Harmonic Associations in Kurtág s Chorale from Játékok, V

Transcription

1 Pesca on Kurtág // Page! of 9! Harmonic Associations in Kurtág s Chorale from Játékok, V Daniel Pesca. ntroduction, form, and summary of linear structures György Kurtág s Játékok (Games) is an ongoing series of piano miniatures, now numering well into the hundreds. The first several volumes contain pedagogical pieces; later volumes, including Volume V, are composed of diary entries [and] personal messages. The Chorale in Volume V is for Benjamin Rajeczky s 80th irthday, placing it in the personal messages category. t is preceded y a Prelude not analyzed in this paper which is a transcription of an early cimalom work y Kurtág, originally composed in 962, nearly twenty years efore the Chorale. The Chorale is in five voices, all moving homo-rhythmically. Within each five-note chord, octave doulings are consistently avoided. Figure is an annotated score, laelling each chord with a Roman numeral. The figure also divides the piece into three parts, laelled A, B, and C. This proposed form cannot immediately e intuited from Kurtág s idiosyncratic markings. First of all, the prolems of rhythm and meter in this piece are formidale. Figure 2 reproduces the key to signs used provided at the end of Játékok Volume V. The key tells us the meaning of the marks over and V; ut it does not help us interpret the relative length of and, or whether the comined duration of and is equal to the duration of, which we might assume given the placement of the arlines. But, then, there are two different kinds of arlines in the piece: dotted and solid. We can safely assume that the solid arlines have greater formal weight; ut neither type seems to denote any sort of metrical periodicity. n the asence of such regularity, what is one to say aout, which is tied over a dotted arline The long phrase marks suggest other kinds of groupings. There are almost always two levels of phrases the right hand etween and V, where there is no large phrase parallel to that in the left hand, is an exception. n total, there are eleven short su-groups, and five long phrases. There are 22 measures, and eight solid arlines. n short, the score conveys mixed messages aout the Form laels are underlined, chord laels are italicized Roman numerals.

2 Pesca on Kurtág // Page! 2 of 9! grouping of the 33 chords. Yet, certain oundaries are clear. For instance, V is a dynamic climax that culminates a long ascent in the outer voices; and V initiates a series of three su-phrases that each descend. t is more difficult, however, to decide where the section that ends with V egins. Kurtág s slurring suggests that elides two long phrases; this point is the modest nadir of the soprano part, and it is a relatively long chord. (Though we cannot decide how its duration compares to that of, say,.) However, the ass part has already started its long linear progression up towards V. The crescendo has already egun, too oth egin at V. V V, then, is another possile formal divide it is the one we will settle on. t does, however, challenge Kurtág s phrase marks. What if we try to respect those phrase marks, and make the first two long phrases into A, the second two into B, and the third into C This parsing puts a formal division etween. This solution has its attractions, ut the motion of the soprano makes it difficult to hear a formal division there. The soprano is stuck on B4 for the first ten chords of the piece, and is finally dislodged in. However, the constant repetition of the B4 has made it seem like a tonic; and so hearing as a cadence is unsatisfying, ecause it feels off-tonic. The return to B4 at V feels cadential and particularly at V ecause of the prominent fifth in the outer voices. We are not necessarily invoking the entire apparatus of tonality y noting that the consonance has a certain acoustical effect, especially with the wide spacing etween the ass and the other voices. 2 The same E-B fifth is, furthermore, a constant feature of V, etween the M and the S. 3 Here it has returned, ut projected over a much larger registral space. So, despite Kurtág s phrase marks, V feels cadential. Furthermore, V feels like a new eginning due to voice-leading continuity. Before V V, the greatest leap in the upper four voices has een a minor third, ut at this point there is a tritone in T. The B also leaps a tritone; and, while the B has had a variale trajectory, the tritone has een foreign to its repertoire so far. Having posited an overall structure, let us egin a more detailed study of the first six chords. Figure 3 shows that in the right hand, set-class [026], contains two instances of the trichord [06], which is immediately projected linearly in the B. The registral distriution of the five-note chords 2 pause here to oserve a fruitful opening for another analysis of the piece: studying the relationship etween the resonances of the ass, played in the overtone-rich depths of the piano, and the other voices high aove. 3 Here introduce a way of identifying the voices of the Chorale (always italicized uppercase letters): S, A, M (for middle ), T, B.

3 Pesca on Kurtág // Page! 3 of 9! helps hear them as 4(SAMT) + (B); many of our oservations will spring from this impression. Figure 4 shows another immediate instance in which the vertical structure of SAMT recurs horizontally in B. Note that, as in Figure 3, the set in question ([0247] this time) occurs twice in the SAMT and then in B; ut now the two occurrences are in different five-note chords. Both Figures 3 and 4 lael the transformations that map the occurrences of the set-classes onto one another. 8 is a recurrent transformation in the right hand. The large phrase V has two su-phrases, and V; the su-phrases are so closelyrelated that we might characterize the second as a variation of the first. The S and M voices are entirely static. Figure 5a astracts the A, which moves up a half-step in and down a half-step in V. Figure 5 astracts the T, which moves successively through an [02] and an [03] in each suphrase. The [03] is inverted; the [02] is not. Figure 5c astracts the B, which inverts etween the two su-phrases. One might say, then, that there is something inversion-like aout the relationship etween and V, ut there are inversions occurring around many different axes. Examining Figures 5a c, we note 6, 0, and 9; 3 maps E4 in the M onto B4 in the S. This suggests a kind of helter-skelter inversion around different memers of the minor thirds cycle starting on C. We need not look far to find this same minor thirds cycle expressed openly in the music: the B outlines it in,,, and V. Since we have found the B to e particularly connotative in these opening chords, let us follow its course further. Figure 6 shows that, in V, the B horizontally unfolds an [027], the same sonority in SAMT in. The repetition of the D/E in this segment of the B draws attention to the inversional symmetry of the set. Figure 7 shows that, in V, the B horizontally unfolds an [0247], the sonority whose transformations are given in Figure 4; Figure 7 compares the horizontal appearance to the vertical appearances at and. The second long phrase of the piece (V ) is not perfectly alanced with the first: it contains seven chords, whereas the first contained six. The extra chord must e somewhere in the su-phrase V ; and the inversional structure of the B of V suggests that is the extra chord. This structure is shown in Figure 8. We shall have opportunity to consider more closely later on; its appearance is, in several ways, a notale event. V introduce a new set-class in the B: [024]. The set-type ends the A section and the the B section at V. This relationship is depicted in Figure 9a, which also shows that the two

4 Pesca on Kurtág // Page! 4 of 9! occurrences together outline C-E-G [048] a major thirds cycle starting on C. We see this structure reflected elsewhere in the section. Figure 9 shows how the motion of the S and B from outlines the same structure via consecutive minor sixths. We also hear the same sonority vertically at other moments in the piece; Figure 9c catalogs several instances. C-E-G appears in open noteheads. Figure 9d analyzes the other two notes in each of these pentachords, discovering symmetries through contrary-motion voice-leading away from the augmented triad. Figure 0 returns to the B to examine the ascending chromatic scale in V. The figure partitions the B into two -related halves, which mirrors the transformational structure of the B given in Figure 8. Figure summarizes some analytical data aout the B in C. The first four notes elong to [0347], as do the pitches in Figure 8. V form an [027], a familiar chord from the eginning, emphasizing the [027] suset. (The [02] suset is emphasized heavily in the B section.) Figure 2 summarizes symmetries the last line, starting with the end of the B, where the last two fourths map onto each other under 0. Examples such as these from across the piece could e multiplied indefinitely; space permits us only to call attention to their presence. And Figures 3a summarize some ways in which the B horizontally projects structures in the SAMT, as it did near the eginning of the piece. Figure 3 is particularly intriguing: the SAM chord in replicates itself in the B of. We have noted instances of every possile interval-cyclic trichord, often in structural roles: [02], [024], [036], [048], and [027]. Clearly this approach has much to say aout this piece; efore we turn our attention to other matters, let us examine just one more example. Figure 4 summarizes the S of the first two sections of the piece. is an [02], and the B section outlines [036]. 2. Harmony The first part of the analysis descried the form of the piece and made some general oservations aout linear organization. The second part will look more closely at the structure of the harmony. Oservations we made earlier will help us along the way. Figure 5 analyzes five-note chords in the piece. The set-class of each of the 33 pentachords in the piece is given, followed y two different Hauptmann scripts for each: a pentachord top-down script (5tds), and a pentachord ottom-

5 Pesca on Kurtág // Page! 5 of 9! up script (5us). There are three more possile Hauptmann scripts for each chord; ut we shall limit our investigations to these two. The space etween the B and SAMT makes us acutely aware of the frequencies etween the latter and the former. On the other hand, the static character of the S makes it a point of reference, against which we hear the other voices moving. The 5us and 5tds quantify these two impressions. Since the SAMT and B are registrally separated, Figure 5 also provides the relevant set-class and 4tds for each SAMT tetrachord. n the last two columns, the figure gives interval vectors for each tetrachord and pentachord. Figure 6 interprets the information given in Figure 5. The figure passes through the A section, taulating linear continuities that is, it associates events with foregoing events. The figure does not provide an interpretation of. shares its 4tds with, as shown in Figure 7. The direction of each arrow shows the direction in which the dyad-class is expressed. A4 in the A and E4 in the M persist, while B3 in the T inverts around B4 (0) in the S to ecome C4. Before continuing through Figure 6, we skip ahead to look at a three instances of 5us/5tds relationships. Figure 8a compares and ; arrows for [06] are two-sided ecause the constituent intervals are reflexive. Figure 8 helps organize the information in Figure 8a. Along the left side, we see the various interval components of the script; the ordinal numers ( 4) in the next two columns tell us how close each interval is to the alpha-note (the B note of, and the S note of ). is the closest, 4 the furthest. n this example, the scripts reverse their order numer relative the alpha-note. The arrows show dyad-class direction. We see that [05] and [0] stay the same, [06] is reflexive, and [04] inverts. 4 This is a more remote relationship that the one we saw in Figure 7. Figure 8a helps us see an [05] among the [0] and [04] components, and an [06] among the [0] and [06] components. But the position of the [05] and the [06] relative to one another has shifted. Figures 9a- compares to using similar methods. The [0] inverts; all other relationships do not. The change of the [0] alters the set-class from [0256] to [0267]. The continuity is easily intuited from the score: the SAMB all move up a half-step, and the T moves up a minor third. The figure shows how the T inverts. B4 in the S of maps onto C5 of under ; and 4 However, when a 5us ecomes a 5tds or vice versa, the intervals expressed the same way invert. For instance, although the way [0] and [05] is the same in the interpretation in Figure 8, Figure 8a shows that they oth invert.

6 Pesca on Kurtág // Page! 6 of 9! A3 in the T of maps onto C of under. These are pertinent oservations in a piece that announces its concern with inversion in the first few chords. The set-class of, [0267], is one that appears at chords and V. Figures 8a analyzed the relationship etween and ; l Figures 20a complete the circle y comparing and, reproducing the relevant information from Figures 8 9 side-y-side. The arrow directions are all the same, and order relative to the alpha-note reverses. Since we are comparing a 5us with a 5tds, order numer relative to the alpha-note does not denote the same voice in each instance; so Figure 20 shows the voice distriution of the different intervallic components. From to, the intervallic component in S sinks to A, the A sinks to M, and the M sinks to T. n other words, the [027] in the SAM of sinks into the inner voices of, a T9 transformation. 0 maps D in the B of onto G in the B of, and B3 in the T of onto C4 in the S of. and are the same set-class, ut their relationship does not end there. Now that we etter understand the relationships scripts descrie, let us continue through Figure 6. After and share their 4tds, and share the same set-class, shown in Figure 4. repeats the tetrachord of. V similarly corresponds to, ut its pentachord set-class repeats that of. V comines features of and. and V have the same pitch-class content, ut the registral arrangement has changed. The S and M are stationary; the B in ecomes the T in V, the T ecomes the A, and the A ecomes the B. V is a T0 iteration of. t relates to as V related to : the B ecomes the T, the T ecomes the A, and the A ecomes the B. So, the T s C4 D4 in V V replicates the B s C D in ; and so on. V replicates the pentachord set-class of, and three of its pitches. 8 maps onto V, keeping every pitch-class the same except one F ecomes D. Figure 2 shows the way the voicing masks the 8 relationship, so it might sound as though the SAM is the same while the BT moves T4. V only use nine memers of the aggregate. V introduces D, a new pitch-class. But the sonority is, again, familiar: it is the same pentachord set-class as. Figure 22 shows that T2 maps onto V; the relationship of V to does not parallel that of V to. The T2 is particularly audile in the way the minor triad in the AMT of moves up into the SAM of V. Figure 23 demonstrates some illusory parallels that make the motion of V V similar to the motion of.

7 Pesca on Kurtág // Page! 7 of 9! There is a rising [02] in the inner voices (though in the later passage it is divided etween two voices), and there is an [05] in the ass (though the dyad-class is expressed in the opposite direction). Figure 24 summarizes some of our findings. Columns show pentachord set-class associations; each pentachord set-class has een expressed twice. The set-class of, [0348], is very different from that of, [0267] (compare, for instance, their interval vectors); yet, in a few chords, the piece unfolds a chain of associations etween them. The order of the set-classes in the music using italicized numers to represent different set-classes is, 2, 3, 4, 3, 4,, 2. Regarding and 2 as an unordered pair, and 3 and 4 as another produces a palindromic structure: /2, 3/4, 3/4, /2. However, the phrase structure oscures the palindrome. ndeed, recalling our earlier analysis of this same passage, we might reflect upon how the symmetries shown etween and V coexist with symmetries on a different level of the harmonic structure. The chain of associations, shown in Figure 24 as arrows etween Roman numerals, applies only to and not necessarily to V V; ut the latter has associations not depicted in the figure. For instance, V repeats the tetrachord of. This relationship is astracted in Figure maps C in the B of onto G in the B of V, and also maps C4 and A4 in the AT onto each other. There is something 9-ish" aout the [04] components of these chords, while the S and M continue reiterating their accustomed pitches. Figure 26 depicts a similar [04]+[05] structure in and V. n V, the [05] component is not [E4 in the M]+[B4 in S], ut [E4 in the M]+[A4 in the A]. n terms of Figure 4, does not easily associate with any earlier chord. t also presents a new pitch-class, F the tritone pole of the S s persistent note. The tritone in the SB is almost unique in the piece: V is the only other chord in which the S is accompanied y a tritone in the B. is thus new in several ways; ut Figure 9c shows one way in which it associates ack to. They are different y just one pitch-class. also shares a structural similarity with : oth set-classes are symmetrical projections of a trichord, a structure we might call [sc]+n[sc]. This structure is applied to and in Figure 27. is an instance of [05]+8[05], while is an instance of [04]+4[04]. Figure 27 also depicts a later chord,, which elongs to the same set-class as and is thus interpretale along the same lines. The symmetry of is transparently reflected in its registral distriution. Figure 9c associates and chords via their inclusion of C-E-G.

8 Pesca on Kurtág // Page! 8 of 9! Features of associate it with,,, V, and V. Figure 28a analyze,, and in terms of their common suset, [025]. and share not only [025], ut two identical pitch memers of their respective [025]s F in the B, A3/B3 in the T. Figure 28 shows that these identical pitches play different roles in each [025] they switch roles under 4. Figure 29 compares the [025]s in, V, and. echoes V in its voicing of the [025] in the AMTB. Figure 8 studied the relationship etween and, and Figure 9 compared and. also shares its pentachord set-class with V and ; Figure 20 compared and. How do these new chords fit into the picture presented in Figure 24 and have dense associations with earlier chords particularly with those in the three left columns of Figure 24. They have, in a way, oscured the difference etween the columns. However, there is still the right-most column, with which we have also associated. Let us propose that part of the cadential" effect of V is that it draws together all four columns depicted in Figure 24. The columns are associated at the opening of the piece, ut V V move towards greater differentiation. Perhaps a short-term musical goal of the piece is to move ack towards the homogeneity of the eginning; and, especially, to ring the contrasting pentachord set-class of into the fold. Let us consider the remaining five chords of the A section non-linearly, eginning with one which will not much help our cause., a memer of [0234], is most strongly associated with and V. These associations are displayed in Figure 30a. t is also an instance of [sc]+n[sc], shown in Figure 30. and V share a [048] suset with, V, and ; in, and V, [048] is prominent in the SAMT tetrachord. All the chords elong squarely in the rightmost column of Figure 24. plays a pivotal role in our narrative. ts scripts connect oth ack to and ahead to V; and V shares its pentachord set-class with. Figure 3 provides the relevant script analyses, and provides the 5us of V, which matches that of and V. is at the center of this formation; its 5tds associates ack, and its 5us associates forward. From to, the [02] and the [05] swap ways, while the other intervals (and, since the alpha-note is identical, pitch-classes) stay the same. From to V, [03] and [05] invert, while [0] and [04] do not. Figure 3 illustrates that there is something 0-ish aout the former intervallic components, and something T4-ish aout the latter. Now let us compare each of these to V. From to V, all dyad-classes reverse direction except [03]. There is something T6-ish aout the [03]; the rest of the chord is 2-ish, as shown in

9 Pesca on Kurtág // Page! 9 of 9! Figure 3c. From V to V, all the intervals except [05] invert. There is something T2-ish aout the [05]; the rest of the chord is 6-ish, as shown in Figure 3d. The inversion is particularly striking ecause the chords are adjacent, ut also ecause D in M maps onto itself under 6. With this point of reference, one can hear B4 in the S of V invert to G3 in the T of V, and A in the T of V invert to G in the A of V. V shares not only a [048] suset with, ut also a 5tds. Figure 32a provides the relevant script analyses, and Figure 32 shows the Tn/n implications. Since the script contains two [04]s, they must go in opposite directions from each other in order to avoid unisons or octaves. We can either see them as oth reversing ( n-ish), or as oth staying the same (Tn-ish). Figure 32 gives the fullest possile picture of the Tn/n implications. Finally, Figure 33 fills out the picture sketched y Figure 24 so as to depict some developments charted in the foregoing discussion.

10 Pesca: Kurtág paper // Figures - Page! Figure. Score with Roman numerals laelling the 33 chords in the piece. A V V V V V V B V V V C V V V

11 Pesca: Kurtág paper // Figures - Page!2 Figure 2. Note on the rhythmic signs in the work. Figure 3. A recurrent trichord in the right hand projected into the left hand n T-2 n -8 n n -8 0 T-2 nn Figure 4. A recurrent trichord in the right hand projected into the left hand n T-4 V n n T-4 V Figure 5a c. nversion structures etween and V V V - -V V V V V V n n n n [02] [03] -0 V [02] [03] -6-6 V V V -9 [02] [03] [02] [03] -0-0 n -7 T- n

12 Pesca: Kurtág paper // Figures - Page!3 Figure 6. A tetrachord in the right hand projected into the left hand. -6 n [02] [03] -0 [02] [03] n -7 T- V Figure 7. A recurrent trichord in 2the right hand projected into the left hand. (See Figure 4.) Figures 9a d. Some C-E-G structures. -8 T-4-8 V V -8 T-4 V T-4 V V V T T-6 V -2 T-6 Figure 8. nversion in the left hand. V V V V V n V V V n n n n n n

13 V T-4 V Figure 0. nversion in the left hand. V Figure. Some tetrachords in the left hand, [027] V. [0347] Figure 2. Some symmetrical tetrachords in the C section. Pesca: Kurtág paper // Figures - Page!4 V n n n n n V n [027] n [0347] n n [027] n n V V n V n n n n V V n 0-0 n n V V V n n 0-0 n n [0347] Figure 3. Right-hand harmonies projected into the left hand in the C section. n T-9 n -3 0 T-3 nt T-3 V n 0 V 0 C C C C Figure 4. Summary of the S in the A and B sections.. w w [02] [036] w n[036] Ó [02] w n Ó

14 Pesca: Kurtág paper // Figures - Page!5 Figure 5. Raw data aout the harmony. lael tetrachord tetrachord script (top note = a) pentachord pentachord script (top note = a) pentachord script (ass note = a) tetrachord interval vector pentachord interval vector [027] a25 [0257] a255 a2345 <2002> <223> [0237] a25 [02347] a225 a234 <20> <222220> [0237] a235 [0348] a25 a344 <20> <22320> [027] a25 [0267] a245 a456 <2002> <3032> V [0237] a25 [0348] a235 a344 <20> <22320> V [056] a45 [0267] a245 a256 <2002> <3032> V [0257] a255 [0257] a255 a46 <02030> <223> V [0237] a235 [02347] a2345 a244 <20> <222220> [048] a35 [0478] a356 a356 <030> <20232> [046] a46 [0256] a456 a45 <> <322> [057] a46 [0267] a456 a56 <02> <3032> [0247] a245 [0248] a245 a345 <0220> <223> [048] a344 [0258] a3445 a235 <030> <2222> [024] a22 [0234] a22 a23 <2200> <43200> V [026] a24 [0256] a234 a345 <20> <322> V [048] a344 [0348] a3445 a345 <030> <22320> V [0257] a255 [0368] a255 a346 <02030> <223> V [0258] a345 [0358] a345 a245 <02> <22230> [047] a45 [0478] a445 a445 <02> <20232> [045] a34 [0457] a344 a3445 <2020> <2222> [056] a45 [0478] a445 a3344 <2002> <20232> [048] a35 [0458] a345 a345 <030> <202420> [045] a45 [0458] a445 a3445 <2020> <202420> [057] a46 [0267] a456 a56 <02> <3032> V [027] a5 [0267] a56 a456 <2002> <3032> V [058] a45 [0458] a445 a344 <0220> <202420> V [0235] a23 [0235] a223 a24 <2200> <3320> V [023] a2 [0237] a25 a4556 <32000> <322> [027] a25 [0257] a255 a2345 <2002> <223> [0237] a235 [0358] a2235 a2345 <20> <22230> [058] a45 [0458] a345 a344 <0220> <202420> [035] a223 [0357] a2234 a2456 <20> <322> [048] a35 [0248] a35 a226 <030> <223>

15 Pesca: Kurtág paper // Figures - Page!6 Figure 6. A provisional interpretation of the data in Figure 5 ( V only). V V V V V V same 4tds as same tetrachord sc as n same tetrachord as T-9 same tetrachord as -3 0 same pentachord sc as same pentachord sc as same pentachord sc as V same pentachord sc as contains [048], as and V contains [025], as did,, V, and V 5tds is the same as 5us of same 5tds as same pentachord sc as V and same 5tds as same tetrachord sc as [02] 5us duplicates 5tds of V w contains [024], as did and V same pentachord sc as same 5us as same tetrachord sc as same 5tds as same 5us as and V 0 [036] T-3 n w n Figure 7. 4tds comparison of and n 4 C C

16 Pesca: Kurtág paper // Figures - Page!7 Figures 8a. 5us of compared with 5tds of n C C [05]: 4 [0]: 2 3 [06]: 3 2 [04]: 4 Figures 9a. 5tds of compared with 5tds of n [05]: 4 4 [0]: 3 3 [06]: 2 2 [04]: n -8 V sounds like: T-4 V

17 Pesca: Kurtág paper // Figures - Page!8 4 Figures 20a. 5us of compared 5 6 with 5tds of n [05]: T S 4 n V sounds like: n [0]: 2 M T 3 n [06]: -8 3 A M 2 n T-4 [04]: 4 S A Figure 2. Transformations etween and V. V V sounds like: n V sounds like: n T-2-8 T-4-8 T-4 V sounds like: n -8 T-4 Figure 22. T2 etween and V. V V V V M A T T T-2 T-2 T-2-9 V V V V Figure 23. llusory parallels: versus V V. V V V V M A T T M A V V V V T T V V V V V M A T T V -9-9 V -9

18 Pesca: Kurtág paper // Figures - Page!9 T-2 Figure 24. Sketch of associations etween V. [0267] [0257] [02347] [0348] tetrachord a25 [0237] V V V V V V Figure ish" interpretation of and V. T V T M A V V V -9 Figure 26. [05]+[04] structures in and V. V V [05]+[04] [05]+[04] [05]+[04] [05]+[04] Figure 27. [sc]+n[sc] structures in,, and. [05]+-8[05] [04]+-4[04] [04]+-8[04] [05]+-8[05] [04]+-4[04] [04]+-8[04] V V n n n -4-4 n

19 [05]+-8[05] [04]+-4[04] [04]+-8[04] Pesca: [05]+-8[05] Kurtág paper // [04]+-4[04] Figures - Page [04]+-8[04]!0 [05]+-8[05] [04]+-4[04] [04]+-8[04] Figures 28a. nterpretations of, V, and in terms of [025]. V n V -4 V n n -4 Figure 29. nterpretations of, V, and in terms of [025]. V V V n n -4 Figures 30a. nterpretations of, V, and in terms of [024], and an [sc]+n[sc] interpretation of. V V or [02]+0[02] V or [02]+0[02] or [02]+0[02]

20 Pesca: Kurtág paper // Figures - Page! Figures 3. 6 a. Script associations etween,, V, and V. d. Some transformational implications of these scripts V n V V T-4 n V -2 V V -6 n V Figures 32a. Script associations etween and V, and corresponding transformational patterns. V V V n n V V V T- -9 n n

21 Pesca: Kurtág paper // Figures - Page!2 Figure 33. Sketch of some associations etween V. [0256] [0267] [0257] [02347] [0348] tetrachord a25 [0237] [025] V V V [048] V V a345 a345 V