Martin G. Georgiev


Multimedia Web Presentation

based on

Tradition and Innovation in my Music

PhD Thesis

Royal Academy of Music

University of London


containing the theoretical text with relevant excerpts from the scores and sound recordings



6.Percussion Concerto No.3 Genesis

Rhythm: regular or irregular? hyper-structuring, metaphors

The 3rd Percussion Concerto, for Marimba and Symphony Orchestra, was commissioned by the Municipality of the City of Varna, Bulgaria, for percussionist Tatiana Koleva and was premiered by her and the Varna State Opera Symphony Orchestra, conducted by myself, in October 2011 at the Opera House in my native city of Varna.

The titles of the three movements are biblical verses, the first two from Genesis, and the third from the Gospel of St John. That opens up the question of titles and their relevance. Whether this approach can be labelled ‘programme music’ or not, I do not know for certain. But in my view these titles are far too abstract and metaphorical to shape a ‘programme’ and they refer to a host of meanings and significations, of which I would not select one, but treat them in their totality. It would be a simplification to say that the first movement is about water, the second about light and so on. Even ‘light’ and ‘water’ open a vast amount of metaphorical significations. Thus my approach to such titles is polysemantic, and the same is valid for The Sacred Flight and A Seasong, even for The Mirror, despite the fact that it is an opera. In the case of the Third Concerto, its general title and movement titles evoke particular atmospheres and moods in my mind, and I have built the musical development upon these evoked responses.

There is a particular aspect of the metric/rhythmic organisation that is relevant for all works in this thesis, but which is particularly evident in the first movement of this concerto.

In the following example I outline the metric structure of the first 14 bars:


Figure 25: Percussion Concerto No.3 Genesis, bars 1-14: metric structure.


Although similar structuring could be seen throughout my music, in this excerpt it is particularly in the ‘foreground’, as the Marimba phrases are built around the barlines in such a way as to make this structuring audible, which is also relevant for the orchestral percussion punctuations and the changes in the orchestral texture.

This approach is inspired by a particular kind of rhythmic/metric structuring, typical for Balkan folk music, as well as for Eastern Orthodox Christian Chant. To describe that I give below the metric structure of the Bulgarian folk dance Krivo Sadovsko Horo:


Figure 26: Bulgarian dance Krivo Sadovsko Horo, metric structure.


This kind of irregular rhythm has been so overused over the last two centuries by Bulgarian and other Balkan composers, that I deliberately wrote my first Symphonic work141 (click)  mainly in 4/4. After that early piece was performed by the National Orchestra of Belgium at the Tactus Young Composers’ Forum in Brussels in 2004, I was surprised to be advised by some composers there to look at the rhythms of Bartok and Stravinsky for some inspiration. In fact, these kinds of folk rhythms could be seen only in a very few bars in my String Quartet – bb. 25-40. (Example 17) They are essential for Apocalyptic Passacaglia on a Theme by John Cage, in a different way which will be discussed in the next chapter. It has been discussed in Chapter 3 that Ligeti and Birtwistle’s approaches to rhythm have influenced my approach profoundly. However, irregular rhythms also do permeate my music throughout, although in a different form.

The kind of meter exemplified in Figure 26 is rationalised by Bulgarian folk musicians in the form of ‘long and short beats’. 142 (click) Thus, in that example there are three ‘short’ beats followed by a ‘long’ beat and other two ‘short’ beats. At the same time they are subdivided into sub-beats (chronos protos),143 (click) forming groups of two or three sixteenth notes, thus the ‘short’ beats have binary and the ‘long’ have ternary sub-structures.144 (click)  Such kind of rhythmic groupings emerge also in the context of Eastern Chant, particularly in the more syllabic chants, as in the following example from Troparion for St John of Rila.


Figure 27: Excerpt from Troparion for St John of Rila, Anonymous author.

Metric structure is designated by numbers and lines.


Although there are neither barlines nor time signatures in the notation and musical thinking in Eastern Chant, I have designated by vertical lines the basic units – the separate words, and by dashed lines the internal subdivisions caused by the accents of the poetic text, which are designated by portato signs above the notes in Figure 27. In numeric values above the stave is given the number of metric beats (corresponding to number of syllables) per sub-unit, and below the stave the number of beats per unit (word). An intrinsic connection between Bulgarian folksong and sacred chant approaches can be thus observed, as the both traditions are anyway the two sides of a single coin, in my view.145 (click)  The difference is that the meter appears augmented double in the chant example comparing to the folk dance, and also that in the chant the rhythmic structuring is much less exposed and more subtle.

In my Marimba Concerto the same kind of structuring is applied, being more similar to the chant approach. It is notated in bars of 2/4 and 3/4, thus the binary-ternary structure is immediately visible in the score (Example 27). What is less apparent is the metric hyper-structure, which I illustrate in Figure 28:


Figure 28: Percussion Concerto No.3 Genesis, bars 1-14: metric structure and hyperstructure.


This is the kind of hyper-structuring that I apply to the overall meter. The irregular 8/4 and 11/4 meters in Figure 28 are augmented versions of the irregular 8/8 and 11/8 in Bulgarian folk music. Although it might be doubted whether such hyper-structure can be heard generally, I would argue that in this case it will, because with the beginning of each hyper-structural unit there is a change in the orchestral background which is clear and noticeable (Example 27). Thus the rhythmic structure in this example is a hyper-augmented irregular rhythm (shifting to regularity in the last unit), with a sublevel of regular crotchet beats, and another sub-sub-level of regularity in the Marimba sextuplets.

However, in most cases the hyper-structuring is not that obvious. It is the change of binary and ternary metric elements that is more clearly audible, which creates the perception of regularity or irregularity. Thus the first 6 bars in Figure 28 create an overall perception of irregularity, which is somewhat ambiguous because of the succession of two 3/4 bars in the middle. Then from bar 6 a 3/4 regularity is created, which establishes a certain expectation, to which the 2/4 bar in b.10 comes as a surprise. After that, regularity is established altogether, to be broken again in b.16 (beyond Figure 28)(Example 27). Thus a continuous shifting between regularity and irregularity is present throughout the metric organisation in the passage. In essence this kind of metric macro-structuring is identical to the morphing rhythm discussed and exemplified in Chapter 3.1, Figures 13, 14, in relation to the general rhythmic processes in my textures. It has a general importance for my music altogether in terms of its overall metric structuring.

Although it looks quite simple in such a schematic representation and in its (deliberately) obvious application from the beginning of the Marimba Concerto, the matter becomes more intriguing when it interplays with texture and surface rhythms, and furthermore with text, as in The Mirror and Three Songs... . In these two works there are two basic approaches in the interrelation of metric structuring with the poetic text: the first is where the accentuated syllables coincide with the main points of the metric structure, and second where the two elements clash. The two approaches are often alternated from bar to bar or from section to section.

I have described hyper-structural irregularity upon sub-structural regularity in relation to the Marimba concerto, while the reverse could be seen in the String Quartet, bars 1-35 (Example 28). The continuous quintuplets are establishing an irregular sub-level, upon which the main level of crotchet regularity is based. In bars 35-36 the sub-level becomes a main level through a metric modulation in which the quintuplet quavers become regular quavers, and then upon this level, changes of irregular rhythm of Balkan folk type are briefly explored in bb.36-40. From b.41 regularity on the same level is established (Example 28).

Similar interplay of levels of chronos protos and regularity/irregularity can be seen in the last of the 7 Pieces... for Piano (Example 26). That interplay has also a particular application in Apocalyptic Passacaglia... which I will discuss in the next chapter.


6.1.Fifth-repeating modes, fourth-repeating modes (tetraphonia, triphonia)

in the Third Percussion Concerto and A Seasong

(click to continue)