containing the theoretical text with relevant excerpts from the scores and sound recordings
In Three Songs... the modal centre is implied within the linear development of the voices. In Figure 21 the modal centre for each of the two lines is given below it.
Figure 21: The excerpt from Figure 19 with the modal centre for each line designated on a stave below it, and the general modal centre designated on the bottom stave. The morphomodal network given on the 5th stave.
I must emphasize that this is how I have been thinking of the modal centres while composing the work and how I perceive them when listening to it. However, in some cases (as given in brackets) the linearly conveyed modal centre is an ambiguous percept, which might also vary for different listeners generally. In this respect I would refer again to Kühl’s ‘fluidity of musical meaning’ 118 (click) and his semantic model119(click) in which certain salient cues120 (click)/elements from the music, as perceived, are extracted to evoke cognitive responses in the process of semiosis, whilst other elements are made redundant. The number and proportion of selected and redundant elements will vary and will cause the perception to ‘fluctuate from person to person, from situation to situation and from time to time’.121(click) In the current context that could be seen as congruent with Thomson’s root analysis through ‘vectoral framing’, where a certain number of ‘vectoral cues’ pointing towards a common root are extracted from the whole of the musical texture. From these, a convincing solution for the perceptual root or tonic is given in an ambiguous context where other methods for chord-to-root extraction do not account convincingly for the perceived overall root or tonic.122 (click) Albeit Thomson’s method is developed within a tonal context, it could be applied with some adaptation here, as in his research it is seen as particularly relevant namely in ambiguous contexts where ‘the harmonic template horizontalizes’ 123 (click) and there is no clear chord structure/progression.
Although a step-by-step adaptation of Thomson’s analytical method for the purposes of analysing modal centre in morphing modality is possible, it would be a lengthy process for which I have no space here. Therefore I give in Figure 21 a complete solution for the modal centre as perceived in my view, as that gives my personal perspective as relevant to the compositional process which created that music.
As regarding the morphomodal network, the first three bars in Figure 21 are developed upon a modal network of three pitches around the centre a (see network on the 5th stave in fig. 21). In this point in the example I see no reason to speculate defining what larger modal network it might be part of, because there are a great number of networks which it could fit in. Instead, I consider it a mode of 2 or 3 or 4 pitches, respectively. In addition, by leaving the matter open, one provides more space for choice as the harmony develops further, increasing flexibility. That can be seen as a general strategy that I have continued to apply beyond this song cycle. From the fourth bar in Figure 21 the span of the network widens and alterations/morphs in its structure are introduced.
Comparing the modal centres for each line in Figure 21, and the way their centres shift, it is evident that often the two separate lines suggest different modal centres simultaneously. At the bottom stave I provide what I consider to be the general modal centre for the total of the texture which centre is thus the centre of the modal network (given on the 5th stave). Comparison with the centres for the individual lines shows that when there is only one line sounding, or where both lines point towards a common centre, that is the perceived centre for the morphopolyphonic texture and respectively the morphomodal network in total. Where there is a shift of centre in one line and no change in the other, the changing centre overrides in the perception of the overall modal centre in this example.
Could this multiplicity of modal centres be considered a form of polymodality? In established approaches to polymodality, (such as Bartok’s ‘polymodal chromaticism’124 (click) or Messiaen’s ‘polymodal modulation’125 (click)) polymodality occurs from the use of several interconnected modes, used either in vertical simultaneity,126(click) or in rapid alternation.127 (click) In contrast, in the present approach the multiple modal centres occur across the same modal network (presented on the fifth stave in Figure 21). Therefore I do not think this is an example of polymodality. Furthermore, I doubt that two modal centres can be perceived simultaneously. In my approach, as I see it, the single modal centre shifts dynamically across the morphomodal network and is sometimes ambiguous. That ambiguity is logical and welcome in the general context of morphing modality. It provides for flexibility and can be controlled or influenced to a significant extent. This stability/ambiguity variable is a key point of influence over harmony in my compositional strategy. Another important variable: staticity/fluidity, which is relevant to both the morphomodal network and the modal centre, is another key factor in my general harmonic strategy.
In contrast, a more obvious and stable approach to the establishment of modal centre is applied in The Mirror. In that opera the modal centre is often focused in a fundamental bass note. That is inspired by the Ison technique in Eastern Chant.
The Ison is a drone which is applied to the chant by sustaining the fundamental pitch in its modal network, as designated by the modal neumes. In most cases Ison is not explicitly notated and is applied following certain rules. However, some explicit designations in a medieval musical manuscript from the early fourteenth century suggest an elaborate and extensive use of Ison in that period, as reported by Elena Toncheva128 (click) (suggesting further that it was in use much earlier in order to have reached this elaborated practice that is designated in the manuscript). Furthermore, she posits that the Ison has a deep spiritual significance in Eastern chant, connected symbolically with the doctrine of the Holy Trinity.129 (click)
In my view, the Ison does not add a different polyphonic or harmonic perspective to the chant. It only supports what is already present in its horizontal harmony designated by the modal neumes, hence it was not explicitly notated up until quite recently, and is often not notated even today, being also not mandatory, but discretionary applied in performance. Instead of a harmonic or polyphonic meaning, it has a particular acoustic130 (click) and psychoacoustic131 (click) significance, which I will discuss further in Chapter 6.1.
In The Mirror, in many instances the modal centre is established by the fundamental bass tone which performs the function of an Ison. It determines acoustically the fundamental pitch in the morphomodal network. In the context of the dense morphing textures it sometimes creates a context in which they could be heard as pitch complexes related as harmonics to a common fundamental pitch. That, together with the spectral similarity of the core modal pitch collections that I use (Chapter 2.1), has important implications for a particular kind of perceptual/spectral integration/fusion in some passages, for example bb.306-315 in The Mirror (Example 18). However, such an Ison does not account necessarily for harmonic stasis, as active changes in the morphomodal network can create intense shifts in harmony over a static drone. In some instances in The Mirror such shifts are so intense, or are combined with such kinds of textures, that the perceived harmony is highly dissonant and quasi-atonal, for example bb.797-819 (Example 12 (starts in b.720), while there are also intermediate stages between ‘modal’ and ‘atonal’ percept, like in bb.857-889 (Example 12 (starts in b.720).
In all these passages, the acoustic and psychological importance of the Ison is still present, and therefore in the opera the endless bass line is not just a harmony-shaping device. It has a symbolic significance, as connected to some ideas from the aforementioned research by Toncheva, as well as the idea that the mirror,132 (click) which itself is central to the beginning and the end of the opera, is perhaps there all the time, although unnoticed. That suggests its further semantic significance for The Mirror as a whole, as connected with the idea that the Ison creates a kind of ‘consecrated space’, which idea has also an acoustic and psychoacoustic dimension (Chapter 6.1). Thus the extreme use of this device in the opera, which is unmatched in any other work in this thesis, has its manifold significances and significations.
I have underlined above two methods for generation of modal centre in my technique: implied centre – internal to the lines and implied through linear vectors, as exemplified in Figure 21; and placed centre – created through a separate element of the texture (Ison/drone), as described in regard to The Mirror in the present chapter, which method is also at work in Three Songs..., in bars 17-20, 52-54 (Example 19), 71, 75 (Example 20) for example.
From this song cycle onwards, the two methods work in alternation and combination in my technique. It should be noted that the placed centre is not exclusive to the bass register or bottom line in the texture. It could shift intensely and transform into a melodic line, or extend from a line, as in in Three Songs... bb.70-78, 90-93 (Example 20). In the example from The Sacred Flight, discussed in Chapter 2 (Fig. 5), after an extended passage developed with an implied centre (from bar 129 onwards)(Example 22), an Ison in the bass is introduced in b.141 while the texture of the same kind continues to develop over it. Then in bar 145 that Ison is transformed into a melodic line that doubles the established main line in the solo strings, thus the modal centre becomes implied again (Example 22). In that passage, in the sections where the implied centre shifts dynamically (which is the more typical condition for the implied centre technique), the morphomodal network is more static in terms of its intervallic structure. In contrast, when the placed centre (Ison drone) is introduced, the intervallic structure of the morphomodal network fluctuates much more intensely. Thus, an overall balance to harmony across this passage is ascertained by the means of interplay between the modal centre and the intervallic structure of the morphomodal network in terms of their staticity/fluidity variance. This kind of interplay I consider all the time when working with this technique.