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<\/a><\/p>\n{fig. 1}<\/strong><\/p>\n He uses this subset exclusively from bar one through the first quarter note in bar seven.\u00a0 The tritone is important in this work as it represents a critical interval for modulation, interesting pivots on axis, and a principle direction that the pitch-class moves towards other than the original minor second.\u00a0 The use of pitch motion to and from the interval of a tritone furthers the idea of its importance.<\/p>\n What isn\u2019t clear from this snippet of the piece is whether G#, or A is tonic of the piece.\u00a0 It seems from this small area that G# is playing the role of the tonic as that is where Bartok departs from, and arrives back at via the octatonic scale.\u00a0 So, for the first variation, though the tonic of the piece, A, may be present, G# is actually playing a tonic in this microcosm (no pun intended) of the piece.<\/p>\n Bartok quickly dashes this G# world, as in measure seven he expands beyond the tritone limit he stuck to for the first six bars and lands squarely on a D and an A.\u00a0 This perfect fifth is a very stark contrast from the previous bars, but not to let the listener settle on D as being the tonic (which we are inclined to do as it is an arrival on the lowest pitch of an interval that is very stable to our ears), he throws this bizarre, upper register Bb, G#, A cluster into the mix [fig 2 below].\u00a0 This is important, as it introduces the second theme\u2019s \u201ccentral\u201d pitch, which is the Bb as well as the idea of the Major 7th, which recurs later on in the piece.<\/p>\n {Fig.2}<\/strong><\/p>\n Bartok, does not stop with that simple introduction of the second theme\u2019s tonic center.\u00a0 Instead, he moves the harmonic language of the work from the wholly octatonic, to the wholly chromatic [Fig. 3].\u00a0 This functions as a transition area, much like you would see in a sonata between the first and second themes, where there is likely to be a modulation.<\/p>\n {Fig. 3}<\/strong><\/p>\n After Bartok has strayed into this wholly chromatic, transitional area, he separates out between the two hands into two independent octatonic subsets [Fig. 4]. {Fig. 4}<\/strong><\/p>\n He uses this chromatic area to launch the listener into the pitch area of the new octatonic subset, of which Bb is the \u201ctonic\u201d (note that the A still sticks around as the tonal center of the piece).\u00a0 Like in the first variation with the G#, Bartok departs and returns to that Bb over an octatonic subset covering a tritone.<\/p>\n Also, like in the first variation, he expands the tritone further to a perfect fifth when he is looking to begin transitioning to the next variation. Unlike in the first variation, he expands his moving line upwards in the right hand so that the perfect fifth is that of A and E [Figure 5].\u00a0 It shows Bartok\u2019s thinking of how he is demonstrating that A is the tonal center, by using it as an axis and expanding out from it to a perfect fifth.\u00a0 He also cleverly keeps the listener from settling on anything else as the tonic with the aforementioned leap to Bb, G# and A when he landed on the D, A Perfect fifth.\u00a0 Bartok, then, once again, strays into the wholly chromatic as if modulating before moving on to the next variation.<\/p>\n {Fig. 5}<\/strong><\/p>\n In the next variation Bartok mixes up the placement of two pitch class sets so that the intervallic content seems more complicated than it really is [Figure 6].\u00a0 This complicated harmonic language starts off the development section. {Fig. 7}<\/strong><\/p>\n Though the organization of the pitches may seem strange, it is really just two interlocking sets of pitches based on the two principle sets that defined the first two themes. These are G#, A and A, Bb.\u00a0 The C# and C are just products of Bartok\u2019s wholly chromatic expansion to a major seventh in measure twenty-three, as well as being included in the G# or Bb based octatonic subsets.\u00a0 Hashing the sets of pitches out, G#,A and C form the same intervallic content as A, Bb, C# of (014).<\/p>\n In variation IV, Bartok uses the A as an axis again, but in each hand departs in a different direction.\u00a0 In the right hand it departs up the octatonic subset of (T013), and including the A, which is repeated, forms the ever-present tritone idea of (9T013).\u00a0 The exact inversion plays itself out in the left hand, being (35689).\u00a0 Bartok makes it clear in this variation that the A is central in its role as an axis [figure 7].<\/p>\n {Fig. 7}<\/strong><\/p>\n Bartok does muck up what should be a clean inversion though, by changing the right hand just before it is about to land back on the A and Bb.\u00a0 He instead lands on a B natural before heading back up towards and E natural, which is just an extension of the octatonic subset that we have been dealing with.\u00a0 What this B seems to be doing there is extending the left hand\u2019s own octatonic subset to that of a perfect fifth, just like the E natural is doing in measures 35, 37 or 38.\u00a0 In other words, it belongs in the left hand rather than the right as far as its placement in the individual octatonic subsets.<\/p>\n In variation V, Bartok really begins to make the tonal center of the piece unclear.\u00a0 Before, Bartok would be fairly precise as to where the tonic center is, by having it (A) be the center of a symmetrical cluster (as seen before, usually an octatonic subset).<\/p>\n Instead, Bartok initially creates the pitch class of E, A, Bb and Eb [Figure 8].\u00a0 These are interlocked tritones, playing on one of the work\u2019s principle ideas.<\/p>\n {Fig. 8}<\/strong><\/p>\n Here, the center of this \u201caxis\u201d tonality is A and Bb.\u00a0 Bartok quickly makes things ambiguous, though, by throwing in a G# making the central cluster comprise of G#, A and Bb [Figure 9]\u00a0 (this cluster plays a large role in the piece, see measure 17 for an example).<\/p>\n {Fig. 9}<\/strong><\/p>\n This seems to reassert A as the center, but for the first time, creates a truly asymmetrical figure around the A with E, G#,A Bb, and Eb.\u00a0 This lends to the ambiguity of the tonal center, with neither the A nor the interlocking tritone figure for which A and Bb is the center, asserting a tonic role.<\/p>\n The last eighth notes before the next variation further skew what the tonic maybe.\u00a0 Bartok uses interlocking fifths of Bb, F and C#, G#, centered around the tonic A, which calls us back to Bartok\u2019s use (although spurious) of the 5th to highlight when he is modulating [Figure 10].<\/p>\n {Fig. 10}<\/strong><\/p>\n This is the important reason for the complex shifting of \u201ccenters\u201d and \u201caxis\u201d, as Bartok is making his modulation into the retransition, which is in the dominant key.\u00a0 The dominant key is not the traditional dominant of A (which is E), but rather Eb.\u00a0 This plays directly into Bartok\u2019s recurring idea of the tritone as the principle interval in the work.<\/p>\n Variation VI begins the dominant section and the retransition of the work into the recapitulation.\u00a0 Once again, Bartok uses a subset of the octatonic scale to create a motion to and from the \u201ctonic\u201d of the section, Eb.\u00a0 In the right hand this is clear in the first bar (measure 52) of the variation.\u00a0 In the second bar he overshoots, seeming to settle on D, but this can be considered more of as a lower neighbor note.\u00a0 On a side note, the right hand in the bar outlines the principle interval of the work, the tritone.<\/p>\n The following bar is what leads one to conclude that Bartok is still in \u201cEb\u201d.\u00a0 He notates a B double-flat instead of an A to clarify that the motion of the scale he is using is not towards the original tonic of the work, but to more of a dominant of the dominant [Figure 11].<\/p>\n {Fig. 11}<\/strong><\/p>\n Skipping to bar fifty-six, Bartok begins his motion from Eb back to A.\u00a0 Since Eb and A are part of the same octatonic scale that he is using, he adeptly just switches hands with the theme of the particular variation, moving away from the tritone and seventh leaps in the left hand to an exact copy of the right hand in measure fifty-two, but in the key of A.\u00a0 Bartok plays out the transposition of the original phrase in the left hand and then continues on to the recapitulation, ending the development section.<\/p>\n Variation VII looks to be a combination of the first two themes of the work, it is a return to the original theme of repetitive eighth notes spread between the two hands.\u00a0 This time, though, he wastes no time in combining the two octatonic subsets surrounding the tonic A.\u00a0 In bar seventy-two he expands out to the interval of a perfect fifth, this is important as it is and arrival point to which the variation was headed, and important to the final variation [Figure 12].<\/p>\n<\/a><\/strong><\/p>\n<\/a><\/p>\n<\/a><\/p>\n
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