Pitch Materials
General Observations
The pitch materials of Velocity Meadows largely revolve around the set with interval normal form1 (11212113).
Throughout Velocity Meadows, a number of pitch collections emerge that are subsets of this primary (11212113) set – hereafter called set A. In the opening 37 bars, the set (3234) (a subset of A) is used to generate pitch material:
Importantly, (3234) is also a subset of the Acoustic collection – our transposition of (3234) at the start of Velocity Meadows fits into the AC-4 collection (or the Ab acoustic scale). The acoustic scale will return throughout the work as a tie-in to Velocity Meadows’ preoccupation with spectralist-inspired harmonic materials.
After slowly filling in the first four pitches set A, the pitch material switches to outline a different subset – (3144) – starting at m. 38:
As the piece progresses, more pitch classes appear to fill in set A, and we hear the set partitioned into subsets in a variety of ways. Importantly, set A can form a hexatonic collection – specifically HEX0,1 :
Transpositions of this hexatonic collection will appear all over Velocity Meadows – particularly in movement two in the melodic material for the solo oboe and at the conclusion of the piece (the oboe outlines a melody with all of the pitch classes from HEX1,2 to end the work).
Additionally, this hexatonic collection is frequently broken down into smaller sets of (318), such as in the solo oboe at the start movement II (m. 62) which presents F – D – F# (HEX1,2).
The last important item to note regarding set A is that it features inversional symmetry within itself along the axis ICC#.
Movement II
A brief look at the second movement will illuminate some of the details of how these pitch materials are used.
The eight measures before the movement (mm. 54-61) serve as a transition and establish the harmonic context for the next two minutes. A rhythmic electronic synth outlines a B-flat minor triad as the oboe oscillates between two subsets of HEX1,2 in ascending arpeggios:
Throughout the movement, there is a progression through various referential collections – primarily hexatonic collections2:
HEX1,2 – HEX2,3 – AC-3 – HEX0,1 – HEX1,2 – HEX2,3 – DIA+1 – HEX3,4 – HEX0,1 – HEX1,2 – DIA-6 – HEX2,3 – HEX3,4 – HEX0,1
The figure below plots this sequence of referential collections to scale and indicates the bar number for each change of referential collection. The acoustic and diatonic referential collections are highlighted in red.
(Click here for a larger view of the figure)
Note that there is a coordinating process at work in the sequence of hexatonic collections, with the steady transposition upwards by a half step between consecutive hexatonic collections (i.e. HEX1,2 to HEX2,3, etc.) being heightened by the increasing frequency of change in referential collection as the end of the movement approaches.
Movement III
Movement III features arpeggiated figures in the harp and piano with sustained tones in the winds and brass which outline a chord progression infused with a number of Neo-Riemannian transformations (particularly, some striking examples of hexatonic poles). In the example below, the C Acoustic collection that marks the moment just before movement III (and the interrupting “rewind” moment in the middle of this section) is indicated with a red box:
(Click here for a larger view of the figure)
As mentioned in the note on form, several materials and parameters combine in this section to create an evocative and hypnotic dream-state for the listener/viewer. A tritone root relationship from the C major sonority in m. 99 to the F#m sonority in m. 102 lurches the listener away from the dramatic conclusion of movement II before a relation by hexatonic pole converts F#m to Bb major.
In his 2012 book, Audacious Euphony, Richard Cohn argues that motion through a hexatonic cycle3 is strongly correlated with musical topics of magic and the supernatural for listeners acculturated to the canon of Western classical music.4 Cohn asserts that there is a theoretical and psychoacoustic basis for asserting the connection between hexatonic cycles and the evocation of themes of magic and the supernatural. Because hexatonic cycles operate on symmetrical referential collections and step “outside” of the usual function of tonal harmony operating on asymmetrical diatonic referential collections, a completed motion through a hexatonic cycle will paradoxically return to the same starting place while also necessarily undergoing enharmonic reinterpretation. In this sense, the harmonic materials of such a cycle feel as though they are “running in place” – advancing forward continuously only to arrive back at the same starting point.
(Click here for a larger view of the figure)
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Interval Normal Form is a sequence of digits used to represent the distance in semitones between pitch-classes on a pitch-class clock, moving clockwise around the circle and saving the largest interval for last. In this analysis, Interval Normal Form (INF) is always indicated using parentheses – such as
(11212113)– and the corresponding Interval Class Vector is always indicated using angled brackets – such as<545662>. ↩ -
Here, I use the convention of Joseph Straus in identifying two consecutive pitch classes of the hexatonic collection. (So HEX0,1 for example would denote the hexatonic collection containing C and C#/Db). ↩
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A hexatonic cycle is a series of Neo-Riemannian transformations that will create a circular chain of all of the major and minor triads that can be constructed in a hexatonic collection. The chain can be constructed by starting on a major triad and alternating between parallel (P) and leading-tone exchange (L) transformations – or by starting on a minor triad and alternating L and P transformations. ↩
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Richard Cohn, Audacious Euphony: Chromatic Harmony and the Triad’s Second Nature (Oxford: Oxford University Press, 2012). ↩