Boundary objects in Informed Phrasing

Introduction

“Phrasing tends to dominate performance expression”, so say Anders Friberg and Giovanni Umberto Battel^[1] , and indeed all means of musical performance converge for the expressive force of communicating the musical phrase. Hence the importance of phrasing, as an aspect of musical performance, is unquestionable. The on phrasing in tonal music (the main focus of this paper), could be very generally characterized by on the one hand relying on personal musical intuition, and on the other, through an ‘informal analysis’^[2] and thus taking harmonic connections, phrase structures (mainly through examination of cadences), motivic developments and stylistic (hence historic) considerations into account. As important as those considerations are, they leave two significantly important features of the musical phrase out of the performer’s awareness. The first is the fact that the phrase moves. In his book Phrase rhythm in tonal music, William Rothstein explains how intrinsic and crucial tonal motion is for the definition of the tonal phrase, and hence is an inherent feature of the phrase^[3] . The second is the notion that the phrase is a hierarchical construction, meaning that a phrase might accommodate smaller phrases to which Rothstein refers as the ‘minimal units that contain tonal motions’^[4] . The simplest example to explicate the hierarchical nature of the musical phrase is the ‘period’ phrase structure. By definition, the period phrase contains two smaller phrases: the ‘antecedent phrase’ and the ‘consequent phrase’, each is delimited by a cadence, yet the two are regarded as mutually depended due to deeper harmonic and melodic dependencies. Yet in practice, there are many examples for deviated versions of the period phrase. The half cadence marks the end of the antecedent phrase, yet then later is recalled in connection to the perfect authentic cadence. The connection between the two cadences is created through deep harmonic and melodic dependencies. The most appropriate analytical method to explicate those important features of the tonal musical phrase is the Schenkerian method of music analysis. This method uses analytical graphs in order to show different levels of tonal motion within a piece of music. By that, the Schenkerian analysis not only addresses the important features of the musical phrase, but even more importantly, it presents their interrelation. It shows that the musical phrase is hierarchical by its nature, and this hierarchy is formed through different levels of contrapuntal and harmonic, hence tonal motion. The Schenkerian method uses harmony and counterpoint in order to clarify long term harmonic and melodic connections. It illuminates the mutual dependency between the period’s antecedent and consequent phrases, instead of dissecting it into different parts. It shows how those components relate to the whole in deep linear connections. The relevance of the Schenkerian method of music analysis for musical performance, and even particularly on phrasing, has been discussed before by many authors, including Schenker himself. Much less has been written on the application of theories of music cognition on musical performance, even on theories with significant relevance for musical performance such as Fred Lerdahl and Ray Jackendoff’s generative theory of tonal music (1983), which relies on Schenkerian principles, as well as on principles of temporal Gestalt units theory. The temporal Gestalt units theory asserts that the musical phrase is a cognitive phenomenon. The human mind, according to several conditions assembles the components of the musical phrase, i.e. the notes of the phrase, and transforms it from a succession of separated units to a one independently perceived entity; the musical phrase. The conditions for forming phrases as independent units assigned by the temporal Gestalt units theory can offer valuable information for the performer about timing, dynamics and even on timbre. The generative theory of tonal music fuses Gestalt principles with the Schenkerian view of musical structures (describing tonal structures through deep melodic and harmonic connections) in order to explicate the innate musical intuition that forms our musical grammar, in a sense related to Chomsky’s generative transformational grammar, to which I will refer in section 2. Nevertheless, these cognitive theories and the Schenkerian method are far from being performative methods, nor are they widely used by performers in their practice, for which an explanation will be suggested in this paper (section 4). Informed phrasing is a doctoral research project which aspires to form performative methods informing phrasing from both the cognitive and the Schenkerian views. A main objective of this project, is to shape the ‘informing’ process as performative, yet containing analytical and theoretical insights that alternatively would be reached in a non-performative manner^[5] . Therefore, the term Informed phrasing in this paper is referred as a performative process that involves analytical and cognitive inquiries which are made by and through the practice of musical performance. In this respect, I attempt in to incorporate analytical and theoretical fields into the performance processes and by that to transform those fields from theoretical terrains into performative methods. In order to fuse analytical methods and cognitive theories into musical performance in a performative manner, I must firstly introduce the concepts that allow those different terrains to relate to each other and to integrate into musical performance. These connections are only possible through the ‘boundary objects’^[6] of these fields: reductions, universal structures and classical improvisation. In this paper, I will present and discuss those boundary objects which relate the aforementioned terrains to each other and to musical performance. Thereafter, I will describe the integration of these boundary objects in the methodology of the Informed phrasing research project.

1. Boundary object: Reductions

Reductions in Schenkerian analysis

The technique of reduction is one of the core elements of the Schenkerian method of music analysis. The Schenkerian method views tonal compositions as hierarchical constructs, distinguishing three main structural levels: the foreground, the middle ground and the background, which shows the deepest, most fundamental contrapuntal and harmonic motions of a tonal composition. The method reduces the ‘surface’ of the composition to reveal patterns of harmonic and contrapuntal motions forming the structural levels. The revealed patterns do not merely represent separated time spans (as in conventional structural analysis), but the patterns function in order to prolong notes that belong to the deep structure of the composition, thus revealing the long term melodic and harmonic connections and dependencies. The result is a graphic presentation of several levels of tonal motions, excluding the musical surface; each level is reduced in order to present a deeper level of prolonged contrapuntal and harmonic pattern, each perceived as a structural level. The Schenkerian examination then provides crucial view on the tonal composition as structurally hierarchical.

Reductions in music cognition

Essentially, the musical phrase can be viewed as a mere succession of sounds, each of which is a unit that separately provides information regarding its pitch, length, articulation and timbre. Yet, when we listen to a musical phrase, we perceive it as one bigger unit, comprising of all the smaller units, i.e. the notes of the phrase. At that point, the perception and interpretation transform from specific singularities to a perception of relativity. Specific principles, defined by the temporal Gestalt units theory, outline the conditions that allow the human mind to relate successive notes to each other. Those principles are ‘proximity’: the relative distance in time between successive notes, and ‘similarity’: the relative distance in pitch between successive notes. According to the temporal Gestalt theory, the musical phrase is a cognitive phenomenon, meaning that in these predetermined conditions, the human mind generates the relations between the notes of the phrase, resulting in what the theory refers to as ‘cohesion’: the assemblage of components into one whole, and ‘segregation’: the separation of this formed whole from the following and preceding parts. In this paper, I view this perceptual process as a process of reduction. The human mind reduces the multiple sources of information, i.e. the notes of the phrase as separated singularities and forms one bigger independently perceived entity: “The whole is other than the sum of its parts” ^[7]. The reduction element of the process is not the main and most important issue. Yet it is indeed a crucial part of the perceptual process that I choose to focus on in this paper, as it enables the connection with Schenkerian analysis and musical performance to be made. According to the temporal Gestalt units theory, the reduction process is hierarchical, which fact forms another link to the Schenkerian analysis. The phrases, formed from the separated singularities, become singularities themselves, which in turn form the next perceptual level, referred by the theory as a ‘passage’. Before I go further with defining Informed phrasing’s boundary objects, I wish to note that even just the notion of the Gestalt conditions for cohesion, that is to say proximity and similarity, provides premises about the performer’s objective in her/his phrasing. Rothstein (1989) defines phrasing as “the delineation and internal shaping of phrases by a musical performer. Includes both the joining of notes into phrases and the separation of these phrases from each other”. According to this definition, the fundamental aim of the performer in her/his phrasing is to create the ‘joining’ and ‘separation’, or the ‘cohesion’ and ‘segregation’ in Gestalt terms. Therefore, the Gestalt provides the performer with insights about the conditions according to which she/he may or may not successfully phrase. Fred Lerdahl and Ray Jackendoff’s generative theory of tonal music presents a point of fusion between Schenkerian analysis and cognition, relying on temporal Gestalt units theory as well as on Chomsky’s universal structure. The generative theory of tonal music explicates the innate musical grammar of the ‘experienced listener’, and therefore her/his ability to perceive and make sense of the music he hears. This musical grammar comprises four areas of analysis: the first two are grouping structure analysis and metrical structure analysis. The interrelation of these two generates the third area: time span analysis, and the interrelation of the three (grouping, metrical and time span analyses) generates the fourth area: the prolongational analysis. Similarly to Schenkerian graphs, ‘the prolongational tree’^[8] presents the harmonic and contrapuntal structural analysis of a composition, as well as multiple structural levels of harmonic and melodic dependencies. There are several differences between the two methods of music analysis, but the most crucial one is the determining force. In Schenkerian analysis, the revelation of the deep structure is done with the motivation of exposing the ‘concealed repetitions’^[9] , while the prolongational tree is a result of the interrelation of rules based on cognitive evidence. In their book, Lerdahl and Jackendoff refer to their theory’s implication for musical performance merely in one paragraph, where they note that the generative theory may have such implications, but that these will not be discussed (p.64). Therefore, the transformation of this theory into a performative method that can be of use to performers as they work on their repertoire, is then one of the main objectives of the Informed phrasing research project.

2. Boundary object: universal structures

Universal structures in Schenkerian analysis

The notion of universal structures was first introduced as part of the Schenkerian analysis^[10] and was manifested through the background structural level, namely the ‘Ursatz’ (see figure 1).

The Ursatz represents the fundamental structure of a tonal composition. In the Schenkerian view, this is the most profound contrapuntal and harmonic formula. The tonal composition is composed out of this formula through a series of prolongations that lead to the musical surface. The Ursatz appears in three different formation: a descending step wise motion from either scale degree 3, 5, or 8 to scale degree 1. All three formations are harmonically supported by a tonic-dominant-tonic progression. The Schenkerian notion is that these formulas are universal for all tonal compositions^[11] . These formulas show the common tonal origin of all tonal compositions, and the Auskomponierung^[12] process of prolongations shows the unique path every composition goes through from the Ursatz to the musical surface.

Universal structures in music cognition

The term ‘universal structures’ was formulated by the cognitive linguist Noam Chomsky as part of his contribution to the theory of generative transformational grammar. In his theory, Chomsky attempts to reveal the innate knowledge that is required for the human skill of speaking. This knowledge enables an individual to produce and understand an indefinite number of sentences, some of which she/he never heard before. Chomsky sets up transformational rules to show the relationship between two structurally different sentences, thus differentiating the surface structure of sentences from their respective deep structure. The rules then transform a deep structure into multiple different surface structures, thereby showing that all grammatical sentences are generated from several forms of deep structure. Chomsky denies the notion that every language is unique. The deep structures are then structurally universal within a language, but one of the revolutionary claims of Chomsky is that those universal structures apply to all the natural languages.
Lerdahl and Jackendoff’s generative theory of tonal music aims to be a musical parallel to Chomsky’s generative transformational grammar. It aims to reveal what innate knowledge is required for the human skill to perceive and make sense of the music he hears. The generative theory of tonal music relies on studies of music cognition (mainly on temporal Gestalt units theory^[13] ) in order to validate basic Schenkerian principles: structural hierarchy which is manifested through several levels of contrapuntal and harmonic prolongations). In turn, the generative theory of tonal music uses these Schenkerian principles as central components of the innate musical grammar, thereby implying that prolongations are an essential part of the human perception of tonal music. Like Schenkerian analysis and Chomsky’s generative transformational theory, the generative theory of tonal music results in a universal structure, the ‘basic form’ (see figure 2).

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One can immediately notice the similarity between this prolongational tree to the linguistic syntactic trees. This tree presents the ‘basic form’ and the ‘normative structure’. The ‘basic form’ is the GTTM parallel of the Schenkerian Ursatz. Yet, while the Ursatz present only one structural level, the basic form shows four levels of melodic and harmonic dependencies. The normative structure refers to the nature of the prolongations and introduces the prolongational functions of ‘tension’ and ‘relaxation’. A right branch (a line that branches to the right out of a longer line) presents a prolongation that increases tension, while left branch is a part of a relaxation process. This universal structure, as opposed to the Schenkerian Ursatz, does not enforce a predetermined melodic line on the structure. It shows that in all tonal compositions there is a process that builds tension through prolongation (of the tonic, by a deep structural half cadence), and at a certain point the tendency is changed to a relaxation process (deep structural dominant to tonic progression). As mentioned above, the innate knowledge of this of this basic form+ normative structure is according to GTTM the reason for the human capability to understand tonal music ^[14].

3. Boundary object: Classical improvisation

Classical improvisation, as I refer to in this paper, is the practice of improvising on classical structures such as the period phrase, the sonata form etc. In Informed phrasing, classical improvisation serves both as a boundary object, enabling the integration of Schenker analysis with music cognition, and as a tool to transform these theoretical ideas into performative methods. The function of classical improvisation as a vehicle for integrating boundary objects into the Informed phrasing artistic research process will be discussed in the next section.

Improvisation in Schenkerian analysis

In his writings, Schenker refers to improvisation mostly in relation to compositional principles. His approach to improvisation evolved alongside the evolution of his theory of structural levels. In his early years, he regarded improvisation as the organic stream of creativity, liberated from any formal constraint. Later, he relates improvisation to composition as he asserts that both practices require the elaboration of harmonic plans, hence contradicting the notion of entire liberty from any formal frameworks ^[15]. Schenker’s notion of improvisation relies on two principles: first, the act of improvisation involves the prolongation of a deep structure that is linked directly to the middle ground and the background structural levels, second, the prolongation that forms the improvisation occurs through diminutions of the fundamental line ^[16]. In relation to composition, Schenker also links improvisation with his notion of Auskomponierung in which the transformation of the background structural level to the middle ground and foreground occurs by and through improvisation. To simplify this, the musical surface of a given composition is composed out of multiple harmonic and contrapuntal plans of different structural depth, in an improvisatory fashion. According to Schenker, the strict inner plan of composition, together with the improvisatory manner of Auskomponierung achieves what he refers as ‘synthesis’: “The conscious awareness with which our geniuses mastered tonal material in this [improvisatory] manner enabled them to create comprehensive syntheses. Their works are not merely pieced together, but are sketched out instantaneously like the free fantasy and are developed from a mysterious fundamental source”^[17] .

Improvisation in music cognition

Lerdahl and Jackendoff perceive improvisation in quite similar way to Schenker, thereby validating Schenker’s first principle of improvisation. They explain (in Lerdahl and Jackendoff 1983, p.106) that the listener’s ability to relate two variations to each other is due to the unconscious recognition of a common fundamental structure. Later they assert that the practice of improvisation relies on that principle of ‘variation’ of a fundamental structure: "In any musical tradition that involves improvisation on a given subject, the performer must actively employ knowledge of principle of ornamentation and variation to produce coherent improvisation. In all these cases, the listener and performer have an intuitive understanding of the relative structural importance of pitches "^[18].

Informed phrasing

In this section, I will discuss how the boundary objects are integrated in the artistic research process of Informed phrasing. I then show two examples of how the boundary objects generate new performative knowledge in Informed phrasing. Recall that the chief purpose of Informed phrasing is to transform analytical knowledge to performative methods, to make this knowledge accessible for the use of musical performers. In principle, the methods would be most comprehensively accessible for pianists, yet not only for these. Experience shows that conclusions derived from ‘pianistic experimentation’ may apply to other instruments as well. Furthermore, since the analytical methods used in this study explicitly pertain to tonal language, the outcomes of the research will serve primarily the performance of tonal music, yet not exclusively, as you can witness in the next section.

Reductions: grouping – positions preferred relationship

According to the generative theory of tonal music, a first reduction of a musical surface occurs through the division of a stream of sounds into groups, thereby creating a multi-leveled hierarchical grouping structure. In piano performance, the most basic notion of reduction is hand position. When we perform a piece of music, we do not execute each and every note by itself. A piece that contains 40 notes will not be performed by 40 executive actions. The efficiency of piano performance at a very basic level groups notes into hand positions, thereby reducing the number of actions needed for the performance of the series of notes. Therefore, several different notes that were grouped together by the hand grip will be executed through one physical gesture, one action. Now, we can utilize the two different kinds of groupings given by the two theoretical frameworks described above, both employing reductions. What would happen if we apply both kinds of reduction in works of music? Figure 3 shows one level of the grouping structure (according to Lerdahl and Jackendoff’s rules of grouping structure) of a passage from Chopin’s etude op.25 no.11 in A minor:

In this particular example, the ‘position structure’; the reduction of the note succession into a series of hand positions, coincides entirely with the grouping structure. This means that whenever we move from one position to another, a change from one cognitive group to the next also occurs. In other words, the transitions between the cognitive groups and the hand positions coincide. As I was practicing the etude, my hypothesis was that this might be the source of the utter difficulty of performing this passage, and that if I could manage to manipulate my perception of the passage in a way that each cognitive group would contain a transition of hand position, I might be able to perform the passage more easily. Therefore, I experimented to see whether my perception of the grouping structure might be manipulated in a way that this manipulated perception would create a grouping structure whose transitions do not coincide with those between hand positions. I would add that in many cases, and especially in arpeggio-like passages, the transitions in hand positions are the source of the difficulty of performance. The manipulation of my perception of the grouping structure included creating Gestalt segregations in spots where I wanted to insert the ‘preferred transition’, and therefore changing slurs, inserting accents, taking time (all means that relate directly to Gestalt principles of cohesion and segregation). The result was a relationship between grouping structure and hand positions as presented in figure 4 (green brackets for cognitive groups and red slurs for hand positions).

The resulting relationship confirmed my hypothesis, and the performance of the passage (and in fact all the proceeding arpeggio-like passages) became enormously easier and smoother. This led me to formulate the ‘preferred grouping-position relationship’:

In this diagram, the green brackets represent a chosen level of cognitive grouping structure, and the red slurs represent the structure of hand positions. Each transition between hand positions occurs within a cognitive group. As mentioned above, the experimental process and most of the implications of the informed phrasing will regard the performance of tonal music on piano. Yet, since Lerdahl and Jackendoff’s grouping structure is not limited to tonal compositions ^[19], as well as the use of hand positions in piano playing, there is no reason for the preferred grouping- position relationship to be constrained to tonal compositions. The preferred grouping position relationship may also apply to other instruments that hand positions form a part of their technique.

Universal structures + classical improvisation

In section 3 I noted the close relationship between universal structures and improvisation (according to Schenker, and Lerdahl and Jackendoff). In Informed phrasing, improvisation on deep-structural, multi-layered analysis becomes a part of the performative process. The performer practices the middle ground of a composition; phrases it (with regard to Gestalt principles of cohesion and segregation), then gradually ‘improvises out’; imitating the compositional process of Auskomponierung, and turns it to a performative process. This improvisation leads to the next structural level; the foreground level. The same procedure occurs once more, to lead to the surface of the composition, resulting in a performance of the written piece, without any added improvised notes, yet with an ‘improvisatory state of mind’. The improvisatory state of mind is a performance practice studied mainly by Prof. David Dolan at Guildhall school of Music and Drama (who also co-advises Informed phrasing). This improvisatory state of mind is characterized by the spontaneous and risk-taking performance of written western music, as opposed to the ‘prescribed performance’ where the performer prepares his/her performance and recreates it, or worse, ‘recycles’ it on stage. The hypothesis is that the above-mentioned improvisatory process results in multiple phrasing and performance possibilities, all deriving from the inner plan and therefore preserving the Schenkerian synthesis, from which the performer can spontaneously and organically choose as she/he performs the composition. The more common approach in the ‘Schenkerian informed performance’ field is that there is only one performance that is derived from a Schenkerian analysis that there is only one way to perform an analyzed piece, the way that the analysis points towards; structurally important notes are highlighted, concealed repetitions guiding decisions regarding dynamics, articulation and timbre, etc. In informed phrasing, the hypothesis is that the improvisatory process will result in multiple performance possibilities, all of which reflect the deep hierarchical structure (for the sake of tonal motion and structural hierarchy of phrases). In this respect, the hypothesis of informed phrasing differs from the conventional approach of deep structural analysis and offers much more exciting and diverse performance possibilities, out of which, the performer may spontaneously select as she/he performs.

In this paper, I presented the potential importance of deep structural analysis for performers. As mentioned above, this importance was noted by many before myself, yet methods of deep structural analysis and music cognition are excluded from the performative process. I would suggest that the main reason for that is that these methods are time consuming. Efficiency is an aspect of great importance in the practice of classical piano performance. Pianists that perform musical compositions of utter technical and musical difficulty try to do it in the most energetically economic way, somewhat ‘effortless’. Since otherwise, playing a Rachmaninov piano concerto would not be possible at all. It is understandable why deep structural analysis is not viewed by performers as a method that contributes to the efficiency of the performative process. Therefore, one of the most significant challenges and aims of Informed phrasing is to make analytical methods accessible for performers in terms of efficiency. The deep structural inquiry can be done in front of the piano and while practicing, with annotations instead of Schenkerian graphs. The revelation of deep structural levels, as well as grouping structures and prolongational analyses, can occur while practicing the musical surface. Informed phrasing would then set the steps towards performative-analytical efficiency and will therefore transform deep structural analyses to performative methods.

Bibliography

Chomsky. N. Aspects of the theory of syntax. The M.I.T press: 1965.

Dolan. D., Jensen H. J., Mediano P. A. M., Molina-Solana M., Rajpal H., Rosas, F. Sloboda J. A. “The Improvisational State of Mind: A Multidisciplinary Study of an Improvisatory Approach to Classical Music Repertoire Performance”. Frontiers in Psychology Vol. 9. 2018

Lerdahl. F., Jackendoff. R. A generative theory of tonal music. MIT Press: 1985.

Rink. J. “Schenker and improvisation”. Journal of music theory vol.37 no.1. Duke University

Rothstein. W. Phrase rhythm in tonal music. Schirmer book: 1989