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musical composition. Doctoral thesis, Canterbury Christ Church University.
proportion in music and how these can be used to generate original compositions.
of English composer Christopher Bochmann.
Denis Gougeon and Lorraine Vaillancourt. and Sir Peter Maxwell Davies for his support and acknowledgment of my work since my study at the Royal Academy of Music. I thank the Portuguese composer Carlos Marecos for his valuable contribution on issues relating to symmetrical harmony. Paulo Matos. I have had the privilege to meet him again and discuss issues of composition. the stage director Paulo Matos. Raquel Alão. to the members of the jury of 10th International Forum for Young Composers – Music & Art Video: John Rea. His comments helped formulate the first ideas for the current thesis. Benoit Gibson. Manuel Pedro Ferreira. Susana Teixeira. to the members of the jury of the competition Opera in Creation 2008: Helena Barbas. to the members of the jury of the International Composer Pyramid: Paul Patterson. Madalena Boléo. Pedro Boléo. A very special thanks to my supervisors Professor Paul Edlin and Professor Paul Patterson who were the first to believe. the Portuguese Symphonic Orchestra. the conductors João Paulo Santos and Christopher Bochmann. to the Activity Director of the Centro Nacional de Cultura in Lisbon: Alexandra Prista. Frans van Rossum. Carlos Marecos. Sandra Medeiros and Sónia Alcobaça. Philippe Boivin and Philippe Hurel. the Århus Sinfonietta and the conductor Søren K. the International Composer Pyramid Ensemble and the conductor Gerry Cornelius. the Gageegoo! Ensemble and the conductor Pierre-André Valade. to the Portuguese journalists who have demonstrated an enormous interest in my music: Manuela Paraíso. particularly regarding the practical aspects analysed in this thesis. encourage and support my research. Andrea Liberovici. Bella Tromba and the percussionists Stephen Burke and Scott Bywater. Alea String Quartet and the harpist Alexander Rider. Professor Roderick Watkins for his precious advice regarding the analytical quality of this thesis. the singers Nataša Šibalic. João Madureira. and finally to the iii . Hansen. the Nouvel Ensemble Moderne and the conductor Lorraine Vaillancourt. My sincerest thanks to all the players and people involved in the performance of my music during my research: the flautist Stina Dawes. a very special thanks to the former artistic director of São Luiz Teatro Municipal in Lisbon: José Jorge Salavisa. the librettist Armando Nascimento Rosa. Joana Baptista and Gabriela Lourenço. Rolf Hind. aesthetics and interpretation relating to my research works. Margarida Marecos. the Portuguese Symphony Youth Orchestra. During my research at Canterbury Christ Church University. Also.Acknowledgments I would like to express my gratitude to Professor Christopher Bochmann. In addition. Christopher Bochmann. Sven Müller and Jorge Salavisa. who not only offered valuable guidance through his teaching but also lent his support in numerous ways.
iv . I am deeply grateful to the composer and friend Paul Evernden who helped me with the revision of this text.support received through staff development and research funding from Canterbury Christ Church University. Finally.
3 Morgan. In European culture.P. A ‘symmetry’ analysis of a musical piece can provide information about the various levels of symmetry which occur in different parameters: counterpoint. preoccupied composers throughout history and. 2 . balance. p. Music Theory Spectrum. whether or not principles of symmetry and proportion have been applied consciously.. a segment of music)3. there is an inherent predisposition in most scores towards balance. it possesses a high level of symmetry and regularity. biology.ac. aesthetics.html> [Accessed 2 February 2011]. 2007. primarily used as an interpretation of commensurability. Laws of musical construction have been developed theoretically over the course of history. 1998. and applied in a wide range of phenomena of both physical objects (planetary systems. visual arts. such as perfectly symmetrical spheres like 1 Hofman-Jablan. geometric figures. of course. 20(1).mi.. laws of physics. 2 Ibid. R. physics.Introduction From the earliest practices to the present day. it is possible to recognise symmetrical structures in the work of various composers.sanu. architecture. proportion and regularity1. chemistry. elementary particles) and abstract systems (mathematical relations. We like to look at symmetrical things in nature. In art and scientific disciplines the theory of symmetry can have an important role in mathematics. Due to the fact that music is a temporal art based on time and meter. Symmetrical Form and Common-Practice Tonality. theory of proportion.rs/vismath/jadrbookhtml/index. in the twentieth century the concern with symmetry and proportion is of particular relevance. Symmetry of Musical Work [e-book] Available at: <http://www. In the majority of musical works it is possible to understand the individual and stylistic marks of their creator.5. etc. The geometrical and mathematical meaning of the term as it is used today in sciences and music theory started being used in the late eighteenth and early nineteenth centuries. Such structural concerns have. the idea behind the concept of symmetry has its roots in Greek philosophy. rhythmical repetitiveness.2. crystallography. symmetrical harmony and symmetrical form. The physicist Richard Feynmam and the mathematician Hermann Weyl noted the following in relation to symmetry: 1) “Symmetry seems to be absolutely fascinating to the human mind. J.
and perfection. Analysis will be provided evincing the common use of these principles in music before the twentieth century as well as in music of twentieth and twenty-first centuries. 1967.84. 4 5 Feynman.planets and the sun.” 5 Due to the fact that music is a temporal art based upon repetition. The inclusion of an analysis of Bochmann’s work Lament is considered to be of special importance as it facilitates the understanding of the application of symmetrical harmony. Princeton: Princeton University Press. 3 . R. The specialist focus of this thesis is placed on the use of principles of symmetry and proportion in the various parameters of the musical language. or flowers which are nearly symmetrical.. contrast. balance. is one idea by which man through the ages has tried to comprehend and create order.5. 1952. in music the perception of symmetry within a time-frame becomes more difficult and demands an a priori recognition of the symmetrical systems at work. beauty. Weyl.. Cambridge. H. p. I will actively seek to demonstrate many theoretical principles relating to composition through the use of real musical examples in preference (due to context) to complex geometrical formulae. The Character of Physical Law. If on one hand characteristics of symmetrical correspondence are easily recognisable in visual arts (specifically non-temporal arts) such as painting. Symmetry. p.” 4 2) “Symmetry. Additional information about English composer Christopher Bochmann’s compositional thinking related to intervallic proportion will be given. MA: MIT Press. the analytical musical research practised by theorists is then not surprising. or symmetrical crystals like snowflakes. etc. as wide or as narrow as you may define its meaning..
Symmetry and Proportion in Music Section 1 .
Additional information and research will be given relating to 3) Christopher Bochmann’s compositional thinking based on intervallic proportion and 4) construction and usage of symmetrical harmony.This section examines the use of the principles of symmetry and proportion in their various musical parameters. 5 . Their application and the ways in which composers have used these ideas in practice will be analysed in 1) music before the twentieth century and 2) music of the twentieth and twenty-first centuries.
p. There are numerous musical examples of symmetrical concepts applied to counterpoint. it is possible to find multifarious examples where composers purposely searched for balance in their compositions. Two of the most fundamental and important compositional principles are repetition and variation. Princeton: Princeton University Press. What is Symmetry in Music?. 1998. Kyrie eleison.1. 6 Morgan. p. p.P. p.S.1. the ‘crab canon’ being a prime example. In music. Symmetry and Proportion in Music before the Twentieth Century Throughout the history of western classical music one can recognise universal governing theories..156. Bach’s A Musical Offering as shown in Figure 1. Departing from the definition “symmetry = harmony of proportions”7. Interpretation. An example of this compositional conceit can be found in the first canon in J.1. H. 6 . 20(1). 1952. and Analysis. Music’s formal structure may be defined as a specific articulation of time. as well as in the polyphonic settings of the ordinarium messae. The recognition of correspondences is vital to the way we organise experience: the human need for order tends to favour symmetrical patterns. For example: Kyrie eleison. Inc.. Christie eleison.. Due to the fact that symmetry necessitates at some level the idea of repetition.. one part moving backward while the other moves forward9. New York: Dover Publications. symmetry being just one of these. where a symmetrical formal disposition of the text would be translated to music8. 27(2). Symmetrical Form and Common-Practice Tonality. the composers imbue their material with a commendable sense of economy. The composition of such a canon consists of two complementary voices.i. symmetry can be initially recognised in ‘rainbow shape’ melodies found in medieval Gregorian chant. Symmetry. D. 1996. 9 David.T. There are various ways and recognisable examples of the application of symmetrical/proportional principles in musical structure and form. International Review of the Aesthetics and Sociology of Music.S. H. Symmetry allows us to comprehend events as a synthesis of matching components and invites us to see wholes as the necessary outcome of a joining of complementary parts6.Bach’s Musical Offering: History. each allowing for unity within the musical form.21. 1945. 8 Kempf. R. one can satisfactorily conclude that by using symmetrical principles in composition. as well as its realisation concerning different styles and systems. Music Theory Spectrum. 7 Weyl. J.
2): the original version of the fugue is followed by its inverted version. Bach.Figure 1. In Contrapunctus 12.S. a 4 rectus et inversus from Bach’s The Art of Fugue. 7 .1 J. the process of inversion can be applied to the whole polyphonic form of the fugue. the complete polyphonic structure of the original fugue was firstly reflected around an imaginary horizontal axis and then translated in time (Figure 1. A Musical Offering (Canon a 2) In a different way.
the whole second part is a literal retrograde repetition of the first one. The first part of this Menuetto al Rovescio (Figure 1. 26.. (rectus et) inversus (bars 14 – 18) Another interesting example of symmetry applied to polyphonic music can be seen in Guillaume de Machaut’s Rondeau Ma fin est mom commencement from Ars Nova..3) is a Tonic-Dominant Dominant-Tonic period with two phrases of equal duration. Bach. 8 . only the tenor voices interchange their positions. After an imaginary vertical axis of symmetry in the middle.2 J. Hob. 10 11 Kempf. cit.XVI:26. 159. The first 10-bar phrase (antecedent) is repeated retrogradely in order to create the consequent.S. Op. The Art of Fugue Contrapunctus 12. A similar procedure is applied to the trio. Morgan. Op. cit. resulting in an interrelation of symmetries11. Another vertical axis could be put at the end allowing the composition to be performed backwards10. p.Figure 1. A similar example from classical homophonic music can be found in the third movement of Haydn’s Piano Sonata in A Major. a 4. p.
Haydn. K.XVI:26/iii (bars 1 – 20) With regards to the formal symmetry. Hob. Op.A.4 W. In the third movement of Beethoven’s Symphony No. p. This can be found in arias (starting with the da capo arias from the Baroque era). can also be found. 156).. K. The most recognisable symmetrical pattern is A – B – A.4. film. in piano-miniatures and songs (especially from the Romantic era). A famous example of this can be found in the first movement of Mozart’s Piano Sonata in C Major. Mozart. Figure 1. in three-part song forms of classical instrumental music. Scherzos. Development and Recapitulation of the Sonata Form follows the same formal pattern but in a more complex and specific way. 9 . in Minuets. Piano Sonata in A Major. In the so called ‘subdominant recapitulation’. op. (Kempf. 545 (first movement). It is worth noting that there is a tendency to keep the symmetry not only in terms of formal balance but also in terms of harmonic functions according to the circle of fifths.Figure 1. cit. 7 in A Major.3 J. 545. The Exposition. and then transposed in the recapitulation so it begins in the subdominant and ends in the tonic (SD – T). formal scheme Other formal symmetrical examples with 5 and 7 parts (usually based on the A – B – A formal pattern). the typical tonal disposition of the exposition (T – D) is maintained. as shown in Figure 1. Piano Sonata in C Major. etc. it is also possible to find multifarious examples. 92 the usual 3-part Scherzo (Scherzo – Trio – Scherzo) is extended 12 The formal pattern A – B – A appears frequently not only in music but also in other art forms such as architecture. ‘Sonata Facile’. etc12.
op. van Beethoven. 3: the symmetrical pattern applied to the harmonic functions (T–D D–T) is clear. op. The 7-part formal type based on the classical rondo with three themes13 can be found in Schumann’s Aufschwung.5b.. Form in Tonal Music. Rinehart and Winston. Op. It is worth noting that at the end of this movement. 7 in A Major. while the second part begins in the dominant and ends in the tonic: A–B (T D – D T). Courante and Gigue14. Schumann. 158. 3 in C major. formal scheme Another interesting example of symmetry is the one found in harmonic relations in tonal music. creating thereby a 5-part form as shown in Figure 1. No. It is interesting to observe how the symmetry of the formal structure is preserved but.6a shows the two complementary two-bar phrases at the beginning of Beethoven’s Piano Sonata No. D. Ibid.M. 164. 2 taken from the Fantasiestücke for piano. Figure 1. p. It appears when the first of the two complementary sections begins in the tonic and ends in the dominant. Symphony No.5 a) L. due to its size and central location within the whole. No. 10 . underling a strong intention of breaking the symmetrical pattern or provoking disorientation in terms of formal understanding.. 1965. In terms of functional harmonic relations.5a.by means of repetition of the second and third parts together. 92 (third movement). specifically used in binary forms such as the dance forms of the Baroque suite: Allemande. Figure 1. 2. after the last recapitulation of A. The 8-bar last section (A) has a clear cadential function after section C assuming the greater importance. 2. similar mirror symmetry is applied in the micro-level musical planning. the proportion in terms of number of bars used in the last section does not correspond to what would be expected by the symmetrical pattern. on the other hand. 12 as shown in Figure 1. there is a brief reference to the musical material of B before the final cadence. Aufschwung. A similar formal/harmonic interrelation 13 14 Green. p. formal scheme b) R. No. New York: Holt.
2. cit. Fugue BWV 846 in C Major (bars 1 – 6) Owing to the fact that the music written between the seventeenth and nineteenth centuries is almost exclusively either tonal or modal (and therefore contains a predefined. van Beethoven. 11 . p. Op. more or less rigid chordal system dependent on key). No. Bach. 3 (bars 1 – 4) b) J.6 a) L. Figure 1. 158. 3 in C major.6b: the disposition of thematic entries Dux – Comes Comes – Dux (T-D D-T)15. Piano Sonata No. The Well-Tempered Clavier (Book I)..applied to polyphonic music can be seen in the exposition of Bach’s Fugue in C Major from The Well-Tempered Clavier (Book I) as shown in Figure 1. the concern given to symmetry is 15 Kempf. Op.S.
there exist multifarious examples of the application of symmetry and proportion in both the structure and form of music as well as in its micro-level parameters. For example. different ways in which these issues were applied to musical composition in the twentieth century. 159. In this regard it is understandable that in music of the twentieth and twenty-first centuries. Its retrograde version T D/D SD D/SD T would be unusual as it does not follow certain tendencies and fundamental laws of classical harmony16.therefore limited. The next chapter will demonstrate with the aid of a few examples. Op. p. 12 . cit. a typical classical harmonic progression with regular succession of functions would be T D/SD SD D/D T. where though there is a greater plurality of styles there still remains a pronounced predilection for a musical language predominantly atonal.. 16 Kempf.
i. Figure 2. E.1.618 and that of the smaller section 0. R. 1971. as shown in Figure 2. resulting also in different modes of expression. 0. Lendvai. A famous example of proportional calculation is the Golden Section (or Golden Ratio).. p. what is important to retain is that the new century has created new ideas. composers started searching for alternative capacities for their musical languages. If this number is multiplied by the Golden Section key number.1 A prescient example of the application of the Golden Ratio in music in order to determine a proportional formal centre can be analysed in Claude Debussy’s (1862-1918) Reflects dans l’eau from Images (1905). Symmetry and Proportion in Twentieth Century Music From the last decade of the nineteenth century on. The principal climax (bars 56 – 61) lies symmetrically over the piece’s overall point of Golden Section19. Debussy in Proportion.e..17. it is usually used to relate the size of different sections of a musical work. the value of the larger section will approximately be 0. p.. London: Kahn & Averill. It comes about when the proportion of the whole to the larger part agrees with the proportion of the larger part to the smaller one.1.2. Op.38218. 1983. If the whole is considered as 1. that seek to radically diverge from conventional forms and/or methods17. Béla Bartók: An analysis of his music. What prior to the twentieth century could be understood as an intuitive search for proportional balance in music later became more concerned with issues such as symmetry and proportion. 19 Howat. It is widely accepted that the first half of the twentieth century demonstrated a great diversity of different composition techniques. cit. p. Irrespective of analytical results and compositional methods (the purely instinctive over the more logical) applied by the composers. both playing a greater role in the compositional process in a more systematic and planned way.4. Cambridge: Cambridge University Press. the result is approximately 58. The Hungarian composer Béla Bartók (1881-1945) is 17 Howat.618. 18 13 . This piano piece has a total of 94 bars.
the result is approximately 274.. stylistically and aesthetically coherent and consistent. For instance. What is Symmetry in Music?. the first movement of his Sonata for Two Pianos and Percussion consists of 443 bars. 27(2). 2) Mesto – Marcia.another well known example of a composer who uses Golden Section proportional principles in the formal calculation of his work. Also with regards to symmetry in terms of harmonic functions. London: Kahn & Averill. the second (starting at bar 18) is a complete inversion of the first. p. that examples of symmetrical realisation within the works are limited. Paul Hindemith’s (18951963) Ludus Tonalis (1942) for solo piano. 23 The axis system is based on the circle of fifths and gives the same function (tonic.. 1971. The four movements of this quartet are organised as follows: 1) Mesto – Vivace. starting and ending the phrase. E. 21 14 . However. (Lendvai. 18. we easily reach an interesting conclusion concerning the use of symmetry in terms of harmonic function.. The subsequent phrases of this mesto also present a kind of general symmetry although not so rigorous and obviously analysed as the one shown here. considered by many to be the twentieth century equivalent of Bach’s The Well-Tempered Clavier21.2b.618. cit. as shown in Figure 2. It is understandable from the previous chapter that in the tonal system of major and minor keys associated with the laws of tonal counterpoint and classical harmony. It is worth noting the structural importance of the G-sharp and its ‘counterpole’ D. Kempf. dominant and subdominant) to the notes situated on the same axis. The material of the mesti introducing the first three movements is then extended and varied in the last. Such examples are easily found throughout the work of this composer20.1-16). The Fugue in F (number III). 1996. D.2a) as purported by Ernö Lendvai23. 20 Lendvai. International Review of the Aesthetics and Sociology of Music. was composed in a system of expanded tonality and free contrapuntal style (with emancipated dissonance). 22 Ibid. If this number is multiplied by 0. Op. 3) Mesto – Burletta (Moderato) and 4) Mesto. creating two symmetrical interrelated parts. p. Béla Bartók: An analysis of his music. 163. pp. Bar 274 is important within the overall form of this movement as it represents the beginning of the Recapitulation. for example. Also the Fugue in Des (number X) is divided into two proportionally balanced parts. the later being the first played retrogradely and upside-down22. If we analyse the first phrase of the first mesto according to the ‘axis system’ (Figure 2. in these two examples there is a small violation of the symmetry by the addition of freely composed cadential lines at the end of both fugues. it is worth having a brief look at Bartók’s Sixth String Quartet.. The symmetrical conception of Ludus Tonalis culminates in symmetrical interrelations between the Prelude and the Postlude. p.160. is divided in bar 30 and reflected by means of an imaginary vertical axis.
24 Messiaen.Figure 2. the outer two note values are the same.B. Olivier Messiaen (1908-1992) was one of the composers who. As an example of symmetry. pp. pour les sept trompettes from his Quatour pour la Fin du Temps (1941)25. the use of non-retrogradable rhythms was. a very important resource24. Paris: Alphonse Leduc. Figure 2. for this composer.2 a) The Axis System b) Bartók’s Sixth String Quartet.17-18. López.. Numerous examples of non-retrogradable rhythms can be found in Messiaen’s music. Tecnica de mi lenguaje musical. arguably. 15 . The most common and simple example of a non-retrogradable rhythm consists of three notes. Non-retrogradable rhythms remain unchanged when read from right to left. 25 Ibid. with a different middle value. O. first movement (bars 1-3) Another recurrent concern shared by twentieth century composers is the rhythmical organisation within the work. contributed most to a specific compositional/technical thinking. 1956. Translated from French by D.3 shows a simple example of a succession of non-retrogradable rhythms (one per bar) taken from Danse de la fureur.
Revista Modus. b) intervals have lost their tonal function. it is possible to underline the concern given to the symmetrical balance in the use of the intervals. major 2 = 2. Figure 2. na música instrumental/vocal. as well as the ‘global’ symmetry. pour les sept trompettes from Quatour pour la Fin du Temps (F to G) As for the use of symmetry associated with pitch. p. only the size of the interval is relevant. perfect 4 = 5 (…). C. The overall textural result is a consequence of the use of four-part counterpoint. the timbre of which is explored aided by the technique of Klangfarbenmelodie28. major 3 = 4. 28 Klangfarbenmelodie (German for ‘tone-colour-melody’) is a musical technique that involves distributing a musical line or melody over several instruments. despite the fact that each note can be transposed to any octave. etc.4a26 shows the dodecaphonic row and its variants used by Anton Webern (1883-1945) in his Symphony Op.126-127. resulting from the superimposition of four different versions of the series used in fixed register. Ph. C. The intervallic realisation of the inversion is done with the pitches in fixed register (E-flat is the only note used in two different octaves). Non-serial criteria in the pitch-organization of Webern’s Twelve-note works. Universidade de Aveiro. forming two inverted cannons: from the prime version (P0) of the series with its inversion (I0) and one of the transpositions (P8) again with its inversion (I8). which allows the intervals to respect the symmetry of each line. rd rd th th minor 3 = 3. Interacção entre estruturas intervalares e estruturas espectrais. the treatment given to a dodecaphonic series is one such example. It is also interesting to observe the distinctive harmony at the beginning of this piece. inversion and retrograde inversion are the most clear and straight forward examples of symmetrical thinking. 26 nd nd From now on intervals will be named by the number of semitones: minor 2 = 1. This terminology is used for certain very clear objective reasons: a) in a panchromatic world (implicit in twelve-tone technique) all semitones are of equal importance. Thus what is presented is a static chord. The processes of retrograde. 2002. (Bochmann. 16 . 27 Marecos.3 Non-retrogradable rhythms in Messiaen’s Danse de la fureur..134).Figure 2. 21 (1928). as shown in Figure 2. D. minor 9 = 13. 2011. pp..4b27.
By careful observation of the second chord. Thus. The Music of Lutosławski. pp. but also by the repetition of their intervallic pattern. The 12-note chords used by the composer can be seen as a set of pitches united by recurrent intervals. C.. harmonic aggregates are perceived by their own characteristics.5a. 6. each chromatic chord tends to be constructed with two or three types of intervals29. Each 6-note group is also symmetrical with interval 6 at the centre. Church Bells from Five Songs (1958. 1994. London: Faber and Faber Limited. In this way.50-51.21 b) Symmetrical harmonic field at the beginning of Webern’s Symphony op.B. taking into consideration its basic harmonic structure (Figure 2. Another interesting example can be found in Lutosławski’s Concerto for Cello and Orchestra (1970). His last song. with interval 7 in the central axis. 29 30 Rae. staring at bar 225 and shown in Figure 2. 11 and 2. By repeating this pair of intervals it is easy to achieve interval 7 which therefore confirms its repeated presence within the aggregate and de facto harmonic character.. 11. p. it is possible to note the rigorous symmetry of its intervallic construction: it is formed by two (also) symmetrical groups of 6 notes each using intervals 2. small orchestra version) is based on only two 12-note chords30.21 With regards to other kind of pitch organisation not involving the use of a twelvetone row. 17 .4 a) Dodecaphonic row (and its variants) of Webern’s Symphony op. Ibid. not only by the recognition of the intervals used. 61. Polish composer Witold Lutosławski (1913-1994) believed that a certain ‘harmonic field’ is better characterised if a reduced number of intervals are used within an aggregate.Figure 2.5b) which is built from intervals 3 and 4 with interval 1 in the central axis.
Figure 2.. his intervallic concern causes him to develop a hierarchical concept based upon a symmetrical intervallic axis. instead functioning similar to a mode from which specific internal characteristics can be explored: the intervallic combinations and its symmetrical relations. Harvey informs the construction of his harmonic spaces according to the harmonic series. By using a symmetrical axis. synthesisers and live electronics (1986).6. 1. a wide intervallic structure is obtained.83-86. pp. 1984. J. His convictions about symmetrical harmony and the concept of ‘bass-in-the-middle’31. 1986. 127(1720). shows the deviation from the ‘gravitational attraction’ of the bass (and building chords upwards from there) to the centre of a symmetrical axis. as shown in Figure 2.5 a) Second 12-note chord in Lutosławski’s Church Bells from Five Songs b) Basic harmonic structure of Lutosławski’s Concerto for Cello and Orchestra Another composer who believes in issues concerning symmetry and intervallic proportion is Jonathan Harvey (b. ‘Harmonic space’ is a term used by Harvey to best define the concept of ‘harmonic field’. 32 18 . moving the gravitational attraction from the bass to the middle. although the comparison between the two reveals some clear differences: 1) the harmonic spaces are built with a succession of intervals that intercalate between small and large. One of the differences between the two concepts is that the harmonic space is rarely used in totality. in his compositional planning there is a recurrent meeting point between intervallic and spectral thinking: in some of his pieces. as can be seen in the first (of seven) ‘harmonic spaces’32 in the piece Madonna of Winter and Spring for orchestra. J.431). The Musical Times. p. Reflection after composition. Contemporary Music Review. 31 Harvey. Nevertheless. from which he constructs his symmetrical structures. 1939). Harvey attributes a primordial gravitation to a low fundamental. Madonna of Winter and Spring. (Harvey. However..
The emphasis is in the original. focal attention is forced. p. providing a fundamental function to the middle axis33. Reflection after composition. etc. rhythm.6 First harmonic space in Harvey’s Madonna of Winter and Spring Jonathan Harvey himself has strong feelings about his engagement towards the use of symmetrical structures with a central axis: “The bass moves into the middle: this is our musical revolution. have been fascinated by harmonic structures which radiate out from either side of a central axis in reflecting intervals. as the central axis is the only common element to all the harmonic spaces used. S. The internal intervallic relations reveal the importance of interval 7 in the harmonic structure. 34 Harvey. myself included. Universidade de Aveiro.62-64. This first harmonic space presents an intervallic structure based on the intervals 5. 19 . Contemporary Music Review. Figure 2. The more or less systematic use of pre-determined compositional techniques and the 33 Santos.C. 1. into the axial middle. 2. timbre e espaço em Madonna of Winter and Spring de J.C. 2005. examples of the application of concepts of symmetry and proportion are easily found within the various parameters: formal organisation. 1984.Harvey. Harmonia. because all relationships converge there: the sounds point to it. M. In the piece Madonna of Winter and Spring the concept of ‘bass-in-the-middle’ is relevant.whereas the harmonic series is presented with a sequence of intervals that become smaller and smaller and 2) the fundamental of the harmonic series is the lowest note of the aggregate. Unless a strong contrary line is taken in atonal music the bass will remain at the bottom of what sounds like dissonant music.83. 6 and 1. Several composers after Webern. But in symmetrical mirroring structures it is forced. whereas in Harvey’s harmonic spaces the intervallic structure is organised from the centre. pp. by adding 5+2 or 6+1.. Phil.. J. choice of pitch material.” 34 Due to the fact that the twentieth century has produced numerous compositional techniques.
creative act, there is an ideal synthesis of all components relevant for great art”35.
in how it relates to all the parameters of his music.
Kempf, Op. cit., p. 163.
music has incorporated a degree of simplicity, following specific tendencies towards postmodernism without resorting to neo-tonality.
of his students would have been influenced in some way by his principles of composition.
common technique can allow for different composers to create highly individual results.
Bochmann has explained in detail his position towards music and musical composition37.
organisation can have an important role in terms of melodic and harmonic construction.
based on a non-functional (non-tonal) context.
All the quotations are taken from the afore-mentioned interview; I have freely translated them.
Therefore. E-flat.2a). O.B.3a). Figure 3. Figure 3. four times within an octave. Béla Bartók: An analysis of his music.. it is only necessary to write three notes of this scale as the intervallic content is repeated ad infinitum (Figure 3.3c) . Paris: Alphonse Leduc. Translated from French by D.87-95. which gives a ‘tonic’ function to the notes C. E.2 It is worth exploring how this applies to the octatonic scale (or Messiaen’s second mode of limited transposition39). Tecnica de mi lenguaje musical. The intervallic pattern of the scale is repeated every minor 3rd. London: Kahn & Averill. 39 Messiaen. The same notes in different octaves have a strong relationship as they function in the same way. 1971. Therefore. López. pp. Also. 1956. Perhaps fortuitously the four ‘tonics’ of this scale correspond to the Axis System as described by Ernö Lendvai40 and briefly explained in the previous chapter (Figure 3.. pp. 23 . F-sharp and A (Figure 3.2b shows the relationship between dominant (V) and tonic (I) as an example.1-16.In tonal and modal music the intervallic content of a scale is repeated in a pattern every octave (Figure 3. the pitches have the same function despite the varying registers or octaves.2c).3b). chords based on an octave equivalent scale never lose their function irrespective of the position they are in (Figure 3. 40 Lendvai.
Thus. 24 ..4). D. 1). 3. it would be expedient to outline briefly the way in which Portuguese composer Carlos Marecos (one of Bochmann’s former students) works. 1. 1.5b). Ph. on the other hand. 3. 3. na música instrumental/vocal. the raw material (Figure 3. it is possible to observe one of the characteristics of a ‘non-octave scale’: the same function given to different pitches (F2 and G-sharp3. Universidade de Aveiro. 2011. the intervallic structure (formed with intervals 1 and 3) constitutes the general harmonic field (Figure 3. the pitches C-sharp3 and C-sharp4 have different functions within the aggregate41. Interacção entre estruturas intervalares e estruturas espectrais. 41 Marecos. interval 15 assumes the equivalence of the structure: the harmonic field starts at D2 and repeats its structure from F3.4 Due to the fact that in some atonal music the sound organisation does not repeat its structure every octave.5a) can be reduced to two notes (Figure 3.60-61. If we give a function (a – h) to each element of the harmonic field (according to their linear intervallic position within the aggregate). In his piece Terra (2009) for string orchestra. Figure 3. pp. for example). The sequence of intervals is repeated after 15 semitones (3.3 As an example of intervallic structures without the octave equivalence. C. providing a ‘tonic’ function to all the notes.Figure 3.
) 45 Bochmann. 2) Each note has its own identity as important as any other note within the aggregate: there are no differentiated functions. We are talking about a musical ‘system’ all based in a semitone scale. intervals 19 and 7 have a high degree of consonance. therefore there are no octave-equivalent functions43: interval 12 is the most consonant combination of two notes. Lisbon:(not published). 43 25 . It refers to music based on equal steps45. Barce. which is based on two types 42 Bochmann.Figure 3.138. 2008. 1922. Bochmann. Bochmann has also created a new term. C. Lição de Síntese: O registo na música serial e o pensamento intervalar. or quarter tone scale. 2003) According to this definition the whole-tone scale is also isobematic as it is constructed with major seconds only. 2004. pp. p. pp. or any combination of two types of steps.5 The functional equivalence of all the elements has very important repercussions42: 1) There is no ‘pole’ or consequent hierarchy. unless the composer creates them purposefully. negating an absolute value (or ‘tonic’).” (Bochmann. (Schönberg.8-9. Armonia.. Évora:(not published). whereas intervals 6 and 1 have a high degree of dissonance44. “We are no longer talking about a major scale based on whole tones and semitones.2-3. or sixth tone scale. A música isobemática. Bochmann’s has a Greek etymology: the word ‘isobematic’ comes from ‘ισο ισος βηµα‘ ισος‘ (meaning equal) and ‘βηµα βηµα (meaning step). Unlike the major scale. Also. where all the steps are equal. Non-serial criteria in the pitch-organization of Webern’s Twelve-note works. Madrid: Real Musical.. C. C. like many other terms used in musical languages. There is a true ‘democratisation’ of all the elements used. The notes are all related to one another.. 44 Schönberg’s refutation of ‘consonance’ and ‘dissonance’ related to the harmonic series will be taken into consideration whenever mentioning these two terms: consonances are the intervals formed by the first overtones of the harmonic series whilst distant overtones create intervals that can be considered ‘dissonant’ when related to the fundamental. Translated from German by R. Revista Modus.13-17. A.. For this issue. 2002. pp.
intervals. it has the value of 193. For example. i. 48 Marecos. M. the frequencies are equidistant and thus possible to relate the harmonic series to the ‘isobematic’ principle described by Bochmann providing that the measurement is made in Hertz. New York: Routledge. Op. pp. 2001. What we actually hear is the ratio between frequencies.1.25. In order to fully clarify my recent observations it is necessary to make one final analysis in association with the harmonic series: Figure 3. Cit. 1. P. what we hear is. In the extreme bass and treble registers. 150-151). 2006.e.. 1. in acoustic terms. pp. the whole-tone scale lacks such distinct contrast as all the notes are separated by the same interval and therefore have the same function. i. 47 26 . the proportion between frequencies is altered48.6 shows the frequencies in Hertz (Hz) of the harmonic series starting from the fundamental C1.6 (if tempered tones are considered).6 46 Simoni.of steps and consequently whose functions are very clear (the leading note for example has a very distinctive attraction to the tonic). ed. However. the relation between frequencies.63Hz. It is interesting to observe that in terms of pure tones. as there is a logarithmic correlation between a frequency measured in Hertz and our perception of that frequency described as a pitch46. (Cook.. when moving the pitches up or down an octave. i.62Hz. E3 with 329.63Hz and C4 with 261.25Hz form a minor 6th. p. in fact.e.63Hz and C4 with 523. 59-60. The ear recognises the same interval in any part of the register47 once the ratio between frequencies is the same. in this case 8:5. Figure 3. London: The MIT Press. the interval formed with the E is a major 3rd: E3 with 329.e. Cognition and Computerized Sound: an introduction to Psychoacoustics. the difference is 68Hz and the ratio between the two frequencies 5:4. If we move the C down an octave.. Analytical Methods of Electroacoustic Music. Considering this interval as a deviation of cycles per second. Music. the same proportions do not exactly reflect what is psychologically perceived. Thus.
34. 11. 47. rhythmic figures (durations). 3. It is worth noting that starting from an interval related to the series and following to a new. Basically. C. This means that the second beat has a different function from the first. 55. duration. …) in which each number is defined as the sum of the two previous terms. 27 . Lisbon:(not published). Bochmann limits the use of different intervals in order to allow the ‘sound world’ created to more readily establish distinct aural references.e. specifically in order to apply it to other musical parameters. 29. 4. 50 Marecos. They are however used to relate the different musical parameters to each other: pitch (intervals). they are not used by Bochmann to estimate the golden section of a particular work or a movement/formal section. structure/form (size of sections). 1. almost every piece of music which is tonality based and written in 4/4 will end with an articulated note on the first beat of the bar. 2005. p. what is the relation between them? If we have a texture… what is the relationship between this texture and any other? Thus. 2003) The proportions used in most of Bochmann’s work are related to the Lucas sequence49: 1. Despite these numbers being directly related to the Golden Ratio. number/density of musical occurrences.Continuing with the ‘isobematic’ concept. 13. If the rhythm for example has a long note and a short note – what is the proportion between the two? Is it a ratio of 3:4 or 2:3 or any other more complex proportion? If we have two notes. Christopher Bochmann believes that everything in music is relative. form. adjacent element also related. the semiquavers. But in music that does not imply tonality or time signature (i.is relative.” (Bochmann. thus being more important that the others in the hierarchy. 49 This is a variant of the Fibonacci sequence (1. 5. 18. etc. 1. O pensamento intervalar. pitch . without hierarchies) everything is equal. 76. 2. everything .. 21. This is somehow automatic because the first beat is the one that resolves. (…) It is a mater of relating one thing to the other. 8. Figure 3. everything is isobematic: the semitones. etc. the triplets. the quavers.7 exemplifies the melodic use of the Lucas numbers. … The choice of these numbers is primarily related to the intervals used. 3. it necessarily equals another interval that will be within the same kind of proportion50. for example: “In a 4/4 bar in tonal music we tend to denominate the first beat as ‘strong’ and the second as ‘weak’. 7.no matter whether we are talking about texture.
4R. 4. in Bochmann’s music the use of these proportions is not done in a linear way. increasing or decreasing: 1. These contours are used in four different ways: in the so-called prime version (P). Figures 3. inversion (I) and retrograde inversion (RI). 7. I will use the following terminology: 3P.7 The same principles of proportion can be observed in the rhythmic organisation: the specific rhythmic figures used in Bochmann’s music are calculated through the division of the unit (e = 1.Figure 3. Such musical coherence is achieved by avoiding using different ‘rules’ for the different musical parameters. However. 11. 1. for example) by numbers relating to the Lucas series: - demisemiquavers (y = e/4). it can be asserted that the use of such exclusive criteria converge to form a unified final result. Therefore. = 3/4e) - grace-notes (an approximation of e/7 or e/11). Thus. The most commonly used contours in Christopher Bochmann’s music are the ones with 3 and 4 elements. 7. 4. 3. xJ . - dotted semiquavers (x. underlining once again the use of the numbers taken from the Lucas series. 51 Whenever mentioning these contours. 11 or 11.9 represent the four types of 3 and 4-element contours respectively used by Bochmann51. 3I and 3RI for the 3-element contours and 4P. 4. 3R. x).8 and 3. 4I and 4RI for the 4-element contours. proportions are demonstrated and used irregularly. and its respective derived versions: retrograde (R). - semiquaver triplets (xJ = e/3). In this way. the use of such numbers can be presented by the order: 7. 3. 28 . The application of these numbers is practised according to another important concept to the composer: the ‘contour’. 3. The Lucas numbers are also recurrently used to multiply the unit (e) or any resulting rhythmic figures by any divisions of the unit shown above (y.
See Appendix. His use of 7 and 11-element contours can be seen occasionally. derived from sums of 3+4 (or 4+3) and 4+3+4 (or 3+4+4.Figure 3.9 It is also possible to find in Bochmann’s music other types of contours (which are a variation or combination of the contours shown above) whose number of elements also relate to the Lucas sequence. Christopher Bochmann designates these concepts for use across all potential musical parameters. 29 . 4+4+3). Form in Lament This piece is divided into two contrasting ‘parts’ . Whilst he himself shies away from such a term. durations. as well as to melody. As already mentioned.mic. composed in 2001. dynamic levels and the number/density of material/musical occurrences. therefore rendering the perception of two individual movements unavoidable.Bochmann deliberately avoids the term ‘movement’ in identifying the two parts.8 Figure 3. 52 The score is published by the Portuguese Music Information Centre and available for free consultation at http://www. In order to gain a better understanding of Bochmann’s compositional principles in action we must look closely at Lament for 15 players52.pt. the characteristics of each ‘part’ are so strikingly different as to appear completely unrelated. The following brief analysis will focus on the use of proportion and contour applied to the formal structuring.
It is once again clear that Bochmann uses the Lucas series when repeating A and B four and three times respectively. Subsections A have a fixed duration of 47e and subsections B.e. thus 47 . However. but rather. Number 65 is not immediately recognisable within the Lucas series. is used to generate the form of the piece and to calculate the proportions between sections and subsections. it can be calculated by adding 47 and 18 together. this melody would sit well within the contours typically used by the composer. The second part of Lament is constructed by the alternation of two elements: A1 – B – A2 – B – A3 – B – A4. respectively.10 By observing the scheme of the ratios between the two parts. finding the notes for formal differentiation. thus using contour 3I.11a.18 = 29 (B2) and 47 + 18 = 65 (B3). they are ‘starting points’ from which other musical gestures are generated. 3 and 1. rather than specific pitches.10). Melody in Lament When speaking of melody in the works of Christopher Bochmann one must remember that any subsequent analysis should focus on intervals used. 47e. This 7-note melody can be 30 . The use of Lucas series lends coherence to the compositional planning. The whole first subsection is constructed through the polarisation of the notes presented in Figure 3. The second part has one subsection only and the proportion is defined by the number 7 (see Figure 3. the proportions between the sizes (durations) of which are: 4. one can see the proportional use of the contour 4I in relation to the formal organisation. Both these numbers are related to the present series.The notion of ‘contour’. Figure 3. In aural terms it is worth stating that these notes are not recognisable as a melody. However. as explained above. 29e and 65e respectively. The first part of the piece is divided into three subsections. i.
18  11.12 demonstrates the use of other types of 3 and 4-element melodic contours in the first part of Lament. can also exemplify the use of the same ‘philosophy’ (Table 3. 31 . Figure 3. Subsection Rehearsal mark Contour A1 17 3I and 4I 53 Here we can use the prescient analogy of photography – words such as ‘focused’ and ‘unfocussed’ constantly appear in Bochmann’s vocabulary when defining the clarity of a musical discourse – to liken the processes of enlargement and reduction with the zoom-in and zoom-out capabilities of a camera. Comparing the two melodies shown above.11 Bochmann’s processes of ‘enlargement’ and ‘reduction’ consist of the substitution of an interval for adjacent intervals also proportionally related. in this case with the Lucas sequence53.divided into two types of contours: 3I and a variation of 4I.11b). Figure 3.12 The subsections A (1 – 4) of the second part of Lament. 7  4. based on parallel chords. Figure 3. 11  7. This succession of notes is the ‘enlargement’ (augmentation) of another recurrent succession used by Bochmann to determine polarising points in his music (Figure 3.1). the following substitutions can be observed: 4  3.
The numbers of the durations indicate the process of multiplication of the semiquaver triplets by numbers contained in the Lucas series. articulated seven times it prefigures the general harmonic conversion to a unison D.13. clarinet and bassoon play a chorale. presenting contour 3I. Once again it is clear that the same principle is applied to various musical parameters. 7 and 29. this time played by the flute. oboe.1 It is worth noting in the previous example that all four versions of both 3 and 4element contours are used. Bochmann uses a limited number of rhythmic figures resulting from the division of the quaver (e = 1) by the numbers of Lucas series.13 At 5 the oboe. clarinet and alto saxophone to the following durations: 18. At the beginning of the piece the strings play a single chord. it is also possible to calculate the values 18. The result of these divisions and the quaver itself can also be multiplied by values corresponding to the afore-mentioned proportions. These 32 . Similar to this last example. 11 and 29 derived from the multiplication of the semiquaver triplets. Figure 3. The 7-element contour is easily analysed by the application of 4I and 3P. with the initial rest included. 11. another chorale appears at 7. In the same way as shown above. The rhythmical articulation of this chord is planned as shown in Figure 3. Durations in Lament As explained earlier in this chapter.A2 19 3R and 4P A3 21 4RI and 3P A4 23 3RI and 4R Table 3.
etc.2 indicates the order in which the dynamic values are used in each phrase together with its corresponding contour types (P. pp 3P A2 pp.2 clearly shows the constant rotation of the last element to the beginning. mp. Table 3. p 3RI A4 p. it is reached by applying another important concept for the composer: ‘rotation’. The idea of rotation is based on the movement of the first element to the end or vice-versa. the dynamic level contour in A2 is unidirectional. Bochmann’s solution to the use of dynamic levels in his music is inherently subjective and does not consider measurement in decibels.). the subsections A (1 – 4) are based on parallel chords with three musical phrases each. However. It is worth mentioning that Bochmann’s approach to the distribution of dynamics is not calculated as systematically nor it is informed as rigorously as the previously discussed aspects: here the application of numerology is conspicuous by its absence.numbers are also expressed by the multiplication of semiquaver triplets and use contour 4I.2 As the table above demonstrates. pp 3P Table 3. but maintaining the coherence which justifies its place alongside Bochmann’s other recurrent processes. a consistent approach to contour and proportion is clearly evident in the two examples (both chosen from the second part of the work) I have analysed (see below). thereby creating an exception to the applied contours hitherto encountered. p. 33 . Dynamic levels in Lament Using Bochmann’s compositional ‘tools’ to analyse dynamic levels in Lament is still possible (though not as straight forward a process as seen with other compositional parameters). the emergence of this exception is not incongruent in Bochmann’s language. Subsection Dynamic level Type of contour A1 p. mp (unidirectional) A3 mp. moving away from the concept of contour demonstrated thus far. I. pp. Table 3. mp. As mentioned above.
Harmony in Lament Although the harmonic/vertical construction of Bochmann’s music (specifically in Lament) does not lend itself to being analysed according to Bochmann’s own ideas of contour. If a different function is given to each interval (a – e. The concept and indeed importance of contour is also identifiable in the first part of Lament. 4 and 1 note(s).3. In B1 (18) the piano plays three gestures of 3 notes. A2 – 1.by deduction then: 3. 3 and 4 note(s). 11 or 3 notes. 3RI and 3P. The types of contours used are respectively: 3P. A3 – 4. 7 and 4 notes used. The three-phrase chorales observed in subsections A (1 – 4) from the second part of the piece are a good example: the number of notes contained in each phrase may be expressed in the following manner: A1 – 3. A4 . Figure 3.The second example is evident in the general dynamic level of the B subsections in the second part of Lament (see piano part for example): p. the section between 2 and 8 (inclusively) can be first characterised by the use of solo lines in the woodwind. 7. it is worth looking in more detail at the way intervals are used.14 shows the first three chords played by the woodwind and brass at the beginning of the piece. in B2 (20) it plays one gesture containing 7 notes and in B3 (22) three gestures of 4 notes each . for example) also demonstrates the application of contours as has been analysed previously. Density of musical occurrences in Lament Similar proportions and contours are also applied to the density of musical occurrences. The number of notes contained in each melodic phrase (4. (unidirectional). interesting 34 . 1 and 3 note(s). mp and pp: contour 3P. 4 and 1 note(s). for instance the number of notes used in a certain melodic line. The application of contours to determine the density of musical occurrences is also inherent in subsections B from the second part of Lament. from the bottom to the top). corresponding to contour type 3R. It is interesting to note that the formation and use of a unidirectional contour is possible through the application of rotational principles as explained above.
14 Finally I wish to draw the reader’s attention to rotational processes occurring in Bochmann’s harmony. as has been seen previously.15). keeping intervals (d) and (e) as they are but creating a new interval (c) – interval 11. Interval (e) is kept as it is and interval (d) is achieved by the application of the process of ‘enlargement’ (4  7).occurrences can be seen. interval (b) is kept the same (interval 4) throughout the progression (the brass sustain D3 and the alto saxophone repeats/re-articulates B-flat2). It is worth stating that the chord in the example is disposed in a way of favouring the balance of the harmonic series. The progression of these 3 notes to chord 3 is achieved in the same way: the upper part of the aggregate is transposed 4 semitones up creating again a new interval (c) – interval 15. i. thus. Figure 3. a proportionally balanced new chord (Figure 3. larger intervals in the lower register and smaller intervals in the higher register. If we take the first chord of the previous example it is possible to rotate the upper interval to the bottom of the aggregate creating. calculated by the sum of 11 + 4. bearing in mind what has been discussed in this chapter: the importance of the interval above the specific pitch. revealing another of Bochmann’s compositional idiosyncrasies. Interval (a) is used in a constant process of ‘enlargement’ (7  11  18) from chord 1 to 3. The three upper notes of the aggregate are transposed 4 semitones up from chord 1 to chord 2.e. 35 .
15 The compositional ideas discussed in this chapter regarding Bochmann’s principles are evident in my own music and thus. the wider implications of Bochmann’s teaching have influenced my overall approach to composition. the relevance of this chapter in my thesis should not be underestimated. the use of proportion is integral in the ‘drafting’ of a new piece and is consequently inextricably linked to the music’s creation. Even if I do not apply Bochmann’s principles in as rigorous a way as he. I will explore the use of proportion in relation to the construction of harmony. in particular symmetrical harmony whose close relationship with intervals is of course prominent.Figure 3. 36 . In the following chapter.
and Schurig. Symmetrical Harmony – Construction and Usage “The harmonic domain is unavoidably inherent to art music. Hofheim: Wolke Verlag.. In music that is not tonal and does not exhibit tonal functions. 2002)54 Based on the main issues examined in the previous chapter.-S. it becomes a problematic issue in every post-tonal music. the current chapter serves as a brief introduction to the way I construct and use symmetrical harmony in order to facilitate the comprehension of the commentaries/analyses pertaining to the seven original compositions contained in the portfolio which will follow in the next section of this thesis. it is not justifiable to use the octave as an equivalent interval in a system that is not based on a mode (or scale) where inherent internal intervallic structures are repeated every octave. ed. 2002. the more recurrent intervals would become familiar to the ear. Polyphony & Complexity.-S. Cox. C. C. specifically Bochmann’s concern with the importance of intervallic qualities/proportion in his music. W.65. From the notion of a ‘central note’ or ‘central interval’.. Theses Concerning Harmony Today. What is essentially relevant is that the musical material can generally be recognised and characterised by the intervals used. F. demanding in each case an individual solution” (Claus-Steffen Mahnkopf. 37 .4. p. the following explanation regarding symmetry takes into consideration some of the intervallic ideas already discussed whilst introducing new approaches to the construction of harmony: - The principles applied when constructing a symmetrical chord are rather simple. As previously maintained. 2002. The symmetrical harmony is constructed through the use of a central note or a central 54 Mahnkopf. as well as lending coherence to its technical and aural organisation. therefore assuming the importance of points of reference and consequently aiding perception of the work. One piece of information that is necessary to retain from the previous chapter is the importance of intervals and the consequent non-equivalence of the octave within the musical material (pitches used). In: Mahnkopf.
once divided at the centre.1a shows the central intervals used to create symmetrical chords consisting of an even number of notes.1b shows examples of symmetrical chords using the same central intervals. Figure 4. These central notes are an example of a possible starting point. the middle axis can subsequently be set anywhere in the register providing the intervallic symmetry used to generate the chord has been respected. A symmetrical chord is a group of more than two notes that. The chords are not built from the bass note up. 55 My starting point is usually E3 or F3 (or interval 1 that corresponds to both notes played together) as it is the centre of the piano (my main working tool) and allows for the same number of notes down and up the register. as well as for allowing the creation of an ‘aural tonic’ when one of these notes (or both together) are polarised. but from the centre. This is a useful resource when working with symmetrical harmony. one must use homogeneous three-note symmetrical chords to define the central axis as shown in Figure 4. 38 . Figure 4.interval55.2a.2b shows examples of symmetrical chords using the central three-note middle axes. Figure 4. Figure 4.1 To create symmetrical chords with odd numbers of notes. offers two equal parts containing the same intervals disposed upwards and downwards.
subtraction of numbers in the sequence, for example 10 = 11 – 1 or 7 + 3; and 6 = 7 – 1.
interval types a chord has, the more complex and dissonant it becomes.
tonal references. Figure 4.4 shows examples of some of these chords.
See ‘Introduction to Christopher Bochmann’s compositional thinking’.
make consistent use of a system that can guide our thinking and organise one’s creativity.
compositional ‘concerns’ whilst at the same time presenting new issues to tackle.
43 . rather than their order of composition. Each of the following commentaries comprises information about the creative motivation behind the work in question as well as a brief analytical overview. The reoccurrence of references to certain technical issues has been unavoidable as all works share a common technical background and their omission would lead to an incomplete picture of the different works in analysis.This section deals with the analysis of the seven original compositions contained in the portfolio. the focus of each analysis is tailored to a different aspect of the work in order to reveal more extensively the potential of these issues in contemporary composition. Although all of them utilise elements of symmetry and proportion. The pieces have been presented in an order designed to help clarify issues.
The concept of ‘open work’ or ‘open form’ is based on principles of total or partial liberty given to the formal linking of musical gestures within a piece. Through the combination of some of his arguments such as the influence of the performance in the (post)creation of a work.4. MA: Harvard University Press. depending on the player. There is only one direct way that links these two fragments.. being put on an almost equal footing regarding the composition of the work as the audience perceives it. to lesser or greater degrees depending on my compositional precepts. in other words.I. The duration of the piece depends on the performance. U. 1989. it is the order of presentation of these gestures which is ultimately decided by the performer. 44 . I wanted to compose a piece where I could use a common principle explored by both Stockhausen and Eco: an ‘open work’ whose formal organisation varies from one performance to another. The emphasis is in the original. The Open Work. and the desire to pay homage to the then recently deceased composer Karlheinz Stockhausen (1928-2007). the 57 Eco. Translated from Italian by A. though each has been carefully calculated to function within a range of specific parameters. 1962)57 The idea for Fragmente-Spiel (or ‘Game of Fragments’) for solo flute arose from the self-imposed necessity to explore a personally unknown compositional path. getting to the ’wrong’ fragment. Cambridge. therefore the original starting point is. The final options are left ‘open’. The motivation behind taking what was for me a ‘new risk‘ in my work evolved from my reading of Umberto Eco’s La definizione dell'arte (1968) in which I was reminded of a previous work of his. The idea for Fragmente-Spiel was to create a labyrinth of fragments where the performer starts on the first fragment and begins a journey eventually leading to the last fragment (number 24). Opera aperta (1962). These ideas were explored by composers such as John Cage (1912-1992) and Earle Brown (1926-2002). which allow the player to act as a creative agent. in a sense. experimental. Fragmente-Spiel for solo flute (2008) “…every reception of a work of art is both an interpretation and a performance of it. p. Cancogni. because in every reception the work takes on a fresh perspective for itself” (Umberto Eco.
Figure I. there does exist a ‘direct’ way as shown in the diagram below. 17 or 18. Although composed specifically to allow for the capricious nature of choice (so that each ‘path’ through the work is as valid as the next).piece can actually last for a long time. 3 minutes. this leads to an inevitable variation in the duration of the piece. At each step (fragment). the player has two or three options available: for example. after playing fragment 1 the flautist chooses to proceed to fragments 2. There is a certain degree of freedom as to the ‘path’ through the piece chosen by the performer.1 shows the direct way towards the end and how the fragments which are out of the main path create a kind of loop. 45 . which is of a fixed duration of ca.
in this piece the principle is used in a more systematic way in order to demonstrate the ‘intervallic thinking’58 linked to the idea of sound symmetry. and in fragment 24 the use of a multiphonic as a conclusive gesture. fluttertonguing. they are ornamental notes. All the other fragments are mostly characterised by the use of staccato. Concern was given to allow some significant identity to fragments 1 and 24. lip glissandi. 47 . two or three symmetrical chords. key clicks and lyrical two or three-note melodies.e. Although this was not the first time I had derived melodic lines from harmonic fields I found it challenging whilst combining the idea of symmetrical harmony with a solo melodic instrument. these intervals are predominantly 7 and 11. However. trills. As is evident. The melodic/harmonic structure is very simple and it can be exemplified through the score reduction and intervallic analysis as shown in Figure I. Hitherto I felt that a perceptible formal structure aided clarity of communication with the audience. 58 See ‘Introduction to Christopher Bochmann’s compositional thinking’ in Section 1 of this thesis. its antecedents are arguably seen in the ‘Alberti bass’ used in classical music.Fragmente-Spiel was the most fragmented piece I had written at that point. clearly creating a beginning and an end. It is only really necessary for the performer to understand the ‘game’ behind the conception of this piece.2. i. However. for each fragment it is possible to analyse one. indeed. This was achieved by the use of extended techniques in both fragments: in the first fragment the use of overtones and humming. This technique of breaking up a chord is not a new compositional resource. which occur frequently in my music. melodic leaps. The idea of deliberate fragmentation of material leads to a ‘chaotic’ formal organisation in relation to the clear and perceptible forms exhibited in my previous works. All the other notes that are not in the example are considered separated intervals that do not belong to the general harmony.
in general. as shown in Figure I. It is worth noting that. This usually provokes the perception of two layers of intervals 48 . the intervals between the notes are.2 It is obvious that my intention when creating these symmetrical chords was not to allow the listener to hear them as clear ‘harmonic fields’.3.Figure I. This is one of the examples where the creative principles regarding symmetrical harmony were utilised for a different aim: the generation of a ‘pitch pool’. when ‘breaking’ a chord. not the ones which were initially planned.
Figure I.3 As for other symmetrical elements in the piece.4 As noted above. based on intervallic relationships. Figure I.sounding concurrently: the ones contained in the ‘harmonic field’ and the ones played melodically. Fragmente-Spiel functions mainly as a study for solo instrument. Figure I. Figure I. the application of symmetrical principles in this piece is rather simple.4b). 49 .4a) and rhythms which can be seen between two different fragments (Fragments 4 and 21. Technical preoccupations concerning the composition of Fragmente-Spiel has in turn opened a door to new musical ideas used in the other pieces analysed in this thesis. it is possible to pinpoint some examples such as the use of both symmetrical contours (Fragment 10.
inspired by the varying sounds/timbres trumpet mutes can create. 1934) Secret Theatre (1984). the dynamics and the contours. who have demonstrated tremendous kindness in accepting the ideas that gave birth to the piece. The idea of superimposing different layers of musical material has been both one of my main preoccupations and compositional resources. Gestures III: (untitled) makes the exploration of musical gestures its priority. i. In this particular work the issue of degrees of musical ‘perception’ depends on the geographical position of the listener within the audience. The percussion works almost as an independent element ultimately being influenced by (and reacting to) the gestures of the trumpets. These pieces work as ’test tubes’ for gestures and ideas that end up together in a piece. Gestures III: (untitled) is the third work bearing this generic title – the two preceding being Gestures I (2006) for solo piccolo and any four instruments (or four groups of any instruments) and Gestures II: conversations about a contour (2006) for clarinet. the only notated materials are the rhythms. To each musical gesture I have associated a different timbre. Gestures III: (untitled) for 4 trumpets in C and percussion (2008) Gestures III: (untitled) was commissioned by Deal Festival 2008 and written in collaboration with Bella Tromba and the percussionist Stephen Burke. the trumpet material is in a constant process of transformation. The importance of gesture as a means to create a functional musical discourse is the overriding compositional ‘concern’ in my cycle. Among the various works which ask for the players to be positioned in unorthodox performance positions in relation to the audience one can highlight Karlheinz Stockhausen’s (19282007) Gruppen (1955-57) and Harrison Birtwistle’s (b. the trumpets’ starting positions are onstage but as the piece develops each player moves around the performance space59. the gestures. in terms of aesthetic control as well as from a compositional point of view. within a certain register the 59 The idea of ‘spatialisation’ in music consists in the use and localisation of sounds within the physical space. not least because of the way music plays with ‘audience perception’.e. constitutes a kind of alter ego in my musical creation. Each player has to improvise the notes according to register indications on the score. In order to understand and contextualise the ideas related to this cycle it is necessary to briefly refer to the other two pieces: - Gestures I is written without any defined pitch. The cycle Gestures. 50 . piano and two percussionists.II. In addition.
as these pieces work as ‘experiences’.1 shows the chords played by the trumpets in Section A. In Gestures II: conversations about a contour the sections vary between those containing rigorous notation (specified pitches and rhythms) and those with freer notation as used in Gestures I. Returning once again to Gestures III: (untitled) and its analysis. as the graphical notation and the movement of the trumpeters around the audience vary from performance to performance. As previously stated. However. Ultimately. the next four chords are used from A until two bars before B. the cycle Gestures works as a ’test tube’ because the final musical result of these pieces is rather different from the expressive continuity I try to explore in my other works.instrumentalist would play any note according to the rhythm and gesture notated. and Gestures II generated the musical material for Four characters taken from a tale (2007) for clarinet. The 51 . rev.25 : 3.25 : 5. Throughout my oeuvre I have the desire of unifying each constituent work and therefore this is a very prominent resource within my musical writing. The fact that all sections are connected without any general pause throughout makes the understanding of these differences even more difficult. At this point all the players are onstage in front of the audience. All the symmetrical chords shown represent the harmonic progression (played by the trumpets) of the first section of the piece. these proportions (devised during the process of pre-planning) aims at creating an irregularity in the size of the different sections. The first seven chords are used from the beginning until one bar before A. the reference to issues of durational proportion became a means to an end. The exact duration of each section depends a lot on interpretation. The remaining three chords are used from C until one bar before D.: 2009) and Fragmente-Spiel for solo flute (2008). the next chord at B. violin. i. Gestures I provided the ‘raw’ musical material for Inventio for orchestra (2007. particularly in relation to proportion it should be noted that the larger structure was conceived in five different sections which are ‘smoothly’ joined to one another. With regards ‘recycling’ the same musical material for use in different pieces (whilst acknowledging this practice is far from new) it has been an idiosyncratic characteristic of my compositional thinking for some time. Therefore. versus a quasi-independent musical layer played by the percussionist. Section A (from the beginning up to D) is characterised by a single gesture on the trumpets using the Harmon mutes to produce a wa-wa effect. violoncello and piano.e.75. Figure II. The proportions (duration) between them are approximately 6 : 4 : 4. guiding and informing the compositional process and providing clear parameters in which to develop the work as a whole. leaving the choice of the notes to the player.
Thus trumpet 1 does not solely play the top note nor trumpet 4 the lowest. creating concords within the harmonic plan of this section. A similar observation can be made concerning the dynamic levels which vary between pp and mf. none of the trumpets play the same dynamic level at the same time. The notes played by the vibraphone in Section A are analysed in Figure II. 4. semiquavers and quintuplet semiquavers in order to create rhythmic irregularity and avoid homophony. triplet quavers. Figure II. It is also worth referring to the concern given to the voiceleading: as there are four groups of chords corresponding to four small subsections (7. thus creating a cross-fade of intensities. with crescendi and diminuendi. the differentiation of the gestures is quite clear. 1 and 3 chords. 4 and 5 are the ones that occur more frequently. 8. All the pitches shown in the example are used melodically (they are bowed) and the durations were chosen specifically to avoid homophony with the trumpets. 3. The recurrence of intervals 6 and 7 here is absolutely intentional. 9 and 11 as a contrast to the ones already established. leaving intervals 2. The chords are orchestrated evenly across the four. the voices are distributed to the four trumpets in a way of achieving internal movement within the ensemble.2a. All these intervals and chords are played by the vibraphone and end three bars before B.2b shows how these notes connect to the symmetrical chords played by the trumpets. 1 and 3: all numbers make part of the Lucas sequence. Intervals 1. Regardless of any inferred harmonic connection between the trumpets and the percussion. Figure II. as stated previously).numbers of chords used are 7. 4. Beyond the beginning of each subsection.1 There is clear evidence of the superimposition of quavers. 52 .
taken together (with each instrument within the ensemble contributing) help to form a more general accompaniment. 4. and linear melody on the vibraphone) allows the creation of musical tension before changing to a new section. 6. Section B (from D to H) of Gestures III: (untitled) is characterised by the movement of the trumpets to new positions around the audience (see ‘ensemble layout’ on the score). playing symmetrical chords that are not related to the general harmony. To a certain extent (and as can be seen throughout this analysis). 7 and 11. The independent harmonic nature of the percussion is used to help demarcate the different musical layers. Gestures III: (untitled) is the first piece I wrote whose instructions in the score include not only the movement of the players but also the direction of the trumpets’ bells in relation to the audience.2 At two bars before B the role of the percussion becomes increasingly independent of the rest of the ensemble. these being the most recurrent and therefore personal in my work. Gestures are treated independently (soloistically) and. The visual as well as theatrical element of this small section represented at the time of composition something new in my work. To a certain extent and due to its relative duration (the smallest of all the constituent sections) it is somewhat unavoidable that it functions as a bridge to Section C. 3. the separate functions of the instruments within the ensemble as a whole greatly influence the overall defining characteristics of the work. In Gestures III: (untitled) the concept of ‘gesture’ is extended to encompass the visual as well as the purely musical aspect of live performance. The use of two intervallic principles (symmetrical harmony on the trumpets.Figure II. the vibraphone plays a melody that is not related to any ‘symmetrical principles’: the notes are chosen by the use of intervals 1. Two bars after C. 53 .
instead relying solely on the performers’ independent choices. at F the same principles apply. At F. the remaining notes are played by the first trumpet. Once again. which starts a completely new gesture once it is placed in the new position. By inferring a circular pattern to the order of melodic gestures (i. At G the choice of the notes is more intuitive but is still based on characteristic intervals. underlining the intention of avoiding a static harmonic field. but also to the visual side announced by the gestures of the percussionist whilst conducting. whilst the remaining three notes are taken by the trumpets 2 – 4 inclusively. the missing note would represent the missing movement.e. The white note in the example is the one played by the second trumpet which is in motion. the trumpets play the chord shown in Figure II. Each trumpet has a specific gesture that passes from one to the other until they all reach a different gesture. Even though I do not use any pre-defined ‘pitch pool’. The concept of ‘gesture’ is not only applied to the musical material.3b. Figure II. where the second trumpet is moving off stage. The position of the listener within 54 . the visual and theatrical side of the piece is explored.3c. but as there is no trumpet player in motion. playing repeated intervals and notes which are unrelated to the general harmony. Trumpet 3 is silent throughout.Starting from D. trumpets 1 and 2 play the symmetrical chord shown in Figure II.3 Section 3 (from H to Q) is characterised by trumpets 1. Trumpets 3 and 4 sustain interval 11 at E and F. At E. This section does not have any defined pitches written and the players have to improvise the notes according to the musical gesture notated. The B-natural is played by the first trumpet which is in motion. trumpet 1 plays an incomplete symmetrical chord with one note missing as shown in Figure II. some symmetrical principles still apply: the three trumpets positioned offstage in a symmetrical way (see diagram in the score) are the ones playing and the percussionist (who is onstage) is conducting them.3a. each trumpet ‘contaminates’ the other by passing on its gestures) the process of transformation adheres to a quasi-symmetrical idea. This is all achieved during a process of slow transformation. If compared to the situation happening at E. The percussion retains its independent role. 2 and 4 (which are already in their new positions around the audience) taking on independent material: one gesture for each player.
Figure II. Section 4 is characterised by the complete liberation of independent musical line within the ensemble.4 shows the symmetrical harmony used in these ‘frozen/static’ harmonic moments and also justifies (symmetrically) the pitches played on the vibraphone. Figure II. The fact that all the players are distributed throughout the available space allows for a clear and contrapuntal perception of all the gestures that surround the audience. 55 . 2 and 3) are used to create harmonic discordance with these chords. and despite the fact that all of the trumpets are still separated around the performance space (please note that trumpet 3 and the percussionist are kept onstage throughout the piece). there is a gestural convergence. their duration indicated. Figure II. all the trumpets are unified in a common gesture in favour of a general sonority. Each player has independent material that is superimposed in a quasi-chaotic way.e. Section 5 (from U to the end of the piece) there is the use of symmetrical harmony alongside the natural harmonic series.4 In the final part of Gestures III: (untitled).5 shows the symmetrical chords played by the trumpets. All gestures used in the fourth section. At P it is beholden on the vibraphone to once again prepare the transition to the new section by virtue of the reintroduction of symmetrical harmony. culminate in material which is placed within bars marked with repeat signs. The proportions used to govern each change of gesture played by the trumpets are calculated in seconds and used in an irregular way. In Section 4 (from Q to U) I revisited an old solo trumpet piece Dialogues (2006) in order to ‘borrow’ some gestural ideas which I thought would complement the dramatic nature of the narrative I had set up in Gestures III: (untitled). The remaining gestures (natural harmonics and unidirectional lines using intervals 1. At this point. i.the audience also has an important role: their own perception of the musical discourse dependent on where they are in the auditorium. regardless of character.
etc. The idea of symmetry is also perceptible in the musical notation: once Sections 1 (first) and 5 (last) are the ones with conventional notation. With respect to the harmonic language. The way in which the narrative of the piece is allowed to progress through the preconceived structure I prepared for it should allow for the focus of the listener to be drawn to the central themes of movement (as they are expressed in physical gestures) and visual symmetry (dependent on the offstage positioning of the players).Figure II. As for the general form. there is no direct symmetrical relation within the musical material used.e. defined metres. The central sections are written with free notation and use quasi-improvisational material. i.5 In this analysis it has been my express intention to systematically show the pitches I generated and the ways in which they were subsequently used. a ‘symmetrical journey’ is implied by the trumpets which start onstage in front of the audience and end the piece moving out of the performance space behind the listeners. 56 . Gestures III: (untitled) exhibits the most consistent formal planning with regards the harmonic fields which characterise each section. for example) whilst coming to what could be convincingly termed a ‘gestural consensus’ at the end of the piece. However. whereby it is clearly evident that the instruments assume more and independent roles (soloistically inclined melodic lines in the trumpets. the exploration of musical gestures was always at the heart of my compositional aesthetic. the use of symmetrical chords acting as the predominant unifying agent within the work as a whole. One may also note that simple elements of symmetry can be seen in terms of instrumental function.
III. Loose messages is intentionally written in order to show different musical objects at any given time. the most fragmentary work in my oeuvre. 62 ‘Mosaic form’ refers to the juxtaposition of contrasting musical gestures [for example. also serving as an instrumental study for the afore-mentioned opera. at other times I sought to create ‘distance’ between the different instrument’s relationships to one another. 60 See ‘Commentaries – Fragmente-Spiel’.e. Loose messages represents a kind of summary of the two pieces previously analysed (therefore. Some of this material then ‘ramifies’. superimposed. Written in ‘mosaic form’62 (in contrast to the more linear narrative which characterises the majority of my other work). juxtaposed. abstract messages. The use of musical ‘fragments’ together with the superimposition of gestures in order to create a soloistic and/or ensemble dichotomy. I believe. 61 57 . sometimes there is a focus on the group’s homogeneity. Unlike Fragmente-Spiel for solo flute (2008)60 which is intended to be a game of fragments. after their initial placement within the narrative are then varied. providing a more heterogeneous (soloistic) sonority. The major difference between these two pieces is in the choice of the final formal progression. This work is in an attempt to consolidate ideas that had accumulated in my mind. By contrast Loose messages is formally organised with the juxtaposition of different musical fragments (or ‘messages’) chosen entirely by the composer and thus not conforming to the idea of ‘open form’ previously explored in the earlier Fragmente-Spiel. i. See ‘Commentaries – Os mortos viajam de metro’. Loose messages was composed after a long period of little creative activity where I was already ‘pre-composing’ the opera Os mortos viajam de metro61. the constituent statements in turn forming dialogues with one another as they pass through the ensemble like distorted. were considered the fundamental aspects in the work’s construction. harp and string quartet (2009) Loose messages is. Loose messages uses material which functions in a similar way to a series of small statements which. though even then the choice is governed by certain parameters. aspects concerning composition already mentioned will not be repeated): Fragmente-Spiel and Gestures III: (untitled). Stravinsky’s Symphonies of Wind Instruments (1920)] as opposed to a more linear/continuous succession/development of the musical material. etc. The ensemble is used to create a seeming narrative of ‘discontinuity’. In Fragmente-Spiel the order in which the 24 different fragments are performed is given to the performer. Loose messages for flute.
focusing on one section at a time. this piece is mainly built upon superimposed gestures played by the individual instruments with a specific focus on timbral differentiation. The following analysis of Loose messages.1 63 The character α (Alpha) was used to differentiate the introductory element. as well as the subsequent subsections. 58 .1. mainly in the use of similar textures and also in terms of notation. it is convenient that this analysis is presented in parts. The piece is divided into three sections. Figure III. the first two sections are subtly connected and the last is a quasi-independent section: Section 1 – Introduction (homogeneous strings) Section 2 – (heterogeneous tutti) Section 3 . as shown in Figure III. As previously stated.(heterogeneous/homogeneous tutti) As a consequence of the individual thinking in the composition of each of these sections. This short section has five musical gestures (or subsections) separated by general pauses: α63 – A – B – B – A. will focus mainly on the formal planning and how this determined the choice of instrumentation and musical content. Section 1 (from the beginning to C) Section 1 (first page of the score) works as an introduction and features the string quartet only. specifically regarding the use of independent lines.Loose messages was commissioned by Sounds New Contemporary Music Festival 2009 – Polish Connections and clearly shows the influence Polish composer Witold Lutosławski has had in my music.
This section is divided into five subsections. 4 and 665. The harmony chosen for the harp material took into consideration the operating characteristics of the instrument.There is a purposeful break in the symmetry of the subsections (gestures) in order to create a formal imbalance at the micro-level. Subsection α is not recapitulated in the end as one would expect (by the suggested symmetrical pattern). Section 2 (from C to K) The introduction of section 2 should surprise the listener: not only its microstructure imbalance (asymmetry) with section 1 but also by the sudden inclusion of both the harp and flute. Subsection α represents a ‘strange object’ within the micro-structure planning. exploring the register of the instrument and using intervals 1. seeking a macro-structure whose durations are balanced. In all of the three musical gestures (α. The harp’s gesture is presented with arpeggiated symmetrical chords based on the intervals 2. A and B). it might not be possible to ‘feel’ these differences as they are stated. the numbers are respectively. And the musical gesture of the violoncello is characterised by melodic lines. 2. It is worth examining the duration (in seconds) of each of these subsections. The use of these proportions only serves for the formal planning. 65 The summation of these intervals total 12 and thus correspond to the octave. each of them with individual characteristics. the acceptance of the octave helped to maintain the symmetry. E. F and H respectively. 59 . The gesture of the flute is essentially based upon the ornamentation of F4 by intervals that became increasingly larger. To facilitate the comprehension of the division of these subsections. where number 21 appears in the extremes and the smaller numbers of the series appear in the centre. the quartet functions as one unified instrument. Section 1 is also characterised by the homogeneity of the string quartet whose individual instruments contribute to the ensemble’s general sonority. D. Subsection C: characterised by the use of a trio with independent material (soloistic). 64 It is possible that the accuracy of these numbers will not be understood during the performance and consequently. constituting an exception or anomaly. All these numbers belong to the Fibonacci series and also underline the symmetry between the subsections A – B – B – A: 21 – 3 – 5 – (21+1). This is done with the express intention of ‘surprise’ when section 2 begins. the rehearsal letters in the score will also be used to name the five subsections. 7 and 11. these subsections start at C. aided with the initial punctuation (col legno battuto) of the two violins and viola. Thus. 13 – 21 – 3 – 5 – (21+1)64.
i. without defined time signature. followed immediately by a 10-second general pause. Subsection H: characterised by the use of (flute + viola) + soloistic material on harp. Subsection F: characterised by the uniformity of the string quartet material (one gesture only) + simple scalic passages on the flute66 + chordal gestures (each preceded by grace notes) on harp. applying 66 The flute plays scales representing the Portuguese knife sharpeners who walk around towns with a bicycle whistling similar tunes on their pan flutes.e. allowing for a sense of freedom to the execution of the solos.2 shows the formal scheme at the micro-level used in section 2 of Loose messages. Subsection E: characterised by the use of violin I + harp with independent (soloistic) material. Subsections C. These three subsections use ad libitum notation. starting with echoes from the other instruments (except violoncello) whose gestures started in the previous subsection. 60 . These two subsections use time signatures and tempo markings.2 Figure III. The subsections D and F present a homogeneous use of the string quartet (one gesture for the whole quartet) contrasted with independent gestures on the flute and harp. Figure III. E and H are characterised by the exploration of superimposed heterogeneous solos (in a trio – duo – trio. respectively). ending with a ‘pointilistic’ gesture (sempre staccato) expressed throughout the ensemble.Subsection D: characterised by the uniformity of the string quartet with one gesture only + flute with a ‘pointilistic’ gesture (staccato) + harp with arpeggiated chords.
The use of symmetry with regards the micro-structure of section 2 should be clear. M. Violoncello – material used at C (section 2). with the addition of tremolo. Subsection K Flute – material used on the strings at B (section 1).e. E and H (with the 10-second pause) last a total of 140 seconds. Viola – material used at A (section 1). String quartet – homogeneous texture. with the addition of tremolo. 61 . Violin I – material used at A (section 1). L. (utilising the expressive capacity of the instrument whilst at the same time acknowledging the cultural associations of this gesture). the total duration of subsections D and F is 70 seconds. Viola – ‘pointillistic’ material used by the flute at D (section 2). The first two are characterised by the heterogeneity of the ensemble where the superimposition of gestures used in the first two sections of this piece are contained. with only one new gesture. Harp – new gesture: glissandi. this influenced the choice of instrumentation as well as the integral character of the musical gestures used. i. It is worth noting the duration (in seconds) of these subsections: subsections C. Violin II – material used at α (section 1). N and O. Violoncello – ‘pointillistic’ material used by the flute at D (section 2). Harp – arpeggiated material and intervals used at C (section 2). Violin I – material used on the strings at B (section 1).a more accurate rhythmic expressivity to the ensemble. Subsection L Flute – tacet. half. Violin II – material used on the strings at α (section 1). Subsection M Flute and Harp – tacet. Section 3 (from K to the end of the piece) This section is also divided into five subsections: K.
The exception is seen in subsection O which does not correspond to this succession. harp and violoncello – tacet. Figure III.3 Figure III.3 shows that there is a diminution/decrease in the number of the instruments used in each subsection. disconnected from the others. This last conclusive ‘loose message’ is differentiated from the rest not only by its musical character but also by the textural use of the ensemble. Harp and string quartet – a dual texture of melody (violoncello) and accompaniment (harp. violins I. Again I wish to draw your attention to the individual subsections’ duration (in seconds): M is half of K whilst O is half of L. with only one new gesture. String trio – again homogeneous. It is interesting to observe the symmetry in this example: the piece starts with a musical gesture (α) which represents an exception to the micro-structure planning of section 1 and ends with a dual texture of melody and accompaniment (O) that. resulting also in a diminuendo in terms of dynamic and of contrast in the gestures used. Figure III. as 62 .4 presents the formal scheme of the whole work at the macro-level. incorporating the micro-level formal schematics of the preceding three sections into the whole. constituting a quasi-independent musical object. Subsection O Flute – tacet.Subsection N Flute. The exception here is subsection N: a smaller duration which does not correspond to the prevailing mathematical scheme. II and viola).
the balance being in the central section. It is also possible to observe the total duration (in seconds) of the three sections: 64 – 210 – 85 respectively. it is the middle section which. by virtue of its greater length. also represents the exception of the micro-structure planning of section 3. Perhaps unsurprisingly. assumes the core of the work’s weight and importance. Note that the formal exceptions appear in sections 1 (1 + 4 subsections) and 3 (4 + 1 subsections). 63 .previously stated.
or segue into one another creating a sense of transformation from one gesture to another. their own intervallic and harmonic characteristics and. to superimpose these with others from within the ensemble. choice of instrumentation used for each subsection. encouraged within me the freedom to assign independent gestures. The subsections are disconnected from one another and link like ‘flashes’: either they are separated by pauses.Intending to complement the previous analysis (which concentrated on harmony and gesture) the present commentary on Loose messages aspires to demonstrate the application of principles of proportion and symmetry found in formal planning at both the micro and macro levels in relation to the density of musical gestures. once established. I believe that the musical discourse of this piece justifies its title. The use of a symmetrical stage layout (see score) and the concern to allow for the timbral individuality of each instrument to stand out/emerge from the ensemble. 65 . The creation of a multi-layered texture not only lends the work a multi-dimensional character but also achieves the density of counterpoint between the instruments I desire. and in the importance given over to total and constituent duration(s).
referring to the fascination Freud had with cocaine when he was alive.IV. This idea was very appropriate to the musical universe I intended to create. The two sisters begin a psychoanalytical dialogue and end up snorting Freud’s ashes as two drug addicts. almost independent of the voices. The form of the piece is clear: 67 ‘The two women of Sigmund Freud’. Although the librettist already conceived the majority of his ideas concerning the plot. Portugal. The two female characters are Martha Freud and Minna Bernays: Sigmund Freud’s wife and her sister. Martha had read a newspaper headline which referred to a love affair between Freud and her sister. The music explores a sound world which was appropriate for a dramatic setting in a cemetery. we both explored certain thematic ideas I had in mind: a macabre theme and only two female voices. See the score in Appendix for an English translation of the libretto. providing a quasi-static landscape. As duas mulheres de Sigmund Freud won first prize which consisted of a commission for a full-length opera: Os mortos viajam de metro68. sopranos. The music played by the orchestra works as a ‘third’ extra character. Five of the short operas entering the competition were then selected for a stage performance where the jury would decide the winning work. One hundred years after their deaths the ghosts of the two sisters meet in a cemetery. 13 minutes) for two female characters and chamber orchestra. Having selected the composers. the organisers of Opera in Creation 2008 then assigned each one his/her own librettist to create a short scene (As duas mulheres de Sigmund Freud). written in collaboration with the librettist Armando Nascimento Rosa. Armando Nascimento Rosa (who is an established playwright) likes to ‘resurrect’ deceased non-fictional characters on stage. 68 See ‘Commentaries – Os mortos viajam de metro’ in the next chapter of this thesis. 66 . This piece was composed for the Opera in Creation 2008 competition. held at the São Luiz Theatre in Lisbon. Minna. As duas mulheres de Sigmund Freud67 [short opera] (2008) As duas mulheres de Sigmund Freud is a short opera in Portuguese (ca.
The Conclusion recovers musical material presented in the Introduction. Apart from the ‘sound effects’ played on the bowed suspended cymbals and another on the horn (depressing the three valves 67 . The Dialogues destabilise the idea of formal symmetry as there is a sense of progression in the musical material used in the central sections. whose clear and incisive strike starts the third part of the Introduction. the gesture is given more resonance and hence timbral consideration (and in so doing enhances the already striking nature of the pizzicato) by using open strings.1) Introduction – A 2) Dialogue (first part) – B 3) Dialogue (second part) – B’ 4) Dialogue (third part. the harmony is somewhat static in the third part of the Introduction. recitative) – C 5) Conclusion – A’ The form is organised in a quasi-symmetrical way. The Introduction is divided into four distinctive and contrasting parts. This furious gesture is interrupted by the suspended cymbal. Figure IV.1 With the objective of creating a ‘ghostlike’ musical atmosphere. symbolising the inconclusive post-mortem. though contrary to my overall harmonic planning does evidence my concern for exploiting fully each instrument’s own individual capacities and characteristics. The Bartók pizzicato on the strings functions purely as an effect/gesture and does not relate to the harmony. with no development.1 shows the eleven-note symmetrical chord played by the woodwind (broken chord) and brass (repeated notes). one single gesture) which prepares the way for a musical ‘explosion’ given to the orchestra (second part) one bar before A. starting with a solo tam-tam tremolo (first part. Figure IV. the inclusion of which.
The use of the natural resources of an instrument to create an independent musical layer is a recurrent theme in my music. Departing from the interval played by the trumpet (interval 3). this time an orchestral tutti (fourth part). The use of symmetrical chords with natural harmonic series usually enriches the way of following a harmonic progression. In the specific case of this section.halfway creating a sound usually known as ‘the wolf’s howl’69). making it more complex in its perception. this was an idea which aided me greatly in the long-term harmonic planning of this piece. The intervals used by the 69 For an example of this effect see Olivier Messaien’s Appel Interstellaire from Des canyons aux étoiles… (1971). where Mahler and Freud met for the first time. Working with two or more different approaches to harmonic thinking simultaneously will obviously allow for greater contrast when one ‘switches’ to a section with only one harmonic approach. the natural harmonics on the double bass are used together with the artificial harmonics played by the remaining strings. destabilising the harmonic symmetry created by the quartet. The harmonic reduction of the third section of the Introduction can be seen in Figure IV. the notes used by the remaining wind instruments complete the total of 11 different pitches that are used in fixed register. The strings (except the double bass) nearly always progress symmetrically as a different layer of musical material. attaining a unison that will prepare the onset of section B (first part of the dialogue).2 The third part of the introduction is also interrupted by a strong and violent gesture.3) and all the notes of this chord progress to F3. Figure IV. the trumpet announces a musical gesture taken from the first movement of Mahler’s Fifth Symphony Trauermarsch (‘Funeral March’) thus underlining the sense of context/space as well as actively seeking to allude to a specific time: early twentieth-century Vienna. The chord used here is a symmetrical twelve-note chord (Figure IV. 68 . These eleven notes are not disposed symmetrically and work as a static ‘harmonic field’ where the notes are played with some considerable time elapsing between them.2.
These lines are constructed with intervals already contained in the harmony played by the orchestra. Intervals 2. The F3 is present in all ‘harmonic fields’ used so far and will have major importance in the following sections as well.4a shows the harmonic progression of section B (at E) and the roots of its construction (the prominent use of interval 7). 4. 7 and 10 are also used but much more sparingly. thus constituting a kind of ‘tonic’ (i.e. 6 and 11.instrumental ensemble to reach F3 are mainly intervals 1. It is also possible to extract some symmetrical harmonic principles out of the melodic lines as shown in the Figure IV. The melodic lines of the sopranos are placed on top of this harmonic progression. The ‘alien’ melodic notes to the harmony are ornamental notes which create contrast (dissonance) within the harmonic field that is being played. Other instruments sustain some of the notes being sung by the soloists creating a sense of heterophony or echo. However. Figure IV. Figure IV.4b. these ‘strange’ notes usually keep the same intervals already contained in the harmony. polarising note) used throughout the piece. 3. 69 .3 In section B and B’ the principles of symmetrical harmony are used to generate the chord progression in order to create a ‘landscape’ (or kaleidoscope effect) in the orchestra.
but they have the potential to be added together as one larger aggregate: a completely new symmetrical chord. is based on the harmonic progression shown in Figure IV.4 Section B’. are all constructed from a common pitch and all use the same intervals) are added up. Figure IV.Figure IV.5. resulting from simple mathematic principles of subtraction (11 – 4 = 7). The process by which one achieves this is rather simple: the four chords (all of which contain only four pitches. there is a repetition of the same idea explored in the second part of the Introduction.5 At R. this time without the repetition marks. There is a common note (F3) which is used to link the chord progression of the section. starting at M. the fact that all the harmonic and melodic material of this piece is related to F3 gives this note a strong attraction and a ‘point of repose’. Although there is no use of tonal functions. This ten-second bar works as a bridge 70 . This equals another symmetrical chord with 9 notes with a new interval (7). The four symmetrical chords are used one at a time.
This musical gesture can be seen often in my music: ornamenting a chord by surrounding the main pitches with a series of quasi-grace-notes. the sopranos respond with simple melodies. with little gestures varied throughout the orchestra. This section is first characterised by its extreme static quality.6 The conclusion of this short opera begins at U. the strings constitute an independent layer of musical material.Dialogue III) has a quasi-recitative flavour with chords played on the vibraphone followed by melodies sung by the sopranos. The same principles of the third part of the Introduction apply (see Figure IV. The vivid gesture played by the woodwind and brass at S and T can also be analysed symmetrically as shown in Figure IV. all maintaining independent melodic lines consisting of small intervals.6a shows the harmonic progression of this section with the chords played by the vibraphone.2 above). The use of this gesture underlines the phrase “The rest is neurosis” which is a reference to Shakespeare’s Hamlet. The last section (C . The strings play moving clusters in order to contradict the static quality of the music played by the rest of the ensemble.for the penultimate section. similar to what happened in the second part of the Introduction. Figure IV. It is worth noting the parallel chord progression on the woodwind one bar after U as shown in Figure IV. After the chord played on the vibraphone. where Hamlet says in scene II: “The rest is silence”. the notes of which are extracted from the previous harmony.7.6b. Figure IV. The homogeneous symmetrical chord 71 .
allows for the creation of a degree of ‘black humour’ and consequently. Figure IV. underlining the intention of symmetrical formal planning. The piece ends with a lyrical melody played by the violoncello. with the exception of the horn solo (three bars after U) and the violoncello solo (starting four bars before the end of the piece). In the next chapter importance will be given to the symbolic aspects related to symmetrical resources in connection with dramatic intentions. The element of subtle humour inherent in the libretto allied with a music whose character is static and induces the sense of the macabre. this last section is based upon the same principles used in the third section of the Introduction. These melodies are clearly influenced by the same intervals used in the soprano lines. internal contrast within the work as a whole. Both melodies were intentionally left to the concluding part of the piece in order to give the idea of reminiscent melodic phrases arising from the sopranos’ silence.7 As referred to previously. an echo if you like. The use of fixed-register-notes (symmetrical and/or non-symmetrical) gives an unavoidable static quality to this piece. 72 . The use of symmetrical elements in this piece is simpler than in the others analysed thus far. one that I deliberately sought to achieve and which I feel complements the dramaturgical aspect of the work. constituting in itself one ‘voice’. The harmony of this short opera can be reduced to a small number of chords which characterise the different sections.constructed with interval 7 is moved down the register in parallel motion (using intervals 4 and 1). It is worth noting the lack of clear melodic material within the orchestra.
and stage direction by Paulo Matos. It was premiered on the 9th April 2010 at S. to such an inhospitable spot.V. with the Portuguese Symphony Orchestra conducted by João Paulo Santos. She has lost the memory of who she is or who she was and is only driven by the all-consuming idea of her own suicide. Luiz Theatre by Raquel Alão. long abandoned by the living. with libretto by Armando Nascimento Rosa. Susana Teixeira. 73 . They are ghosts of 70 71 ‘The dead travel by metro’. and to my sister Inês. who wisely balanced the hours of my days. there are also other characters. Short synopsis In a long since abandoned tube station. In this underground metro station where trains no longer pass through. after the short-opera As duas mulheres de Sigmund Freud being awarded the first prize in the Opera in Creation 2008 competition71. the rainy and the sunny ones. a Young Suicidal Woman wants to bring her life to an end with a revolver. See ‘Commentaries – As duas mulheres de Sigmund Freud’. The following analysis will comprise a symbolic description of the musical material and its formal position within the whole. Os mortos viajam de metro70 [opera in one act with prelude] (2010) Os mortos viajam de metro is dedicated to my parents. but none of them knows what brings them there. It was commissioned by São Luiz Theatre in Lisbon. Margarida Marecos. this chapter is presented in order to exhibit other issues related to operatic musical composition. Characters Young Suicidal Woman/Ophelia Florbela Espanca Virginia Woolf Agatha Christie Sylvia Plath Sarah Kane The opera is set in a disused tube station. Sandra Medeiros and Sónia Alcobaça. Alda and Carlos. Madalena Boléo. In order not to repeat what was said thus far. See the score in Appendix for an English translation of the libretto. Os mortos viajam de metro is an opera in one act with prelude (in Portuguese).
Sarah Kane. [scene 4] – Agatha Christie VII. Among them. none of them knows the identity of the Young Suicidal Woman. Sylvia Plath and Sarah Kane. [conclusion] 74 . Sarah Kane. Sylvia Plath. Sarah Kane XIII. which may offer the key to release them from this strange limbo. Agatha Christie VIII. Florbela Espanca. However. Agatha Christie XVII. the connections between poetic creation and the urge for death are fictionalised in a serious and lyrical parody giving voice to feminine icons of our collective consciousness. [scene 10] – Agatha Christie. Young Suicidal Woman XI. Sarah XII. is also Agatha Christie trying to solve the mystery. [introduction] IV. [interlude] XVI. Florbela Espanca Virginia Woolf. Virginia Woolf XIV. [scene 7] – Sarah Kane. Florbela Espanca. [interlude] IX. [scene 2] – Florbela Espanca V. In this opera for six female singers. [scene 12] – Young Suicidal Woman. [scene 11] – Agatha Christie. Virginia Woolf. In order to understand who this lonely young girl is it is necessary to decipher the name of their surroundings – namely the metro station. Virginia Woolf XV. [scene 9] – Sylvia Plath. [scene 13] – Kane. [scene 14] – Virginia Woolf. [scene 3] – Virginia Woolf VI. Formal organisation and musical symbolism The opera is divided into 19 movements as shown below: PRELUDE I. [scene 8] – Virginia Woolf. Agatha Christie XIX. [scene 6] – Young Suicidal Woman X. Young Suicidal Woman (Ophelia). Florbela Espanca. [scene 1] – Young Suicidal Woman ACT III. [introduction] II.female writers. Sylvia Plath. Virginia Woolf. Florbela Espanca XVIII. Sarah Kane. by which singing is the only means of communication with each other. whom have committed suicide: Florbela Espanca. Sylvia Plath. [scene 5] – Sylvia Plath. Agatha Christie.
without any intervallic relationship with the rest of the musical material (introducing a small theme developed at the end of scene 7). both trumpets and both bassoons. 2. the remaining five are purely instrumental.The music is continuous. trombone. Violas’ melody (interval 1). The constituent material is exactly the same and consists of five juxtaposed gestures: - 1.e. playing upon the audience’s perception and memory: the Prelude’s Introduction introduces the first character who commits suicide with a revolver. Repeated note (F3) and symmetrical chords played on second horn. violoncellos and double bass. The musical material used in the Introductions [from the beginning of the Prelude to rehearsal mark 2 (Introduction 1) and from the beginning of the Act to rehearsal mark 24 (Introduction 2)] can be considered to be a leitmotif serving to represent the metro station. i. It also appears in a shortened version in the two Interludes [from rehearsal mark 40 to 42 (Interlude I) and from rehearsal mark 72 to 74 (Interlude II)]. Quarter-tone glissandi (emerging from a symmetrical chord) on first horn. save for a pause between the Prelude and Act. ‘against’ the harmonic field. The Introduction of the Prelude and the two Interludes function as instrumental preparations for the entrances of the Young Suicidal Woman (referred to as YSW for the remainder of the chapter). The macro-form of this opera could be understood as follows: A – Prelude: [introduction] and [scene 1] The opera starts with an orchestral introduction which sets the general mood of the drama. The Introduction to the Act is an exact repetition of the Introduction to the Prelude. 3. By using exactly the same introduction for the beginning of the Act my express intention was to create the same emotional ‘background’ to serve as a link (to show a clear psychological bond) with the new character who enters in scene 2. 75 . All the movements described as ‘scenes’ involve the characters.
parallel movement of a symmetrical chord. while the others are used mainly colouristically and on occasion as a disruptive ‘effect’. 5.1 After the presentation of these musical gestures.1 shows a harmonic reduction relating to the five afore-mentioned gestures. I deliberately maintained the same orchestration for the above gestures each time they appear in the score so as to strengthen their characterisation. this gesture is recurrently used in my music. Melody on strings (violins and violas). 76 .4. the orchestra culminates in a climax from where a new subsection emerges.6b). etc. The text presented in this scene represents the character’s last words: the 72 73 As stated in the previous chapter (see Figure IV.) contribute to the sonority of the overall atmosphere. consisting of ornamenting a symmetrical chord with small melodic intervals72. A rapid and nervous gesture on the flutes. This subsection is entirely based on the beginning of As duas mulheres de Sigmund Freud73 but with an enlarged orchestration. un-pitched percussion. Figure V. The other small gestures (piano muted string. See ‘Commentaries – As duas mulheres de Sigmund Freud’. Figure V. The five gestures listed above work in a very systematic way. Scene 1: This is characterised by the four attempts from the YSW to end her life with a revolver. oboes and clarinets. horn valves effect.
At the end of the fourth suicide attempt the same melodic material (as sung by the YSW at the beginning of this scene) is ‘re-played’. By seemingly recapitulating at this point I devised a way in which to directly influence the audience’s perception of the narrative. From this point onwards. The second chord of the example shows a certain imbalance in terms of symmetry although does retain the regularity of proportions used hitherto. The musical gestures of this scene are mainly based on the YSW’s first attempt to commit suicide (scene 1) with variations of the musical material and occasional insertion of new gestures.2a) introduces the entrance of a new character: Virginia Woolf.last will and testament. particularly by way of introducing the character of Virginia Woolf to the action. At the end of this scene the gesture played by the strings (Figure V. this gesture will be recurrently used throughout the opera. Figure V. the material of the first attempt inspires scene 2. Florbela Espanca’s material at the beginning of scene 2 uses exactly the same melodic intervals as those at the beginning of scene 1. Thus. namely that this new character was also going to attempt to commit suicide. Agatha Christie (scene 4) and Sylvia Plath (scene 5). and the material of the fourth attempt inspires scene 4. 77 . The fact that the Prelude ends with an orchestral explosion (without voices) also gives symmetrical formal coherence to the first part of the opera. thus creating a sense of formal symmetry. The four attempts are musically presented in four different subsections of the scene which will influence the musical material of the whole opera. as mentioned before. the material of the second attempt inspires scenes 3 and 5. intimating the sense of recapitulation. In this section of the opera four of the characters introduce themselves through either solos or duos: Virginia Woolf (scene 3). B – Act: [introduction] to [scene 5] As indicated above the Act starts with the same introduction which prepares the entrance of Florbela Espanca (scene 2).2b shows the intervallic analysis of the chords used to generate the musical material played by the strings.
serving as harmonic support (or foundation) from whence the melodic lines emerge. symbolising the simplicity of this character. The music. Figure V. describing the conversation the characters are having.2 Scene 3: This is a dialogue between Virginia Woolf and Florbela Espanca which serves to introduce the two women to each other and the audience. based on the YSW’s fourth suicide attempt.Figure V. Like the gesture in the previous example.3) introduces the entrance of a new character: Agatha Christie. is simple and sparse. The general musical gesture is based on the YSW’s second suicide attempt from scene 1. this one too is recurrently used throughout the opera. see Figure V. At the end of this scene the gesture played by the solo violoncello (constructed from successive symmetrical chords using intervals 7 and 1.3 Scene 4: This is a recitative where Agatha Christie reveals the reasons for her being here: there is a woman constantly attempting to commit suicide whose identity is a mystery needing to be solved. 78 .
The first Interlude begins with an expressive gesture played by the first violin (solo) and it is harmonised by the remaining strings. The orchestral music serves again as a ‘harmonic foundation’ to the vocal melodies. The gesture played by the solo violoncello is taken from As duas mulheres de Sigmund Freud and Loose messages (although here it is based on different intervals) and prepares the first Interlude (Figure V. all the characters converge on stage leading to conflicts and/or passionate encounters. This part of the opera is the most dynamic. underlining the use of this specific atmosphere whenever a scene is characterised by dialogues introducing new characters. characterised by its ferocity. the scene is characterised by the use of melismas as well as all round virtuosity. increasing in both levels of intensity and numbers of characters involved: - Scene 6: Here there is a recapitulation of a variation of the material from the first scene. There follows six self-contained scenes.4 C .Act: [interlude I] to [scene 11] The third part of the opera starts with a musical interlude that prepares the second appearance of the YSW who attempts suicide again. Occasionally the voices are doubled by the orchestra in order to emphasise the most dramatic phrases as well as to give more importance to specific areas of the story whose success is dependent on their clear perception and understanding by the audience. this material is juxtaposed in closer proximity than before.4). before recapitulating the musical material from the beginning of the two Introductions (as shown before). this time with a syringe. 79 . Figure V. From a vocal point of view. However. This prepares the arresting climax which will culminate in the second entrance of the YSW. there is a dialogue which introduces a new character: Sylvia Plath.Scene 5: Like scene 3.
Figure V. She is the sixth character to show up and the first one to interact with the YSW. This is the first time the five characters meet. The fractious mood is maintained from the previous scene symbolising the continual conflict between these two characters. Florbela Espanca (the only Portuguese character in the opera) is characterised by melancholic lines reminiscent of Fado Music74. almost always responds in an offensive way. The text for each character becomes shorter in this scene. often about the sea or the life of the poor. culminating in a slow waltz in G minor (Figure V. Sarah Kane (whose admiration for the work of Sylvia Plath is well documented) recognises the older woman and freely expresses her happiness at their acquaintance. The music becomes more and more expressive and lyrical. The first. These are occasionally connected with the gesture played by the solo violoncello shown in Figure V. The main characteristic of this scene is the contrast between Sarah Kane and Florbela Espanca. 74 Fado (Portuguese for ‘destiny’.5 Scene 10: This interrupts the previous moment with the entrance of Agatha Christie. 80 . After the orchestral climax (which is an exact repetition of the climax used after the YSW’s third suicide attempt in scene 1). The entrance of Virginia Woolf is associated with the idea of a ‘harmonic landscape’ used in scenes 3 and 5.3 (see above).5) which is played while these two characters dance.Scene 7: Sarah Kane enters the drama. Sarah Kane begins a vocal solo based on the Violas’ melody (interval 1) presented in the Introductions (see above). On the other hand. all endeavouring to find out the identity of the YSW. Scene 9: This begins with the nervous entrance of Sylvia Plath who believes she is being pursued. ‘fate’) is a musical genre which is characterised by mournful tunes and lyrics. Scene 8: This is the first scene to include more than two characters at the same time. whilst the music becomes more and more fragmented using different musical gestures for each line. a very active character.
this time between Virginia Woolf and Agatha Christie both seeking to identify the name of the abandoned metro station and with it also the name of the YSW. The three scenes: - Scene 12: This scene has the third and last entry of the YSW. Scene 14: This is the moment of Ophelia’s liberation and the music’s texture is written in a minimalist way. demonstrating a progressive reduction of the duration of each scene featuring the YSW. however. all the voices are unified by sharing common melodic contours whilst the orchestra obsessively maintain an ostinato.Act: [interlude II] to [conclusion] The fourth and last section of the opera begins (as in the previous section) with an interlude which prepares the YSW’s third entry. At this point however. The discovery is made by Virginia Woolf (both she in real life and the fictional Ophelia committed suicide by drowning themselves). after the climax. This last appearance is the shortest of all. evidence that there is clear intention to provide symmetrical coherence to the formal planning of the opera. this time. It is worth noting that in the Introductions and Interludes the repeated note 81 . the vocal lines between Virginia Woolf and Agatha Christie are reversed. Scene 13: This is the moment of the revelation: the name of the unknown metro station is discovered: Elsinore. The conclusion begins with a staccato and ‘pointilistic’ gesture scored for the woodwind which is followed by the regular pulsating rhythms prevalent in both the Introductions and Interludes. The final chorus represents a ritual and symbolises a typical musical gesture in opera: the unification of the voices in order to prepare the finale. but also on the regular pulsating rhythms characterising the Introductions. D . After her final vocal entry the music recapitulates the same recitative of scene 11.Scene 11: This is another recitative. – prompting the identification of the YSW: Ophelia. there is a coda. This recitative is less sparse than the one in scene 4: it is not only based on the YSW’s fourth suicidal attempt in scene 1. during which the YSW uses a knife to try and cut her wrists. The conclusion is almost a palindrome of the Introduction.
On the one hand. except Agatha Christie. 82 . The recurrent use of the same material which is superimposed. All the characters are sopranos apart from Florbela Espanca and Agatha Christie who are mezzi-soprani. It was always my intention in this work to create a musical ‘landscape’ with the orchestra for the vocal lines to both inhabit and explore.6. The characters and their vocal material All the female characters of Os mortos viajam de metro committed suicide. she is “the ghost of a ghost”: a fictional dead character. condemned to suffer eternity in purgatory as penance for their committal of a mortal sin: suicide.(effectively a pedal) used was F3 and in the Conclusion it is E3. The afore-mentioned palindrome is presented with some variation symbolising the characters’ existence: destined to endless repetition. dramatic and depressing universe. As it can be seen from the previous formal description there was no attempt to define the characters with recognisable thematic material. This theme (which I encouraged the librettist to explore fully) has become more and more important to my musical imagery. extended and reduced was applied in order to create a cyclical musical universe. Ophelia is the ‘outsider’ one that never existed in ‘our world’. The opera’s sound world shares obvious similarities with As duas mulheres de Sigmund Freud: this was intentional as the latter work was a preparatory study for Os mortos viajam de metro. All the musical material in this opera tries to reflect only one scenario. 75 See ‘Symmetrical Harmony – construction and usage’ in Section 1 of this thesis. The tessitura of the characters was planned in order to differentiate between an all-female ensemble as shown in Figure V. juxtaposed. varied. The theme of self-destruction connected to each of the characters (celebrated in real life for their creativity) prompted the exploration of a dark. reiterating what was said previously about my practice in pitch polarisation specifically in order to provide clear aural reference75.
Figure V. other melodic gestures were derived as seen in Figure V. 21 (1912). 83 . This technique was pioneered by Arnold Schönberg in works such as Pierrot Luniare. From a recurrent melody initially sung by Ophelia in scene 1 which is based on intervals 7 and 1.7. I chose to use this vocal technique for Agatha Christie as hers is perhaps the most mysterious character in the opera and I wanted this to be highlighted by the uniqueness of her articulation. result in sense of a long recitative that travels through all the scenes of the opera.6 To symbolically unify the characters (and thus highlight the enduring fact that they all share a similar fate – they are all dead) I specifically did not differentiate between the intervallic content of their melodic lines. The mostly syllabic and parlando word setting together with varied melodic contours. There was the preoccupation of making the text even clearer for Agatha Christie who sings mostly in sprechgesang76.7 The audibility and comprehension of the text was my priority when constructing the vocal lines for the opera. Op. Figure V. She represents the 76 Sprechgesang (German for ‘spoken-song’ or ‘spoken-voice’) is a musical term used to refer to a vocal technique between singing and speaking.
the vocal lines. or characters’ entrances. i. The orchestral texture is reduced during the voices’ interventions in order to allow for a clear understanding of both the text and the melodies. or simply link different gestures. On the other hand. this material takes on the mantle of leitmotif. these ‘false-beginnings’ are always perceived in a different way due to our cumulative memory.e. the contrast between sections with voice and those that are purely instrumental (where the orchestra is used to its full potential) is recognisable. These solos trigger new sections. imitating. However.detective of the group. The music written for the orchestra is manly continuous and underlines the importance given to this ‘seventh character’: either it is very much in the foreground or it provides background ‘harmonic landscapes’. As the audience begins to recognise these gestures over the course of the whole work the ‘general atmosphere’ (the musical language of the ‘landscape’) will become more familiar. thus it is necessary that her deductions should be easily heard. Thus. The solos played by the violoncello assume a very important role within the orchestra. the audience will always expect the presence of Ophelia on the stage whenever the orchestra plays the same recurrent musical material. The instrumental sections consistently give the idea that the opera is always starting from the beginning again. the vocal lines of Sarah Kane are the most ‘pointilistic’ and fragmented for the simple reason that she is the most contemporary character of them all. I feel this is justified because the vocal style is mainly quasi-recitative and therefore transparency within the instrumental density is required. 84 . The orchestration I considered the orchestra to be my seventh character in the opera: it is the instrumental music which establishes an initial atmosphere of the abandoned metro station. to a degree.
it is appropriate to reflect upon other tools and motivations also connected to musical creation.1. 80 The death of the Portuguese Nobel laureate for fiction. Despite the form of the video inspiring the composition of the piece.1. – 1.0. – Pno. they were composed simultaneously and share several compositional concerns intrinsically linking them.VI. – 1. Diurne: alter ego was the winning work of the 2010 edition of the project. including weekend workshops in both France and the UK. even though both pieces analysed here share the same compositional technical concerns analysed in the previous chapters.1. – Pno. Diurne: 1. darkness and light.1.1. for example the idea of musical discourse and its ‘psychological consequences’ with the audience./Cel. 85 . – 1Perc. Nocturne: rituel was purposely written to work as a stand-alone musical work. Diurne: alter ego was written for the International Composer Pyramid79 project and was premiered on 4th December 2010 in Canterbury (England) by the ICP Ensemble. The titles Nocturne and Diurne represent one of the oldest dichotomies in human history: night and day. the specific instrumentation is slightly different.1. This piece represents a homage to his works which I hold very dear.2.1.1. Nocturne: 1.1.1. Though both pieces arose from very different commissions.1.0. – 1Perc. I regard such ideas an important component of composition and so wish to analyse briefly what I see as the causes and effects concerning these issues. which started with a Call for Scores in January 2010.1. Nocturne: rituel & Diurne: alter ego for 15 players77 (2010) In addition to what has previously been said and in order to conclude this thesis. The piece received its world première on 26th November 2010 in Montreal (Canada).1. The following analysis will focus only on the work as a self-contained musical statement. Nocturne: rituel was written for the Nouvel Ensemble Moderne and the conductor Lorraine Vaillancourt. as so justifying being analysed concurrently.1.1. – 1.1. Though the reception of such extra-musical associations is dependent wholly on the subjectivity of the listener. conducted by Gerry Cornelius. then Diurne is characterised as being its 77 Despite the two pieces using the same number of instruments.1. If on one hand Nocturne is ritualistic and inhabits the sombre world of a funeral march80. – 2. José Saramago in June 2010 had a profound impact on me. after being selected to participate in the 10th International Forum for Young Composers Music & Art Video78. 78 This piece was written to the video Agora Obscura by David Manseau. Twelve composers were selected and given tuition and mentoring. 79 This is a three-year project organised by Sounds New and Coups de Vents.
lasting 6 bars. together with muted trumpet (Harmon mute) plus bowed suspended cymbal. it was a conscious decision on my part that each piece draw on existing material.1 shows a graphic representing the macro-structure of this piece. which is repeated four times (the first bar is repeated five times). Figure VI. Section A makes use of musical gestures which are mainly inspired by the two Introductions to Os mortos viajam de metro: 1) an insistent regular pulse where 2) sparse gestures are superimposed. D and E) have the total duration of 4’21’’. The other instruments try to ‘un-focus’ the lyricism of this melody. All the constituent sections are characterised by a single musical atmosphere that is maintained for the pre-determined period of time. ornamenting it with ¼ tones. C. the winds sustain the notes of the chord. Section C is a small variation of the previous section: the winds recapitulate the gestures previously played by the celesta and glockenspiel. notes that do not belong to the general harmony and effects such as multiphonics or the horn’s ‘wolf’s howl’82. formed of more energetic and diverse material. appreciate the capacity the existent material had (and perhaps still has) to be so substantially revised as to function in a completely new. Diurne the most ferocious and rhythmic material. The duration of section A is 5 minutes and the following four sections (B. equally viable context. the common element to all the musical material used in these two pieces is their intervallic structure. These two pieces ‘recycle’ material from Os mortos viajam de metro81 and. The piece ends with a sudden emergence of a melody on the strings.alter ego. in this case from Os mortos viajam de metro and in doing so. proportion and symmetry. 81 82 See ‘Commentaries – Os mortos viajam de metro’. based around G minor. See ‘Commentaries – As duas mulheres de Sigmund Freud’. The macro-structure in Nocturne: rituel consists of five sections. 86 . Section B is based on the movement of the strings using glissandi where fast gestures (on celesta and glockenspiel) are superimposed. ornamenting them with ¼ tone glissandi and the piano and percussion play the same notes melodically. Section D is characterised by a static harmonic field whose notes always appear in their fixed register: the strings repeat a musical gesture which appears rhythmically independent from the rest of the ensemble. taken together both works form a suite or diptych: Nocturne reuses the most lyrical and expressive elements from the opera.
Diurne: alter ego is divided into 4 sections: Section F is characterised by the fast juxtaposition of three energetic gestures. By consciously playing this musical ‘game’. aural recognition and identification of the material’s appearance is enhanced: once the musical material is not developed. which is both hypnotic and meditative. At Section I. clearly (here through repetition over a longer time span) our aural memory will recognise more readily the change to a different section. the principal one being the dual between the piano and marimba. piano and double bass. These chords are mainly taken from the end of scene 1 in Os mortos viajam de metro. 87 . by delaying the eventual transition between two contrasting segments of material. This impact is due to the idea of playing with the listener’s sense of anticipation. Once a specific musical gesture is established.2 shows the macro-structure of the work as a graphic. achieved by maintaining the same gestures for a long period of time. Section H is based on the juxtaposition of two gestures: the first is characterised by its rhythm. Section G is superficially based on Section A of Nocturne: rituel. This section is only 8 seconds long. where the gestures are transfigured and played in a more chaotic order. The work ends with a quasi-tonal melody.Figure VI. Nocturne:rituel ‘develops’ according to consonant gestures (innately established as recognisable to our ear). The intention was to establish an aural focus. underlining my recent tendency to imbue the final bars of my scores with some object/gesture redolent of a musical ‘departure’. Figure VI. the composer is heightening the individual listener’s aural perception: when the music does move/change it is consequently felt/experienced more keenly. the second by its inherent drama where the whole ensemble play dense chords. the instrumentation also owes something to a traditional jazz trio: suspended cymbal.1 Nocturne: rituel is principally characterised by its long and atmospheric section (A). I insert a musical gesture which clearly has its roots in jazz music. our consciousness has time to understand the differences between sections.
Diurne is characterised by the fast and chaotic juxtaposition of various musical gestures. The fact that the piece ends just after the appearance of this gesture underlines its structural importance: it is our lasting impression of the work. This narrative style can also be seen in films such as Being John Malkovich. In Nocturne the ‘journey’ is slow. thus ‘disorienting’ our consciousness. The piece ends in a new musical ‘world’ from that presented from the start and throughout (and even more different if compared to Nocturne). The expression ‘musical journey’ is perhaps what best defines one of the concepts behind these two pieces: the audience is transported by means of both diverse gestures and musical references. By including a musical gesture commonly found in Jazz at the end of the piece. 84 The idea of insanity: to put a character (for example. Eternal Sunshine of the Spotless Mind and Synecdoche. but also to transport the spectator to a different universe. 88 .Figure VI. in Diurne it is both fast and fragmented.2 As a contrasting response to Nocturne. The way in which my music communicates with the audience and how best I can utilise the mutually inclusive elements of surprise and contrast are key factors concerning 83 For example. the speed at which these gestures are presented means that memorising (and subsequently recognising) one type of material as distinct from another is trying for the audience. specifically in a poly-stylistic language or as simple quotation. This is a resource very much used in the temporal visual arts and entertainment (in both cinema and animation). New York all of them written by Charlie Kaufman. and used as a humoristic ‘trick’83. Adaptation. abruptly transports the audience to a completely different world. where the cutaway gags are not exclusively used to be funny. The work’s short duration also strengthens the effect of free-association of musical styles. creating contrast with the current narrative. Shakespeare’s Hamlet) in a different play (for example. the animated sitcom created by Seth MacFarlane Family Guy. in Beckett’s Waiting for Godot). Here I intend it to serve as a disruptive schism within the narrative84. The effect of the final gesture leads us to forget everything that was played before. conversely.
– all these factors together pose the musical questions that I believe it is my job as a composer to find solutions for: they are my motivation.me at each piece’s genesis. the like of which constitutes both my compositional language and. etc. the duration it requires to establish itself. which way it is going to be prepared (if at all). nor elicit a response the weight of which I try to bring to each and every composition I set out to write. the starting point is never a technical principle or stylistic conceit. my 'voice’. it is perhaps a creative idiosyncrasy influencing both the way I think about music and how I approach the act of composition itself and. The musical gesture and its position within the form of the piece. how a specific gesture will psychologically effect the listener’s perception of the piece. 89 . the way it is going to be resolved (or not). the weight it has at the moment of its appearance. as such forms the indelible mark on each and every work I write. though essentially elusive no less real. I am aware that these issues will not be perceived uniformly by everyone.

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