which the pioneers of modern stereo recordings did not begin to develop until the early sixties.

In the principal theme of the second movement, the left group of strings is taken over by that on the right (see Fig. 99 on p. 59), while in the principal theme of the fourth movement, the right orchestra is answered by the left, in accordance with the fact that – as opposed to the energetic short-tempered impulses of the beginning of Movement II – the mood of the finale is relieved and joyous. We have already experienced the crucial importance of the fact that the two orchestras are united at the recapitulation of the second movement (likewise the sound becomes ’centralized’ in bs. 74 and 114 of the finale).

Melodies appealing to ’emotions’ – as the secondary themes of Movement III – come forward consistently from the left, whereas thoughts of ’spiritual’ content come from the right. It is not even conceivable otherwise: at the end of Movement IV, where the fugue-theme returns in ’diatonic’ form, the tune is heard from the right-hand stage – the spiritual quality of the thought is in this way significantly extended.

Further it can be observed that the ’impressionistic’ character goes hand in hand with the spatial polarization of the tonality; and conversely, the more ’expressionistic’ the character of the music, the more the external space loses its importance and the tonality becomes homogeneous – mono-sounding. This in itself conceals exceptional possibilities! E.g., at the climax of Movement I – when all our attention is focused on the inner dynamics and tension – Bartók suddenly transforms the polarized sound into ’mono’ sound, that is, he makes the two orchestras play the same parts. The reverse is just as effective; but as opposite laws apply to the ’chromatic’ and ’diatonic’ techniques, in the diatonic world this also comes to pass the other way round: the homogeneous sound becomes a ’stereo’ sound at the climax – in much the same way as when we have ascended a hilltop, the landscape all at once opens up before us. The opposition of the left and right often produces the sensation of ’here’ and ’away’ (the music of the next movement offers an interesting example of this).

Ferenc Liszt also writes about this symbolism in a poetic letter (Florence, 1839) on Raphael’s painting Saint Cecilia. ’The painter places Paul and John on the left of the picture: the former is deeply absorbed in himself, the outer world ceases to exist for him; behind his giant figure immense profoundities are lurking. John is a man of "attractions" and "feelings"; an almost feminine face looks out at us. On the other hand, Augustine on the right of Cecilia, maintains a cool silence ... he abstains even from the most sacred emotions – constantly fights against his feelings. On the right edge of the picture stands Magdalene in the full splendour of her worldly finery; her whole bearing suggests worldliness, her personality radiates a sensuousness somewhat evocative of Hellas... Her love stems from the senses and adheres to visible beauty. The magic of sound captivates her ear faster than her heart is possessed by any supernatural excitement.’

Movement III is a magic nature music. Its form again rests on symmetry – on a five-part ’bridge form’ (the order of the themes being A-B-C-B-A): on the one hand, the dirge melody of the first and last sections, and on the other, the alluring siren music of the second and fourth sections rhyme with each other; the sharp flashes of the third theme mark the centre of the bridge. To put it another way, the form of the movement delineates a spacious cupola, rising from the sobbing dirge-melody (A) up to the ethereal siren-song of the secondary theme (B); then an undulation – stirring up the whole orchestra – prepares the midpoint: the ’light’ effects of the climax (C), (see: Fig. 56 on p. 36) in order to lead back to the starting point, in reverse order of the themes (melody B and finally, A).

Erich Doflein believes the xylophone rhythm at the beginning of the movement to have been inspired by the wooden drum of Japanese No dramas. That Bartók resorts to such sound-effects not for their own sake is proved by these very pages of the score. From theme 1, the sobbing lament song, the ’fume’ of a gong-stroke rises to the ethereal clear dolce-melody of the celesta-violin (theme 2); in the recapitulation, however, since the order of themes is reversed, the previous dolce-melody is suddenly stopped by the ’snapping’ of the strings (produced by slapping the strings against the fingerboard), and leads back to the dirge. And whereas the dirge-melody and its nocturnal F# tonality is deepened by the shuddering sound of the timpani (i.e. the lowest drum effect), a high-pitched cymbal effect indicates the centre of the movement – and the key of light: C.

Fig. 102

As in the previous movements, the peak of the cupola (the counterpole of the movement) also transmutes the action in its content – and this is movingly expressed by the recapitulation of the secondary theme:

Fig. 103

The most essential effect often escapes the attention of performers: this theme reappears in canon, and from the ’imitating’ part of the canon (cello) Bartók requires a more intensive dynamism than from the ’leading’ violin: the cello is piano, the violin pianissimo. Thus the effect arises: the melody becomes a recollection, a memory image: with the help of the canon, it shifts in space and time (attention and mind are divided into two) – it takes place on a divided double-stage and, owing to the stressed imitating part, a stronger light is thrown on the more distant stage. We point this out because in Bartók’s recapitulations, canon melodies of slow space usually play the role of ’memory’, remembrance, reminiscence.

Here the reminiscence effect is enhanced by something else. The violin is heard from the left, and the imitating cello from the right side of the stage. As on modern stereo stage, the left is associated with ideas of ’inside and here’ – while the right with ideas of ’outside and far’.

The’memory’ character makes us realize why the tune must end with the break of the strings (a strong pizzicato so that the string rebounds off the fingerboard). As a consequence of the crack, the basses groan and the dirge-melody returns.

The finale contains the poetic solution of the work. The solution lies in the fact that the leitmotif of the work, the ’closed’ fugue-theme – which hitherto occurred in a narrow a chromatic form – reappears towards the end of this movement in a wide diatonic form: in the ’open’ sphere of the natural overtone scale (see Fig. 107 on p. 65).

The transformation from closeness to openness is already revealed by the principal theme: the ’circular’ melodic lines of the first movement are here extended to ’straight’ scale-lines:

Fig. 104

Bartók’s closed chromaticism can be represented by the symbol of the ’circle’, while his open diatony can be seen in the symbol of the ’straight line’. The themes also become assimilated to these emblems: the chromatic system is most naturally combined with the circular, whereas diatony with the straight melodic line (scale-line). The opening and closing themes of the Sonata for Two Pianos and Percussion, Music for Strings, Percussion and Celesta, and of the Fourth String Quartett are shown here:

Fig. 105

In Dante’s Divine Comedy, the symbol of the Inferno is also the circle, the ring, whereas his Paradise is symbolized by the straight line, the arrow, the ray. The concentric circles of the Inferno narrow till they reach the Cocytus – the circles of Paradise, however, expand into the infinite Emphyreum. In the Comedy we frequently come across the transformation of the circle into straight line, and vice versa. The poet approaches, for instance, the denizens of the Purgatorio in this way: ’You, who are bent by life, keep circling to straighten out again’ (Purg. XXIII); or later on, looking into the light-river: ’Into roundness it seemed to change its length’ (Purg. XXX).

How characteristic of Bartók’s simplicity that when the diatonic fugue-theme returns, he is satisfied with a unisono melody (on the G string) – the artistic solution is achieved virtually without the assistance of technical means. Even when repeated, the melody is coupled only with simple major-triads, through which the sound becomes solid and solemn, like an organ – signifying that the fugue-theme which was born out of the resounding chaos of the first movement, through the piercing humour of the second movement, and the spell of nature in the third, has finally arrived at its poetic fulfilment.

But what does this ’openness’ actually mean? The hypnotic effect of the first movement is the result of the fact that — during the progress along the fifth-circle — at every moment, in every phase of the circumvolution, we are necessarily aware of the positions the theme occupies in relation to the centre. Bachofen’s mythological analyses call our attention to how deeply and indelibly the ritual act of ’going round’ has its roots in human nature (the excitement of ancient circus-games or of modern horse-races, Dante’s journey through the rings of hell or the lovers of the Magic Flute going round the circles of the ’fire and water ordeal’ would produce quite a different impression on us should we disrupt this outer framework of the action).

In the closing movement all this happens differently. Here each new episode opens up before us with the result that the material of the former section ’bursts open’:

Fig. 106

What at first appears as a sort of ’montage’ or ’mosaic’ form, is in reality a conscious constructional principle, thus constituting a striking contrast to the single-arched ’wave-form’ of the first movement. — If our earlier observations were correct, we should expect to find the decisive turn again after the central theme: in the unexpected ’change of scene’ of b. 114 (a change in key, too, because instead of the expected C major, it switches over to the F# counterpole!). (See: Fig. 176 on p. 93).

The diatonic entrance of the fugue-theme marks the most beautiful ’opening’ of this kind. This is already reflected in the scale of the melody: its notes are derived from the natural overtone sequence (C-D-E-F#-G-A-Bb-C) – that is, the theme is introduced not as a melody but rather the projection of a harmony:

Fig. 107

This is the source of the pervasive clarity, the hymnic floating of the theme and, as mentioned earlier, its open spatial effect. Over the theme — again from the right — a piping major-sixth organ point particularly underlines this effect (the major sixth in Bartók’s tonal world may justly be called the ’pastoral sixth’). This theme is the key to the comprehension of the work. Is it not conspicuous how vividly this tune — this unisono melody — is pervaded by the metrical pulsation of ancient hymns, suggesting a text, the Hellenistic sense of form: infinite in its asymmetry, but at the same time, clear in cadence and lilt – like the conscious revival of the famous Seikilos hymn,

Fig. 108

of that Seikilos ode which is simultaneously both a drinking-song and an epitaph, wisdom and love of life – a balance between life and death.