As the form diagram indicates, the conflict between both layers is crucial to the structure of this piece (see Example 10). The cycle that is repeated throughout this piece is created by a symmetrical 4/4 backbeat pattern in Layer 2 that conflicts with Layer 1, which alternates between 20/16 and 15/16 bars reinforcing an F# tonal center—four bars of 5/16 and five bars of 3/16, respectively (see Example 11). Given that Layer 1 is three sixteenth notes longer than two repetitions of Layer 2 (similar to the cycle heard in "A Crane Came from Van"), every four repetitions of Layer 1 will realign with a downbeat in Layer 2. However, as illustrated by the vertical dashed barline at the beginning of the fifth system in Example 11, even though both layers are aligned on a similar downbeat, Layer 1 now begins on beat 4 of Layer 2. Thus, all sixteen 4/4 bars in Layer 2 are unique with regard to their alignment with Layer 1. Layer 1 is heard seven times in total before an 11/16 bar (5/16 + 6/16) disrupts the cycle in order to realign with the downbeat of Layer 2 when the cycle repeats. This conflict between layers 1 and 2 continues throughout most of the composition, making the tension generated by these cycles significant to the piece's structure.
"Etude No. 1"
[4.2] Another example of structural cycles is in "Etude No. 1," the sixth track on An Ancient Observer (2017) and the only solo piano composition discussed in this article. While the cycles in this piece are not used in the outer sections like they were in "Entertain Me," the amount of time that cycles are heard in this short composition implies that these dissonant formations are an important structural component of this composition: 75 of the recording's total 128 seconds contain phrases with cycles, comprising 59% of the piece (see Example 12).
[4.3] In "Etude No. 1," Layer 1 is a four-bar 5/8 pattern (2+3) that is repeated throughout the entire composition (see Example 13). This pattern as well as the others used throughout this piece are primarily "white key diatonic," emphasizing C as a tonal center. In the first cycle, 0:05–0:36, Layer 2 is a 7/8 pattern (3+4), which helps create a series of unique metrical alignments and contrapuntal intervals between these two voices; I have illustrated these between the staves of Example 14. In this cycle, Layer 2 realigns with a downbeat of Layer 1 every seven bars of 5/8, but given that Layer 1 is based on a four-bar pattern, the downbeats of each layer only realign every twenty-eight bars. The hypermeter in Layer 1 is further complicated by the addition of a new melodic voice first heard in m. 17 in the piano's left hand. This voice follows the 5/8 pattern established by Layer 1, but lasts for eight bars. Even though both layers realign in m. 37 after the seventh repetition of the 5/8 pattern of Layer 1 (indicated in the example with an *), this event occurs in the middle of the eight-bar hypermeter that is now reinforced by the new melodic content in the piano's left hand. This cycle is disrupted in m. 49, when the sixth note of the 7/8 ostinato in Layer 2 coincides with another statement of Layer 1 at the beginning of the next phrase.
[4.4] After repeating a similar cycle using 5/8 and 7/8 patterns (0:39–0:51), from 0:51–1:04 Hamasyan uses similar 5/8 and 7/8 patterns but adds a 3/8 metrical layer (Layer 3) that is formed by a C5 repeated every three eighth notes (see Example 15). Given that this phrase is sixteen bars long, the only point at which all three layers share a downbeat is in m. 85 at the beginning of the phrase. Layers 2 and 3 are also cut short in m. 100 in order to maintain the eight-bar hypermeter established in Layer 1, disrupting the cycle in order to maintain this symmetrical phrase structure used throughout the composition.
[4.5] This leads directly to the fourth and final instance of cycles in this piece from 1:04–1:23, which uses the original 5/8 ostinato (Layer 1) and an elaborated version of the 3/8 ostinato (Layer 3′) heard in the previous cycle (see Example 16). Unlike the previous phrase, this cycle is eight bars longer, which leads to an implied resolution of both layers 1 and 3′ in m. 125. (Layer 3′ is not heard on the downbeat of m. 125, but if it were it would be on the downbeat). This is the only instance of cycles in this piece in which both layers resolve at a shared point of alignment, which is significant given that this is the end of the last cycle heard in this composition: after this cycle is completed the 5/8 meter from Layer 1 continues without conflict until the end of the piece. The use of multiple incomplete cycles throughout this piece builds tension, which eventually resolves at the completion of the fourth and final cycle, suggesting these cycles are an important component of this piece's structure.
Developmental Cycles
"Vardavar"
[5.1] One example of the developmental approach to cycles can be heard in "Vardavar," the fifth and final track on EP No. 1 (see Example 17). Layer 1 is introduced at the beginning of this composition, which is a 5/16 + 5/16 + 3/16 + 5/16 + 5/16 + 4/16 + 5/16 pattern structured in a 3 + 4 grouping that reinforces a C tonal center given the harmonic rhythm and bass line articulated in the piano's left hand (see Example 18). Starting around 3:14, however, Hamasyan introduces the first cycle in this piece (see Example 19). Here, given that the chords are repeated, Layer 1 (consisting of piano, bass, and kick drum) sounds twice as long. At the same time, a symmetrical 4/4 backbeat pattern in Layer 2 is introduced in the cymbals and snare. The chords in this section largely use the same pitch content from the beginning of the piece (CDEB from the opening becomes CGDE), but they are articulated as chords rather than a single melodic line. In this phrase, both patterns are the same length of 32 total sixteenth notes, but they do not share any points of alignment other than the downbeat of mm. 1 and 3 in Layer 2, which is also the beginning of each Layer 1 repetition. Thus, this complete cycle has the effect of unveiling a symmetrical 4/4 structure hidden underneath the asymmetrical rhythmic pattern heard throughout the beginning of the piece.
[5.2] After this first cycle, the next section returns to the unison asymmetrical ostinato used in Layer 1 for one more section. The final section of the piece, however, reduces the tempo and forms a new cycle (see Example 20). Here, on the one hand, Layer 2 returns to a symmetrical backbeat pattern similar to the first cycle in this piece, albeit now in a slower 2/4 meter. On the other hand, the earlier 5/16 + 5/16 + 3/16 + 5/16 + 5/16 + 4/16 + 5/16 in Layer 1 is developed into a new pattern using diminution: 3/16 + 3/16 + 2/16 + 3/16 + 3/16 + 2.5/16 + 3.5/16. This new complete cycle still retains the shared points of alignment on beat 1 of both layers, but adds an additional point of alignment on beat 3 of Layer 2, coinciding with the beginning of the second sub-phrase of Layer 1. However, given that the second repetition of Layer 1 begins on beat 2 of Layer 2, both layers need to be played twice before they both return to a shared point of alignment at the beginning of the phrase. In other words, the asymmetrical Layer 1 has been transformed to better fit with the more symmetrical backbeat pattern in Layer 2, creating four points of alignment rather than the two heard in the initial cycle. This suggests a development of Layer 1 at the end of the composition, in that it is transformed to better fit the symmetrical groove of Layer 2 (see Example 21).
"The Grid"/"Out of The Grid"
[5.3] The last two tracks on Hamasyan's 2015 album Mockroot also combine to form a similar large-scale developmental approach like the one discussed in "Vardavar" (see Example 22). The original Layer 1 that is introduced at the beginning of "The Grid" is based on a 5/16 + 5/16 + 7/16 + 5/16 + 5/16 + 5/16 pattern, emphasizing a G tonal center (see Example 23). The first cycle starts around 1:43 in "Out of the Grid," using a similar melodic pattern from Layer 1 (G–Eb–B–G–F–C) in counterpoint against itself in both layers (see Example 24). In this cycle, Layer 2 uses this melodic pattern in a consistent 5/16 ostinato, while Layer 1 uses the same melodic pattern but in a 4/16 + 4/16 + 5/16 + 4/16 + 4/16 + 4/16 pattern. The ostinato in the pattern of Layer 1 can be understood as a development of the original layer, in that it retains a similar six-bar phrase structure, but removes one or two sixteenth notes from each bar. Each repetition of Layer 1 creates a point of alignment with a strong beat in Layer 2. However, both layers do not reach the same point of alignment in which they share a downbeat and complete the cycle until after Layer 1 repeats six times and Layer 2 repeats five times. My transcription illustrates that in addition to creating unique points of alignment between the two layers, unique contrapuntal intervals are also formed at the beginning of each Layer 1 statement, creating tension that pushes the phrase forward until the end of the cycle.
[5.4] Similar to "Vardavar," the music returns to the original Layer 1 metric structure following this initial cycle, after which a new and final cycle is introduced (see Example 25). This cycle retains the same 4/16 + 4/16 + 5/16 + 4/16 + 4/16 + 4/16 pattern in Layer 1, now with a more driving rhythmic pattern based on three repeated sixteenth notes. This is juxtaposed with a new (4/16) pattern in Layer 2 that creates a symmetrical 4/4 backbeat pattern. Like the previous cycle, this passage continues on as if it will form a complete cycle, but after m. 3 of the eighth melodic statement in Layer 1, Hamasyan disrupts the cycle by increasing the tempo and returning to the original Layer 1 rhythmic content to conclude the second half of this six-bar phrase. Thus, unlike "Vardavar" which altered the original asymmetrical layer to fit a more symmetrical backbeat, "Out of the Grid" develops the original Layer 1 to make it seem like this pattern will form a complete cycle in this new symmetrical groove pattern, but eventually the cycle is disrupted and the music returns to the original metric pattern of Layer 1 (see Example 26).
[5.5] Both "Vardavar" and "The Grid"/"Out of The Grid" illustrate different large-scale strategies using developmental cycles. The former uses complete cycles and maintains the new symmetrical layer through the end of the composition, suggesting a more permanent transformation of the original layer. The latter ends with an incomplete cycle before returning to the original asymmetrical patterns heard throughout the piece, suggesting only a temporary disruption to the metrical framework. One possible reason that these patterns are used in this fashion as part of the large-scale formal development of a composition might be explained by Hamasyan's comments about his music:
"My idea was to try to weave these folk melodies into jazz improvisations," [Hamasyan] says. "My first attempts were terrible! The challenge is that folk music is modal, with no chord changes. So you are trying to find harmonies for a music that's not supposed to have harmonies. That's tough" (Lewis 2013).
In light of the difficult task of finding suitable harmonies for repetitive, modal folk melodies, it is possible that Hamasyan uses these ostinati and cycles in order to create a sense of progression in the large-scale form of his music, in addition to (or sometimes in place of) large-scale harmonic motion that might fulfill this function in other contexts.