Microsoft Word - ME_Diss_Apr_22_part_IFourteen Bagatelles for piano op. 6: No. I, III, IV, V, VI, VIII, and XI
by
Department of Composition Eastman School of Music
University of Rochester Rochester, New York
2011
All Rights Reserved
Michaela Eremiášová (1974) was born in Prague, Czech Republic. Throughout
her studies and professional experiences as a composer of concert, jazz, and film music
she has had the opportunity to compose for various types of vocal and instrumental
ensembles, from soloists to orchestra, and in various genres and styles such as opera,
jazz, ethnic, and electro-acoustic music. Her personal study and research of various
musical traditions and techniques of composition is exemplified in the eclecticism of her
music.
Eremiášová’s music has been performed by ensembles such as Phil Wilson's
Berklee Rainbow Band, New York City Opera, the Arabesque Winds, ITB (Institut
Teknologi Bandung) Choir from Indonesia, Chamber Choir Hymni from Denmark, Duo
vio-Link-oto, Eastman Triana, Eastman Chorale, Eastman Trombone Choir, and the
Novus Quartet, among others. Here collaborations include work not only with great
performers but also with contemporary painters, poets, modern dance choreographers as
well as with experimental and mainstream film makers. One of her closest collaborators
is her colleague and husband, Colombian composer Jairo Duarte-Lopez, who is also a
PhD candidate in Composition at Eastman. Together, they co-composed and produced
the orchestral theme for the Toronto Blue Jays for the 2008 and 2009 baseball season as a
commission by Rogers Sportsnet (Toronto, Canada). In 2008, this score was broadcast
during 102 games on Canadian cable television. They also co-composed and produced
music for two documentaries for Discovery Channel Latin America. In addition, their
co-composed chamber work Car Crash Opera, for an animated film by Skip Battaglia,
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was selected as one of eight out of eighty submissions to be showcased at the 2009 New
York City Opera’s VOX Festival. In 2010, Michaela and Jairo were commissioned by
the Kurt-Weill Festival, the Eastman School of Music, and the George Eastman House, to
write music scores for live performance to eight short silent films from the 1910s to
1930s by renown European film makers Lotte Reiniger, Walter Ruttman, and László
Moholy-Nagy. The total program was over sixty minutes of music and was premiered at
the Arsenal Theater in Berlin’s Sony Center in January 2011. These scores were also
performed live at the George Eastman House and the Rochester Institute of Technology.
Eremiášová’s collaborative works with experimental film makers such as Stephanie
Maxwell, Jean Detheux, Skip Battaglia, Peter Byrne and Carole Woodlock, have been
featured in over sixty national and international film festivals such as Siggraph Computer
Animation Festival - Visual Music in New Orleans, Anima Mundi Festival in Sao Paolo,
Brazil, backup_festival in Weimar, Germany, and 27e édition des Rendez-vous du
cinéma québécois in Québéc, Canada, among others. Several of the collaborative projects
have been recognized with awards including the ASIFA Award for Excellence in
Experimental Techniques, Best Experimental/Animation/ Music Video award, Best New
Art Award, Best Impact of Music in Experimental, Performance Art and Art Films: Gold
Medal for Excellence, and Best Experimental Short award.
Since the fall of 2008, Eremiášová has been co-instructor, along with her husband, of
Film Scoring Techniques for the Department of Jazz Studies and Contemporary Media at
Eastman and has been teaching the same course at the Eastman Community Music
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School since the fall of 2010.
Eremiášová holds a Bachelor of Music in Composition from the Conservatory of
Jaroslav Jeek; a Diploma Degree in Jazz Composition from Berklee College of Music,
and a Masters in Musicology from Charles’ University in Prague. She pursued doctoral
studies at the Eastman School of Music while serving as a teaching assistant in
orchestration, and Renaissance and Baroque music history courses. She also worked as a
teaching instructor in film scoring techniques and composition. Her composition teachers
at Eastman were David Liptak and Carlos Sanches-Gutierrez. She had additional study
with Mario Davidovsky.
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Abstract
This essay is dedicated to an analytical study of the Fourteen Bagatelles op. 6 by
Béla Bartók. The main focus is based on the impact of Slovak and Hungarian folk music,
and its modal heritage, upon Bartók’s fourteen Bagatelles: No. I, III, IV, V, VI, VIII, and
XI. These pieces are analyzed with an emphasis on folk-music sources, which are the
core of Bartók’s Bagatelles. The structure and modal content of folksong are the main
characteristics of his compositional style, newly developed during the years 1904 - 1908.
The goal of this research paper is to examine Bartók’s use of modes, their
transformations and the influence of folk music on these seven Bagatelles. The selected
Bagatelles are each based on one primary mode or set of notes. The further development
of the modal property has a crucial impact on the formal and harmonic structure of the
pieces.
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Table of Contents
Section Title Page
I. Introduction 1
Béla Bartók – Life and Work in 1904-1908 2 II. Slovak and Hungarian folk music, and its modal heritage 4 Slovak and Hungarian folk music 4 Tone systems 11
III. Analyses of seven Bagatelles 16
Bagatelle No. I 16 Bagatelle No. III 19 Bagatelle No. IV 24 Bagatelle No. V 26 Bagatelle No. VI 33 Bagatelle No. VIII 36 Bagatelle No. XI 43 IV. Conclusion 44 Bibliography 46
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Example 1 Maqm Hijz, Maqm ehnaz and Verbunkos modes 7
Example 2 Pentatonic scale 8
Example 3 Pure Pentatonic scale in folksong 9
Example 4 Pentatonic scale with scale degrees 2 and 6 as ornamental 9 notes Example 5 Pentatonic scale with scale degrees 2 and 6 as real notes 10
Example 6 Byzantine Modes versus Gregorian Modes 12
Example 7 Diatonic, Soft Chromatic, Hard Chromatic and 12-13 Enharmonic Genus
Example 8 The I. authentic Byzantine mode with the letters of the 13 Greek alphabet Example 9 Hard Chromatic versus Maqm ehnaz 14
Example 10 Diatonic First Authentic versus Maqm Bayyti 14
Example 11 Turkish, Arabic, Byzantine and Western notes 15 between whole-tones Example 12 Bagatelle No. I: mm. 1 – 2 16
Example 13 Bagatelle No. I: mm. 1 – 3 17
Example 14 Bagatelle No. I: mm. 16 – 18 17
Example 15 Bagatelle No. I: mm. 5 – 6 18
Example 16 Bagatelle No. I: G half-diminished (Locrian) scale 19
Example 17 Bagatelle No. III – score 20-21
Example 18 Bagatelle No. III -Verbunkos Phrygian scale 22
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Example 19 Bagatelle No. III - melodic structure 22
Example 20 Two harmonic entities in the Verbunkos Phrygian mode 23
Example 21 Bagatelle IV in D minor pentatonic 24
Example 22 Bagatelle IV – modal transformation in mm. 1 – 2 25
Example 23 Bagatelle IV – modal transformation in m. 8 25-26
Example 24 Slovak folk song 27
Example 25 Bagatelle No. V – score 28-30
Example 26 Bagatelle No. V - Gm and Dm harmonic entities 31
Example 27 Bagatelle No. V – modal transformations 31
Example 28 G Minor Pentatonic scale 32
Example 29 Bagatelle No. V: mm. 51 – 64 32
Example 30 Bagatelle No. VI: mm. 1 - 7 34
Example 31 Bagatelle No. VI - Verbunkos Phrygian scale 34
Example 32 Bagatelle VI – modal transformation 35
Example 33 Bagatelle VI - symmetrical modal formation 35
Example 34 Bagatelle No. VIII: mm. 1 – 10 37
Example 35 Bagatelle No. VIII: mm. 1 – 4 38
Example 36 Bagatelle VIII – main motif 38
Example 37 Bagatelle VIII – axis system 39
Example 38 Bagatelle VIII – main motif in m. 24 40
Example 39 Bagatelle VIII – main motif in m. 25 40
Example 40 Bagatelle VIII – main motif in m. 26 40
x
Example 42 Bagatelle XI: mm. 1 – 7 43
Example 43 Bagatelle XI: mm. 8 – 16 43
1
I. Introduction
In the introduction of the score for the Fourteen Bagatelles op. 6, Béla Bartók
described his compositional style as “a reaction against the exuberance of the romantic
piano music of the 19th century, a style stripped of all unessential decorative elements,
deliberately using only the most restricted technical means.”1 As this quote suggests,
Bartók felt a need for change in his musical compositional style that would differ from
the traditional romantic style. The Bagatelles were composed in 1908 and are considered
the first series of short piano pieces which exposed Bartók’s elaborate new musical
language. 2 This new language involved a combination of folk and contemporary
techniques and concepts, as noted by Antokoletz in the article “The Musical Language of
Bartók’s 14 Bagatelles for Piano.”3
The Bagatelles clearly represent Bartók’s unique compositional style, which he
developed between 1904 and 1908. This stage of Bartók’s compositional career is
specifically important for two reasons. These years indicate the beginning and the
development of his folk music interest, and the rise of his new compositional style
starting in piano music, which is primarily influenced by his ethno-musicological
research.
1 Peter Bartok, “Notes of the Editor in 14 Bagatellen für Klavier,” in Béla Bartók’s 14 Bagatellen für Klavier (Budapest: Editio Musica, 1998), 40-47. The words come originally from Béla Bartók and were part of his introduction for the publication of 14 Bagatelles in 1940 which were not used in this edition. 2Grove Music Online, “Bartók, Béla, §3: 1908-14,” by Malcolm Gillies, http://www.oxfordmusiconline.com/. 3 Elliott Antokoletz, “The Musical Language of Bartók’s 14 Bagatelles for Piano,” Tempo, New Series, No. 137 (Jun. 1981).
2
The Fourteen Bagatelles, op. 6, is a collection of unconnected short piano
compositions. In other words, it is not a multi-piece that provides an organic unity of the
pieces.4 In my analysis, I am particularly interested in modal property that is primarily
based on an Eastern European modal heritage. Thus I have selected only certain
Bagatelles (No. I, III, IV, V, VI, VIII, and XI), because they best display this modal
property as a major base for the harmonic content and the structure of the pieces.
Béla Bartók – Life and Work in 1904-1908
In 1904, after his graduation from the Budapest Academy of Music, Bartók
revealed his interest in folklore for the first time. He felt that his musical language was
influenced by Romantic composers. For instance, his first opus-numbered pieces,
Rhapsody op.1 for piano and Scherzo op. 2 for piano and orchestra stylistically and
formally reflected Brahms, Strauss, and Liszt. Bartók was truly inspired by folk music
after he heard Lidi Dósa, a Transylvanian-Hungarian peasant girl singing a popular
Hungarian art song based on more complicated formal and tonal transformations. 5
Affected by Lidi Dósa’s songs, Bartók revealed himself in a letter to his sister in
December 1904: ”Now I have a new plan: to collect the finest Hungarian folksongs and
raise them, adding the best possible piano accompaniments, to the level of art-song.”6
The first sign of this change in Bartók’s compositional style can be seen in his first
4 “The idea of the multi-piece entails a sense of incompleteness in the individual pieces, but it does not automatically follow that a multi-piece thereby forms a complete whole that corresponds to a multi- movement work.” From Grove Music Online, “Multi-piece,” by Peter Foster, http://www.oxfordmusiconline.com/. 5 Bartók transcribed this folk song for voice and piano, and it was published as “Székely Folk song” in Magyar Lant, from Benjamin Suchoff, “Bartók’s Odyssey in Slovak Folk Music in Bartók Perspectives,” in Bartók perspectives: man, composer, and ethnomusicologist, 16. 6 Grove Music Online, “Bartók, Béla, §3: 1908-14,” by Malcolm Gillies.
3
publications, dated in February 1905: the setting of a Székely (Transylvanian) song Piros
alma (Red Apple) BB34, and a collection of settings of four folksongs BB37.
In 1905, Bartók received a grant for research on folk song in Transylvanian
villages and also established a collegial relationship with Zoltán Kodály. In 1906 he
collected about 120 tunes in the village of Grlice (now Gemerská, located in Slovakia in
the time of Bartók, Grlice represented a Slovak-Hungarian language border) and together
with Kodály made the first volume of transcribed Hungarian folk songs.
In the compositions written between 1908 and 1910, such as Fourteen Bagatelles,
Two Elegies, Two Roumanian Dances and Ten Easy Piano Pieces, folksong in Bartók’s
music became more than just a melody with an accompaniment; he incorporated it into a
more complicated compositional scheme, based on the formal and modal or tonal unity of
folksong. As noted by Dobszay, the greatest effect of folk music is an attachment to
modality, the great synthesis within which Bartók managed to unify the free use of
twelve notes and the widening of the results of permutational functional thinking.7 As
expressed by John Weissmann, Fourteen Bagatelles and Ten Easy Piano Pieces “may be
considered the best of introductions to modern music.”8
7 László Dobszay,“The Absorption of Folksong in Bartók’s Composition,” Studia Musicologica Adademiae Scientiarum Hungaricae, T. 24 (Budapest 1981). 8 John Weissmann, “Bartók’s Piano Music,” Tempo, New Series, No. 14, Second Bartók Number (1949- 1950).
4
II. Slovak and Hungarian folk music, and its modal heritage
Slovak and Hungarian folk music
Bartók’s intensive ethnomusicological research first focused on folk song in
Slovakian and Hungarian regions. Thus, it is suitable to assume that Slovakian and
Hungarian folk music was the main source for the Fourteen Bagatelles. This is apparent
mainly because of the fact that Bagatelles No. IV and V are actually based on folk
melodies from Slovakia and Hungary. 9 In order to better understand Bartók’s
compositional concepts in the Fourteen Bagatelles, it is important to reveal some of the
basic points of historical background and characteristics of Slovakian and Hungarian folk
music.
Slovakia is surrounded by Czech Republic, Poland and Hungary. It was a part of
the Czechoslovak Republic (Czechs, Moravians, and Slovaks) from 1918-1989. There are
three historical periods that had an impact on folk music in Slovakia. The first stage (ca
6th – 9th centuries) is characteristic for “pre-harmonic, old-style” songs that are mainly
associated with rituals to influence fate and control nature. Songs of this time were
generally based on a range of a second or third with short, repeated rhythmic formulas.
An ambitus of a fourth can be found in a repertoire of farmers’ fieldwork and harvest
songs, and songs for weddings and other rituals. A range of a fifth can be traced in old-
style shepherds’ songs in mountainous areas with improvisatory techniques. The second
stage (A.D. 863 – ca. 18th century) includes monophonic songs mainly based on Lydian,
9 Suchoff, 17 – 22.
5
Mixolydian, Hypoionian, and Dorian modes. Byzantine culture had its impact on Slavic
culture since the Byzantine missionaries Cyril and Methodius brought Christianity to the
Great Moravian Empire. The last stage (before 19th century) includes three types of
songs:
1. Songs with old-style rhythms and open construction (ABCD, AABB),
2. “New-Hungarian” style syncopated songs,
3. Songs reflecting Western melodic and harmonic influences.
The second and third types are based on closed forms such as AA5BA (A5 refers to
phrase A repeated a fifth higher). All three types of songs are based on major-minor tonal
principles.10
There was a long period of time (1526 - 1914) when Hungary, Slovakia, Moravia
and Bohemia were together as possessions of the Habsburg Empire, and later the
Austrian-Hungarian Empire. Therefore it is possible to find some musical similarities,
especially in Hungarian and Slovak folk music, in terms of strophic form, ornamentation,
modal quality, rhythm and mixed meter. The oriental aspect found in Hungarian folk
music is very peculiar however, and can be traced to different ethnic groups such as
Genghis Khan’s Mongols who reached the Carpathians in 1241, the Turks who ruled
Hungary from 1526 – 1686 (Ottoman domination) and the Gypsies who might have come
along with the Turks.
10 The Garland Encyclopedia of World Music, Europe,“Czech Republic and Slovakia,” by Magda Ferl elinská and Edward J. P. O’Connor, 722-726.
6
Due to constant interaction with various ethnic groups, political, economic and
religious changes, Hungarian folk music is certainly a great source of multiple cultural
elements. The oldest songs come from peasant music that includes old-style songs based
on the pentatonic mode, songs found in the “psalmody” style, and the “lament” style
(children’s and ritual songs, funeral laments). According to Judith Frigyesi, it is possible
to assume that these old-style songs were based on Finno-Ugric (Magyarorszg –
originally the Finno-Ugric nation) musical elements that existed before the Hungarian
conquest. 11
During the period of the Hungarian kingdom (11th – 15th centuries) the music of
the Magyars was influenced by Gregorian chants and European melodic styles. Although
there is no surviving evidence of the repertoire sung in this time, based on the influences
of all these cultures we can assume that the music had to involve Finno-Ugric, Turkish,
and medieval European folk and chant elements.12
According to Peter Manuel,13 the Gypsy community had a special impact on
secular Hungarian music. Gypsy musicians were kept as slaves by Ottoman and Eastern
European aristocrats. They specialized in a varied mixture of “exotic” and novel-
sounding melodies from different regions. They had preserved some Turkish musical
material. This may explain the occurrence of the Turkish modes, Maqm Hijz and
11 The Garland Encyclopedia of World Music, Europe, “Hungary: History of Folk Music,” by Judith Frigyesi, 736-739. 12 Ibid. 13Peter Manuel, “Modal Harmony in Andalusian, Eastern European, and Turkish Syncretic Musics,” Yearbook for Traditinal Music vol. 21 (1989).
7
Maqm ehnaz, in 17th century Hungarian folksongs.14 The existence of the so-called
Verbunkos modes15 might have developed from these types of Turkish scales, especially
the Verbunkos mode, called Kalindra. Comparing the modes Kalindra with Maqm
Hijz, we can see the identical pitch content. See example 1.
Example 1: Maqm Hijz, Maqm ehnaz and Verbunkos modes
Maqm Hijz Kalindra (Harmonic minor with lowered 2 and raised 3)
Maqm ehnaz (with Western tempered intervals)
Verbunkos Minor (Harmonic minor with raised 4) Verbunkos Aeolian (Natural minor with raised 4)
Verbunkos Dorian (Natural minor with and raised 4 and 6)
Hungarian vocal songs are characteristic for being established on a strophic
structure, and for two rhythmic styles they are usually played in: the style parlando-
rubato and the style giusto. Parlando-rubato theoretically refers to the natural rhythm of
the spoken text. Speaking of practice, the music reflects metrical line-schemes based on
poetic rhythm. When asymmetrical rhythmic formations appear, they become steady
14 “Modal Harmony in Andalusian, Eastern European, and Turkish Syncretic Musics.” 15 W. Marvin, handout, “Scales, Modes and Collections in Western Music,” from Loya Shay, “The Verbunkos Idiom in Liszt’s Music of the Future: Historical Issues of Reception and New Cultural and Analytical Perspectives” (Ph. D. diss., King’s College, London, 2006).
8
patterns within the performance. Bartók called this phenomenon frozen rubato. The
rhythm in giusto style is based on a metric framework; however, there is certain
flexibility in the durational values. Parlando-rubato occurs mainly in solo performance,
giusto is typical for choral performance. It is important to note that Hungarian songs are
usually syllabic; however, ornamentation is in many cases crucial. According to older
recordings, ornaments were much longer and structurally more substantial before the 20th
century.16
The various melodic types of Hungarian folk music include several general
characteristics such as fifth-shifting,17 the use of the pentatonic scale, and related types
such as major-mode, descending, octave-range types, psalmody and lament styles.18 All
these styles were simply divided by Bartók and Kodály into old, new and mixed styles.19
As I already mentioned, the mode of tunes in the old style can be found in the pentatonic
scale. See example 2.
Example 2: Pentatonic scale
(F) G Bb C D F (G) (Bb)
According to Bartók, there are three basic forms of the pentatonic scale in old
style Hungarian songs:
16The Garland Encyclopedia of World Music, Europe, “Hungary: Genre, Style and Performance,” by Judith Frigyesi, 740-741. 17 Ibid. In other words, fifth-shifting refers to a melodic structure where the second half of a melodic line appears a fifth lower in the exact or tonally adjusted version of the 1st melodic line, found in László Vikár, “What Is Old and What Is New in the Traditional Music of the Volga-Kama Region,” Studia Musicologica Academiae Scientiarum Hungaricae, T. 37, Fasc. 2/4 (1996). 18 The Garland Encyclopedia of World Music, Europe, “Hungary: Melodic Types,” by Judith Frigyesi, 741- 742. 19 Béla Bartók, “Hungarian Folk Music,” transl. by M. D. Calvocoressi (London: Oxford University Press, 1931), 11.
9
Example 3: Pure pentatonic scale in folksong
2) The pentatonic scale, in which the scale degrees 2 and 6 appear as ornamental
notes – see example 4.21
Example 4: Pentatonic scale with scale degrees 2 and 6 as ornamental notes in folksong
3) The pentatonic scale, in which the scale degrees 2 and 6 appear as real notes.
However they usually appear on a weak beat, never at the end of a melody. The
20 Bartók, 10-11. 21 Ibid.
10
appearances of additional scale degrees transform the pentatonic scale to Dorian,
Aeolian, or Phrygian modes. See example 5. 22
Example 5: Pentatonic scale with scale degrees 2 and 6 as real notes in folksong
The dominance of pentatony in Hungarian peasant music was first recognized by
Kodály. As he points out, pentatony is the fundamental layer of the Hungarian melopoeia.
The rhythmic aspect comes from dance and language. 23
22 Bartók, 17 – 18. 23 Zoltán Kodály, “Folk Music and Art Music in Hungary,” Tempo, New Series, No. 63 (Winter, 1962- 1963). “Melopoeia is the art of forming melody; melody; -- now often used for a melodic passage, rather than a complete melody.” found in http://dictionary.reference.com/browse/Melopoeia.
11
II. Tone systems
There are two important tone systems that had a crucial impact on Eastern
European modal development: the Byzantine and Arab systems. Both systems share the
same heritage of the Greek tone system.
The Byzantine system of eight modes, the Oktoechos, is ascribed to John
Damascene (676 – ca754 A.D.). In fact, it goes back to Oktoechos of Severus, the
Monophysite Patriarch of Antioch (ca. 512-19 A.D.). The Oktoechos also means a
liturgical book of the Eastern Churches, in which the hymns for the cycle of eight
consecutive Sundays are arranged in accordance with the eight modes. It is a remnant of a
calendar system used by the Sumerians, Akkadians and other ancient nations of West
Asia. The origin of this calendar, called the Pentecontades Calendar has a conception of
seven seasons and seven winds. Each wind corresponds to a god. The Ogdoas, a supreme
divinity ruled over these seven gods as it is mentioned in the Eighth Book of Moses.24
The set of eight notes consists of two sub-groups, the authentic tones and the
plagal tones. Each of the plagal tone is related to its corresponding authentic tone.
Therefore, the first four tones are the authentic tones and the second four are the plagals.
24 Hans Wilhelm Haussig, A History of Byzantine Civilization (New York: New York Press, 1971), 70.
12
Byzantine modes Gregorian modes
I. authentic I. Dorius
II. authentic III. Phrygius
III. authentic V. Lydius
IV. authentic VII. Mixolydius
I. plagal II. Hypodorius
II. plagal IV. Hypophrygius
IV. plagal VIII. Hypomixolydius
Regarding the species of modes, Byzantine music does not recognize major and
minor scales as western music does. Byzantine music instead identifies four main modal
species: Diatonic, Enharmonic, Soft Chromatic, and Hard Chromatic. The Diatonic
category includes four modes: I. authentic and I. plagal, IV. authentic and IV. plagal.
The Enharmonic category consists of two modes: III. authentic and III. plagal. The
Chromatic category appears in two kinds of modes: Soft Chromatic mode applied to II.
authentic mode, and Hard Chromatic mode to II. plagal mode.25 See example 7.
Example 7: Diatonic, Soft Chromatic, Hard Chromatic and Enharmonic Genus: 26
Diatonic:
25 H. J.W. Tillyard, “The Modes in Byzantine Music,” The Annual of the British School at Athens vol. 22 (1916/1917-1917/1918). 26 Byzantine scales have precise tunings that have some intervals smaller than the Western semitone. The quartertones notated in example 7 are only approximations of a more complex intervallic structure found in Byzantine and Greek modes.
13
Enharmonic:
Byzantine civilization dates from the reign of the first Christian emperor,
Constantine the Great (ca. 300 A.D.). It is based on three primary factors: extension and
continuation of the Roman Empire,27 Greek tradition, and Christian religion.28 As already
mentioned, Byzantine civilization is considered to be a continuation of ancient Greece.
The notes of the I. authentic Byzantine mode are named after the first seven letters of the
Greek alphabet. See example 8.
Example 8: The I. authentic Byzantine mode with the letters of the Greek alphabet
The notes of the I. authentic mode: D E F G A B C
The first letters of the Greek alphabet: pa vu ga dhi ke zo ni
The first letters of the Greek alphabet in Greek: πα βου γα δι κε ζω νη'
27 Steven Runciman, Byzantine style and civilization (London: E. Arnold & co., 1933), 27. 28 Egon Wellesz, A History of Byzantine Music and Hymnography, 2nd ed. (Oxford: Clarendon Press, 1961), 31.
14
In opposition to the theory about Byzantine civilization being a continuation of
ancient Greece, the influence of Semitic and even Iranian civilizations was emphasized
on the Hellenized countries, which were the most important part of the Byzantine
Empire. 29 There is no doubt of the oriental impact on Byzantine music, which is
especially noticeable due to the chromatic and tuning alterations in the modes presented
in example 7. The Arabo-Turkish names were applied to the Byzantine modes by Greek
theorists, as for example Christodulus Georgiades.30 Therefore, it is hardly a coincidence
that the Hard Chromatic II. plagal mode versus the Turkish Maqm ehnaz, and
descending Diatonic I. authentic mode versus the Arabic Maqm Bayyti are identical.
See examples 9 and 10.
Example 9: Hard Chromatic versus Maqm ehnaz
Hard Chromatic:
Example 10: Diatonic First Authentic versus Maqm Bayyti
Diatonic I. authentic:
15
In comparison with the Western tone system, which distances notes by the same
interval (100 cents = half-tone) and therefore divides the octave into twelve tones, the
Byzantine, Arab and Turkish tone systems use microtones, three tones between each
whole-tone. 31 See example 11.
Example 11: Turkish, Arabic, Byzantine and Western notes between whole-tones32
Turkish, Arabic, and Byzantine notes between whole-tone
Western notes between whole-tone
31 Garland Encyclopedia of World Music, The Middle East, “The Eastern Arab System of Melodic Modes in Theory and practice: A Case Study of Maqm Bayytí: The Invervals of Modern Arab Music,” by Scott Marcus, 36. 32 Garland Encyclopedia of World Music, The Middle East, “Contemporary Turkish Makam Practice: The Abstract Level: Makam Theory,” by Karl Signell, 48.
16
Bagatelle No. I
Regarding the modality of the Bagatelle No. I, there is some unique pitch content
based on two modes: C# Aeolian in the right hand and C Phrygian in the left hand.33 The
combination of both modes offers several modal formations. In mm. 1 – 2, the first three
ascending notes in the right hand and the first three descending notes in the left hand
together create a 5-note set of the C# symmetrical (whole – half – half –whole) modal
formation. It is identical to Messiaen’s third mode of limited transposition. See example
12.
W H H W - P - (PALINDROME)
In mm. 1 – 3 the pitch content expands into a 7-note set of C symmetrical (half –
whole – half – half – whole – half) modal formation. 34 See example 13.
33 The score of the Bagatelle No. I is written in the dual key signature, with four sharps in the upper staff and four flats in the lower staff. 34 The term “symmetrical modal formation” is based on author’s theoretical construct and is not derived from an existing theory.
17
H W H H W H
- P - The same pitch material also appears at the end of the piece (mm. 16 – 18) in a
more extended version. The entity of the type of the octatonic mode formed from this
content also can be considered symmetrical. See example 14.
Example 14: Bagatelle No. I: mm. 16 – 18
W H W H H W H W
- P -
18
The combination of C# Aeolian and C Phrygian, illustrated in the examples 12 –
14, creates a new modal symmetrical formation, surrounding note E. This pitch becomes
the center of a palindrome, the first and last note of two related Octatonic partials:35
I. = E, F, G, Ab, Bb
II. = E, D#, C#, C, Bb
Partial II is the second transposition of partial I. 36
M. 5 in the right hand and the first part of m. 6 in the left hand include a 5-note set
of the whole-tone scale. See example 15.
Example 15: Bagatelle No. I: mm. 5 – 6
The descending G half-diminished (Locrian) mode appears in the left hand in the
mm. 9, 11, and 15 – 17. See example 16.
35 Octatonic, as a designation for the scale or pitch class collection, is generated by alternating whole tones and semitones. A scalar order of the collection can begin with the semitone or the whole tone (the forms were termed ‘Model A’ and ‘Model B’ by van den Toorn). Only three distinct transpositions are possible. The collection is therefore a ‘mode of limited transposition’ under Messiaen’s definition (1944). From Grove Music Online, “Octatonic,” by Charles Wilson, http://www.oxfordmusiconline.com/. 36 E Octatonic mode based on partial I: E F G Ab Bb B C# D E
1st transposition: F F# G# A B C D D# F 2nd transposition based on partial II: F# G A Bb C C# D# E F#
19
Example 16: Bagatelle No. I: G half-diminished (Locrian) scale
In the 1920s scholars approached the Bagatelle No. I as a bitonal composition
because of the dual key signature. This view tended to divide the piece into two distinct
layers operating simultaneously yet separately. It is more accurate, however, to view this
Bagatelle as a united entity based on transformations of one particular mode. The pitch
material at the beginning and end of the piece can be considered a type of a C
symmetrical modal formation (see the examples 13 and 14). As László Somfai points out,
Bartók himself did not classify this piece as “bitonal,” or “polytonal.” He presented this
work as “simply a Phrygian colored C major.”37 Thus, the function of the dual key
signature in this Bagatelle offers a combination of two separate voices that creates a third
layer of cohesive chromatic material that resembles the melodic color of Hungarian and
Slovak folksong.
Bagatelle No. III
Although Bagatelle No. III does not include any reference to specific folksong
material; the piece carries certain folk elements such as the periodic character of the
melody, repetition, basic song structure, monophony, modality, melodic downward
motion, and static accompaniment. Because of these characteristics, it is possible to
37 László Somfai, “Nineteenth-Century Idea Developed in Bartók’s Piano Notation in the Years 1907 – 14,” 19the-Century Music, vol. 11 (1997).
20
assume that the folk elements implied in Bagatelle No. III come from folk song found in
Hungarian or Slovak regions. See the score in example 17.38
Example 17: Bagatelle No. III – score
38 Score in public domain, score analysis is by Michaela Eremiášová.
21
In this piece there is a prominence of one mode that can be found with many
names. The so-called Verbunkos Phrygian scale (Phrygian with raised 3)39 does not
appear only in the Hungarian Gypsy music repertoire, but also in the Arabic repertoire as
39 W. Marvin, handout, “Scales, Modes and Collections in Western Music,” from Loya Shay, “The Verbunkos Idiom in Liszt’s Music of the Future: Historical Issues of Reception and New Cultural and Analytical Perspectives” (Ph. D. diss., King’s College, London, 2006).
22
Maqm Hijz.40 Its first tetrachord also corresponds with the following modes: the Arabic
Maqm ehnaz, and the Byzantine Hard Chromatic mode. See example 18.
Example 18: Bagatelle No. III -Verbunkos Phrygian scale
According to the mode, the tonal center is B. However, regarding the melodic line
in the left hand; there are two pitches that frequently appear throughout the piece: F# and
C. Although the note B occurs on weak beats, together with F# it creates a melodic frame
of the periodic antecedents. The note C appears in consequents. See example 19.
Example 19: Bagatelle No. III - melodic structure
The range of the B Verbunkos Phrygian mode is emphasized by a frequent
appearance of B4 as the highest note in the right hand, and B3 as the lowest note in the left
40 Garland Encyclopedia of World Music, The Middle East, “The Eastern Arab System of Melodic Modes in Theory and practice: A Case Study of Maqm Bayytí: The Invervals of Modern Arab Music,” by Scott Marcus, 36-44.
23
hand (except one occurrence of A3 in the left hand in m. 22). Thus it is possible to assume
that the Bagatelle is centered on B.
The melodic line in the left hand together with some of the pitches in the right
hand (G, A, B) offers two harmonic entities, derived from the mode: B7 ( I ) and CMaj7
( bII ). See example 20.
Example 20: Two harmonic entities in the Verbunkos Phrygian mode
The B Verbunkos Phrygian mode appears in several transformations to other
modes, such as the octatonic and chromatic modes. In mm. 3 – 10, pitch material in the
left hand is based on five notes of the Verbunkos mode. In mm. 11 – 14, the mode is
transformed to five notes of an octatonic collection, and it is further transformed in mm.
15 – 18 to a 6-note chromatic collection that completes, with the music material in the
right hand, an aggregate.
In the Bagatelle No. III I peruse the pitch content through chromatic pitch space
with the main interest in Bagatelle’s modal material, based on one particular mode
derived from Hungarian modal heritage, which includes the Byzantine, Arabic, Turkish
tone systems and the Verbunkos modes. Example 19 illustrated the pitch content with an
emphasis on the B Verbunkos Phrygian mode, its modal transformation, and its impact
on the harmonic and formal structure of the piece. See examples 19 and 20.
24
Bagatelle No. IV
As noted by Antokoletz, the Bagatelle No. IV uses an old Hungarian folksong as
the source, collected by Bartók in 1907 in Felsöiregh.41 If we only consider the pitches on
down beats in the melodic line of the right hand, then the song is based on the D minor
pentatonic scale. Referring to Bartók’s idea of three basic forms of the pentatonic scale in
old style Hungarian songs, this Bagatelle is based on the third type of the pentatonic scale
(cf. example 5 in section II - Slovak and Hungarian folk music), in which the scale degree
six appears as a real note. This note Bb occurs only on off-beats. See example 21.
Example 21: Bagatelle IV in D minor pentatonic
In mm. 1 – 2, the appearances of the additional scale degrees (E, Bb) from the
melodic line and chordal accompaniment transform the pentatonic scale into the Aeolian
mode. See example 22.
41 Elliott Antokoletz, “The Musical Language of Bartók’s 14 Bagatelles for Piano.”
25
Example 22: Bagatelle IV – modal transformation in mm. 1 - 2
On the first beat of m. 8, the pitches in the right and left hands include an almost
complete G Mixolydian mode. See example 23. On the second and third beats of m. 8, the
notes in the right and left hands create a symmetrical modal formation. See the 2nd part of
example 23.
26
W min3 H H H H min3 W - P –
It is understandable that Antokoletz approaches this Bagatelle from a harmonic
point of view. His focus is primarily on intervallic properties of the chordal
harmonization of the Hungarian tune. However the modal content of the song, built on
the D minor pentatonic scale, is the essence for the chordal harmonization and the modal
transformation.
Bagatelle No. V
Bagatelle No. V includes a Slovak folk song that is actually a Hungarian tune,
published in the second volume of Bartók’s Slovak folk songs collection. See example
24.42
42 Benjamin Suchoff, “Bartók’s Odyssey in Slovak Folk Music in Bartók Perspectives,” in Bartók perspectives: man, composer, and ethnomusicologist (London; New York: Oxford University Press, 2000), 17.
27
Example 24: Slovak folk song
The translated text43 of the Slovakian folk song is as follows:
Oh, in front of our house, in front of our house,
in front of our doors, in front of our doors,
Oh, a handsome lad, a handsome lad is planting a white rose.
According to Benjamin Suchoff the structure of this Slovak folk song is based on
the symmetrical Hungarian pentatonic scale. The circled notes in example 24 suggest the
scale degrees A and E are neighbor and passing tones that switch the pentatonic scale into
the Dorian mode.44 This modal transformation is typical in old-style folk melodies, as is
noted by Bartók in his book, Hungarian Folk Music. If the other degrees of the
pentatonic scale appear as real notes (usually on weak beats), they change the pentatonic
scale into a different mode. It is possible to notice that in terms of rhythm, the basic
pattern is preserved in a simplified version. This Slovak folk song is based on a mixture
of duple and triple meter, while the Bagatelle no. V is simply in duple meter. Regarding
the modal content, Bagatelle No. V is based on the G and D minor pentatonic scales and
their transformations: the Aeolian and Dorian modes. See the score in example 25.
43 Peter Bartok, “Notes of the Editor in 14 Bagatellen für Klavier,” in Béla Bartók’s 14 Bagatellen für Klavier (Budapest: Editio Musica, 1998), 40-47. 44 Suchoff, 17.
28
Example 25: Bagatelle No. V – score:45
45 Score in public domain, score analysis is by Michaela Eremiášová.
29
30
The melodic line of the entire piece is based on asymmetrical periodic structure,
in which the antecedent is built on the D pentatonic/Dorian modes, and the consequent is
built on the G pentatonic/Dorian modes. The property of the modes has an evident
impact on the structure of the chord in the right hand, which accompanies the main
31
melody in mm. 1 – 20. Its harmonic function implies two harmonic entities, G and D
minor, derived from the D pentatonic/Dorian and G pentatonic/Dorian modes. See
example 26.
Example 26: Bagatelle No. V - Gm and Dm harmonic entities
The modal transformation from the D minor pentatonic to the D Aeolian in the
left hand occurs in mm. 5 -11, and the G minor pentatonic scale is established in mm. 12
– 19. See example 27.
Example 27: Bagatelle No. V – modal transformations
The passage in mm. 20 – 27 is based on the G minor pentatonic scale. See
example 28.
Example 28: G Minor Pentatonic scale
The same melody appears in the right hand in mm. 28 – 45 with a different
chordal accompaniment. For the first time there is an appearance of a harmonic
progression derived from the G Dorian mode.
The chordal accompaniment in the right hand (in mm. 51 – 56) changes the
character of the G pentatonic mode to the G Mixolydian mode, and in mm. 57 – 62 to the
D Dorian mode. A short transition to the G minor pentatonic mode appears in mm. 63 –
64. See example 26.
Example 29: Bagatelle No. V in mm. 51 – 64
The main melody appears again in the left hand in m. 54 and is based on the G
minor pentatonic scale.
33
As Suchoff correctly points out, the chordal accompaniment is derived from the
melody.46 As with the Bagatelle No. IV, Bagatelle No. V is another example of the use of
folk song modal material, which has a crucial influence on the harmonic and formal
structure of the piece.
Bagatelle No. VI
The melodic framework of the Bagatelle No. VI resembles folk song. This can be
assumed because of its modality, repetition, variation and its clear repeated rhythmic
pattern. See example 30.
46 Quote from Benjamin Suchoff, Bartók’s Odyssey in Slovak Folk Music, 17.
34
Example 30: Bagatelle No. VI: Sentence47 in mm. 1 – 7
The modal content at the beginning of the Bagatelle (mm. 1 – 2) in the right hand,
is built on a 6-tone set (B C D# E# F# A#). The first five pitches of the set, except the
scale degree four (circled in the following example), correspond with the Verbunkos
Phrygian scale. See example 31.
Example 31: Bagatelle No. VI - Verbunkos Phrygian scale
47 Sentence is a musical term adopted from linguistic syntax that represents a complete musical idea. The construction of the beginning (the presentation of a basic idea and its repetition) determines the construction of the continuation. From Arnold Schoenberg, Fundamentals of Musical Composition, (Oxford: Alden Press, 1973).
35
At the end of m. 2, the 6-tone set in the right hand gets expanded into another
modal formation, which consists of two overlapped tetrachords, based on B octatonic and
D# pentatonic modes. See the modal transformation in example 32.
Example 32: Bagatelle VI – modal transformation
By the end of m. 7, the modal content in both hands creates an 11-tone
symmetrical modal formation. See example 33.
Example 33: Bagatelle VI - symmetrical modal formation
H H H H H W H H H H H
36
Although we do not know if this Bagatelle is based on a folk song source,
Bartók’s compositional procedure follows the same steps, traced in previous Bagatelles
No. I, III, IV and V.
Bagatelle No. VIII
Bagatelle No. VIII represents Bartók’s more complicated compositional concept
of folk song. According to Forte, the overall structure has an “unfolding” character based
on a primary set of notes. 48 As Forte explains the unfolding in his analysis, there is a set
of three predominant tones in mm. 1 - 4: C, G, and B. The role of C can be considered as
a preparation to B. The next important tones are Eb (D#) in m. 5, followed by B in mm. 6
– 8, and G in mm. 9 – 10. 49 As Forte points out in his sketch 37, these structural notes (G
– B – Eb – B – G) are not only prominent in mm. 1 – 10, but they also continue to appear
throughout the rest of the Bagatelle in slightly different groupings: G – Eb – B – G (in
mm. 16 – 24), and G – B – G (in 25 – 32).50 These notes clearly reflect an equal division
of the octave in three major thirds (G – B – D#/Eb – G) and are obviously the main
pillars of the Bagatelle’s melodic and harmonic structure according to Forte’s theory. In
my analysis, I focus on a single primary motif, its elaboration and its impact on harmonic
and melodic structure of the Bagatelle. See Example 34.51
48 Allen Forte, Contemporary tone-structures, (New York: Teachers College, Columbia University, 1955), 75. 49 Forte, 75-76. 50 Forte, 169. 51 The first three systems of example 34 are based on the score from public domain, the score analysis and the fourth system in the same example were made by Michaela Eremiášová.
37
Example 34: Bagatelle No. VIII: mm. 1 – 10
In mm. 1 - 6, there is a clear embellished statement that ends in the middle of m.
6. (There is a breath mark in the score). The passage in mm. 1 - 6 consists of two parts
based on the main motif in mm. 1 - 2 and its slight variation in mm. 3 - 4, and therefore
the tones C#, B, A, C and D# are predominant in this part. See example 35.
38
Example 35: Bagatelle No. VIII – mm. 1 - 4
The framework of the main motif (C#5 - B4 - A4 - C4) is C#5 - A4 - C4, if we
consider B4 as a passing tone. It is transposed into the bass in the left hand (G#3 – E2 –
G2), and has an important harmonic and structural role in the first section (mm. 1 - 10).
See examples 36 and 37.
Example 36: Bagatelle VIII – main motif
This section A (mm. 1 - 10) can be perceived as a kind of asymmetrical period
with its antecedent (mm. 1-6) and consequent (mm. 6 - 10). The predominant tones in
section A are C# (m. 1), E (m. 5), G (m. 9) and Bb (m. 10), and are based on the axis
system.52 See example 37.
52 Axis system is based on the circle of fifths. If, in the circle of fifths, C is considered the tonic, than F will be the sub-dominant, G the dominant. D is the relative of F (S function), A the relative of C (T function) and E the relative of G (D function). This can be applied to the whole circle of fifths, in which case the three principal functions are periodically repeated. The 'axis' grouping consists of minor-third-related tonalities that split the octave symmetrically into four parts. From Roy Howat, “Bartók, Lendvai, and the principles of proportional Analysis,”Music Analysis 2/1 (March 1983), András Szentkirályi, “Some aspects of Bartók’s Compositional Techniques,” Studia Musicologica Academiae Scientiarum Hungaricae, T. 20 (March 31, 2008), Ernö Lendvai, Tonal Principles in Béla Bartók. An analysis of his music, (England: Stanmore Press, 1971), 1 -16.
39
Example 37: Bagatelle VIII – axis system
Section B (mm. 12 - 23) can be considered as a sort of development. In mm. 12 -
15 the main motif appears again in a transposed version, and is partly inverted (m. 12).
The leaps of the motif are expanded and are based on the AUG8/or Min9 that is the frame
of the main motif in its original version. It is interesting to follow some modal formations
in this section: the octatonic triad (G, Ab, Bb) in upward motion in the right hand in m.
16, an octatonic tetrachord (F#, F, Eb, D) in downward motion in the right hand in m. 17,
an octatonic hexachord (Ab, Bb, Cb, Db, Eb, E) in upward motion in the right hand in m.
18, a whole tone 5-note set (E, D, C, Bb, Ab) in downward motion the right hand in m.
18, and two overlapping tetrachords (F#, G, Bb, B / B, C, Eb, E) in upward motion in the
right hand in m. 21, which correspond with the first tetrachords of the Turkish Maqm
Hijz, the Arabic Maqm ehnaz, the Byzantine Hard Chromatic mode, the Verbunkos
Phrygian mode and the Verbunkos Kalindra mode.
40
The original motif in mm. 1 - 2 appears again in a rhythmic diminution in m. 24.
See example 38.
Example 38: Bagatelle VIII – main motif in m. 24
In m. 25 the motif occurs in a transposed and slightly varied version. The basis of
this motif is on G - Eb - G. See example 39.
Example 39: Bagatelle VIII – main motif in m. 25
In m. 26 the same motif appears in a modified and transposed version. See
example 40.
Example 40: Bagatelle VIII – main motif in m. 26
As Forte noted, the last section A1 consists of two phrases, which create a period,
antecedent in mm. 24 - 25 and consequent in mm. 26 - 27. They are related to section A.
41
The last part in mm. 28 - 32 can be perceived as a coda. It is obvious from this
part that Bartók wanted to emphasize the tonal centre of the piece based on the tone G.
Also, the important appearance of F# in m. 28 and m. 31 has an evident tonal resolution
to G. See the score – example 41.53
Example 41: Bagatelle VIII – score
53 Score in public domain, score analysis is by Michaela Eremiášová.
42
43
Bagatelle No. XI
The Bagatelle No. XI is the last example of Bartók’s compositional procedure,
based on more intricate modal content, and its impact on the melodic and formal structure
of the piece. For instance, an 8-note set of a symmetrical modal formation, based on
octatonic pentachords at the beginning of the piece, creates a foundation for the first
section A (mm. 1 – 16) of the Bagatelle’s song-form (AA1BA). The melody based on this
formation occurs in mm. 1 – 7 in the right hand, harmonized in fourths. (See example
42.) In mm. 8 – 16 the melodic line transforms into a transposed and slightly modified
version and creates another symmetrical modal formation. (See example 43.) The circled
notes in example 43 are the modifications of the melody in example 42.
Example 42: Bagatelle XI: mm. 1 - 7
H W H W W H W H - P -
Example 43: Bagatelle XI: mm. 8 – 16
H W W H W W H H
44
IV. Conclusion
The crucial characteristic of Bartók’s elaborate new musical language in seven of
the Fourteen Bagatelles is the use of modal symmetrical formations and transformations.
As I already emphasized, folk song plays a crucial role in Bartók’s compositional
procedure. As noted by Manuel, there are significant categories of secular, modal,
monophonic or heterophonic folk songs in Eastern Europe, which include different
formal sections in discrete modes and often use various tonic ground-notes.54 This aspect,
described by Manuel, is followed by Bartók in his seven Bagatelles. The pitch content of
each separate piece is built on one particular mode, or set, that is expanded and therefore
transformed into other modes. The primary mode, or set, allows for further modal
transformations and symmetrical formations, chordal harmonization and the overall form
of the individual Bagatelle. As brought up by Suchoff, the chordal accompaniment in
Bagatelle No. IV is derived from the melody, based on the Hungarian folk song. We
already know from the analysis that the melody is based on one specific mode--D Minor
Pentatonic mode--which creates a foundation for the piece.
The most effective analyses, therefore, should take the source of the music as a
point of departure. Some published articles refer to individual Bagatelles, 55 but
54 Peter Manuel, “Modal Harmony in Andalusian, Eastern European, and Turkish Syncretic Musics,”75. 55 Elliott Antokoletz, “The Musical Language of Bartók’s 14 Bagatelles for Piano,” [article on-online], Zoltán Kodály, “Folk Music and Art Music in Hungary,” [article on-online], László Dobszay, “The Absorption of Folksong in Bartók’s Composition,” [article on-line], Friedemann Sallis, “La transformation d’un heritage: Bagatelle op. 6 no 2 de Bela Bartok et Invencio (1948) pour piano de Gyorgy Ligeti,” Revue de Musicologie, T. 83e, No. 2e (1997), László Somfai, “Invention, Form, Narrative in Béla Bartók’s Music,” [article on-line], László Somfai, “Nineteenth-Century Ideas Developed in Bartók's Piano Notation in the Years 1907-14,” Vol. 11, No. 1, Special Issue: Resolutions II (Summer, 1987), János Kárpáti, “Perfect and Mistuned Structures in Bartók’s Music,” Studia Musicologica Academiae Scientiarum
45
nevertheless most of the analytical treatises, such as Forte’s analysis of Bagatelle No.
VIII 56 and Antokoletz’s analyses of six Bagatelles,57 focus on a harmonic content, and
exclude the importance of modal quality that has such a crucial impact on the overall
structure in Bartók’s Bagatelles.
Bartók himself hinted about his compositional thinking when he said that
Bagatelle No. I is written in “simply a Phrygian colored C major.”58 There is a reason he
did not characterize his work as a bitonal composition. Bartók’s compositional approach
followed the monophonic or heterophonic aspect, so essential in folk song.
Hungaricae, T. 36 (July, 1995), [article on-line], Suchoff, Bartók’s Odyssey in Slovak Folk Music in Bartók Perspectives, Allen Forte, Contemporary tone-structures. 56 Forte, 75. 57 Antokoletz, “The Musical Language of Bartók's 14 Bagatelles for Piano.” 58 László Somfai, “Nineteenth-Century Ideas Developed in Bartók's Piano Notation in the Years 1907-14.”
46
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Bartók, Béla. Hungarian Folk Music. Trans. by M. D. Calvocoressi. London: Oxford University Press, 1931. Dobszay, László.“The Absorption of Folksong in Bartók’s Composition.” Studia Musicologica Adademiae Scientiarum Hungaricae, T. 24 (Budapest 1981). Forte, Allen. Contemporary tone-structures. New York: Teachers College, Columbia University, 1955. Foster, Peter. “Multi-piece,” From Grove Music Online, http://www.oxfordmusiconline.com/. Frigyesi, Judith. “Hungary.” The Garland Encyclopedia of World Music, Europe, Vol. 8, New York and London: Garland Publishing, Inc., 2000. Gillies, Malcolm. “Bartók, Béla, §3: 1908-14,” Grove Music Online, http://www.oxfordmusiconline.com/. Haussig, Hans Wilhelm. A History of Byzantine Civilization. New York: New York Press, 1971.
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47
Encyclopedia of World Music, The Middle East, Vol. 6, New York and London: Routledge, 2002. Marvin, W., handout, “Scales, Modes and Collections in Western Music,” from Shay, Loya, “The Verbunkos Idiom in Liszt’s Music of the Future: Historical Issues of Reception and New Cultural and Analytical Perspectives.” Ph. D. diss., King’s College, London, 2006. Runciman, Steven. Byzantine style and civilization. London: E. Arnold & co., 1933. Sallis, Friedemann. “La transformation d’un heritage: Bagatelle op. 6 no 2 de Bela Bartok et Invencio (1948) pour piano de Gyorgy Ligeti.” Revue de Musicologie, T. 83e, No. 2e (1997). Schoenberg, Arnold. Fundamentals of Musical Composition. Oxford: Alden Press, 1973. Signell, Karl. “Contemporary Turkish Makam Practice: The Abstract Level: Makam Theory.” The Garland Encyclopedia of World Music, The Middle East, Vol. 6, New York and London: Routledge, 2002.
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