Atonal Music

The attitude to use whole numbers to point out notes in the twelve-tone chromatic scale dates back to about a century ago. Although the trend to quantify and to catalogue has always been present in Western music, it was with the dissolution of the tonal system that this trend became urgent, especially among those composers who were looking for new forms of expression.

All’inizio del XX secolo molti compositori furono attratti dal fascino dei collegamenti accordali ciclici a distanza di intervalli regolari. Questi collegamenti permettevano di allontanarsi in maniera decisa dal sistema tonale, basato sul rapporto di quinta, per indagare le caratteristiche dei rapporti intervallari che dividevano l’ottava in parti uguali. Andò così affermandosi una tendenza alla ripetizione periodica di elementi musicali su livelli di trasposizione che tornavano alla posizione iniziale, in una sorta di progressione statica. Alcuni spunti ereditati dalla tradizione novecentesca hanno fornito le basi per sviluppare una tecnica di composizione musicale a carattere ricorsivo denominata ‘caleidociclica’. Applicato alla composizione, un caleidociclo (termine derivato da alcuni procedimenti grafici di M. C. Escher in cui le parti di un oggetto siano copie su scala diversa dell’oggetto stesso) impiega le proprietà verticali degli accordi per regolarne anche lo svolgimento orizzontale. Il calcolo razionale, connaturato a questo specifico modo di affrontare la composizione, non resta comunque mai fine a se stesso, proponendosi piuttosto come banco di prova per saggiare la capacità del musicista di passare da un’applicazione meccanica delle regole e delle tecniche a un’altra ben più flessibile, complessa e creativa.

"Carter's music poses struggles of opposition, for instance in timbre (Double Concerto), space (String Quartet No. 3) or pulse (String Quartet No. 5). His preference for the all-interval tetrachords, 4–Z15 [0, 1, 4, 6] and 4–Z29 [0, 1, 3, 7], is also well known. From these facets of Carter's music, I develop a narrative interpretation of his Petrarch sonnet–inspired solo flute piece, Scrivo in Vento (1991). Specifically, I forge narrative pathways by imagining the two tetrachords as active agents opposed in competition. Previous Scrivo analyses (Capuzzo 2002; Childs 2006) stress continuity by revealing Q-transforms and common-note voice leading between the tetrachords. While acknowledging such features, my analysis emphasises oppositional struggle by tracing the tetrachords as separate entities which cooperate and conflict as they manoeuvre to outdo each other.

The analysis advances three theses: (1) it guides listening to and reading Scrivo in a way which resonates with Carter's concern for the aesthetics of oppositional struggle, his choice of a sonnet as inspiration and his affinity for all-interval tetrachords; (2) it shows that music-analytical detail can be organised into dramatic narratives by (a) projecting dramatic roles onto categories asserted by a formal theory and (b) treating the formal theory's relations metaphorically as actions performed by each role as the musical work unfolds; and (3) it shows how detailed pc-set analysis can support a Heraclitean view of music: a flux of opposing forces seeking and resisting unity."

"Carter's music poses struggles of opposition, for instance in timbre (Double Concerto), space (String Quartet No. 3) or pulse (String Quartet No. 5). His preference for the all-interval tetrachords, 4–Z15 [0, 1, 4, 6] and 4–Z29 [0, 1, 3, 7], is also well known. From these facets of Carter's music, I develop a narrative interpretation of his Petrarch sonnet–inspired solo flute piece, Scrivo in Vento (1991). Specifically, I forge narrative pathways by imagining the two tetrachords as active agents opposed in competition. Previous Scrivo analyses (Capuzzo 2002; Childs 2006) stress continuity by revealing Q-transforms and common-note voice leading between the tetrachords. While acknowledging such features, my analysis emphasises oppositional struggle by tracing the tetrachords as separate entities which cooperate and conflict as they manoeuvre to outdo each other.

The analysis advances three theses: (1) it guides listening to and reading Scrivo in a way which resonates with Carter's concern for the aesthetics of oppositional struggle, his choice of a sonnet as inspiration and his affinity for all-interval tetrachords; (2) it shows that music-analytical detail can be organised into dramatic narratives by (a) projecting dramatic roles onto categories asserted by a formal theory and (b) treating the formal theory's relations metaphorically as actions performed by each role as the musical work unfolds; and (3) it shows how detailed pc-set analysis can support a Heraclitean view of music: a flux of opposing forces seeking and resisting unity."

In this essay, I explore historical and theoretical issues germane to an understanding of an 1885 piano composition with an intriguing title: Liszt’s Bagatelle ohne Tonart—a bagatelle “without tonality” or “without a key.” After briefly describing the work’s history and musical associations with other compositions by Liszt, I survey two present-day approaches that reveal ways in which the work defies tonality: octatonic interpretations via set-class examinations, and Schenker-influenced prolongational models. I then turn to focus instead on how the Bagatelle fit within the framework of nineteenth-century musical thought; how its processes were supported by contemporaneously evolving theories of chromaticism. Partly through an analysis based on the practice of Gottfried Weber (1779–1839), I demonstrate that the Bagatelle is not a piece “without tonality” as much as it is one “without the fulfillment of the tonic.” It maintains harmonic tension by avoiding anticipated resolutions, as well as by preserving a sense of ambiguity as to what the actual “missing” key is. Next, I consider why Liszt was prompted to write a piece in such a manner. We know that he was a proponent of musical progress—of Zukunftsmusik (“music of the future”)—but for this fact to be relevant we must confirm, first, that Liszt had definite ideas about a Zukunftsharmoniesystem; and second, that such a system is reflected in the processes exhibited by the Bagatelle. I argue that the Bagatelle’s traits are indeed in accordance with theoretical views about music’s future direction, to which Liszt subscribed. Relevant theories of Karl Friedrich Weitzmann (1808–80) and François-Joseph Fétis (1784–1871) are assessed. Lastly, in a “Schoenbergian epilogue” I explore connections between Liszt’s operations and Schoenberg’s ideas, addressing historical associations that conjoin their views of composing “ohne Tonart.” I conclude that the 1885 Bagatelle’s attenuation of tonality was part of a tradition that extended from the mid-nineteenth into the early twentieth century—one that stretched from Liszt and his contemporaries through Schoenberg and his pupils and beyond, embracing along the way the theoretical prescriptions of Weitzmann, Fétis, and Schoenberg himself. The various threads of theory and analysis explored in this essay contribute to an understanding of the same strand of musical evolution: the increasing circumvention of tonality to the point that a piece could be written “ohne Tonart.”  (NB: For this article, the author was awarded the  2006 “Emerging Scholar Award” by the Society for Music Theory.)

This paper will examine Arnold Schönberg’s influence on the modern jazz world through the teachings of one of its most influential theorists and pedagogues Dennis Sandole, mentor to John Coltrane, James Moody, Art Farmer, Jim Hall, Pat Martino, and many other important jazz artists.

This paper suggests that Schönberg’s work was a substantial influence on Sandole and that Schönberg’s compositional innovations such as the use of trichords, tetrachords and hexachords, octave displacement techniques, the use of combinatorial hexachords, chromatic completion, and the use of major thirds tonal relationships were key aspects of Sandole’s jazz improvisation and compositional pedagogy. Some of these concepts would be utilised by John Coltrane to change the musical language of modern jazz permanently.

Through analysis of all three men’s work, this paper will illustrate conceptual connections between Schönberg’s compositional practice and Sandole’s pedagogical literature which would go on to influence John Coltrane’s creative output and that of many great jazz practitioners ever since, helping to solidify Schönbergian thinking within the syntax of modern jazz.

The paper tracks the origins of horizontal and vertical synthesis in early Schoenberg. Influenced by Wagner and Brahms, this synthesis was evidently first used in Schoenberg's Op. 7 String Quartet. This paper presents evidence that, in Op. 7, Schoenberg referenced Wagner's Prelude to Tristan und Isolde (and the Tristan chord itself), cementing its place as Schoenberg's prototypical vagrant chord that would lead to his early atonal techniques.

This study aimed at deciphering the inner logics of György Ligeti's Piano Etude No. 11 and its relations with form. Two parameters were derived from pitch-class set theory and used for statistical analyses: the sum ∑ of the six components (ic1 to ic6) of the interval vector, which measures the complexity of a chord, and the ratio (ic1 + ic2 + ic6)/∑, which measures its dissonance. The results have shown that the music is polyphonic and constructed from two complementary guidonian hexachords. The melodies generated from two short motifs, phrase structures, rhythms, average dissonance and complexity of harmony all vary between the parts and contribute internally to the tripartite form and progression. Polyrhythms result from the superposition of cyclic rhythms whose periods are coprime integers. The relations between hidden cyclic patterns of sound and pitch are reminiscent of the medieval motets. The outcome is complex but coherent. Download at URL: http://hugues.bedouelle.free.fr/music.html

The third and final piece for my masters final portfolio. This piece was also written instinctively and was predominantly a way for me to explore extended techniques on the bassoon and double bass.

Most notable influences whilst writing include:

Luciano Berio: Sequenza XII per Fagotto Solo (solo bassoon)
Brian Ferneyhough, Trittico per G.S. (for solo Double Bass)

"The complexity of atonal musical structures has led theorists to offer varying analyses of atonal works. This ambiguity stems from the intricacies of human perception: Is it possible to state a definitive analysis when perceptions differ? In order to justify a segmentation, the analyst must provide supporting evidence in the music. Due to the wide range of perception, this evidence yields analyses that are more or less persuasive, but neither correct nor incorrect. David S. Lefkowitz and Kristin Taavola, however, propose a mathematical model that defines a correct segmentation.

This thesis briefly compares Lefkowitz and Taavola’s mathematical theory to James Tenney and Larry Polansky’s perception-based theory. Tenney and Polansky’s theory is rooted in visual Gestalt perception and provides the foundation for Dora A. Hanninen’s segmentation theory. I then employ Hanninen’s analytical framework to identify segmentational boundaries that support published analyses of two atonal works: the fourth of Anton Webern’s Fünf Sätze, Op. 5 and an excerpt from Arnold Schoenberg’s Klavierstücke, Op. 11, No. 1. I apply two of Hanninen’s three segmentational criteria: the sonic, which refers to acoustical properties, and the contextual, which refers to categorizations, such as set-classes.

Lefkowitz and Taavola note that Tenney and Polansky’s theory cannot be applied to polyphony. Although Tenney and Polansky concede this point, Hanninen encourages the use of her theory for polyphonic segmentation. She does not, however, provide a method for addressing polyphony. Thus, I combine aspects from Lefkowitz and Taavola’s simultaneous analysis with Hanninen’s theory in order to formulate a basic method for segmenting polyphonic music.

I find that sonic and contextual criteria in the music strongly support the analyses by George Perle, Allen Forte, Gary Wittlich, and Charles Burkhart. Due to the emphasis of set-class theory for atonal analysis, there is an inherent reliance on contextual criteria; however, sonic criteria also reinforce their segmentations and sometimes may even support their contextual criteria in places lacking local sonic criteria. Thus, the musical structures strongly support the segmentations, validating the diversity of analyses and suggesting that atonal music can legitimately be heard in different ways."

The better quality pdf is downloadible from here: "http://www.leoalmanac.org/wp-content/uploads/2013/07/LEAVol19No3-Mailman.pdf
Through recent artistic practices and technology of interactive systems for music, composition and improvisation have more and more blended and interconnected with each other – a sui generis situation now called comprovisation. The concept of comprovisation applies equally well to the spontaneous generation and manipulation of computer graphics, especially as such graphics are systematically coordinated audio-visually, while being subject to spontaneous manipulation by a performer.
This is explained in terms of the Fluxations and FluxNoisations Human Body Interfaces, interactive dance systems that generate music and graphics spontaneously in response to hand and body movement. They enable spontaneous expressive shaping of coherent complexity and variety. Thus a multi-layered multimodal experience arises. The aesthetic experience of this multimedia spectacle relates to experiences of various prior music and visual art of the 19th, 20th, and 21st centuries, as well as to hypothetical physical realities. Thus a kind of cybernetic phenomenology of art is pursued and enacted through an embodied cybersynthesis of art with simulated alternate reality. Call it a pragmatic speculative realism, an adventurous technoetic ‘what if.’ As compared to more traditional forms of improvisation, the opportunities for risk-taking and aesthetic exploration rise to a new level of uncertainty, as the reactions of the improviser simultaneously draw from and target both visual and aural modalities, such that the intentions toward each fuse together."

Bu makalenin amacı, yirminci yüzyılda yaşamış olan Avusturyalı
müzisyen ve teorisyen Arnold Schönberg'in atonal müzik uygulaması
üzerinde somutlaştırdığı müzik estetiği anlayışını tarihsel ve teorik koşulları
içerisinde açıklamaktır. Bu bağlamda, öncelikle Schönberg'in müziğinin
eleştirel bir şekilde eklemlendiği klasik üçlüsel armoni ve onun tarihsel önseli
kabul edilen antik armoni kavrayışlarının ana uğraklarını kışça açıklayacağız.
Söz konusu kapsamda, Antik Yunan dünyasından Pythagorasçıların ve
Aristoxenus’un çalışmalarının önemi belirtilecek ve Avrupa Orta Çağ
organum müziği, Musica Enchiriadis ve Scolia Enchiriadis gibi tonal dönem
öncesi temel uğraklara değinilecektir. Ardından üçlüsel armoni fikrinin kısa
bir yapısal analizi sunularak tonalite fikri açıklanacaktır. Son olarak,
yukarıda verili olan arka plandan yola çıkarak Schönberg'in atonal müziğinin
olanaklı bir yapısal analizini sunacak ve nihayet, onu müzik estetiği açısından
klasik batı müziği geleneği içerisinde konumlandırmaya çalışacağız. Bu son
bölüm konu ile ilgisinde 12 ton müziğinin dizi, matris, yansıtma, tersine
çevirme ve yansıtıp tersine çevirme gibi temel kavramlarının kimi teknik
analizlerini de içerecektir.

This is the final proof of the first chapter of my new book (Cambridge, 2019), which uses Schenkerian analysis as a measuring stick to distinguish "tonal" from "atonal" in Schoenberg's Op. 2, no. 2 and Op. 11, no. 1.  It also considers how a "musical idea" is projected atonally in the latter piece.

Morris's Arc (1988) for String Quartet flows; it flows with substance, and with purpose. By flowing, I don’t just mean in the trivial sense that all music flows because it is unfolding in time and time flows. Rather I mean that there is continuity to its various surges of eventfulness; these surges are not disjunct or sudden. And by substance I mean both that its sound is as a sensuous fluid material and that the unfolding of its constituent events presents a coherent organization, thus binding together into a statement that seems meaningful in retrospect. By purpose I mean not only that there is a local logic to the consequence of one note following another, but also that the flow of events enables the material to organize into processes that forge a trajectory toward a goal.
    The analysis first focuses on local details considered in terms of pitch and pitch-class formations as arising from twelve-tone rows; then it delves into aspects of form, process, and texture. These are considered in terms of emergent properties in flux. The modeling of these properties and their flux employs some mathematical formalisms, but the reader can rely on the fact that every mathematical definition and formula is described carefully in prose as well.
    In Arc, the twelve-tone pitch class details and the surging emergent qualities projecting form are not completely separate from each other. Rather, all these features interact. Thus not only does the article weave together connections between such facets as form, process, and texture, but it also connects these to the twelve-tone rows and pitch-class configurations that are more straightforwardly part of the compositional plan (and more usual in analyses) of Morris’s music.

[Download the pdf below, or contact the author jmailman@alumni.uchicago.edu, for a digital offprint. It can also accessed through JSTOR: www.jstor.org/stable/10.7757/persnewmusi.52.2.0249 ]

PREVIOUS STUDIES OF TWELVE-TONE MUSIC
suggest that participants can learn a twelve-tone row and
identify it in a forced-choice test (Bigand, D’Adamo, &
Poulin, 2003; Krumhansl, Sandell, & Sergeant, 1987).
However, these findings invite speculation about the
extent to which participants were attuning to intervals
to complete the task. The present study builds upon
these previous experiments by specifically investigating
whether participants implicitly attune to repetitive
interval patterns embedded in twelve-tone melodies.
After passive exposure to a monophonic twelve-tone
melody dominated by intervals 1 and 3 (in semitones),
musician listeners with no formal training in nontonal
music theory demonstrated learning of the frequent
intervals (and directed interval pairs) in both forcedchoice
and ratings tasks. Experiment 2 tested a new
group of participants with similar backgrounds,
although this time the twelve-tone melody heard in
familiarization was predominated with intervals 2 and
5. Participants showed learning of directed interval
pairs, but not intervals (possibly due to the more tonal
nature of interval successions within familiarization).
These findings have pedagogical and analytical
implications.

Atonal Music and Infinite Fragmentarity

The concept of fragmentarity not only constitutes the central idea of Ernst Bloch’s philosophy of music, but also the whole of his aesthetics, even of his entire ontology –which can already be characterized as a Marxist ontology of creative, utopian imagination. In spite of the fact that the focus of his musical interest was chiefly classical, tonal music and that, unlike Adorno, he gave relatively little attention to atonal and dodecaphonic music, we would like to show that Schönberg’s atonal music occupied, by way of the problem of fragmentarity, a specific place in Bloch’s socio-utopian ontology. At the same time, we want to highlight problematic aspects of Bloch’s concept of fragmentarity. This concept is perhaps overly connected with the aesthetics of romanticism, and its use to describe new music is in this way limited. The last part of the text is then a corrective of this position using the thinking of Emmanuel Levinas, especially his aesthetics and some of his notes on the event nature of music. In fact, from the point of view of Levinas’ critique of ontology, Bloch’s fragmentarity too is overly connected with the idea of totality, albeit only utopianly sketched. In the conclusion itself, we will then attempt to point out the possible combination of Bloch’s conception of new music as a fragment and Levinas’ event approach to music in the broader framework of the aesthetics of ambiguity.

This research is an analysis of Ether-Cosmos no. XIII-XVII by Wiboon Trakulhun, the researcher focuses on how these compositions managed, by analyzed in the issues of pitch organization and rhythmic organization, which showed the composer’s identity.

The study of pitch organization showed that Ether-Cosmos no. XIII is free atonal music throughout the piece, the set appears in the piece is mostly abstract subset. In parts of EtherCosmos no. XIV-XVII are atonal music base on serialism but there are tonal music element hidden in some part of piece. In addition composer also emphasizes the symmetry in every pieces.

Composer give the rhythmic and meter the asymmetry and ambiguity by various process such as emphasizing the syncopated rhythms, irregular rhythmic groupings, augmentationdiminution including additive process, by using the metric displacement technique and using
2 meters simultaneously to create the character of polymeter and polyrhythm.

Overall results showed that composer used same set but the set reflect different sound quality because the difference of pitch organization in each pieces, including the using of various rhythmic technique. These methods created the rhythmic displacement. In addition, atonal music
from Ether-Cosmos by Wiboon Trakulhun has a symmetrical identity significantly.

While studies of musical modernism in film have generally focused on techniques, case studies, or broad scoring practices, less scholarship has been devoted to experimentalism in specific film genres. The thriller genre frequently adapts and transforms avant-garde devices developed by concert composers. Modernistic sounds became codified within the thriller at the same time that the genre matured in the New Hollywood cinema of the 1970s. To take one example, a standard thriller trope is a rhythmically-isochronous, near-twelve- tone melody for scenes of urgency; such motifs pepper chase cues in David Shire’s Taking of Pelham 123 (1974) and Michael Small’s Marathon Man (1976), and can be heard in present-day film and television scores. Techniques seemingly more at home in horror scores are updated in thrillers via a number of means, including jazzified serialism, tape-manipulation and musique concrète, and polystylism. These methods reflect—and encode—timely cultural anxieties towards surveillance, governmental malfeasance, and urban alienation.

Focusing on Shire’s contribution to the genre, particularly those strategies used to evoke what he calls an “awe of irresolution,” demonstrates the adoption and longevity of these tropes. A confluence of jazz, electronics, and Cagian techniques flows through The Conversation (1974). At climactic moments, sound design, underscore, and diegetic music bleed into each other, creating a sonic morass that reinforces the film’s thematic preoccupation with concealment and mishearing. Examining the use of harmony and orchestration in Zodiac (2007) reveals how Shire’s Ivesian textures (many redolent of “The Unanswered Question”) contribute to the film’s epistemology of radical insolubility.

This edited transcript of a public pre-concert discussion with composer, theorist and critic Benjamin Boretz not only touches on early personal encounters with Babbitt but also ranges over issues of reception of his music, listening experiences, transfor- mations of music’s temporality, connections to Schoenberg, Webern, Cage, and postmodernism, stylistic changes over Babbitt’s career and composerly poetics, as well as motivations and consequences for pre- compositional structures and systems. The discussion took place on 22 November 2015, at the first of three recitals during the 2015–16 concert season at Spectrum, in New York City, in which Augustus Arnone for the second time performed all of Milton Babbitt’s solo piano works, this time in honour of the composer’s centenary.  (Access:  http://dx.doi.org/10.1017/S0040298216000322)

Conlon Nancarrow’s music has been the subject of analysis by some of the most astute composers and academics in modern music. His music and its accompanying scholarly literature are a potentially rich source of material for improvisation. As Nancarrow was influenced by expert jazz improvisers with virtuoso technique such as Art Tatum when constructing this music, this is a logical outcome.

Nancarrow’s work had made a substantial impact on the output of electric guitar virtuosos such as Frank Zappa and Shawn Lane, as the sheer speed of the linear material along with the dense polyrhythmic fabric present in the music had pushed these influential players to increase their technical capabilities of the instrument to a new much higher level. This in turn has had substantial impact on current electric guitar practice.

The video performance of an electric guitar piece based on Nancarrow’s Third Study for Player Piano (Boogie Woogie Suite) is performed on electric guitar improvisation based on melodic, intervallic, and rhythmic material within the piece against two tracks of pre-recorded electric guitars also performed by me following the harmonic structure of the piece and utilizing the polyrhythmic devices contained within the original music. The performance is roughly the same length as the original piece (3’ 22”), and demonstrates Nancarrow’s rhythmic, harmonic, and melodic concepts (including what he himself called “licks”) within an improvisational format.

Perpetuum Mobile

This piece was written using a nine-tone (Nonatonic) scale  (C#, D#, E#, G, A#, C, D, E, F#) constructed by 20th Century Jazz Theorist and Pedagogue Dennis Sandole (teacher of John Coltrane, James Moody, Jim Hall, Pat Martino amongst many others). My use of pitch material of a jazz origin such as Sandole’s was purposeful in order to conceptually align this work with Nancarrow’s clear jazz influences in his “Boogie Woogie Suite”.  This particular scale allows for liberal use of a trichord that includes a minor third and major third which features prominently in Nancarrow’s “Suite”.

I constructed this piece using octave (registral) displacement techniques combined with a rhythmic texture of sixteenth note rhythms similar to the constant “left hand” ostinato motion of Nancarrow’s Study#3. The octave displacement of lines creates a two part texture of predominately staccato attacks and the use of changing time signatures and registers in a variety of rhythmic note groupings was meant to give the illusion of two separate rhythmically independent parts unified by one basic scalar tonality. The few cascading arpeggio sections that feature liberal use of sustain pedal were inspired by Nancarrow studies 5, 27, 37, and 45c.

The general absence of harmonic writing places the emphasis on the rhythmic and contrapuntal elements of the music and the faux “player piano” sound is an obvious nod to Nancarrow and seems to work with this essentially staccato and rhythmic nature of the piece.

I wrote this composition not to imitate Nancarrow’s work directly, but to allow his overall musical approach to influence my own musical language.

RESUMEN
Este trabajo se propone un análisis de las transformaciones contemporáneas de la idea de música, así como del cruce de discursos y disciplinas que intentan dar cuenta del alcance estético,  sociológico y terapéutico de aquellas transformaciones, las que, como se mostrará, nutren el debate filosófico.  Finalmente, a la luz del pensamiento del filósofo alemán Peter Sloterdijk, se esbozará una lectura del mundo como sistema polifónico de sonidos y una analogía entre la música y la vida humana.
La música que atesoramos, que nos habita y secuestra, provoca un ahondamiento, una receptividad hacia emociones que de otro modo nos serían desconocidas. Los intentos de desarrollar una psicología, una neurología y una fisiología de la influencia de la música sobre el cuerpo y la mente se remontan a Pitágoras y la magia terapéutica, pasando por Schopenhauer y Nietzsche, hasta llegar a Sloterdijk, quien plantea como basamento de este interrogar, como pregunta estrictamente filosófica, exploratoria de la experiencia musical: ¿dónde estamos, cuando  escuchamos música? A la que podríamos añadir ¿a dónde nos dirigimos cuando escuchamos música?  O, mejor aún, ¿hacia dónde somos conducidos?
Adolfo Vásquez Rocca

Abstract: The following article sought to determine which were the implications of the junction between text and music and in which way it dictated, determined or aided the compositional process of a large-sized atonal and athematic piece. Thus, based on previous researches and in musical analysis, an explanation about the symbiotic aspects between the two languages and the essential structural elements in the compositional process is shown.

Babbitt’s relatively early composition Semi-Simple Variations (1956) presents intriguing surface patterns that are not determined by its pre-compositional plan, but rather result from subsequent “improvised” decisions that are strategic. This video (the third of a three-part video essay) considers Babbitt’s own conversational pronouncements (in radio interviews) together with some particulars of his life-long musical activities, that together suggest uncanny affiliations to jazz improvisation. As a result of Babbitt’s creative reconceptualizing of planning and spontaneity in music, his pre-compositional structures (partial orderings) fit in an unexpected way into (or reformulate) the ecosystem relating music composition to the physical means of its performance. http://doi.org/10.30535/smtv.5.3

Some music, more than others, prompts heightened awareness of the passage of time—certainly some passages from Beethoven’s late sonatas and quartets, or, in Feldman’s Rothko Chapel, the chord conspicuously sustained by the chorus whose time is marked by the toll of chimes. Ben Boretz’s string quartet Qixingshan (2011) is in this category, but with a difference: its self-conscious temporality is much more infused with teleology or directedness. It puts its ears ever to the future—in this case perhaps a future of geological change, change which is usually slow, but which in some geological formations can also be violently quick.  The article presents an analysis of the Boretz's quartet Qixingshan. Connections to Stravinsky, Gershwin, 12-tone theory, canon, and palindrome are discussed.

Nello spazio temperato dodecafonico, basato sulla divisione dell'ottava in dodici parti uguali, alcune collezioni di note possono trasporsi un numero di volte inferiore a 12, prima di riprodursi identiche. Queste collezioni sono legate ai circoli di intervalli sottomultipli di 12 (cioè 1,2,3,4,6) ed alla suddivisione dell'ottava in parti uguali; le più semplici sono il tritono e la triade aumentata: il primo è sei volte trasponibile e divide l'ottava in due parti uguali, la seconda è quattro volte trasponibile e divide l'ottava in tre parti uguali. Tutte le collezioni simmetriche per trasposizione devono essere composte da tritoni e/o triadi aumentate: non possono essere composte da 5 o 7 note, perché 5 e 7 non sono multipli né del numero 2 né del numero 3; tuttavia, in qualsiasi modo si voglia sovrapporre un tritono ed una triade aumentata, senza raddoppi, il risultato sarà sempre equivalente alla stessa collezione di 5 note (0,1,4,7,8), e in qualsiasi modo si vogliano sovrapporre due tritoni ed una triade aumentata, senza raddoppi, il risultato sarà sempre equivalente alla stessa collezione di 7 note (0,1,2,5,6,8,9), complementare dell'altra. Queste due collezioni sono le uniche costituite da soli tritoni o triadi aumentate a non essere simmetriche per trasposizione Le collezioni simmetriche per trasposizione sono 16, ossia:-il totale cromatico-il tritono e la sua collezione complementare di 10 note-la triade aumentata e la sua collezione complementare di 9 note-tre collezioni di 4 note (formati da diverse sovrapposizioni di due tritoni), e le loro complementari di 8 note-cinque collezioni di 6 note, di cui due costruite sulla sovrapposizione di due triadi aumentate, e tre formate da diverse sovrapposizioni di tre tritoni.

This is the second piece for my Masters' final portfolio.

The methodology behind this trio includes a mixture of pre-compositional processes and instinctive composition.

The rhythmic aspects of the piece were composed instinctively, however, when it came to the harmonic language there are some parameters present. Due to the nature of these parameters the general structure and development of the music was also affected.

Elliott Carter's pan-intervallic language when concerning harmony or pitch material was the model which inspired the piece. Although I did not make use of his more common methodology of assigning specific intervals to specific instruments or for example, making use of all-interval tetrachords and all-trichord hexachords, and other interval based chords (that is something I am working on now).

I did, however, assign specific intervals to sections of the piece; more specifically I began with only one interval available to me (the octave or notes in unison) and progressively added more and more intervals: 2nds/9ths, 3rds, 4ths/11ths and so on. This continued till the last section where they were all available to me.

When it came to the gestural nature of the piece Ferneyhough and Ligeti were once again important reference points and figures.

Pieces that were of particular influence to me whilst writing this include:

György Ligeti: Trio for Violin, Horn and Piano, Musica Ricercata, Cello Concerto I & II, Etudes 1-XI
Brian Ferneyhough: Time and Motion Study I (for bass clarinet)
Luciano Berio: Sequenza IV for Piano
Elliott Carter: A Mirror on Which to Dwell
Bela Bartok: Contrasts for Violin, Clarinet and Pianoforte

This thesis argues that harmonic function did not disappear entirely the day that Schoenberg ‘freed music from the shackles of tonality.’It is rather easy to assume that harmonic function cannot exist without tonality. However, within this thesis I aim to demonstrate a system of functional harmony that can operate independently of tonality, and to show how it can suggest form in early post-tonal music. With a focus on voice-leading, this thesis suggests there are continuities with preceding harmonic practice that current analytical methods, such as set theory and transformation theory, while making other relevant observations, miss.
The approach used is built on the observation that not all interval classes are treated equally by Schoenberg. The most significant is his treatment of ic6, which still functions as we would expect it to in tonal music: by resolving in contrary motion by semitone to ic4. The ic6 can be a subset of a larger set, and, likewise, so can the ic4. The other vertical sonority that Schoenberg takes specific care with is pcset 3-12 (the augmented triad), which again functions in a way reminiscent of tonal voice-leading. One pitch class will remain in the following set, while the pitch class an ic4 higher will resolve up chromatically. Again, the initial pcset 3-12 can belong to a larger set and so can the resultant set.

UN ABISSO DI GEOMETRIE introduzione ai 21 Solfeggi per flauto solo di Antonio Zanon. Analisi di francesco bellomi Certi oggetti sonori celano la loro vera identità fino a quando qualcuno, guidato dal proprio istinto o dal semplice desiderio di capire, non comincia a toccarne la superficie, a cercare una chiave, una frattura. Questi solfeggi, nella loro enigmatica geometria, si lasciano scalfire solo dallo strumento, leggero e sottile, dell'analisi. Oppure bisogna avere il fiuto che hanno certi esecutori e cogliere i segnali che la partitura offre e nasconde allo stesso tempo. Quando ho iniziato non sapevo dove e come cercare il codice, la chiave. Poi, mentre il lavoro procedeva, la struttura mi è sembrata emergere lentamente da sola, fino a quando non è parsa chiara e nitida. A questo punto ho mostrato i miei risultati all'autore che mi ha soccorso mostrandomi gli appunti preparatori del suo lavoro. Studiando quegli appunti mi si è poco a poco spalancato davanti un abisso di geometrie. Quello che credevo di aver individuato con le mie prime rilevazioni era appena qualche traccia di superficie. Niente a confronto dell'enorme costruzione sotterranea di questi brani. In quei giorni provavo uno strano senso di vertigine, come quando, dietro a qualcosa di apparentemente semplice, si scopre un universo di complessità. Continuavo a trovare numeri, metri, intervalli, lettere e ogni cosa era calata in una fitta rete di interconnessioni, di rimandi. Anche quando qualche tabella o qualche serie sembrava non avere rapporti con tutto il resto, io "sapevo" che il collegamento ci doveva essere, bastava cercarlo nel modo giusto. Era solo questione di tempo di determinazione o forse di fortuna. Alla sensazione di essere un osservatore esterno di una struttura che emerge si è sostituita la sensazione di essere entrato "dentro" la struttura. Come quando da studente entravo dentro il grande organo del conservatorio per vedere e capire il funzionamento della macchina dall'interno. Qualcuno da fuori azionava i tasti ed i registri secondo un programma stabilito dalla partitura; io, dentro lo strumento, ero avvolto dai suoni delle canne e dai rumori delle parti meccaniche, ero "dentro" il suono e dentro il complesso concorso di azioni che lo produceva. Ora credo che la "macchina" che verrà indagata attraverso l'analisi che segue sia una macchina geometrica, composta di un numero grande ma finito di elementi. Il funzionamento di questa "macchina" segue anch'esso un criterio geometrico e non casuale in modo tale che le combinazioni sonore che ne possono scaturire siano un numero relativamente grande ma finito. Ovviamente questi solfeggi non presentano tutte le combinazioni sonore possibili sulla base degli elementi di partenza. Presentano invece una unica traiettoria scelta fra tutte le possibili, un unico agglomerato geometrico scelto nella sterminata estensione di tutti gli agglomerati possibili. Questo cristallo preciso ed irripetibile, unico e allo stesso tempo molteplice è costruito, numero dopo numero, simmetria dopo simmetria, con il più impalpabile ed evanescente dei materiali: il suono. Una manciata di variazioni di pressione dell'aria che portano fino alle nostre orecchie questa specie di labirinto di specchi la qui complessità (ma sarebbe più giusta chiamarla semplicità) strutturale è assolutamente inafferrabile, anche dal più perfetto ascoltatore (ammesso che esista). Le "architetture di invenzione" di questi solfeggi non sono che lo sfondo, l'ambiente dentro il quale l'esecutore deve muoversi. Compito dell'esecutore è quello di percorrere questo