Interview with Trans Indigenous Composer Mari Esabel Valverde

Mari Esabel Valverde is one of 13 transgender composers—and to my knowledge, the only trans BIPOC composer—in the US who are listed in the Institute for Composer Diversity database. You can find more information about Valverde’s music through the links below, including contact information, how to purchase her music, and how to donate to her surgery fund. Do consider including her fabulous music in your courses. I urge everyone to do something to help QTBIPOC music-makers.

Composer profile for Valverde

Video recording of Our Phoenix (2016)

Donation to Valverde’s surgery fund

History and Bibliography of the Global Musical Modernisms website

By Gavin Lee

“Global musical modernisms” is a term I proposed to the US Society for Music Theory’s Global Interculturalism and Musical Peripheries interest group (formerly the Global New Music group), co-founded by Tomoko Deguchi and myself, who served as co-chairs from 2017-2020 (Deguchi remains a co-chair of the group). We are, of course, not the only people to have discussed modernisms in a global framework. For example, across the Atlantic Ocean, Björn Heile independently published his seminal 2019 article, “Musical Modernism, Global: Comparative Observations.” 

Because the discourse from the study group has mostly been published online as introductory essays, readers may not be as familiar with them, but as is often the case, new inclusive concepts have been discussed by BIPOC people who you may wish to cite. This bibliography includes writings by BIPOC and other authors on conventionally modernist as well as popular music, from which you can glean that BIPOCs and our allies have been pushing against the boundaries of Western musical modernism. There are two main sources: Musicology Now’s 2018 “Global Perspectives” series (reprinted on this website in 2020), and Gavin Lee ed., Global Musical Modernisms website (2020 ff.). In 2019, the Global Interculturalism and Musical Peripheries interest group convened a seminar on global musical modernisms, which led to articles by Ya Hui Cheng (2021) and Tomoko Deguchi (2021) (see also, Jungmin Mina Lee 2018). Writings on underrepresented composers have been contributed by Amy Bauer, Frederico Barros, Anton Vishio, Ron Squibbs, Jay Arms, Paul David Flood, and Megan Lyons.

As defined in G. Lee ed., Global Musical Modernisms, the term refers to “all forms of music received and appropriated as ‘modern’ in any location around the globe, crossing the boundaries of post/tonality and musical genres. The focus is on art, avant-garde, experimental, modernist, and popular music, by global (African, Middle Eastern, Central/ South/ Southeast/ East Asian, Latin American, Australasian etc.) music-makers, minority music-makers from the West, and music-makers from the peripheries of Europe and North America.” Rather than attempting a “theory” of global musical modernisms, this definition serves to correct asymmetries in music studies (that fall under a broad definition) of “modernism,” which has tended to focus on a narrow concert repertoire from Western Europe and North America. With this decentering approach in mind (in contrast with an effort in theorizing global musical modernisms—not that the two are necessarily incompatible), it is important to remember that this is a descriptive rather than prescriptive definition based on submissions received, which have thus far included modernist and popular music and not other genres. In its earlier incarnation, the expansion of genres from modernism to popular music was articulated under the term “global new music” (G. Lee, 2018), before the Global Musical Modernisms website was launched. The website includes contributions on composers from the “peripheries of Europe and North America,” such as Helena Tulve and Per Nørgård (though the vast majority of submissions have been on BIPOC composers); this should give pause to dichotomous conceptions of “Western” and “global.” Forthcoming research on the website includes articles by Sophie Brady, Bjorn Heile, Lena Heng, Ralph Locke, and Eshantha Peiris. Other on-going related research include a book by Heile and a special journal issue co-edited by G. Lee and Chris Miller, in which I embark on a belated theorization of global musical modernisms, beyond the descriptive, decentering definition given above. Readers are of course free to produce publications examining the epistemic affordances of the specific formulation of “global musical modernisms”–what can this term offer to us that was not already found in pre-existing research? 

More research on music that could fall under “global musical modernisms” (but mostly pre-date the term) can be found in the bibliography of the SMT Global Interculturalism and Musical Peripheries group.

Bibliography (writings from the study group and this website)

A) Lee, Gavin, ed. 2020-. Global Musical Modernisms.

Arms, Jay M. 2021. “Rahayu Supanggah’s “Paragraph” and the Problems of Intercultural Collaborations”

Barros, Frederico. 2021. “Guerra-Peixe’s Academic Trio.”

Cheng,Ya-Hui. 2021. “Whose Authorship? Authenticity in Chinese Popular Music under Global Modernism”

Deguchi, Tomoko. 2021. “The Appeal of the Foreign in Toshio Hosokawa’s Opera Matsukaze.”

Flood, Paul David. 2021. “Per Nørgård’s Two-Tone Infinity Series in “Wie Ein Kind” (1979-80).”

Lyons, Megan. 2021. “Hale to the King: “Three Brevities for Solo Flute” by Hale Smith.”

Squibbs, Ron. 2021. “Jōji Yuasa – Cosmos Haptic for piano (1957)”

B) Musicology Now’s “Global Perspectives” series. 2018.

Bauer, Amy. 2018. “Global Perspectives—The Music of Helena Tulve.”

Cheng,Ya-Hui. 2018. “Global Perspectives—Rock under the Red Flag: ‘A Piece of Red Cloth’ by Cui Jian”

Deguchi, Tomoko. 2018. “Global Perspectives—Significance of the Parts in Music of Tōru Takemitsu.”

Lee, Gavin. 2018. “Global Perspectives—Global New Music: From Avant-Garde to Rock, Korea to Estonia.”

Jung-Min Mina Lee. 2018. “Global Perspectives—The Story of Unsuk Chin’s Cello Concerto.”

Vishio, Anton. 2018. “Global Perspectives—The Art of Derivation: Jo Kondo’s Paregmenon.”

Akin Euba: African Art Music, Intercultural Composition and Creative Ethnomusicology

Björn Heile

The Nigerian composer Akin Euba (28 April 1935 – 14 April 2020) described his mission as the creation of an ‘African Art Music’. This, he explained, would be ‘a form of music [that is] universal to all Africa [… and that]  in order to be truly African must use the stylistic and instrumental materials of African music or, at least, a preponderance of them’. <1> As this suggests, his life and work exemplify the tensions of postcolonial Africa: between tradition and modernity, African heritage and European training, and a colonial past and an independent but uncertain future. While it is a matter of debate whether he ever fully managed to reconcile these conflicts and contradictions, his proposed solutions proved influential among a younger generation of composers.

Born in Lagos, he studied Composition at Trinity College London with Arnold Cooke and Eric Taylor (1952–7) before embarking on a Master’s in Ethnomusicology at UCLA in the 1960s. Although, Euba was surrounded by traditional music in his youth, it is one of the ironies of the postcolonial situation that he had to travel to California to formally study the music of his own country. His education and training up to that point were entirely in European classical music, and it was only during his studies in London that his consciousness of himself as an African composer began to emerge. He concluded his education with a PhD on Dundun Music of the Yoruba, under the supervision of Kwabena Nketia, the leading authority on African music and a fellow composer (PhD 1974).

            Euba had a varied career, teaching at the Universities of Lagos and Ife and working for the Nigerian Broadcasting Corporation, before moving to Bayreuth (Germany) to work at the Institute of African Studies (1985-91). He eventually succeeded his teacher Nketia as Andrew W. Mellon Professor of Music at the University of Pittsburgh (1993-2011). In addition, he set up the Centre for Intercultural Music Arts, London and the Centre for Intercultural Musicology at Churchill College, Cambridge.

            As a composer, he pursued the idea of ‘intercultural music’, by fusing Western modernist techniques, including serialism, with African (especially Yoruba) music, that reflected his own ethnic background. One may see a contradiction between his earlier African nationalism and his later interculturalism. However, there is a connection to the model of cosmopolitanism as a series of concentric circles originally proposed by the Stoics.<2> In a similar way, Euba’s Yoruba heritage formed the innermost circle, Pan-Africanism (which he regarded as separate) the next, and so forth, up to the outermost, intercultural or ‘global’ circle. His model for combining African traditions with European techniques lay in the work of Béla Bartók, who also inspired his notion of ‘creative ethnomusicology’,the employment of ethnomusicological research for composition. This is also something he shared with his teacher Nketia.

            Unfortunately, little of Euba’s oeuvre is available as a score or in recording, never mind both. The culmination of Euba’s oeuvre is arguably his opera Chaka (1970, rev. 1995-98), a setting of the play by the great writer and first President of Senegal, Léopold Sédar Senghor (1906-2001), on the eponymous King of the Zulus. However, I want to focus instead on his contemporaneous piano cycle Scenes from Traditional Life (1970) (Verlag Neue Musik, Berlin, NM 689; recording from African Music Publishers).<3> Although he later learned the dundun drum, the piano was Euba’s first instrument; he is perhaps best known as the ‘father of African pianism’, a concept that encapsulates his approach to both African art music and intercultural composition. He explained the principles himself:

The piano, being partially a percussive instrument, possesses latent African characteristics. Techniques in the performance of xylophones, thumb pianos, plucked lutes, drum chimes, for which Africans are noted, and the polyrhythmic methods of African instrumental music in general would form a good basis for an African pianistic style.

As characteristic elements of African pianism, he lists:

Thematic repetition, direct borrowings of thematic material (rhythmic and/or tonal) from African traditional sources, the use of rhythmic and/or tonal motifs which, although not borrowed from specific traditional sources, are based on traditional idioms and percussive treatment of the piano.<4>

            Scenes from Traditional Life exemplifies these ideas. As the preface to the score indicates, the title refers to Schumann’s Scenes from Childhood. This does not fully explain ‘traditional life’, and the composer has suggested that ‘the connection between title and work is nebulous’.<5> What is striking at first glance is the predominance of two-part writing: both hands are used melodically, typically independently of one another; chords are relatively rare and appear as percussive effects more than harmonic events. Indeed, along the lines of Euba’s own comments, many of the textures are more reminiscent of an ensemble of two xylophones or two mbiras (played by one or two players) than Western classical piano music. That said, if there is a precedent for the pianistic textures and playing techniques employed in Scenes in the repertoire, it is in the work of Bartók, such as the cycle Out of Doors.

There are three pieces in this cycle, all in a kind of ternary form. The most notable common structural feature is cell construction. These cells consist of short, rhythmic-melodic phrases in one hand, which are repeated and varied like ostinatos, and combined with other cells in the other hand. The pieces differ in character, particularly in terms of rhythmic-metric construction. Uzoigwe has identified the rhythmic pattern underpinning the first piece (ex. 1) as a variant of the Yoruba version of the West-African timeline pattern (a rhythmic organisation in which seven impulses, normally quavers or crotchets, are distributed over a 12/8 cycle).<6> The second is a study in shifting additive metres: it starts in 17/8 (sub-divided into 4+6+4+3) with an irresistibly dancing lilt, and takes on 13/8, 14/8 and 10/8, all in changing sub-divisions (except the 17/8 which remains largely invariant); and on some occasions, different polyrhythmic sub-divisions occur simultaneously in the two hands (ex. 2). The third and final piece features syncopation on various metric levels (ex.3). According to Uzoigwe, it is based on a further syncopated version of a rhythmic pattern characteristic of Highlife—a form of popular music common in West Africa (and at the root of more recent developments such as Afrobeat)—which is itself derived from the Timeline mentioned earlier.<7> In a sense, then,  the work is about ‘African rhythm’, but whereas, as Kofi Agawu has pointed out, this term is often used generically and vaguely,<8> Euba explores three distinct rhythmic-metric techniques that all have very specific origins.

Ex. 1: Akin Euba, Scenes from Traditional Life, No. 1, bars 1-9.

Ex. 2: Akin Euba, Scenes from Traditional Life, No. 2, bars 1-6.

Ex. 3: Akin Euba, Scenes from Traditional Life, No. 3, bars 1-12.

Omojola and Uzoigwe briefly point out Euba’s use of twelve-tone technique in the work, both claiming that the series rarely appears ‘intact’.<9> In fact, Euba’s use of the technique is not as free as they make it seem. The key is that he freely repeats all pitch classes from the series that have already been sounded, which is not uncommon among serial composers. Another specific technique is that he splits the series into tetrachords, and that within each tetrachord, the order of pitch classes may vary. Once one is aware of these peculiarities, it becomes easier to identify the serial structures underpinning the work, although it is fair to say that dodecaphony is used primarily for melodic invention; not for overall structural coherence. The music examples show a complete unfolding of each piece’s basic series – given the free repetition of already sounded notes, this can take a little while!

It might be tempting to sum up Euba’s work in the formula ‘African rhythm with European pitch structure’, but it is more subtle than that. For instance, by composing for piano and employing staff notation, Euba already departs from traditional practice, and his rhythmic-metric manipulations go well beyond the original material, even if that remains recognisable. Conversely, Uzoigwe has argued that Euba’s twelve-note rows show a preponderance of the intervals used in the dundun drum music of the Yoruba, namely minor and major thirds and perfect fourths and fifths, whereas minor seconds and tritones, which are rare in dundun music, are generally avoided.<10> In this way, the dodecaphonic structure is suffused with a West-African sensitivity.

In works like Scenes from Traditional Life, we can see Euba’s vision of African art music taking shape. Euba goes beyond the notion of a ‘fusion’ between African and European elements, since both intersect in complex ways that can no longer be disentangled. The result is music that is as distinctively African as it is modernist.

<1> Quoted from Joshua Uzoigwe, Akin Euba: An Introduction to the Life and Music of a Nigerian Composer, Bayreuth African Studies Series 25 (Bayreuth, Germany: E. Breitinger, Bayreuth University, 1992), 71.

<2> For the Stoic notion of concentric circles, see Martha C. Nussbaum, Cultivating Humanity: A Classical Defense of Reform in Liberal Education (Cambridge, Mass: Harvard University Press, 1997); cf. also Marilyn Fischer, ‘A Pragmatist Cosmopolitan Moment: Reconfiguring Nussbaum’s Cosmopolitan Concentric Circles’, The Journal of Speculative Philosophy 21, no. 3 (2007): 151–65.

<3> I would like to thank Jennifer Lynne LaRue for the information about the recording. There is also an excellent lecture recital on the work of Nketia and Euba by Eric Moe, on YouTube.

<4> Quoted from Bode Omojola, ‘African Pianism as an Intercultural Compositional Framework: A Study of the Piano Works of Akin Euba’, Research in African Literatures 32, no. 2 (2001): 157.

<5> Uzoigwe, Akin Euba, 64.

<6> Uzoigwe, Akin Euba, 68–69.

<7> Uzoigwe, 69.

<8> Kofi Agawu, ‘The Invention of “African Rhythm”’, Journal of the American Musicological Society 48, no. 3 (1995): 380–95,

<9> Uzoigwe, Akin Euba, 65; Omojola, ‘4. African Pianism’, para. 5.

<10> Uzoigwe, Akin Euba, 65.

Björn Heile is Professor of Music (post-1900) at the University of Glasgow. He is the author of The Music of Mauricio Kagel (2006), the editor of The Modernist Legacy: Essays on New Music (2009), (2009), co-editor (with Peter Elsdon and Jenny Doctor) of Watching Jazz: Encountering Jazz Performance on Screen (2016), co-editor (with Eva Moreda Rodríguez and Jane Stanley) of Higher Education in Music in the Twenty-first Century and co-editor (with Charles Wilson) of The Routledge Research Companion to Modernism in Music. He specializes in new music, experimental music theatre and jazz, with particular interests in embodied cognition, global modernism and cosmopolitanism.

He is Principle Investigator of the research network ‘Towards a Somatic Music: Experimental Music Theatre and Theories of Embodied Cognition’ and is currently writing a book with the working title A Global History of Musical Modernism for Cambridge University Press. This blog originates from research carried out for that book.

Global Musical Modernisms blog posts (2021 collection)


Featuring posts on music of the following composers from Indonesia, Japan, China, Brazil, Denmark, and the US:

César Guerra-Peixe (Brazil), Trio (1960) (author: Frederico Barros, Federal University of Rio de Janeiro) Guerra-Peixe’s Academic Trio

Hale Smith (US), Three Brevities for Solo Flute (1969) (author: Megan Lyons, University of Connecticut) Hale to the King: “Three Brevities for Solo Flute” by Hale Smith

Per Nørgård (Denmark), Wie Ein Kind (1979-80) (author: Paul David Flood, University of California, Irvine) Per Nørgård’s Two-Tone Infinity Series in “Wie Ein Kind” (1979-80)

Rahayu Supanggah, Paragraph (1991) (author: Jay M. Arms, University of Pittsburgh) Rahayu Supanggah’s “Paragraph” and the Problems of Intercultural Collaborations

Cui Jian (China), Nothing to My Name (released in 1989) & Li Jinhui, Drizzle (1927) (author: Ya-Hui Cheng, University of South Florida) Whose Authorship? Authenticity in Chinese Popular Music under Global Modernism 

Jōji Yuasa (Japan), Cosmos Haptic (1957) (author: Ron Squibbs, University of Connecticut, Storrs) Jōji Yuasa – Cosmos Haptic for piano (1957)

Toshio Hosokawa, Matsukaze (2010) (author: Tomoko Deguchi, Winthrop University) The Appeal of the Foreign in Toshio Hosokawa’s Opera Matsukaze


Global Musical Modernisms is a forum for all forms of music received and appropriated as “modern” in any location around the globe, crossing the boundaries of post/tonality. The focus is primarily but not exclusively on art, avant-garde, experimental, and modernist music, by global (African, Middle Eastern, Central/ South/ Southeast/ East Asian, Latin American, Australasian etc.) composers, minority composers from the West, and composers from the peripheries of Europe and North America.

Authors in each volume serve as peer editors for each other, shaping each post into an accessible piece of writing (with analytical graphs where appropriate) that is a scholarly guide to global musical modernisms and a multi-media teaching resource.

Guerra-Peixe’s Academic Trio

By Frederico Barros


The year was 1960 and Brazilian composer César Guerra-Peixe submitted his Trio, for violin, cello and piano to a contest held by the Brazilian Ministry of Education’s radio station.<1> Click here for the score and recording. On the surface, the piece is illustrative of Guerra-Peixe’s output of the period, but some of its specificities offer interesting points of discussion. From the modal techniques employed and explicit nationalism to the clear structure and tightly-knit thematic work, the Trio shows how Guerra-Peixe positioned himself in the debate about Brazilian music at the time. Some old-school motivic analysis may help us better understand what this means.

The sonata-allegro begins with the first thematic group’s theme 1 (A1), played by violin and cello two octaves apart and clearly related to the Brazilian northeastern region:


Figure 1: Guerra-Peixe – Trio, 1st mov., A1, m. 1-11, violin part


Showing why musical materials are related to a place or human group is a complex endeavor. However, at least in this case, we can let the composer himself speak. In the essay Os Cabocolinhos do Recife,<2> Guerra-Peixe presents examples very similar both to A1 and B2 (figure 5 below).


Figure 2: Examples of Cabocolinhos melodic figures collected by Guerra-Peixe<3>


The origin of the piano accompaniment in A1 (figure 3) is harder to trace, but its rhythmic structure, repeated until m. 10, combined with the range of a major second (with some variation) in the highest voice can be convincingly linked to the “elements of the berimbau” that Guerra-Peixe would later say were present in the Trio.<4>


Figure 3: Guerra-Peixe – Trio, 1st mov., A1, m. 1-2, piano part


The second theme of the first group (A2), by its turn, is based on the cell c from A1—whose rhythm was also heard in the piano left hand in A1 (as shown in fig. 3):


Figure 4: Guerra-Peixe – Trio, 1st mov. Cell c (from A1) and A2 (m. 26-29)


Finally, the piece’s tonal plan goes from D Lydian (A1) to F# Minor (A2), and then to B Dorian on the first theme of the second group (B1). It then reaches A Lydian on the second theme of the second group (B2), the closing theme that brings back the Lydian sound of A1, to which it is clearly related:<5>


Figure 5: Guerra-Peixe – Trio, 1st mov., B2, m. 70-74, piano right hand


From the first group to the second—the foundational polarity of sonata form—the piece descends a minor third, as if going from major to relative minor, but here making a homologous move from D Lydian to B Dorian. Despite B2 being in the dominant region, the modalism present in the Trio takes over the role of the tonal relations in a conventional sonata-allegro. This serves as an entry point into a significant aspect of this piece: Guerra-Peixe stayed rooted in principles from the Western tradition while infusing them with elements of different origins; following sonata procedures by the book, but employing material seen in his time and place as possessing a distinctive Brazilian character.

Some years later, Guerra-Peixe would state that he wrote the Trio in a deliberately academic fashion, hoping it would make it fare better in the contest.<6> Furthermore, the elements indicated above are all fairly common in the Western tradition, usually being considered indicators of good compositional technique, even if somewhat dated. However, these elements tend to be considerably subtler in other works of the composer from the same period, putting the Trio in a somewhat special place in his oeuvre and raising the question of whether we should take all this at face value.

Born in 1914, Guerra-Peixe’s formative years were marked by the rise of the first Modernist generation in Brazil. It was a period of both aesthetic modernization and of coming to terms with the idea of a national art, and throughout the following two decades this two-fold task would converge. In this very same process, the first modernists would oppose those who came before them with charges of eurocentrism and traditionalism, but slowly sliding into being themselves the new established tradition—at least that’s how many of their successors saw them. To add insult to injury, this took place through the participation of many of those modernists in the Getúlio Vargas dictatorial regime.<7> To put it bluntly, during the 1940s younger composers such as Guerra-Peixe tended to see their nationalist-modernist peers as uninteresting, repetitive, and in many cases as actual sellouts.

It was the time when Guerra-Peixe joined the Música Viva group—centered around German composer Hans-Joachim Koellreutter—and got into twelve-tone music, first radically opposing any form of nationalism but then gradually starting to experiment with combining the two trends. His stint with dodecaphony lasted until around 1949, when questions that had been bugging him for a while about who his music could reach and its social utility reached a peak.<8> Guerra-Peixe then plunged both into the Brazilian countryside and in a creative crisis that would eventually lead him to abandon the twelve-tone technique for good in favor of a music that fed heavily from the proto-ethnomusicological researches he had been doing around that time.<9> Having joined the nationalist bandwagon now, he would criticize his new colleagues by turning their own principles against them, with charges of poor knowledge of the country’s traditions and lack of compositional chops.<10>


Figure 6: Guerra-Peixe in 1950


Guerra-Peixe used to show off his knowledge of Brazilian regional cultures by ditching traditional elements of Western music in favor not only of melodic ideas and rhythms—a practice that at the time was common currency for nationalists worldwide—, but also structures, timbres and forms he learned during his countryside excursions. An eloquent example is the first movement of his String Quartet n. 2, from 1958: at first it may seem like an odd sonata-allegro, then one starts wondering if it isn’t a rondo… only to finally, with some luck, find out that the composer employed the form of the cateretê from São Paulo. To make matters even more complicated, we are not dealing with a song form or equivalent, but with something more akin to a sequence of dances or a ritual whose development is mirrored in the piece.<11>

Thus, the meticulous melodic construction and compositional prowess shown in the Trio can be understood as a deliberate act in a very specific sense. Without getting into value judgments, even if Guerra-Peixe may have misevaluated the jury—he received the second prize and the winning piece, by Marlos Nobre, cannot be said to be conservative, after all—, the Trio reveals that he considered them conventional both on aesthetic and technical grounds. It is true that nationalism would bring Guerra-Peixe and the jury together, but he tended to favor (and boast) a more nuanced view of Brazilian music. When we look at the technical side things get even fuzzier, though, as Guerra-Peixe would often also derive procedures from Brazilian folk sources, perhaps risking a relative alienation of an audience more attuned to the Western canon.

That’s much less perceptible in the Trio. We won’t find some alternative form here, but a proper sonata-allegro, and as such the thematic material is orderly presented. While rhythms from one Brazilian state, Bahia, serve as accompaniment to melodic figures from another, Pernambuco, purposefully blurring geographic frontiers, these work in tandem to form a more general, less localized idea of Brazil. Finally, the specific modal elements he resorts to here may sound Brazilian, but below the surface they serve to put very Western structural forces in motion.

This is not to say that elsewhere Guerra-Peixe would always avoid the Western concert music tradition—be it modern or classic-romantic. On the contrary, these are always present in some shape or form, but often transformed: harmony, timbre, developmental procedures, and other aspects of Western musical thinking would be to some extent impacted by the folkloristic investigations he engaged in from the 1950s on. Threading the line that separated his aesthetic demands from the taste of an imagined jury, he ended up exposing some shortcomings of the modernist project he was himself stumbling upon but couldn’t quite fathom at the time, touching on things we are still grappling with today: alternative theories of form, sound, discourse, and drama, amounting to other ways of thinking about music itself which may not even fit in these categories.



<1> Rádio MEC’s II Concurso de Composição Música e Músicos do Brasil.

<2> GUERRA-PEIXE, C. 2007. Estudos de folclore e música popular urbana. Samuel Araújo (org.). Música editada. Belo Horizonte: Editora UFMG.

<3> Ibid.

<4> Liner notes by the composer for the LP Documentos da Música Brasileira, v.17, LP 356-404-203, MEC/Secretaria de Cultura/Funarte. The berimbau is an instrument mostly associated with the capoeira, from Bahia. It plays two pitches—usually close to a major second in Western theory—that are subject to timbral variations through various playing techniques.

<5> FARIA, A. G. 2000. “Guerra-Peixe e a estilização do folclore.” In: Latin American Music Review. vol. 21, no. 2.

<6> See note 4 above.

<7> SCHWARTZMAN, S., H. M. B. BOMENY, V. M. R. COSTA. 2000. Tempos de Capanema. São Paulo, SP: Paz e Terra: Editora FGV; SQUEFF, E., J. M. WISNIK. 2004. Música. São Paulo, Brasil: Editora Brasiliense.

<8> It’s worth mentioning at this point that the Second International Congress of Composers and Music Critics took place in Prague, Czechoslovakia, in 1948 and brought many of the Socialist Realism directives to music. Its influence was strongly felt in Guerra-Peixe’s circle of relations, as Claudio Santoro, one of his colleagues in the Música Viva group, attended the congress as a delegate of the Brazilian Communist Party (PCB).

<9> See ARAÚJO, S. “Introduction” (GUERRA-PEIXE 2007); ARAÚJO, S. 2010. Movimentos musicais: Guerra-Peixe para ouvir, dançar e pensar. Revista USP, (87), 98-109. USP.

<10> For a detailed discussion, see BARROS, F. César Guerra-Peixe: a modernidade em busca de uma tradição. Doctoral dissertation. Departamento de Sociologia. São Paulo, Brazil: Universidade de São Paulo. 2013.

<11> FARIA, A. G. 2007. “Modalismo e Forma na obra de Guerra-Peixe” in: FARIA, A.G.; BARROS, L.O.C.; SERRÃO, R. Guerra-Peixe: um músico brasileiro. Rio de Janeiro: Lumiar.



Frederico Barros is Music History professor at the Federal University of Rio de Janeiro. He has a PhD in Sociology and MPhil and BA in History. Research interests include concert and urban popular musics and arts during the 20th and 21st centuries, modernism, and nationalism.

Hale to the King: “Three Brevities for Solo Flute” by Hale Smith

By Megan Lyons


If one were asked to name a prolific atonal composer, the answers would likely include Arnold Schoenberg, Anton Webern, or Alban Berg; an unlikely answer would be Hale Smith. Growing up, Hale was involved in classical and jazz ensembles, and these musical experiences shaped his eventual approach to composition. A student of Marcel Dick, a colleague and friend of Arnold Schoenberg in the 1920s, Smith combined atonal and serial techniques into his works alongside African-American rhythmic elements. Horace Maxile describes Smith’s oeuvre as reflecting “a sensitive interaction between the worlds of the African-American vernacular and music of the European tradition.” <1>

Three Brevities for Solo Flute, one of Smith’s lesser-known works, was composed in the middle of his career, in 1969. The first movement, dedicated to flutist Nancy Turetzky, opens with two iterations of pitch-class set (027) through a T3 transformation. This trichord is quartal and open to possibilities, a feature Smith utilizes to his advantage in several of his works, such as Evocation. The trichord (027) appears here as a succession of two interval-class (ic) 5’s and is found frequently in jazz-themed works by Smith. <2> The other primary trichord employed by Smith in this movement, (016), appears more sporadically, and is related to (027) though it may seem audibly disconnected. Ic5 is maintained between the two trichords, yet the whole tone found in (027) is contracted into a semitone in (016). Smith utilizes the common ic5 in dyadic moments in order to illicit uncertainty and blur the lines between the two trichords. The dichotomy between these two trichords is further emphasized as (027) is symmetrical and (016) is asymmetrical. Smith plays upon the contrast between these two trichords through alternation and by focusing on their audible difference, the whole tone and semitone. This alternation can be seen in Example 1, which shows the frequency of these two trichords in mm. 1–15. This opposition is played out on a large scale as exactly halfway through the movement, the piece is performed in imperfect retrograde; the symmetry is altered as two measures of unrelated material are inserted in different locations for each half of the piece.


Example 1: Movement I, mm. 1–15


Dedicated to composer Wallingford Riegger, the second movement supposedly features the basic motive of Riegger’s Second Symphony. <3> While the opening movement was characterized by trichords, the second movement emphasizes tetrachords instead. Smith introduces a melodic and rhythmic motive early on in this movement; this (0123) motive is repeated with slight rhythmic variation throughout the movement. The second movement does not end symmetrically as the first did; instead, Smith concludes the movement with an (0235) tetrachord instead. Example 2 shows the opening (0123) motive and the evolved (0235) motive at the conclusion. The interval content of the pitch collection changes from <321000> to <122010>, with the most notable difference being the inclusion of ic5 in (0235). The contrast between the iterations of the motives (0123) and (0235) calls back to the contrast between semitones and whole tones in the first movement, although this time the initial set expands rather than contracts.


Example 2a: Movement II mm. 1–2

Example 2b: Movement II mm. 27–31


For the third and final movement, dedicated to jazz flutist Jerome Richardson, Smith shifts to serialism: complete tone rows are introduced within a traditional ternary form. As seen below in Example 3, four distinct internal trichords and three distinct internal tetrachords can be derived from this row. In retrospect, the compositional choices of the first two movements are found in the row of the third movement. The first movement utilized mainly (027) and (016) trichords while the second movement featured (0123).


Example 3: Movement III Matrix and Subsets


In his analysis of Smith’s Evocations, Maxile notes four row forms that have the same boundary tones, with Smith often linking tone row statements with common tones. <5> The four primary row forms employed in the third movement of Three Brevities are P6, R6, I6, and RI6, clearly linked through pitch-class (pc) 6. P6 is presented first, with pc6 repeated utilizing the rhythmic pattern from the first movement of two sixteenth notes followed by an eighth note. This is unsurprising as Smith is “a motivic kind of composer in that [he] tend[s] to work with a few key motivic ideas” to unify a composition. <6> RI6 follows yet the opening tetrachord is repeated prior to the entire row form being heard. This repeated tetrachord is a member of (0123) and is reminiscent of the second movement tetrachord motive. The beginning of I6 elides with the end of RI6 and once again features the three-note repetition of pc6 from the opening of the movement. Following the sounding of I6, one would expect R6 to appear, yet it does not; Smith’s composition moves to seemingly unrelated material for the B section, recalling motives from the prior movements as well as subsets of the four main tone rows.

One such subset, a hexachord from R6, is repeated four times before continuing on to unique material in the B section. Prior to the return of the A section, the hexachord from R6 is heard again, but this time in retrograde, an allusion to the first movement. This second presentation of the R6 hexachord is the retrograde of the initial presentation. A full iteration of R6 ultimately concludes the movement, completing the four pc6-based row forms.

The retrospective cohesion of Smith’s work is expected given his comments on his own compositional process. In an interview, Smith stated how “one must be able to extract from one’s ideas all of their possibilities. You have this entity that has all sorts of implications.” <7> One such entity is Smith’s near-obsession with ic5, found repeatedly through his compositional choices in this work. The duration of the piece is set at 5 minutes and 15 seconds; the first movement is 50 measures long; the time signature of the second movement is 5/8; and finally, his persistent use of ic5. The connection of ic5 to Smith’s jazz-like pieces is well-known, yet it must be asked: why ic5? Perhaps it allows him to venture into complex musical realms while maintaining a connection to tonality as a perfect fourth/fifth. Perhaps, like Bach, Smith wanted his name to shine in his works; after all, Smith is five letters long. This is only a small sample of Smith’s ability to extract all possibilities from a single entity. Cohesion in Smith’s compositions can be further explained through his idea of a nucleus. “Everything relates from the smallest nucleus through the finished fruit, through the tree itself.” <8> For Three Brevities, the nucleus is without a doubt the row form of the third movement, without which the rest of the piece cannot be understood.

Smith received critical acclaim during his career, having his pieces performed by the New York Philharmonic, the Cleveland Orchestra, and more. Being an active composer in the 1950s and 60s, Smith found himself in the middle of racial discussions: he was often seen as a spokesperson or representative asked to speak on behalf of black artists. Smith stated: “the tendency among many people still is to assume that the black American composer is not on an equal level with his white counterpart.” <9> Smith’s words are reminiscent of Phil Ewell’s groundbreaking work with “Music Theory’s White Racial Frame,” which acknowledges the deficit of Black composers and their work within the Western music canon. <10> Both Smith and Ewell advocate for a reframing of Western music standards to be inclusive rather than exclusive, specifically in regards to the race of composers. In 1971, Smith stated “I have faced the question as to whether or not my work was worthy of appearing on programs of music by the recognized masters of my art.” <11> It is clear, through scratching the surface of just one of Smith’s pieces, that his work is more than worthy of being programmed, analyzed, and included in the Western canon.

The score for Three Brevities for Solo Flute is published by ED Marks Music Company and is available for purchase through Subito Music Corporation. A wonderful performance by Laurel Zucker on flute can be found at the following YouTube links: first movement, second movement, and third movement.




<1> Horace J. Maxile, “Hale Smith’s ‘Evocation’: The Interaction of Cultural Symbols and Serial Composition.” Perspectives of New Music 42, no. 2 (2004): 122, accessed January 30, 2020,

<2> Maxile, 126.

<3> This claim remains unconfirmed, as there are no public recordings of the Second Symphony nor is the score accessible to the public. For more reading on Reigger, see his Britannica Encyclopedia page.

<4>  Hansonia Caldwell and Hale Smith, “A Man of Many Parts,” The Black Perspective in Music 3, no. 1 (1975): 71, accessed January 30, 2020, doi:10.2307/12143081.

<5> Maxile, 125.

<6> Caldwell and Smith, 71.

<7> Caldwell and Smith, 61.

<8> Caldwell and Smith, 65.

<9> Caldwell and Smith, 66.

<10> Phil Ewell’s blog can be found here: His plenary paper at the 2020 SMT national conference can be found here: The MTO article based on the plenary session can be found here:

<11> Hale Smith, “Here I Stand,” in Readings in Black American Music, 1st ed. New York: W.W. Norton, 1971: 286–287.


Megan Lyons is a PhD candidate and graduate teaching assistant in music theory and history at the University of Connecticut. Her research areas include music theory pedagogy, Amy Beach, Joni Mitchell, and post-tonal music. She has an article in Engaging Students: Essays in Music Pedagogy, a forthcoming chapter in Teaching and Learning Difficult Topics in the Music Classroom, and presented at the 2020 annual meeting of the Society for Music Theory.


Per Nørgård’s Two-Tone Infinity Series in “Wie Ein Kind” (1979-80)

By Paul David Flood

When Danish composer Per Nørgård discovered the art of the schizophrenic Swiss painter Adolf Wölfli at an outsider art exhibit in 1979, he was struck by the fractal construction of these paintings and their similarity to his infinity series, a compositional system based on an integer sequence which he claimed to have “discovered” and used in his works throughout his “hierarchical period” of the 1960s and 70s.<1> Nørgård’s study of Wölfli’s tormented life influenced his subsequent compositional output during the early 1980s, sonically framing his existential crisis of how his “ideal” world may be envisioned.<2> At the heart of these works is the notion of conflict between “idyll and catastrophe” within the human experience; the apperception of unhappiness as a necessary part of experiencing happiness.<3> This essay suggests how Nørgård’s crisis manifested in his compositional technique by analyzing his unconventional use of the infinity series in his first work inspired by Wölfli, Wie Ein Kind.


Adolf Wölfli, General view of the island Neveranger, 1911.


Written between 1979 and 1980 on a commission from the Nordiska Körkomittén, Wie Ein Kind frames conflict through its exploration of childlike experiences.<4> The first and third movements, “Wiigen-Lied” and “Trauermarsch mit einem Unglücksfall,” bear motivic similarities and set a nonsense text written by Wölfli. In the first movement, the soloist’s wails and distant cries evoke the image of a street vendor, or a mother calling to her child from a tower. In the third movement, the soloist attempts to conform with the choir but suffers from an embarrassing stutter which keeps them rhythmically misaligned with the choir. The second movement stands in contrast to its bookending movements. Set to Rainer Marie Rilke’s “Frühlings-Lied,” the movement’s harmonic simplicity and playful texture depicts childlike joy and sensual awareness.<5> A later section of this movement employs a reduced form of Nørgård’s infinity series called the two-tone infinity series. As Wie Ein Kind is the first piece written in the Wölfli period of Nørgård’s oeuvre, Nørgård’s reduction of his own technique signifies the manifestation of his crisis in his composition.

The infinity series is a recursive integer sequence built upon the outward projection of intervals, in both directions, beginning from the very first interval of a given row, counted in semitones.<6> This process of intervallic projection can also be used to reduce an infinity series into a two-tone infinity series. I will introduce the infinity series, demonstrate how Nørgård may have reduced his original series into a two-tone infinity series, and discuss the two-tone infinity series within mm. 98-129 of “Frühlings-Lied.” (Note that measure numbers referenced in this essay align to the score which has been made commercially available by Edition Wilhelm Hansen.<10>) These measures contain four units with similar motives in the tenor and alto voices that are constructed by the two-tone infinity series. Each successive unit is varied from its predecessor in texture, pitch collection, and rhythm of the outer voices.


Figure 1: Nørgård, “Frühlings-Lied,” mm. 97-132. Annotated to show beginnings of each unit.


Figure 2 is an infinity row based on the ascent of two semitones from the starting pitch C. This series will be called Inf. C+2, indicating the starting pitch and the respective ordered pitch interval.

Figure 2: The first twelve pitches of Inf. C+2.


The aforementioned process of constructing an infinity series is one in which the ordered pitch intervals from one note to the next are projected to determine the succeeding pitches in a series. Starting from the beginning of the series, the interval of two rising semitones between C to D will determine the following two pitches. The projection of intervals occurs in such a way that every other note is related, as shown by the blue and red arrows in Figure 2. Each interval projects two notes in opposite directions: the first note to be projected will move in relation to the starting pitch, but in the opposite direction of the interval being projected . In other words, the ascent of two semitones between C and D will project a descent of two semitones between C and the Bb after the D. The next note will be projecte d in the same direction as the interval between C and D, but will do so in relation to the D. The ascent of two semitones from C to D will project the same interval between D and the E after Bb. Therefore, in the context of Inf. C+2, the two-semitone ascent from C to D will project itself such that the third note of the series will move two semitones below C, to Bb, and the fourth note of the series will move two semitones above D, to E.  The series then continues with the interval between D and Bb, a descent of four semitones, leading to D and C as the next two pitches in the serie The process continues toward infinity (or at least where the composer decides to stop).<7>

In Wie Ein Kind, Nørgård uses what is called a two-tone infinity series, a reduced form of the infinity series which contains and repeats the same two pitches which began the original infinity series. The repetitive ordering of these two pitches can be identified through the very process of reduction. To convert Inf. C+2 into a two-tone infinity series, we consider the pitches C and D as numerical values 0 and 1. Each successive pitch will be given a value in relation to the starting pitch; Bb is -1, E is 2, Ab is -2, and so on (these values are given based on the number of whole steps above or below C).<8> Each value will then be added to or subtracted from by a multiple of 2 until it becomes either value 0 or 1, as demonstrated by the blue numbers in Figure 3. If the value is above 1, it will be subtracted by a multiple of 2, and if the value is below 0, it will be added to by a multiple of 2.<9>



Figure 3: Process of reduction from Inf. C+2 to 2TInf. C+2.


Given the above examples, provided for technical context, I now turn to the two-tone infinity series that is present in “Frühlings-Lied.” Between measures 98 and 129 are four units based on the two-tone infinity series. Nørgård se ts a larger two-tone infinity series as the basis of these units, including only the consecutively repeating pitches within that series in these units to create what he calls a “pishop” rhythm . A pishop rhythm is the extraction and tying-together of these consecutively repeating pitches from their larger two-tone series.  Repeated notes from the larger series are converted into tied notes in the score, creating the pishop rhythm. Pitches that do not have a repetition before or after themselves are replaced by a rest, as shown in the Figures 4.1 and 4.2  in which the pishop rhythm in the tenor line is isolated to reveal the series 2TInf. E-9.


Figure 4.1: Nørgård, “Frühlings-Lied,” mm. 98-105, tenor.



Figure 4.2: Conversion between tenor pishop rhythm and 2TInf. E-9.


At first glance, there may appear to be discrepancies in this conversion, but these are intentional and unique to each unit. For example, the pishop rhythm containing an eighth note tied to a quarter note is most likely a textural choice, as it is not an indication that three consecutively repeated pitches exist in the two-tone infinity series (this would not be possible based on the process of reduction). In addition, the large distance between the two pitches of the series used in “Frühlings-Lied” means that neither pitch can be identified with values 0 or 1 as in the technical example above. Nørgård’s use of the two-tone infinity series in other works does allow for this identification of numerical value, and even though the series in question does not possess this quality, it is still considered a two-tone infinity series for functional purposes.<11> Nørgård’s use of a two-tone infinity series that is non-derivative is perhaps another manifestation of his crisis and the transition into his Wölfli period.

The introductory unit in mm. 98-105  features two infinity rows in the inner voices while the basses sing in fifths below. The second unit in mm. 106-113 features variation in the outer voices while the content in the inner voices remains the same. Here, the soprano part enters above while the fifths in the bass move by glissandi. The third unit in mm. 114-121 sees multiple variations. First, the soprano line from the previous unit does not return. There is an additional pitch B added to the tenor line. A possible explanation for the addition of this pitch is to align with the first bass’ Bs on m. 115 and m. 116. The most important variation here is disruption of the pishop rhythm at the end of measure 116, where the rhythmic values proceed from quarter note on G, to eighth note on E, to half note on G, rather than three consecutive occurrences of two tied eighth notes. In addition, the alto and tenor parts fall out of alignment for a brief moment in measure 116, where the alto sings an eighth note on beat two but the tenor holds on for a bit longer with a quarter note. The fourth and final unit in mm. 122-129 sees the return of the soprano line with shorter durations of the material from unit two, and the removal of the glissandi from the bass. At the beginning of this unit, the tenor briefly sings a unison D with the alto. This culminating two-tone unit presents slightly obscured inner voice lines, informed by the two-tone infinity series, with motives in the outer voices to provide accompanying texture.

Nørgård’s use of his infinity series in its reduced, non-derivative form harkens as a point of no return, a glimpse into something that once was but which cannot be revived in its original form. Much in the same way, Nørgård’s study of Wölfli challenged his former vision of the ideal world to accommodate outsiders  such as Wölfli. <12> Nørgård did not necessarily intend for this music to be ekphrastic in its content — that is, he did not attempt to illustrate any particular artwork through musical composition. Instead, the Wölfli works originate from Nørgård’s desire to situate himself as a medium through which the “cries and phantasms of a lonely person, afflicted for decades, who suddenly demanded entry into Per Nørgård’s music” could be heard.<13> Wie Ein Kind frames Nørgård’s struggle to abandon his fixation for order in favor of the opportunities presented by chaos: to embrace the outsider, Wölfli, in his shifting ideology and compositional style over the next few years.



<1> Erling Kullberg, “Beyond Infinity: On the infinity series — the DNA of hierarchical music,” in The Music of Per Nørgård: Fourteen Interpretive Essays, ed. Anders Beyer (Brookfield, VT: Ashgate Publishing Co., 1996), 71.

<2> Jean Christensen, “Part I—New Music in Denmark” in New Music of the Nordic Countries, ed. John D. White (Hillsdale, NY: Pendragon Press, 2002), 41.

<3> Erling Kullberg, “Wie Ein Kind for choir a capella,”

<4> Kullberg, “Wie Ein Kind.”

<5> Per Nørgård, Wie Ein Kind (Copenhagen: Edition Wilhelm Hansen, 1996), iii.

<6> For a mathematical explanation of the infinity series, see the entry on the Thue-Morse Sequence in the On-Line Encyclopedia of Integer Sequences:

<7> Jørgen Mortensen, “Construction by the projection of intervals,”

<8> Note that these values are not to be confused with pitch class set theory, in which C is also 0 but D is 2.

<9> Jørgen Mortensen, “An infinity series with only 4 or 2 different variants,”

<10> The score for Wie Ein Kind  is available for purchase at:–Per-N%C3%B8rg%C3%A5rd/.

<11> Kullberg, “Wie Ein Kind.”

<12> Christensen, 42.

<13> Jørgen I. Jensen, “The Great Change: Per Nørgård and Adolf Wölfli” in The Music of Per Nørgård: Fourteen Interpretive Essays, ed. Anders Beyer (Brookfield, VT: Ashgate Publishing Co, 1996), 9.



Paul David Flood is pursuing his Master’s degree in Musicology at the University of California, Irvine. His research focuses on developments of Nordic musical identity and modernism in Denmark. He is currently working on his Master’s thesis, titled “Embracing the Outsider: Framing Conflict in Per Nørgård’s Wölfli Works.” Additional interests also include contemporary music reception, music and philosophy, vocal literature, and the Eurovision Song Contest. He received his B.A. in Music from Westminster Choir College in 2019 and is an active choral singer.


Rahayu Supanggah’s “Paragraph” and the Problems of Intercultural Collaborations

By Jay M. Arms

The 1986 First International Gamelan Festival and Symposium (Expo ’86) was a catalytic event in the globalization of Indonesian gamelan music. Though gamelan ensembles had already been established in different nations and cultural settings around the world—largely because of university ethnomusicology programs—Expo ’86 marked the first formalized event to bring international groups together. The event engendered numerous intercultural collaborations among its participants, especially between composers of experimental music. One of the composers to attend Expo ’86 was Rahayu Supanggah (b. 1949). By the time of Expo ’86, Supanggah had already established himself as a leading composer in Indonesia, served as director of the karawitan (classical gamelan music) department at the conservatory in Surakarta, Central Java, and received his Ph.D. in ethnomusicology from the University of Paris Diderot. <1> Despite Supanggah’s achievements, his music was relatively unknown among the North American and European composers he met at Expo ‘86. <2> The symposium brought together artists of diverse nationalities, inspiring dreams of what American composer Philip Corner imagined as a “quasi-international avant-garde tradition.” <3>

Taking part in that shared dream, Supanggah later participated in a five-week residency in 1991 with New York based composers’ collective and repertory ensemble Gamelan Son of Lion. <4> During his residency, Supanggah regularly rehearsed with composer-members of the group, participated in collective composition projects, and recorded a one-hour free improvisation with Corner. <5> After getting acquainted with Gamelan Son of Lion’s post-Cagean approach to playing and composing for gamelan, Supanggah composed Paragraph (1991), an experimental composition that renders both the enticing and challenging aspects of intercultural collaboration audible. Supanggah explains that this piece “represents a part of my experience working with American gamelan players, just as a paragraph is a portion of a larger essay.” <6>

Intercultural collaborations are challenging by nature. As Supanggah observes, even in situations where all parties meet with the best of intentions and mutual respect, the realities of post-colonial hegemony often lay just beneath the surface: “Up to the present time, the majority of collaborations between artists from different cultures or countries has been … with more orientation towards the West.” <7> In composing Paragraph, Supanggah had to orient his approach toward the abilities of his Gamelan Son of Lion collaborators. Whereas Supanggah is a recognized master of both traditional Central Javanese music and experimental composition, the musicians of Gamelan Son of Lion were relative novices in Karawitan, having focused almost exclusively on idiosyncratic ways of writing and performing gamelan music. This discrepancy became axiomatic to Supanggah’s concept for this piece, writing: “In [my] compositional process, I usually work with musicians who are familiar to me. This, however, is a new experience for both composer and musicians. As a way of sharing with these new musicians, I have used some fundamental Javanese techniques in this piece, as well as some new ones.” <8>

Paragraph consists of five distinct, but contiguous sections (labeled I–V). It uses the two common Central Javanese scales pelog (seven-tone hemitonic) and slendro (five-tone anhemitonic). <9> These scales are notated using a form of cipher notation known as kepatihan that assigns Arabic numerals to different tones: 1, 2, 3, 4, 5, 6, 7, for pelog and 1, 2, 3, 5, 6 for slendro. It is critical to note that although some notes between scales share the same numeral, that does not necessarily mean they are of the same pitch. <10> Though traditionally these scales are not mixed, Gamelan Son of Lion composers experimented with combining these scales to create new ones beginning in the 1970s. In Paragraph, Supanggah does not combine the scales, but instead, juxtaposes them in such a way that each retains its own identity while sometimes sounding simultaneously.

The opening of the piece (Part I) uses the pelog scale and features a simple repeating cycle. The instruments used here are mostly keyed metallophones that each play one octave of the scale. From the highest octave to the lowest, these metallophones are called peking, (labeled SP in Example 1), saron (SB), demung (DM), and slenthem (SL). These instruments join the piece one at a time in descending order from highest to lowest in a gradual process of accumulation. Such processes are fairly typical of Gamelan Son of Lion compositions, and Supanggah’s adoption of it here may be a nod to the group for which the piece is composed. In Example 1, all parts are notated together despite entering one at a time to save space in the score.


Example 1. First phrase of Paragraph


Once all of these melodic instruments are present, the large gongs begin to articulate a colotomic structure reminiscent of a karawitan composition. After a few repetitions of this complete texture, a brief transition played in unison leads to Part II, in a tempo twice as fast as that of Part I and using a different pathet (mode) of the pelog scale that ushers in a new character. This lively, jubilant section expresses a feeling of excitement in terms of both tempo and tonality, alternately cadencing on pelog 6 and 7. The mood seems to suggest the sheer joy of playing together and the sense of excitement swells before coming to an abrupt halt.

Part III follows immediately with more contemplative, pensive mood. It consists of an improvisation played on gender (multi-octave metallophone), suling (end-blown bamboo flute), and Chinese erhu (bowed spiked fiddle). This improvisation is modeled on the Central Javanese practice of pathetan, short pieces in free rhythm in which three or four instruments weave together their semi-improvised melodies that diverge from and converge to goal tones. <11> The use of pathetan, a subtler genre of Central Javanese music, suggests more than a mere aesthetic contrast to Part II. Whereas the composer-musicians of gamelan Son of Lion have a proficiency in playing the basic instruments of a gamelan, pathetan requires a deeper knowledge of Javanese music theory than most of the musicians have had. By including a pathetan in this composition, Supanggah brings into focus some of the limitations of collaboration itself: the abilities of all collaborators shape the potential of the results. For Paragraph, the pathetan was played by Supanggah, his colleague composer I Wayan Sadra, and ethnomusicologist Barbara Benary, excluding the musicians who lacked such skills.

Part IV begins immediately as Part III comes to close. The ensemble gradually re-enters the piece through another accumulating process that layers different ostinati in the slendro scale. Once all of the ostinati are cycling, the texture devolves into a free improvisation involving all manner of instruments. <12> This section taps into the egalitarian idealism often associated with free improvisation and which some members of Gamelan Son of Lion projected onto gamelan ensembles in general. <13> This improvisation builds in intensity, and then begins to simplify and become quieter, leading to the fifth and final section.


Example 2. Layered Ostinati in Part IV


The parable of collaboration culminates in Part V. This section brings together the themes that preceded it in stark juxtaposition. Some of the instruments return to the pelog material of Part II, while other instruments introduce a new melody in slendro, creating haunting effect. The jubilant melodies from Part II emerge first, insistently silencing the collective improvisation of Part IV and asserting one vision of unification out of the chaos. But that vision is subverted shortly thereafter by the slendro material that articulates a contrasting, even incompatible vision of its own. The mixing of these scales is highly unusual in a traditional setting, and the dissonances created through this juxtaposition are recognizable even to the uninitiated listener. We learn at the end that no true synthesis has occurred in the course of the collaboration. Each theme remains effectively unchanged by the encounter and unobservant of the other cohabitating the musical space. The piece is suddenly brought to an end by a stroke of a gong, with no resolution of the dissonant mash-up.

Throughout the piece Supanggah guides the listener through a journey. Each section can be understood to represent a certain aspect of the collaborative process: methodical discovery; excitement; realization of limitations, exploration; and finally, Paragraph presents a skeptical outlook on the nature of intercultural collaborations. It is a well-crafted composition that techniques of New York experimentalism and Central Javanese karawitan alternate. But Paragraph does not simply celebrate its syncretism or reassure the listener of an unproblematic multiculturalism. Supanggah encourages us to consider the kinds of compromises that must be made in such collaborations and who is expected to make those compromises. He writes, “It is not uncommon, due to a high level of enthusiasm and willingness to make sacrifices, for a participant to be ‘willing’ to throw off his own identity, and subsequently melt and become or make something new … based on inadequate (mutual) understanding.” <14> In some ways Paragraph can be heard as such a capitulation to the limited abilities of the group. But the ending juxtapositions suggest a more complicated interpretation in which the composer refused to compromise his own artistic sensibilities and instead utilized the imbalanced experiences of the performers to formulate a deeper meaning for the composition.





<1> See Vincent McDermott, “Gamelans and New Music,” The Musical Quarterly 72, No. 1 (1986): 16–27 for more background on Supanggah.

<2> Today Supanggah is internationally recognized for his own compositions, scholarly writings, and for his numerous high-profile intercultural collaborations such as Peter Brook’s Mahabarata (1994), Ong Keng Sen’s Lear (1995), and Robert Wilson’s I La Galigo (2004), and Garin Nugroho’s Opera Jawa (2006) and Setan Jawa (2017).

<3> Philip Corner quoted in Jody Diamond, “Philip Corner: You Can Only Be Who You Are,” Balungan 2, No. 3 (1986): 23.

<4> The residencies were organized by composer Jody Diamond as part of the Festival of Indonesia, a series of NEA sponsored events that took place in different locations around the United States. The residencies produced several compositions and collaborations between American and Indonesian composers that are documented and recorded in Jody Diamond, “Interaction: New Music for Gamelan,” Leonardo Music Journal 2, No. 1 (1992): 97–98.

<5> Rahayu Supanggah and Philip Corner, “Together in New York,” Setola Di Maiale (2015): SM2760.

<6> Rahayu Supanggah, Program notes for Paragraph, Concert program for Experimental Composers From Indonesia: New Music by Rahayu Supanggah and I Wayan Sadra November 20, 1991. Accessed August 8, 2020,

<7> Rahayu Supanggah, “A Story of Arts Collaboration,” Proceedings of the First Asia-Pacific Arts Forum (2000): 399.

<8> Rahayu Supanggah, Program Notes for Paragraph.

<9> The score for Paragraph is published by the American Gamelan Institute. Accessed August 8, 2020,

<10> In fact, the tuning of each gamelan is unique, and compositions generally sound different when transferred from one gamelan to another. Gamelan Son of Lion’s scales share two common tones between the scales known as tumbuk. Pitch 6 is the same between slendro and pelog, and slendro 5 is the same pitch as pelog 4.

<11> See Benjamin Brinner, “At The Border of Sound and Silence: The Use and Function of Pathetan in Javanese Gamelan,” Asian Music 21, No. 1 (1989/90): 1–34.

<12> In the recording and premier performance, this improvisation involved the full gamelan, clarinet, electric bass, erhu, piano, suling, trombone, and violin, though any other instruments would also be accepted.

<13> For example, See Daniel Goode, “How Can the Orchestra be More Like the Gamelan?,” New Music Box, accessed October 2, 2020,

<14> Rahayu Supanggah, “A Story of Arts Collaboration,” 403.




Jay M. Arms is a lecturer of ethnomusicology at the University of Pittsburgh where he teaches the West Javanese gamelan ensemble. His research focuses on the globalization of gamelan music and its intersections with American experimental music and ethnomusicology. He is the co-editor of the journal Balungan that regularly publishes articles and scores related to gamelan and its related arts.

Whose Authorship? Authenticity in Chinese Popular Music under Global Modernism 

By Ya-Hui Cheng


In his discussion of literary forms during the period of global modernism, Ramazani (2016) argued that the commonly used scheme of foreign form and local content (abbr. FFLC) neglected transcultural materials and favored Western centricity, a trend inherited from colonialism. To comprehend the local elements, Ramazani suggested three schemes to examine local aspects: foreign form and foreign content (FFFC), local form and foreign content (LFFC), and local form and local content (LFLC). Those schemes complement FFLC to formulate additional analytic devices in studies of global modernism in the twentieth-first century, or geomodernity as specified by Gavin Lee (2019).  


A similar challenge occurs with the study of transcultural meaning in musical discourse when defining authentic musical vocabulary from the otherness in world music programs in the West. The main issue remains similar to Ramazani’s in that the boundary between foreign and local aspects is hard to delimit and easy to oversimplify or mistakenly dichotomize. Similarly, the notion of otherness in studies of cultural displacement resonates with the condition of intimacy between private and public realms. <1> These perspectives form the debate on the music for young adults in China in the Post-Mao era when China opened its domestic market to the free world. At the time, the most well-known youth music was Northwestern Wind rock, which integrated foreign and local elements to present the intimacy between the public and private realms. The styles of rock music from the free world inspired youth in China. In the meantime, the ongoing domestic root-seeking program also motivated youth to consider renovating the cultural tradition. Chinese youth adopted folk songs from the Northwestern province and synthesized them with the Western rock to present a type of rock sonority that was replete with Chinese characteristics. This music received global attention when Cui Jian performed his Northwestern Wind rock song Nothing to My Name at the 1989 Tiananmen Domestic Incident. After that, the image of Cui Jian and his rock signified Chinese youth rebellion, which has been frequently studied. <2>  Among the authors who have addressed this phenomenon, de Kloet used “rock mythology”, which includes a list of assumptions about the rebellious spirit of rock in China and elsewhere, to argue that many of these studies proliferated rock’s public intimacy from the West to China. <3> They transformed the Northwestern Wind rock into a collective global memory of Chinese youth rebellion. 




Cui Jian, Nothing to My Name (released in 1989).


Whereas global memory could conflict with local memory (Huyssen 2003), Chinese songwriters stayed tied to the local cultural environment. They claimed that sociopolitical rebellions were not their concern (Cui Jian and Zhou Guoping 2012). Instead, it is the expressive quality from Northwestern folksongs that depicted their sentiments and motivated them to renovate this tradition. This renovation coincidentally connected them with the global pop trend through its cultural roots. Cultural insiders supported this statement and claimed to own the music’s authorship because their heritage of this folk tradition can be traced to centuries long ago (Brace 1991).


Audiences outside of China interpreted the sounds to be derived from global impacts or from Western pop cultures and presumed its raw expression to be from the spirit of Western rock. There is an apparent discrepancy within this interpretation. The examination of the structure of the Northwestern folksong and its social function can clarify the debate. Northwestern folksong often utilizes a two-part format, similar to verse and chorus. This music is distinct from folk music in other provinces in China. Partly, its motivic pattern is concise, and partly, its phrase structure is symmetrical. These features of Northwestern folksong resemble similar elements in the music of the West, which in turn suggests a musical connection between China and the West has existed in the folk tradition. Furthermore, Northwestern folksong had been the primary resource to produce communist Red songs and disseminate the Red ideologies during the wars between the Chinese Communist and Nationalist Parties before 1949 and before the importation of Western folk-rock into China. By transforming Northwestern folksong into rock in the 1980s, this music continued the propagandistic function to support the socialist social reform across the nation. This is evident when Cui Jian stated that his songs were devices to arouse reform, and this music is “the most comfortable musical language” for him to depict the socialist style of individualism. <4>


Likewise, folk-rock produced in Taiwan and Hong Kong from the 1970s was popular in China. Unlike the rock music made by the youth in mainland China, music from Taiwan and Hong Kong mimicked Western rock to build the Western-influenced youth culture. If “the discourse of mimicry is constructed around an ambivalence,” as Bhabha suggested, the mimicry signified a prototype that resulted in variation in the folk-rock of Taiwan, Hong Kong, and China. <5> Young adults in China received the spirit of rock from Taiwan and Hong Kong, but they adjusted the musical language by adopting the authentic folksong to describe their cultural intimacy. The outcome expresses liberation from the Western influences because the applied musical language is from Chinese cultural tradition, which, coincidentally, is comparable with that of the West. The liberation reconfigured the colonial concept of mimicry from the Westernized Chinese societies of Taiwan and Hong Kong. It removed the notion of the spirit of Western rock, established China’s own youth characteristics in the Post-Mao era, and declared that any foreign production that wishes to be accepted by the Chinese people must connect with the Chinese cultural tradition and absorb the local socialist attitudes. 


The integration of Chinese tradition in popular music production can also be found in the 1930s Shanghai Jazz period in the first Chinese popular song—Drizzle. This song was written by Li Jinhui in 1927 and recorded in 1928 and 1934, respectively. Li adopted the verse form and Chinese pentatonic music to present the modern style of sounds that Chinese audiences referred to as a “familiar and simultaneously strange” listening experience. <6> For Li, the ambiguous listening experience indicated his strategies in songwriting. Li suggested that while most Chinese people only listened to Chinese theater music, he intended to create a fusion style of music that integrated Chinese tradition and music from modern societies such as America and Japan. By doing so, he implemented the concept of modernity to everyday listeners while retaining the Chinese characteristics to attract traditional Chinese theater goers (Li 1982). The music that indicated familiarity with Chinese cultural insiders resulted in the estrangement of cultural outsiders and vice versa. The quality of authenticity became vague as its delimitation depended on the listener’s cultural background.  



Li Jinhui, Drizzle (1927).


In effect, although Ramazani suggests a multi-purpose framework that revives the contents of cultural diffusion, my work on the Chinese fusion style of popular music suggests another dimension for consideration. Transcultural aspects are not the sole factor in the studies of local and foreign influences in content or form. Delimitation and authorship should be part of the discussion. If using the previous example of adaptable Chinese melodies, materials from the local aspect are subtly selected because they coincide with that of the global aspect. Chinese songwriters primarily adopted folksong that contained similar structures as Western popular music. If we study those Chinese popular songs, how can we delimit the local and global elements? In an intensively globalized world, when a sophisticated cultural understanding purposely aims to present multiple contextual meanings for any global citizen to feel related to the original source, who can claim the authorship or make a cultural delimitation? 





<1>. The special issue of intimacy in the Journal of Critical Inquiry, where Berlant specified that intimacy “involves an aspiration for a narrative about something shared” (1998): 281, has been an inspiration in this article.  Intimacy speaks the inner sentiment in the private realm which could turn into public sentiment when a shared feeling is discovered and expounded.

<2>. Jones 1992, Barmé 1999, de Kloet 2001, Baranovitch 2003, and Mittler 2016.

<3>. De Kloet 2001.

<4>. Cui and Zhao 2012: 41.

<5>. Bhabha 1994:122.

<6>. See CCTV The Last Century Pop Music of China.


Ya-Hui Cheng, a native of Taiwan, is Assistant Professor of Music Theory at the University of South Florida. Her current research focus is on the emergence of Chinese popular music including jazz, rock and hip hop and their impact on the capitalist and socialist societies of Taiwan and China. Other than popular music study, Dr. Cheng also works on Giacomo Puccini’s operas. She was the recipient of the National Opera Association Dissertation Competition Biennial prize for her Puccini research and is the author of book Puccini’s Women: Structuring the Role of Feminine in Puccini’s Opera.


Selected Bibliography:

Aaendt, Hannah. The Human Condition, 2nd edition. Chicago: The University of Chicago Press, 1998.

Baranovitch, Nimrod. China’s New Voices: Popular Music, Ethnicity, Gender, and Politics, 1978-1997. Berkeley: University of California Press, 2003. 

Berlant, Lauren. “Intimacy: A Special Issue,” in Critical Inquiry, Vol. 24, No. 2, Intimacy (Winter, 1998): 281-88.  

Barmé, Geremie R. In the Red: On Contemporary Chinese Culture. New York: Columbia University Press, 1999. 

Bhabha, Homi K. The Location of Culture. New York: Routledge, 1994.

Brace, Tim. Popular Music in Contemporary Beijing: Modernism and Cultural Identity,” in Asian Music, Vol. 22, No, 2, Views of Music in China Today (Spring – Summer, 1991): 43-66.

Cui, Jian, and Zhou Guoping. Ziyou fengge (FreeStyle). Guangxi Normal Large, 2009.  

De Kloet, Jeroen. Red Sonic Trajectories: Popular Music and Youth in Urban China. Amsterdam: University of Amsterdam, 2001. 

Foucault, Michel. “What is an Author?” The Norton Anthology: Theory and Criticism. New York: Norton (2001):1622-36.

Huyssen, Andreas. Diaspora and Nation: Migration into Other Pasts. New German Critique, No. 88, Contemporary German Literature (Winter, 2003): 147-64. 

Jones, Andrew. Like a Knife: Ideology and Genre in Contemporary Chinese Popular 

    Music. New York: Cornell University Press, 1992. 

Lee, Gavin. “The Promise of Global Music Modernism.” Paper presented at the Annual Meeting of the Society for Music Theory, Global Interculturalism and Musical Peripheries Interest Group, Columbus, OH, November 9th, 2019. 

Li Jinhui. Wo he mingyueshe (I and Brighten Moon Troup) vol. 1 / 2 in Wenhua Shi liao Congkan Vol. 3 (1982): 90-127. 

Mittler, Barbara. A Continuous Revolution: Making Sense of Cultural Revolution Culture. Cambridge: Harvard University Press, 2016. 

Ramazani, Jahan. “Form,” in Hayot, Eric and Rebecca L. Walkowitz, eds. A New Vocabulary for Global Modernism. New York: Columbia University Press (2016): 114-29. 

Jōji Yuasa – Cosmos Haptic for piano (1957)

By Ron Squibbs

Jōji Yuasa (b. 1929) is one of the most important Japanese composers of the second half of the twentieth century and the early part of the twenty-first century. Along with his compatriot, Tōru Takemitsu (1930-96), Yuasa was a member of Jikken Kōbō (The Experimental Workshop), an interdisciplinary group of composers, artists, and writers that sought to define a characteristically Japanese avant-garde aesthetic in the 1950s. Musicologist Luciana Galliano has described the aim of Jikken Kōbō as follows: “The group’s intent was … to mediate Japanese sensibility with the tantalizing, unknown material of western contemporary music in order to achieve an original compositional expression which corresponded, in turn, to personal expressive desires.” <1> One of Jikken Kōbō’s activities was a series of concerts that featured music by Western modernist composers—among them Schoenberg and Messiaen—as well as new works by the group’s members. Yuasa’s Cosmos Haptic (1957) for piano, the opening measures of which are shown in Example 1, is a representative work from this period. (The score is available from Schott Music.)

Example 1: Jōji Yuasa, Cosmos Haptic for piano (1957), mm. 1-4. <2>

A recording of the work may be heard here.

One of Yuasa’s sources of aesthetic inspiration at this time was the traditional Japanese Nō theater. <3> Characteristic of Nō is the slow and stylized intonation of text in which the durations of individual syllables vary within an eight-beat pattern known as honji. “Differing from metric systems with four or eight beats such as are found in Western music, … honji is essentially based on a substructure of single beats. These are assumed to be even, as in a metronomic continuity, but, actually, each beat has its own ma [space] which shapes the substance of its continuity.” <4> Variations in the durations of the beats are known as mitsuji, which Yuasa has cited as an inspiration for the final movement of his Projection for Seven Players (1955-56), the work immediately prior to Cosmos Haptic. <5> A pattern of eight articulations of varying duration, likely also inspired by mitsuji, may be observed at the opening of Cosmos Haptic. Eight articulations are presented in the upper staff in Example 1, with the eighth-note rest in m. 3 dividing them into two groups of four. The first three articulations decrease in duration, with the duration increasing again from the third to the fourth articulations. The durations among the four articulations in the next group (in mm. 3-4) also first decrease, then increase.

Another source of inspiration for Yuasa was the harmonic language of modern Western composers, both twelve-tone and non-twelve-tone. Among twelve-tone composers Yuasa favored Webern, the temporal nature of whose music suggested an affinity with Eastern aesthetics. Describing his discoveries in the 1950s, Yuasa wrote, “I was the then finding that a commonality existed between the timespace of Nō and that of Webern’s music.” <6> Webern’s austere approach to twelve-tone composition provided a model for Projection for Seven Players (1955-56). For Cosmos Haptic, on the other hand, Yuasa turned to harmonic resources associated with Messiaen. <7> In his implementation of these harmonic resources—such as Messiaen’s modes of limited transposition—Yuasa preferred an austere style that he associated with the music of Varèse and Jolivet more than with that of Messiaen. <8>

The opening measures of Cosmos Haptic present two of Messiaen’s modes of limited transposition. The harmonic units articulated on the surface of the music are four-note groups, an initial group along with three of its transpositions: F♯-G♯-C-D in the upper staff, C♯-D♯-G-A in the middle staff, and A♭-B♭-D-E, and F-G-B-C♯ in the upper staff. When these four-note groups are combined in successive pairs, instances of two of Messiaen’s modes result: Mode 4, C-C♯-D-D♯-F♯-G-G♯-A, is presented in mm. 1-3 and Mode 2, C♯-D-E-F-G-A♭-B♭-B, in m. 4. <9> Additionally, the combination of these two eight-note modes results in the presentation of the aggregate of all twelve chromatic pitch-classes, which is completed by the final chord in the passage. Aggregate completion is a structural principle that is fundamental to twelve-tone composition but is observable in the music of some non-twelve-tone composers as well. <10>

A further characteristic that Yuasa’s Cosmos Haptic shares with the work of modern Western composers is the symmetrical disposition of its pitches around axis points within pitch space. <11> Each of the four-note groups in Example 1 is symmetrical around a different axis pitch. Within the first group, the pairs of pitches F♯5/G♯5 and C5/D6 are both symmetrically disposed around G5, which is not sounded but serves as a point of orientation around which the other pitches are situated. The axis pitches for the remaining groups are D4, A5, and F♯6. Overall, the roving axis pitches indicate motion in the treble range that moves higher as the excerpt progresses. Stepping back from the level of local details to take in longer spans of music, analysis according to axis pitches suggests the slow unfolding of a deliberate process. The eight-note group in mm. 1-3, for example, is symmetrical around a pair of axis pitches, A♯4/B4, which precisely fill in the space between the A4 at the top of the lower four-note group and the C5 at the bottom of the upper four-note group. The eight-note group in m. 4 is symmetrical around the pair of axis pitches, C♯6/D6. One member of this pair, D6, appears on the downbeat of m. 4 as part of a three-note fragment, repeating part of the first four-note group. Rather than appearing to be a merely incidental detail, D6 may be interpreted as a link in pitch space between the first and second eight-note groups.

The structural role of symmetry becomes even more prominent in the dramatic conclusion to the first section of the work, a portion of which is shown in Example 2. In this passage, musical materials from the opening of the work are transformed and recontextualized. The first four-note group from mm. 1-3 in Example 1 reappears as the upper strand of the middle staff in m. 11 (the first measure of Example 2) in a rhythmically concentrated form. The lower strand of the middle staff of the same measure presents a new four-note group, a transposition up a major second from the four-note group that had appeared in the middle staff in mm. 2-4. As a result of this transposition, the combination of the two four-note groups in m. 11 does not produce an instance of Messiaen’s Mode 4, as it had done in mm. 1-3, but instead forms a new instance of Messiaen’s Mode 2: D-E♭-F-F♯-G♯-A-B-C. The transposition also causes the previous pitch axis of A♯4/B4 from mm. 1-3 to shift up a minor second to B4/C5 in m. 11. This new pitch axis is maintained in m. 12, where the notes of Mode 2 from m. 11 are revoiced in a way that highlights its dissonant intervals: two minor ninths in the outer staves surround two tritones in the middle staff.

Example 2: Yuasa, Cosmos Haptic, mm. 11-13. <12>

The transformation of previously heard materials continues at the beginning of m. 13, where the four-note group in the upper strand of the middle staff recalls the four-note group from m. 4. In m. 13, this four-note group combines with the four-note group that had been introduced in the lower strand in m. 11 to form a new instance of Messiaen’s Mode 4: D-E♭-F-F♯-G A-B-C. At this point, both the upper and lower four-note groups from mm. 1-3 have been transposed up by a whole step. Consequently, the pitch axis has shifted upward again, to C5/C♯5. This shift of axis creates a momentary disruption in the equilibrium of the passage, which is restored in the middle of m. 13, where the axis returns to B4/C5, where it had been in mm. 11-12. At this point the transposition of Mode 2 that had been introduced in mm. 11-12 returns in a new voicing: the minor ninths that appeared in the upper and lower staves in m. 12 have now been inverted to become major sevenths in m. 13.

Further transformations of materials in Cosmos Haptic include the reshaping of the eight-note mode from mm. 1-3 into an unaccompanied melody (not shown). This melody, whose range and contour suggest an affinity with the nōkan (Nō flute), forms the basis for an extended middle section. <13> Musical gestures related to the work’s opening recur intermittently during this middle section and return at its closing. The slow processes of transposition initiated at the start of the work continue throughout, so that its conclusion does not form a closed circle with its beginning, but rather suggests an opening out to an as-yet-undetermined future.

Cosmos Haptic is a pivotal work in Yuasa’s development as a composer. From this point forward, Yuasa has continued to forge a personal synthesis between harmonic resources typically associated with Western modernism and what he refers to as “traditional Japanese concepts of time.” <14> Among his later works are four more bearing the title Cosmos Haptic. This series includes solo, chamber, and orchestral works, the most distinctively Japanese among them being Cosmos Haptic III – Kokuh for twenty-string koto and shakuhachi. <15> In these works and many others, Yuasa has succeeded in generating an oeuvre that richly rewards repeated, attentive listening.

<1> Luciana Galliano, The Music of Jōji Yuasa, ed. Peter Burt (Newcastle upon Tyne: Cambridge Scholars Publishing, 2012), 8. For more on Jikken Kōbō, see Galliano, The Music of Jōji Yuasa, 5-33, Peter Burt, The Music of Tōru Takemitsu (New York: Cambridge University Press, 2001), 39-49, and Luciana Galliano, Yōgaku: Japanese Music in the Twentieth Century, trans. Martin Mayes (Lanham, Maryland: Scarecrow Press, 2002), 150-66.
<2> Jōji Yuasa, Cosmos Haptic. Copyright © 1957 Schott Music Co. Ltd., Tokyo. Copyright © renewed. All rights reserved. Used by permission of European American Music Distributors Company, sole U.S. and Canadian agent for Schott Music Co. Ltd., Tokyo, publisher and copyright owner.
<3> Jōji Yuasa, “The World of Nō as I Perceive It, Concerning Some Problems in Music,” Perspectives of New Music 31, no. 2 (Summer 1993): 186-91.
<4> Jōji Yuasa, “Temporality and I: From the Composer’s Workshop,” Perspectives of New Music 31, no. 2 (Summer 1993): 220.
<5> Yuasa, “Temporality and I,” 220. Projection for Seven Players and Cosmos Haptic, the latter performed by Takahorio Sonada, its dedicatee and a member of Jikken Kōbō, are both included on the CD Music from Experimental Workshop, Fontec FOCD3417. An example of mitsuji in the context of Nō chant may be found here.
<6> Yuasa, “Temporality and I,” 218.
<7> Galliano, The Music of Jōji Yuasa, 26.
<8> Galliano, The Music of Jōji Yuasa, 21-25.
<9> On the modes of limited transposition, see Olivier Messiaen, The Technique of My Musical Language, trans. John Satterfield (Paris: Leduc, 1956), vol. 1, 58-62, vol. 2, 50-54.
<10> On aggregate completion in Varèse, see Robert Morris, “Equivalence and Similarity in Pitch and Their Interaction with PCSet Theory,” Journal of Music Theory 39, no. 2 (Autumn 1995): 207-43.
<11> On inversional symmetry and axis pitches, see Joseph Straus, Introduction to Post-Tonal Theory, 4th ed. (New York: Norton, 2016), 232-44. On the use of pitch space as a structural principle, see Jonathan Bernard, The Music of Edgard Varèse. (New Haven: Yale University Press, 1987). For an approach to Cosmos Haptic that makes use of pitch-space graphs similar to Bernard’s, see Ron Squibbs, “Structure of Time, Structure of Space: Eastern and Western Influences in Jōji Yuasa’s Cosmos Haptic” (paper presented at Music Theory Society of New York State Annual Meeting, Ithaca, NY, April 10, 1999).
<12> Jōji Yuasa, Cosmos Haptic. Copyright © 1957 Schott Music Co. Ltd., Tokyo. Copyright © renewed. All rights reserved. Used by permission of European American Music Distributors Company, sole U.S. and Canadian agent for Schott Music Co. Ltd., Tokyo, publisher and copyright owner.
<13> An example of nōkan performance may be found here.
<14> Yuasa, “Temporality and I,” 218.
<15> Recordings of all of the works in the Cosmos Haptic series may be found in the Discography.

On the Keyboard: Piano Works of Jōji Yuasa. Ronald Squibbs, piano. Aucourant Records AUREC-0501-1.
Music from Experimental Workshop. Various performers. Fontec FOCD3417.
Piano Transfiguration. Aki Takahashi, piano. Camerata CMCD-15145~6.
Nanae. Nanae Yoshimura, 20-string koto, Kifu Mitsuhashi, shakuhachi. Camerata 32CM-189.
Cello ~ Japanese Sounds. Tsuyoshi Tsutsumi, cello, Akira Wakabayashi, piano, Seizan Sakata, shakuhachi. Sony Records SRCR 2291.
TIME of Orchestral Time: Works by Jōji Yuasa. Various performers. Fontec FOCD9288.

Acknowledgement: Jōji Yuasa, Cosmos Haptic. Copyright © 1957 Schott Music Co. Ltd., Tokyo. Copyright © renewed. All rights reserved. Excerpts used by permission of European American Music Distributors Company, sole U.S. and Canadian agent for Schott Music Co. Ltd., Tokyo, publisher and copyright owner.


Ron Squibbs is Associate Professor of Music at the University of Connecticut, Storrs. He has published on the music of Iannis Xenakis and has presented on the music of Xenakis, Yuasa, Rudhyar, John Luther Adams, and others. He has recorded piano music by Yuasa and Rudhyar for Aucourant Records and by Peter Garland for Cold Blue Music (forthcoming). Further information on his research may be found at