There is a thread of epistemic theory connecting the discourse of twentieth-century aesthetics and phenomenology, which asserts that works of art open up or disclose a sort of ‘world’, so to speak, as well as an associated view of reality that accords with the subject’s primordial and embodied sense of being. This idea was asserted most notably by Martin Heidegger in his essay “The Origin of the Work of Art” (1935-57), and by Maurice Merleau-Ponty in his essays “Cézanne’s Doubt” (1945) and “Indirect Language and the Voices of Silence” (1952). This ‘world’, which essentially accounts for the essence of aesthetic experience, is neither completely subjective nor objective; inasmuch as it exists solely for, and can be accessed only by the subject, it is necessarily always related to an experience of something in the empirical world. In this way, it is comprised of both ‘real’ and ‘unreal’ types of experiential data; the former correspond to empirical information, as obtained through sensory perception, while the latter characterises the quality of the lived experience, and generally refers to psychic and somatic projections of spatial, temporal, emotive, and conceptual knowledge. The ‘unreal’ categorisation of ‘world’ is not to suggest that the experience is fictional in any sense; on the contrary, it is indeed a real experience that is categorised as surreal, or ‘unreal’, only in relation to experiences of objective or absolute time and space.
For the purposes of this discussion, the concept of ‘world’ can be taken in the somewhat more abstracted sense of phenomenal ‘space’; that is, an environment that is felt and experienced as the lived or present consciousness. The concept of phenomenal ‘space’ will be given thorough consideration in subsequent discussion; however, for the time being, it suffices to suggest that phenomenal ‘space’ is characterised as being multi-dimensional or total - that is, integrating multiple dimensions of experience into one singular episode, so to speak. Moreover, although the phenomenal realm is dependent upon the cognition or acquisition of particular sensory stimuli, it is categorically concerned with essences and will, at some point, simultaneously transcend the merely perceptual.
In fact, the emergence of phenomenal ‘space’ in the capacity of aesthetic experience can even be traced back beyond the level of immediate perceptual information, which itself arises from the given or quantifiable elements of the art work. Musicologist Jean-Jacques Nattiez addressed this issue by devising a semiological tripartite of musical experience, consisting of three symbolic dimensions: the poietic, the esthesic, and the neutral. The poietic refers to certain phenomenal experiences associated with the initial influence or event that inspires the creation of an artwork, and the resultant aesthetic or intellectual experience belonging to the beholder of the artwork is the esthesic. The neutral, however, is understood to be the physical trace, as Nattiez (1990, pp.10-16) suggests, which contains all the tangible or analysable elements held within the musical or artistic work itself. human beings are symbolic animals; confronted with a trace they will seek to interpret it, to give it meaning. We ascribe meaning by grasping the traces we find. Clearly, then, the neutral conforms to the domain of immediate, sensational content, and not wholly to the phenomenal experience. Thus, these neutral elements - that is, that which can be analysed in music, most likely from a score - should be distinguished from what the listener can, or tends to, perceive in music and, even further, from what the listener may claim to feel or experience from the music. Such a distinction lends support to the contention that there are things that can be analysed but that one would not claim to perceive (or, much less, experience) as such, even if such things happen to determine the presence of the things perceived. Yet, as Nattiez reminds us:
…human beings are symbolic animals; confronted with a trace they will seek to interpret it, to give it meaning. We ascribe meaning by grasping the traces we find. (1990, p.128)
The trace, it seems, is our only palpable contact with the aesthetic experience and, surely, the aesthetic experience arises from the work of art, and not independently of it, no matter how distant the connection or how inadvertent the trigger may be (Nattiez, 1990, p.166).
In music, these given elements, which can also be understood as the collective or public symbols of the art object, can be identified as pitch and frequency, register, timbre, duration, amplitude, dynamic change, motive and phrase, texture or density of sound, and harmonicity or inharmonicity. Insofar as these phenomenal ‘spaces’ also arise from the given elements of the work, a qualitative description of phenomenal space first requires a description of the work itself and the compositional elements that play a part in the construction of a perceptual ‘world’. Various compositional choices will affect a listener in particular ways and although it is clear that each listener will experience a completely subjective and unique ‘world’, it would still seem feasible to suggest that there will be more generalised features common to each subject’s experience. Surely, different compositional styles are united, in part, because they share certain aesthetic assumptions. It is, then, also acceptable to suggest that there will be particular traits shared among different ‘worlds’ that have been created according to a similar aesthetic methodology. To explore this notion within the minimalist compositional approach, it would be worthwhile to first consider some of the general aesthetic assumptions which underlie minimalism, before turning to specific musical examples to illustrate this point.
Perhaps the most vital facet of the minimalist aesthetic - which is, by and large, shared among visual art, film, architecture, and music - is advocacy of a reductionist attitude. That is, the utilitarian contention that “less is more,” or that, in other words, only the necessary materials, processes, and forms need be used in order to foster the revelation of an aesthetic or functional ‘essence’ or ‘meaning’. The purpose of the reductionist attitude, then, is in service to an explicitly self-referential end in which focus is directed toward the perception of the thing in itself (Mertens, 1983, p.88). However, in positing the nature of the thing’s essence, to which the aesthetic meaning refers, the different artistic media seem to diverge conceptually. In visual art and, for the most part, in film, the essential is recognised as the given object or activity, and not within or around it. In painting and sculpture, for instance, simple geometric forms and shapes are often chosen as artistic material precisely because they are familiar, or, in other words, because they are not typically presented in isolation of some narrative. This is evident, for instance, in the works of American minimalist sculptors Donald Judd and Tony Smith, whose pieces deliberately emphasise blunt forms, shapes, and colours, either through repetition or enlargement. Thus, by abstracting or de-familiarising these basic shapes or movements from any sort of context, the viewer is forced to focus on the thing in itself and, by extension, its essential nature.
In minimalist architecture, the essence of the thing-in-itself refers to a functional essence; that is, the essence of the space according to its intended purpose (Blaser, 1972, p.50). In the case of a house or apartment complex, the architectural reductionist aesthetic - which was reflected most prominently in the projects of German architect Ludwig Mies van der Rohe - dictates that the exterior and interior structures should serve to illuminate the concept of what it means to dwell, or that which is essential to the concept of dwelling. In earlier projects such as the Farnsworth House of 1951, Mies van der Rohe extended the exterior walls into the landscape and used glass to surround the interior space so as to engage the feeling of the living space extending into the natural landscape (Drexler, 1960, pp.15, 22). Moreover, the interior also maintained an open concept in that room divisions were often created by way of vertical partitions instead of complete wall closures.
In minimalist music, the idea of the essential typically points inward; that is, entering inside a sound, process, or surface texture itself, and away from conscious comprehension of outer macro-structures, especially those representing the chronological perception of passing time (Bernard, 1993, p.19). This can be seen most notably in the works of American composers La Monte Young and Terry Riley, who are seen to have begun the tradition in the early 1960s, as well as Steve Reich and Philip Glass, who further transformed the fundamental structure to one emphasising process and repetition throughout the later 1960s and 1970s. Contemporaneous composers such as John Adams, Louis Andriessen, and Arvo Pärt are also often viewed as adhering to the minimalist aesthetic, given their tendencies toward reductionism. According to Young, the minimalist tendency in music is connected to the idea of “getting inside [sounds] to some extent so that we can experience another world” (Potter, 2002, p.46). Thus, while minimalist visual art tends to focus on the experience of the thing itself, minimalist music focuses on the quality of the somewhat surreal ‘world’ that is created within the thing itself. This implied sense of perceptual interiority does, in a sense, presuppose the presence of a so-called dwelling space and therefore, perhaps, asserts something fundamentally shared between music and architecture.
Music, being inherently time-based, is therefore also appropriately situated to transform the temporal aspects of phenomenal ‘space’ and experience. Minimalist music, given its general lack of directionality or teleological design, tends to produce a sense of suspended or frozen time (Mertens, 1983, p.91). This essentially ‘unreal’, yet lived temporal experience is typically created through the use of sustained or repeated sounds and patterns. These elements create a more multi-dimensional sense of phenomenal ‘space’ in music in that they extend the reduced sound or aural object over time. In so doing, the listener is, in a sense, positioned so as to approach the internal and oftentimes surreal ‘world’ of the sound. Accordingly, the view held throughout this discussion asserts that the combination of reduction and stasis give way to a particular type of spatiotemporal complex, or environment.
Insofar as one aims to experience another world beyond the mere perceptual elements of the sound itself, it is also important to consider the notion of automatism and its role in contributing to the aesthetic experience. In general, automatism refers to something external - a feeling, an idea, a perception, etc. - that was not built directly into the aesthetic object, yet emerges unconsciously when one is engaged with the explicit elements of the work. The term ‘external’ should not be associated with any connotation relating to the strictly empirical, objective, or even representational world per se; in the context of automatism, ‘external’ simply accounts for the fact that the character of the ‘space’ or ‘world’ that arises is external to the aesthetic object itself, and that it is externalised in the psyche of the beholder.
It is important to note that in visual art, these so-called extra or meta illusions, which are external to the immediate art object, do not play a part in expressing the meaning of the artwork. Artists Robert Morris, Sol Le Witt - and, to an extent, also Steve Reich - share a particular opinion regarding intended and unintended meaning. Morris iterates the view by suggesting that we receive the gestalt of the work of art immediately, as an impression, but that there will always be a period (that occurs over time) of divergence into different levels of perception. Thus, he claims that immediate impressions do not always account for complete experience (Bernard, 1993, pp.19-20). Reich expresses a similar notion of temporal divergence in relation to the psychoacoustic effects that emerge in generative and process-based music, which one could also exchange for the visual ‘side-effects’ that arise in Le Witt’s terminology. That said, although these artists do not deny the phenomenon of external evocation in art, they do, however, render it insignificant, or secondary to the meaning of their work (Bernard, 1993, p.11).
With the above noted exception in Reich’s aesthetic, this view regarding extra or ‘automatic’ phenomena is not necessarily held as stringently in minimalist music. As initially suggested by Young, the endeavor undertaken in minimalist music is to employ reduction and sustaining material so as to get into the ‘world’ of the sound; indeed, to enter inside the sound, or become close to it in some phenomenal way. It would seem, then, that the notion of some type of ‘space’ being revealed or opened up to the beholder of a work of art implies the notion of automatism. This phenomenal exteriority does not, however, contradict the interiority or sense of looking inward expressed above; the latter describes the localisation of essence in the sound, while the former describes the localisation of ‘world’ in the listener. In contrast, then, to the views espoused by the minimalist visual artists, it is contended here that so-called ‘automatic’ extra-musical phenomena - that is, conceptual elements beyond the theoretical or acoustical content of the musical form or material - in fact hold an important position in the development of the phenomenal ‘spaces’ that are founded in aural sensation.
Finally, it is also important to distinguish between two types of automatism: namely, ‘perceptual’ and ‘phenomenal’. The former refers to that which is perceived, and is typically founded in sensory data, while the latter refers to that which is experienced or felt, and is normally constitutive of the subjective, or lived psychosomatic experience. Moreover, each form of automatism associates with a particular type of ‘world’ or ‘space’; that is, either a perceptual ‘world’, or a sort of phenomenal ‘space’, as was illuminated in the foregoing. The two categories of automatism are related insofar as the phenomenal emerges from the perceptual, however they are distinguished in that the phenomenal experience is characterised as having a total, or complex, and ‘unreal’ quality that transcends the sensory.
In several compositions by minimalist composers La Monte Young and Arvo Pärt, both perceptual and phenomenal ‘worlds’ arise as a result of a shared attitude regarding reduction, stasis, and the evocative possibilities of automatic phenomena. Although less explicit than Young’s notion of experiencing another ‘world’, Pärt’s approach to the technique of tintinnabulation (that is, emulation of the sound of bells) can be considered an extension of entering inside a particular sound itself; musicologist Paul Hillier (1997, p.20) argues that although bells are generally understood to ring out, they can also serve to pull the listener inward so as to create the sensation that ‘inside’ and ‘outside’ are one and the same. Although the compositional techniques employed by Young and Pärt diverge in many ways, both share an acute apprehension toward the combination of reduction, stasis, and automatism; indeed, these similarities are reflected in the nature of the phenomenal ‘spaces’ that arise.
In the majority of the music La Monte Young has composed since the late 1950s, notions of reduction and sustained material manifest predominantly in the use of a few select harmonically-related tones or intervals, which are typically determined by the strictures of just intonation and are given considerably long durations. Two compositions are particularly reflective of this approach: namely, The Second Dream of the High-Tension Line Stepdown Transformer from The Four Dreams of China (1962) and The Well-Tuned Piano (1964). These pieces employ a sense of sustained harmony through the use of drones, as in The Second Dream, and the quick repetition of several neighbouring tones, as in The Well-Tuned Piano.
Although Arvo Pärt’s overall compositional aesthetic does encompass a predominantly minimalist attitude, several of the works he composed during his tintinnabuli period of 1976 to 1979, including Für Alina (1976), Cantus (1976), Fratres (1977), Tabula Rasa (1977), and Spiegel im Spiegel (1978), are especially representative of a similar reductionist stance. In these works, the musical material is, for the most part, restricted to a single triadic entity and its diatonic counterparts. Although the two composers differ somewhat in relation to the use of overtly melodic gestures, one fundamental characteristic shared between the two is an attraction to the prolongation of simple harmonic structures. Quite unlike the progressive harmonies that have characterised a good deal of Western music since the Baroque era, both Young and Pärt employ a non-functional or ‘static’ harmony. In other words, although harmonic relationships are established within a given piece, these relationships remain largely unchanged throughout the duration of the piece. Moreover, one notes the use of a drone or pedal point, as it were - that is, a particular timbre, pitch, interval, or triad that carries throughout the entire piece - in order to effect the presence of a singular sound guiding the entire structure.
In music, the concept of perceptual automatism can refer, amongst other things, to the psychoacoustic or spectral effects (such as overtones, sum and difference tones, and beating patterns) that emerge from the overlapping frequencies and intervallic relationships as given in the musical material. In other words, it describes those aural phenomena that connect with, yet cannot be pointed to, the quantifiable elements of the work, and which arise somewhat automatically (or without conscious deliberation) in the act of engaged listening. For instance, when two tones of frequencies 150 Hz and 100 Hz sound together, the difference tone of 50 Hz and the combination tone of 250 Hz will also be detectable even though they are not explicitly given to the listener. Tones that are tuned according to the harmonic series, such as those set by systems of just intonation tend to produce other harmonically-related frequencies called partials, which are specific sets of resonant overtones linked to the harmonic series (Gann, 1997).
Emergent psychoacoustic effects arise as one of the timbral focuses of The Second Dream and The Well-Tuned Piano. Young’s affection for the acoustic and psychoacoustic behaviour of held frequencies can, in part, be attributed to certain childhood experiences. Young was born in Idaho in 1935, but his family relocated to California in 1940 where La Monte spent the better part of his youth and early adulthood. During his brief time spent in Idaho, Young states that he became interested in the static sounds of electric power transformers, and the wide, open spaces of the Western landscape (Potter, 2002, p.23). Despite his time spent studying serialist technique - first in Los Angeles and later as a graduate student at Berkeley - Young became increasingly more experimental throughout the latter half of the 1950s in his work with long tones. At the same time, Young became interested in Indian classical music, both aesthetically and ideologically, and began to intuit theories about just intonation as well as the practice of holding a single tone so as to expose the notes that ‘live’, so to speak, within it, as would have been done in the development of the raga (Holmes, 2002, p.249). These ideas did not, however, crystallise in Young’s compositions until after his relocation to New York in 1960, where he has since remained. Throughout the 1960s, Young continued to develop his personal compositional approach - though many projects, such as the Dream House, were typically done with the visual aid of his partner Marian Zazeela - in addition to his more improvisatory work with The Theatre of Eternal Music (1960 - 1963).
The Four Dreams of China is a set of four pieces composed in December, 1962. Each piece is restricted to a collection of four tones, which Young refers to as the Dream Chord; The Second Dream focuses on the tetrachord of F, B-flat, B-natural, and C. Young dictates that the texture of the piece should exemplify long sustained tones and silences, and that only certain intervals or combinations of pitches may sound together simultaneously. He advocates such restrictions in order to emphasise a specific group of overtones that emerge from intervallic relationships such as the unison, fourth, and fifth. Harmonically, then, it could be conceived that the perceptual ‘world’ of the sound is a very spacious one, revealing myriad other possible sounds as one is permitted to ‘live’ there for some time. As such, these perceptual phenomena tend to imply a sort of spacious quality inherent in the sounds; in other words, there is the sense of a single fundamental sound, which is also complex insofar as other tones are emerging from within it. Effectively, then, psychoacoustic phenomena are set up or prepared through the use of particular harmonic relationships. However, the actual coming-to-be of a perceptual ‘world’ is achieved only through stasis, or sustenance of sound, which essentially gives the sound the ‘space’ it requires to envelope the listener. Indeed, the appearance of outer stasis serves to effect the impression of internal change, as if one is almost physically (or, perhaps, somatically) inside the sound.
The Well-Tuned Piano was initially begun in 1964, however Young continued to work on the piece throughout the 1970s and into the 1980s. In contrast with the held tones and intervals of The Second Dream, The Well-Tuned Piano employs passages of rapidly repeating neighbouring tones in order to induce the perception of sustained sound. Psychoacoustic effects emerge in The Well-Tuned Piano by virtue of overlapping tones, which are generally arranged as groups of just semitones (Potter, 2002, pp.86-88). As such, the exterior texture of The Well-Tuned Piano is decidedly more varied than that of The Second Dream. In fact, The Well-Tuned Piano is mostly comprised of two different textures: one in which discrete tones are played in slow succession at a relatively subdued tempo, and another in which different permutations of a few tones are constantly repeated with considerably greater force and in extremely fast succession. The latter section also requires lifting the dampers of the piano, so as to let the tones and their spectral counterparts blend.
As a result, a highly complex, conglomerated cluster of sound or ‘cloud’, as Young describes the effect, emerges (Potter, 2002, p.83). Indeed, the overall resonant quality is quite consistent. As such, the static, yet harmonically rich cluster appears to sustain in much the same way as the held tones and overtones of The Second Dream. In this case, then, suspension of a unified, texturally spacious atmosphere is achieved through repetition in conjunction with pitch restriction. Interestingly, Young (1987, p.7-8) has also cited the way in which he would use the beatings produced by the overlapping frequencies of the ‘cloud’ sections as rhythmic pulsations to which he could match the pace of his playing. Naturally, then, the performer’s connection to the sound is also characterised by a certain sense of disclosure over time. In other words, it could be argued that the performer is guided by the piece itself, as it unfolds over time, rather than by an internal sense of timing. According to Young, The Well-Tuned Piano marks the first instance of this type of “real-time” engagement in a musical performance.
Just as in The Second Dream, the combined effect of repetition and reduction is a sort of ‘shimmering’ stasis, so to speak, in which the listener’s perceptions are continually, albeit minutely, transforming over time even though the overall or macro feeling of the sound remains largely unchanged. Thus, the psychoacoustic effects that emerge are taken as perceived elements, while the feeling of inner spaciousness essentially outlines the spatial aspect of the phenomenal quality of the associated aesthetic experience. Of course, this phenomenal ‘space’, being multi-dimensional, is as much temporal as it is spatial. In a way, the extended drones that connect the entire piece serve to suspend one’s experience of duration into the extended presentation of a single moment, as in the immediate impression of a temporal whole. It would seem, then, that the quality of spaciousness, which arises through sustenance of sound, is conjoined with consciousness of the moment, or feeling of the present-time in itself. Thus, the ‘unreal’ spatiotemporal environment here is spatial in its being expansive, and temporal in its sense of staying.
Throughout 1971 and 1976, Pärt largely abstained from composing, and instead spent his time studying early music in order to overcome what he felt to be a sort conceptual barrier, so to speak, in his process (Hillier, 1997, p.32). During this time, he also became curiously affected by the idea of tintinnabulation - that is, generally speaking, the sound of bells - and returned to composition in 1976 with a transformed approach (Hillier, 1997, p.86). Bells possess a particularly rich and complex texture, which is determined by their shape and material, and is a mixture of both inharmonic and harmonic frequency spectra. They are also characterised as having a highly resonant quality in their overall sound, enabling the complexities within to extend perceptibly over time. Essentially, then, tintinnabulation can be described more broadly as the emulation of an unfolding sound that is at the same time changing in its complexity and nuance, yet static given its acoustical connection to the same object. As such, Pärt’s iteration of tintinnabulation is not necessarily in the sense of the timbre of bells per se, but rather in the experience of being immersed or focused within a single sound that is simultaneously still, yet continually moving over time.
As in the case of Young, a sense of extremity arises in relation to such notions of expanded duration and space. Indeed, the idea of experiencing something eternal or infinite certainly evokes a sense of the ‘unreal’ in relation to the limits of empirical experience. One could argue that part of Pärt’s attraction to this notion of stillness and concentrated focus arose from his connection to the Hesychastic and monastic traditions of the Eastern Christian orthodox church; a practice into which he was born and maintained throughout his later life (Hillier, 1997, pp.7-9).9] Pärt was born in Estonia in 1935, where he lived until his emigration to Berlin in 1980. Although working concurrently with Young, Pärt’s early experiences with music were notably different on account of the disparate social and cultural climates that separated the United States and Eastern Europe during the Cold War. Unlike Young, Pärt’s knowledge of early twentieth-century avant-garde music was mostly self-taught. In fact, Pärt’s decision to emigrate to the West in 1980 came as a reaction to governmental restrictions that were placed on his ability to attend international performances of his music, and in view of the generally disapproving attitude with which his seemingly radical music was received in the Soviet Union (Hillier, 1997, pp.27-33).
Für Alina, composed in 1976 for solo piano, was Pärt’s first attempt at manipulating the tintinnabuli aesthetic. Like the later tintinnabuli works, a single triadic harmony is sustained throughout the entire piece, accompanied by slow-moving melodies in the upper registers. These melodies are comprised of both consonant and dissonant pitches, reflecting the complex texture present in bells. Additionally, the damper pedal is held throughout most of the piece, allowing the consonances and dissonances to merge into one conglomerated sound circling the ever-present harmonic drone. Indeed, a similar sense of hovering or suspension was produced in the ‘cloud’ clusters of Young’s The Well-Tuned Piano.
Pärt solidified this technique in works such as Fratres, composed in 1977 for an unspecified early music ensemble (later rescored for various other ensembles), and Spiegel im Spiegel, composed in 1978 for violin and piano. In Fratres, the dominant interval of A - E is maintained as the bass structure throughout the entire piece, with punctuating reinforcements placed at the end of each section. The melodic notes, which are heard in the upper voices of the piano as series of chords and intervals, and in the viola as singular lines of changing density, maintain a circular presence around the dominant pedal. Neighbouring dissonant tones are occasionally introduced in order to give the subtle sense of pulling or branching away from the drone of the pedal. However, the melody always returns to the dominant, creating an overall sense of settling or stillness. This sense of circular motion is apparent in the first few lines of section 3 (figure 1), particularly in the way in which the melodic motion of the piano extends above and below the sustained tones. One also notes a sense of dissonant texture given the presence of C and C# within the same line. A more macro sense of dissonance is also detected in relation to the dominant pedal; in this example, a neighbouring F is held directly against the E.
Figure 1: Arvo Pärt, Fratres (1977), section 3
Figure 2: Arvo Pärt, Fratres (1977), section 5
In section 5 of the piece (figure 2), the dissonant texture has now been moved to the B, which juxtaposes the A of the dominant pedal. Toward the end of the piece, however, the dominant triad is prolonged in isolation. Although not prescribed explicitly by Pärt, lifting the dampers throughout the entire piece (that is, with minimal or no changes), allows for a gradual (that is, over time) and natural clearing of previously heard dissonant resonances. In the final section of the piece (figure 3), the dominant pitch is presented in solitude, creating a particularly acute sense of stillness and purity of sound. Indeed, the sense of circular motion is similarly extended into the timing of the piece, as shown in the manner in which the time signatures cycle about 9/4 into 7/4 and 11/4.
Figure 3: Arvo Pärt, Fratres (1977), section 9
Again, a similar approach can be traced in Spiegel im Spiegel. In this piece, the tonic octave is continued throughout, while the arpeggiated melodies above circle the notes of the tonic triad. As figure 4 demonstrates, there is a similar sense of circularity around the diatonic pitches; first in the movement from F to G in bar 49 - 50, followed by the movement in bar 51 from C/E to D, and finally as a return to the stillness of the tonic centre in bar 53.
Figure 4: Arvo Pärt, Spiegel im Spiegel (1978), bars 49 - 53
Indeed, it would seem that the subtle way in which Pärt extends the triad - such that every note seems to emerge from within - tends to create the impression of movement within the sound structure. In this way, a dimensional space is created that could, perhaps, be likened to the experience of standing in the center of a bell itself. As such, the perceptual ‘space’ produced in Pärt’s tintinnabuli music refers to the sense of resonance, consonance, and dissonance that arises as a result of the sustaining of a unified texture. On this point, it is interesting to note that Pärt’s attraction to the notion of spatial circular experience could also have developed from the physical or somatic associations of sound being diffused throughout large orthodox churches and cathedrals. In these buildings, one becomes surrounded by a flow of sound - that is, a continuity of sound, which is non-localised and tends to fill the reverberant space (Hillier, 1997, p.179). Indeed, these aesthetic experiences are characterised by the way in which beginnings and endings appear to merge. Interestingly, a good deal of Pärt’s music also references the structures of early music. However, unlike the medievalism Pärt seems apt to revive, his music maintains allegiance to equal temperament. Nonetheless, the textural disposition illustrated in medieval polyphony and monody seems to reflect the functional setting of tintinnabulation; that is, the sense of one melodic line creating contour around a single pitch or collection of related pitches, such as a triad, so as to produce the sense of two voices merging into one.
Moreover, as with Young’s music, the phenomenal ‘space’ created in Pärt’s music is, then, comprised of both spatial and temporal senses of lived experience. However, whereas Young’s temporal landscape suggested the idea of suspended ‘moment’ time, the circularity of Pärt’s tintinnabuli works creates what Hillier (1997, p.2) describes as a sort of mythic time, in which experiences of past, present, and future amalgamate into one. This truncation of memorial time, current time, and anticipated time is not to be confused with Young’s truncated experience of duration and continuum; the latter is characterised as the experience of a single moment suspended over perceptible time, while the former is the experience of a truncation of many moments into a single unit.
Despite these differences in the quality of the phenomenal experience, there are several fundamental similarities that can be drawn between the approaches of Young and Pärt. These similarities stem from a common inclination toward the conceptual methodologies espoused in the minimalist aesthetic. As suggested in the foregoing, one of the most important elements found in the music of both composers is the notion of stasis. In both cases, stasis served a three-fold purpose: first, in order to effect the impression of a singular unit of sound, and by extension an impression of unified experience; second, in order to turn the listening experience inward, away from the superficial surface; and, third, in order to give some sense of temporal suspension, however that should manifest in terms of particulars. As such, one perceives a single sound, however the sound is active in terms of complexity at its micro level. In further relation to stasis, both composers also demonstrate a general lack of directionality, or teleological design in their compositional approach. Thus, despite the fact that the particular qualities of the phenomenal experience varied somewhat in each case, one notes a mutually expressed sense of ‘looking inward’; in other words, the exterior remained static so as to expose the more meaningful movements that occur within.
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 In music, these are usually outlined in some form of a score. Of course, music that is not based on a score, including a good deal of improvisatory and electronic music, requires a broader categorisation of the given, even though the quantifiable aspects - pitch, dynamics, duration, timbre, etc. - are still intact. Within the realm of electronic music, for instance, recordings often serve as the physical ‘object’ itself. In these cases, then, the given ought to refer more generally to the aural object with which the listener engages directly. One might also wish to exchange ‘harmonicity’ and ‘inharmonicity’ for ‘consonance’ and ‘dissonance’, however these terms also have considerable import within the phenomenal experience and therefore do not, strictly speaking, belong solely to the perceptual or empirical realm.
 Architect Ludwig Mies van der Rohe (1886 - 1969) famously espoused this view.
 The positing of multi-dimensional spatiotemporal environments in describing the phenomenal quality of the aesthetic experience inevitably suggests a sense of appropriation (albeit unintentional) of certain architectural metaphors. In general, the minimalist aesthetic in music seems to align with minimalist architectural practice in several ways: primarily, however, in order to expose the essence of the function of spaces, and to emphasise the impression of an immersed ‘whole’. In minimalist music, there is a sense of temporal connection, which is established in the truncation of certain elements of absolute time. In minimalist architecture, there is a similar sense of spatial connection in the notion of intertwined spaces, which are established through the use of an open plan and either a lack of connecting walls, or an extension of exterior walls into the landscape. A similar sense of perceptual automatism arises in minimalist architectural practice in connection to the smaller refinements or subtle details that occur on the inside of the building once the simplistic exterior structures have been set in place. For instance, Ludwig Mies van der Rohe often preferred the use of glass in order to produce interesting effects that would alter the inside space without causing changes to the exterior. In both approaches, then, it is implied that simplicity of exterior structure and interior design outline a sense of non-prescribed ‘space’, - indeed the essence of space itself - giving it greater importance by putting it into view. Interestingly, although it is not categorised within the minimalist aesthetic, another particularly potent architectural metaphor for this notion of ‘looking inward’ is found in the idea of ‘architecture of the veil’, a phrase that is often used to describe the construction of certain types of Mosques. This metaphor reflects the view that the important movements or events occur on the inside of the structure, and not on the outside; indeed, encouraging the idea that one must physically enter the building in order to understand its meaning. As such, the exteriors of these buildings are typically quite plain, while the interiors are usually complex, dazzling, and visually active.
 Note that perceptual phenomena are not strictly subsumed under the category of ‘real’ experiential data. Indeed, certain sensory illusions, though not necessarily ‘unreal’ as such, can also not be defined as quantifiable phenomena. Moreover, although the phenomenal realm emulates a fully subjective sense of spatiotemporal experience, one recalls that the data of the phenomenal ‘space’ consists of both ‘real’ and ‘unreal’ elements.
 Although instances of what could be construed as a sort of modulation occur within pieces such as The Well-Tuned Piano and Spiegel im Spiegel, they are typically quite brief and are generally always immersed within the sustained pitches or sounds that underlie the piece.
 There has been some dispute as to who exactly introduced just intonation into Young’s practice. Although Young does claim to have theorized the need for such a system quite early in his musical career, there are circulating claims that it was in fact Tony Conrad, former member of The Theatre of Eternal Music, who made Young aware of the mathematics of just intonation (Doty, 1989, p.1).
 The liner notes for The Second Dream describe this particular inversion of the Dream Chord as the intervallic ratios 18/17/16/12, however there is some discrepancy about the actual pitches. Several consulted sources (Mela Foundation, 2011; McCroskey, 2011) suggest F, Bb, B, and C, while others (Potter, 2002) instead give G, C, C#, and D. The latter combination reflects the overtone series according to a fundamental pitch of C. In the same text, Potter also gives D, G, G#, and A as the Dream Chord at the time of For Brass (1957).
 The Second Dream was composed under the auspices of equal temperament, however one notes that, even here, Young is anticipating his use of just intonation given his interest in intervals such as the unison, 5th, and 4th, which are the purest (or least tempered) intervals of equal temperament.
 The Hesychastic tradition, as reflected in several Eastern Christian and Catholic churches, emphasises a practice of stillness and quiet so as to approach a more inward-looking, physically transcendent state. Monasticism implies a contextual view of the reductionist attitude in terms of material renouncement.
Sarah C. Davachi holds a Bachelor's degree in philosophy from the University of Calgary, and a Master's degree in electronic music and recording media from Mills College in Oakland, California. As a composer of electronic and electroacoustic music, Davachi engages in practices of analog and modular synthesis, multi-channel sound diffusion in alternative spaces, and studio composition. Her work as a musicologist concerns areas of experimental and electronic music, organology and archival study of auditory collections, and phenomenology and perception. For the past five years, Sarah has also had the unique opportunity to work at the National Music Centre in Canada as an interpreter and archivist of their collection of electronic and acoustic keyboard instruments. She has been artist in residence at The Banff Centre for the Arts (Canada), and will be in residence at STEIM (Amsterdam), WORM (Rotterdam), and EMS (Stockholm) in the spring of 2013.