Conclusion

In the preceding seven chapters I have outlined a multitude of traditions that make up the fabric of my technique and style. Various elements of these numerous traditions and practices lay the foundations of my compositional method discussed throughout this text, Morphing Modality, which is a synthesis of approaches, techniques, mindsets and concepts.

In the core of this technique is the concept of horizontal (linear) harmony and monodic modal modulation from the theory and practice of Eastern-Orthodox Christian Chant (Eastern Chant) (Chapter 1), which concept I have integrated in my compositional technique within a broadened and refined concept of ‘modality’ (Chapter 2). Its technical basis could be seen as a particular relationship between two main factors: the background intervallic network and the foreground texture.

The background modal/scalar network/grid, which is dynamically shifting/morphing in time, is built from interlocked intervallic spaces, confined between scale degrees, and the relationships between the sizes of these intervallic spaces is seminal for the resultant sense and colour of harmony. The size of the intervallic spaces in the network could vary from a small microtonal second to an augmented second (acoustically equivalent to a minor third). I consider the network to be ‘modal’ if not more than two intervals of a minor or small second appear consecutively in its structure, and if there are no consecutive augmented seconds (Chapters: 2.1, 5, 6.1). The network can have a cyclic structure, and if so, the type that is most often employed is that with an octave-repeating cycle. However the structure of the cycle of the mode could be also fifth-repeating or fourth-repeating, both present in Eastern Chant and in my music (Chapter 6.1). While other kinds of cyclic structure are also possible, the cyclic nature of the scale is not mandatory, nor is it necessary for the network to span endlessly, covering the full theoretically-possible scope of the acoustic pitch space. A modal network could consist of just two or three adjacent intervallic spaces, and still be a complete, structured and musically meaningful ‘mode’ (Chapter 4).  I accept and support the assertion that ‘mode’ within the contemporary context of my music is a scalar network with a determined modal centre (Chapters: 2.1, 4). The complex concept/percept of modal centre involves not only the background morphing modal network but also its interaction with the foreground texture. I have outlined two methods for creating a modal centre: implied and placed (Chapter 4.2).

The modal network is not static, but shifts continuously in time through fluctuations and alterations in its intervallic structure (Chapters: 1, 2) and through shifts in the position of the modal centre (Chapter 4). These changes are seminal for the conveyed sense and colour of harmony, which can be manipulated by the composer through controlling the process of change of this background intervallic network and the position of the modal centre (Chapters 2, 3, 4). An important principle in the process of alteration and fluctuation of the network involves the presence of pivotal pitches that remain constant within the process of change, while movable pitches shift their position and thus alter the structure of the network (Chapters: 1, 5).^{163 (click)}  In that respect an important correlation between the technical and technological principles in the process of modal change in morphing modality and the technique of morphing images from the visual arts was described in Chapter 1.3. On the basis of this correlation, a specific transference of principles between these two techniques was made possible, and due to these and various other similarities between the two processes (outlined in Chapters 1 and 2) the concept and method of morphing modal network (morphomodal network) emerged. For the overall process of morphing modal modulation the modal centre is also responsible, as it was made evident that its shifting position across the morphing modal network could create modulations without the aid of any changes in the intervallic structure of the network (Chapters: 2, 4). For the process of morphing modal modulation the particular interaction of the network with the foreground texture is also seminal (Chapters: 1, 2).

The foreground texture could be monophonic, homophonic, heterophonic, polyphonic, or an intermediary state of texture resulting from a ‘morph’ between these main types (Chapter 3.2).

The prototype for texture in this approach is the monophonic texture of Eastern Chant (Chapter 1.1). The two constituent components of this monophonic texture are contour and rhythm (Scheme 1). The interaction between these two components produces the complete monophonic texture of the chant. This logic is manifested in the Byzantine neumatic notation which uses separate types of neumes – for contour and rhythm, which interact, thus conveying the complete texture of the chant, while its modal structure/intervallic content, is designated by a third type of neumes (Scheme 1, Chapter 1).

The interaction between the background intervallic modal network and the foreground texture (constituent of contour and rhythm in their interaction), creates the complete sounding fabric of the monophonic chant with its unique capability to convey a particular kind of perceived harmonic structure through a single line (Scheme 1). This harmonic structure I conceptualise as horizontal harmony (Chapters 1, 2). The roots for such a concept were traced back to Classical Antiquity (Chapter 1.2). Furthermore, there is some specific evidence from music psychology that such a structural division of the monophonic (melodic) texture into a set of interacting functional components, namely: intervallic/scale structure, contour and rhythm, is inherent in the mechanisms of our auditory musical processing and memory. ^{164 (click)}

The essence of the functionality of horizontal harmony and monophonic morphing modal modulation lies in the fact that the line moves through a limited intervallic set, which creates a stable representation in the mind and memory of the listener/performer/composer. The majority of the traditional scalar/modal structures employed by the cultures of the world (including Eastern Chant and Western Classical music) would facilitate the stability of such representation due to various perceptual/cognitive factors, some of which were mentioned in Chapters 2.1, 6.1. (Some of them are biological, innate, and others are cultural.) This fact has determined my preference towards this kind of scales/modes, not only due to their perceptual processing advantages, but more importantly due to the importance these acquire for the process of horizontal harmony and monophonic morphing modal modulation. When the monody moves through the limited and structured intervallic set of the modal network, a stable representation is created in the memory which conveys a sense of coherence, due to the aforementioned perceptual factors. This coherence is then challenged when a change in the modal network is introduced because the monody introduces pitches which do not conform to the already established in the mind stable modal representation, albeit some of the previously introduced pitches continue to re-emerge. This creates a sense of disruption – the coherence is perturbed. However, as the movement of the line continues through the altered intervallic network, it gradually conveys another limited and structured intervallic set, which is also stable and coherent, due to the aforementioned perceptual factors that determine perceptual coherence of such particular intervallic structures, described above as modal (Chapters: 2.1, 6.1). Furthermore, the two instances of the modal network are similar, although not identical, the second being an altered instance of the first, due to the presence of the constant pivotal pitches in the network, and the particular logic in the repositioning of the movable pitches in the process of morphing of the modal network, described above (Chapters 1, 2, 6). Thus the overall perception is that of a gradual transformation of the colour and sense of the morphing horizontal modal harmony (Chapters 1.2, 1.3, 2.1).^{165 (click)}  The perceptually smoothest change in the modal network would ensue if the greatest number of components between the two different instances of the network would remain unchanged. That happens when only one scale degree alters position while all the others remain constant, which as a result alters the size of only two intervallic spaces, which are the ones adjacent to the scale degree which moves (e.g. the first two changes in Fig. 7). This is also the basis for the modal scale degree fluctuation (Chapter 1.2). The most radical change is when the greatest number of intervallic spaces is altered, which is the case when there is only one pivotal pitch and the remaining structure is altered (e.g. the last change in Fig. 17).

Because this kind of harmony and harmonic change is conveyed through linear means, it takes a certain amount of time for the change to be registered and perceived as such by the mind. This change is much more gradual than the instant harmonic change that is perceived when a chord is followed by another chord (Chapter 4.3). That underlines another close resemblance between this kind of monophonic modal modulation and the image metamorphosis or image morphing technique in the visual domain, whereby the concept of morphing modal modulation developed (Chapter 1.3).

The application of this concept of horizontal harmony and monophonic morphing modal modulation in the context of a multi-voiced texture is discussed and exemplified in Chapter 2. In that instance of linear, non-contrapuntal polyphony, the rhythmic interaction of the voices and the interaction of their contours make the resultant verticals between them irrelevant both compositionally and perceptually. That is because it is practically impossible to both rationalise/construct them and also to hear them as a succession of intervals and chords. Rather, it is the linear aspect that is evidently most salient. This texture, identified as polyphonic (morphopolyphonic) (Chapter 3.1), has been composed as a set of independent lines, and their contours and rhythms were constructed to emphasize to a maximum the linear aspect of their interaction. However, unlike the atonal linear polyphony from the twentieth century, it conveys the sense of modal harmony, which is constantly shifting, morphing, because the background morphing modal network and its interaction with the foreground monophonic texture of each line functions precisely as described above in relation to Eastern Chant with its monodic horizontal harmony and monophonic modal modulation (Scheme 1, Chapter 1). Furthermore, because all the lines follow simultaneously the same background modal network and its shifting/morphing processes, their interaction with this network and with each other conveys a common sense of harmony, conveyed linearly, rather than vertically/contrapuntally, and associated with the sense of horizontal morphing modal harmony, as described in Chapters 1 and 2. The fact that these independent linear components make a common harmonic sense as a whole is also due to perceptual factors underpinning the overall intervallic structure of the modal network (Chapters 2.1, 6.1) and the logic of its morphing processes, as described above. This intervallic structure provides perceptual coherence and in some instances even partial spectral fusion, due to the particular kind of similarity of its pitch structure to a harmonic spectrum (Chapter 2.1), as well as the inherent cultural schemata for the auditory recognition of such scalar/modal structures as coherent (Chapters 2.1, 6.1).

Although simple in its basics, the complex interaction between contours, rhythms, timbres and registers within the morphing texture on one side, and the interaction between that texture and the background morphing modal network (Scheme 1, substitute ‘monophonic’ with ‘polyphonic’) requires an intensive process of decision making involving many intuitive choices. This intuitive process is set, however, against the robust theoretical/practical system of morphing modality and its working methods, outlined throughout this text. (The briefest summary of these working methods is in Chapter 4.3 and the present Conclsion). This system is always in the back of my mind in the process of composing. The simplicity of its organisational principles makes this technique very clear and economic operationally, flexible artistically, and provides a wide scope for intuitive choice making. Particularly important for me personally is that it provides for a significant liberation of the various textural components from vertical, intervallic and chordal considerations and coordination, while retaining a fine control and influence over the sense and colour of harmony (Chapter 4.3).

The same system of principles is applied to a great number of differing textures and is valid for all works included in this thesis, except for Apocalyptic Passacaglia... (for Snare Drum solo and Videoscape) in which no definite pitch is employed.

An important issue stemming from this approach is the concept of textural consonance and dissonance (Chapter 2.1). As the morphomodal harmony is not conveyed through vertical intervals and chords, the perceived balance of ‘consonance’ and ‘dissonance’ of the sonority in the complete fabric of music (Scheme 1) does not depend on theoretically-consonant or theoretically-dissonant intervals or chords, on their relationships, resolutions etc. It does not even depend necessarily on perceptual consonance and dissonance for any particular vertical combinations of sounds, unless these are situated at perceptually salient points in the texture, or sustained over a long enough temporal span (Chapters 2.2, 4.3), but it became clear that this is more often not the case in these compositions, except for the particular modal clusters that are deliberately employed as verticals (Chapter 2.2) or the kind of dyads that are particular to the song cycle (Chapter 4.3). Ultimately, in the majority of musical situations in these works the perception of the overall balance of ‘consonance’ and ‘dissonance’ of the sonority is a result of the interaction of all attributes relevant to texture, including textural density, articulation, tempo and timbral combinations. Thus the issue of ‘consonance’ and ‘dissonance’ and their balance becomes a complex feature of the texture in its totality, and thus the concept of textural consonance and dissonance is introduced in Chapter 2.1, and exemplified with excerpts from the score of The Mirror. As outlined in that chapter, the balance between textural consonance and dissonance is a key factor that I consider in the process of composition. Although in terms of how it is perceived, the precise balance of these factors would differ interpersonally in line with the variability in perception discussed in the introduction and Chapter 3. Most important is that within the framework of morphing modality the full pallet between very dissonant – quasi-atonal, and very consonant – clearly modal (or even quasi-tonal) sonorities could be composed within the same technique and harmonic system (Chapter 4.3). It provides the capability for either smooth transitions or juxtapositions which are integrated within the same background harmonic framework, enhancing integrity within the contrasts, as opposed to the eclectic intermix of contrasting harmonic devices, techniques and systems which I had used in the past.

The modal clusters which are deliberately used as verticals are naturally coherent elements in this technique, because they are simply verticalisations of the same background morphing modal network that governs the pitch content of all textures in these works. The perceptual significance of these verticals – modal clusters, lies with their spectral similarity, which is determined by the spectral similarity of the modal network that they verticalise (Chapter 2.1). Indeed, the modal cluster trichords (Chapter 2.2) could be seen as microscopic chunks from a harmonic or close-to-harmonic spectrum.

Another important aspect of flexibility involves the intervallic structure of the scalar network where deep integration between semitonal and microtonal elements was pursued (Chapter 5). Indeed, within the fundamental theoretical framework that I outline in this text, a semitonal and equally tempered scalar structure need not have any prominence a priori. In fact it does not have any such prominence for a great number of world cultures, Eastern Chant including, and even in the Western tradition it has a limited historical span. However, its importance, both theoretically and practically, for the contemporary Western tradition, within which my music is performed, cannot be underestimated. That made it necessary to look at the issue of integration of semitonal (and equally tempered), and microtonal elements. Amongst the reasons that such an integration is seamless within the framework of morphing modality (Chapter 5), is because this compositional method works within a very broad (but structured) theoretical and practical framework of ‘modality’ (Chapter 2), which encompasses the broadest possible range of ‘modes’ including these which are neither tempered nor entirely semitonal, but microtonal to varying degrees (Chapters: 2, 5). Thus in its understanding of ‘mode’, this technique integrates the semitonal and microtonal domains within a single, broader domain within which these two sub-domains fit, and operates that broader domain through the modal organisational principles of morphing modality, outlined above. Therefore within this technique these principles are equally pertinent to both sub-domains – the semitonal and the microtonal. That is why in the String Quartet both semitonal and microtonal elements co-exist naturally, because the principles of morphing modality provide the capability for integration between such microtonal and semitonal elements, and for smooth transition between passages that are entirely semitonal and ones that employ microtonal elements extensively (Chapter 5).

Although my practice is informed in depth by the highly detailed use of microtonal features in Eastern Chant, as it is by the semitonal Western tradition, the process of morphing facilitates not only smooth transitions and integration between the various elements, but also the creation of new elements which do not exist traditionally. This is also valid within the narrower semitonal, equally-tempered domain, where in the process of morphing between the traditional classes of diatonic, ‘chromatic’ (i.e. with augmented seconds), fifth-repeating, fourth-repeating modes etc., a great variety of ‘modal’ structures emerge, some of which structures do not exist historically (Chapter 2.1). Thus the process and concept of morphing is also an important tool for creating new modal structures and harmonies, which are a natural product of the compositional process, and bear a deep logical connection to each other and to all traditional elements of harmony in these compositions.

It has some relevance to mention here that the morphing images technique has specific scientific applications, more particularly in re-creating continuous processes from a selection of still images, which for instance is used for creating models of certain processes in medical science and space science. In my work I see morphing as a general tool for creating musical processes through gradual transformation and transition between various elements of pitch structure, texture, rhythm etc., in the process of which numerous intermediary elements form. Their continuous sequence, in which also the logic of pivotal/constant and movable/changing elements is retained, creates at the outset an impression of morphing. Due to this logic, the intermediary elements retain intrinsic connections between each other. Furthermore, a connection between seemingly unrelated components and elements could be created through this kind of gradual transformation, where the key is to find common features which could serve as pivotal elements, around which the changing elements would create the transformation. Throughout this thesis the concept of morphing is discussed with relevance to the following aspects of music composition: morphing modality (Chapters 1-6), morphing polyphony (Chapters 2, 3), morphing rhythm (Chapters 3, 6), morphing texture (Chapter 3).

Regarding musical form, morphing is also discussed as relevant, and it is contrasted with the principle of ‘cuts’ or ‘incision’ inspired by Lucio Fontana’s visual artworks, and that of ‘windows’, as discussed in Chapter 7.1.

Other aspects of rhythm were discussed in Chapters 6 and 7, regarding the importance of the two main concepts or rhythmic/metric regularity and irregularity and their interaction, with further implications for micro- macro- and hyper- structuring of meter and rhythm, and a particular connection between that interaction and the concept of morphing rhythm was established in Chapter 6. In Chapter 7 the importance of ‘rhythm-box-rhythm’ to the majority of the submitted compositions was discussed.

To what extent these compositions (and my method in general) are traditional, and to what extent innovative, is a good question, but it is part of a bigger question – what is traditional and what is innovative? Probably I am, after all, an ultra-traditional composer? But if I am to use a vacuum cleaner, helicopters, noises, human bodies, electronics, kitchen rags, magic squares, theory of chaos, fractals, carrots, is that not going to be traditional as well? Is music not a traditional domain by nature?

It is evident that Kukuzel, Bach, Beethoven, Stravinsky, Ligeti were all highly original innovators. It is also evident that they were all very deeply rooted in the traditions that preceded their work. That particular traditionalism did not deprive their music of originality, quite the contrary – it supported their inventive ideas. Without the solid support of tradition they would have never managed to materialise their inspirational innovations. Thus, in my view, tradition is the indispensable source of innovation. The higher a tree grows, the deeper the roots must reach. Otherwise collapse is inevitable. But from everything that was discussed above it seems evident that in my work as an artist and researcher I have been most interested not in what is particularly traditional – ‘old’, or innovative – ‘new’, but in what might be timeless.

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