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[1] In addition to the conceptual ideas Isang Yun shares in his interview—which, as I will suggest below, have profound implications for music theory and analysis far beyond Yun’s music specifically—we should take note of the value the interview format itself holds for the production of new knowledge. All of this illustrates the value of thinking through ideas in dialogue (Chua 2022)—resisting the Western assumption that philosophical thinking and theory-making (and, by extension, composing) are fundamentally solitary endeavors (Ahmed 2006; Collins 2000). ~ [2] In his interview with Akira Nishimura, Isang Yun describes aspects of his “linear musical language” through which characteristic linear gestures “ranging from fine microtonal tremors to tremolos wider than a third” animate musical processes that at once form cohesive, living wholes and “transform without end.” [...]the actual content of those musical styles are seldom explicitly present in his music; rather, Yun folds traditionalideas—say, the gestural impetus of an A-ak court melody—into a “more general grammar” that also reflects his training in high-modernist compositional techniques in Europe. [8] Yun explicitly contrasts this process of selection, variation, or adumbration with Western compositional methods, in which form and content are in a dialectical relation.

In 1996, during my guitar studies, I read for the first time about microtonal guitars. I was so fascinated about it. Trying to experiment to hear microtones in my instrument, I created a 36EDO scordatura system, which I have been using now for 25 years. In this article, I would like to present my ideas in a personal and biographical way about how I decided to create my 36-divisions system and to compose with it. I would also like to explain about the challenges and the decisions I took as a composer during this time.

The contribution to knowledge, and the core of the research, is a tonal foundation based on glissandi using compositional techniques derived from synergy of glissandi, microtonality, and isorhythm. The techniques are performed on specially constructed guitars in 18, 24, 30, and 36 tet (tone equal temperament). Guitar based musical artefacts demonstrating some possible techniques are arranged on two compact discs: CD1 ‘Experimental Miniatures’ and CD2 ‘After Twelve’.

In the case of Carrillo, both his microtonal theory and his ideas on mathematical metamorphosis draw on his extensive training in the European classical tradition, while indulging his tendency towards self-aggrandizement via personal experiment and mythology, and his desire to exalt the present and potential future of Mexican music. [...]Czech composer and theorist Hába—who moved to Berlin with his teacher Franz Schreker in 1920—and the Russian emigre Wyschnegradsky were soon to pioneer microtonal systems independent of tonal models. The various theoretical writings of this Berlin-centered group appeared to take a more pragmatic, systematic approach to the topic of microtonality than that offered by Carrillo’s fanciful declaration of “The Thirteenth Sound,” with its focus on microtonal expansion as “transcendental event” (Carrillo 1923, 2), as well as its echoes of Mexican revolutionary discourse in 1920s Mexico (Madrid 2015, 145; Pareyón 2022). The generation of microtonal divisions followed from the “law of division” found in the sixth octave of the overtone series, but can also be found in much music of the past, as well as in folk repertoires.

Music is a vital part of most cultures and has a strong impact on emotions [1–5]. In Western cultures, emotive valence is strongly influenced by major and minor melodies and harmony (chords and their progressions) [6–13]. Yet, how pitch and harmony affect our emotions, and to what extent these effects are culturally mediated or universal, is hotly debated [2, 5, 14–20]. Here, we report an experiment conducted in a remote cloud forest region of Papua New Guinea, across several communities with similar traditional music but differing levels of exposure to Western-influenced tonal music. One hundred and seventy participants were presented with pairs of major and minor cadences (chord progressions) and melodies, and chose which of them made them happier. The experiment was repeated by 60 non-musicians and 19 musicians in Sydney, Australia. Bayesian analyses show that, for cadences, there is strong evidence that greater happiness was reported for major than minor in every community except one: the community with minimal exposure to Western-like music. For melodies, there is strong evidence that greater happiness was reported for those with higher mean pitch (major melodies) than those with lower mean pitch (minor melodies) in only one of the three PNG communities and in both Sydney groups. The results show that the emotive valence of major and minor is strongly associated with exposure to Western-influenced music and culture, although we cannot exclude the possibility of universality.

I offer a translation of, and commentary on, Julián Carrillo’s Leyes de metamorfosis musicales, Chapter 1 (self-published originally as Julián Carrillo, Leyes de metamorfosis musicales [Laws of Musical Metamorphosis], 1949). In my commentary, I show how Carrilo’s text brings together a unique constellation of theoretical interests, encompassing whole-tone collections, microtonality, and pitch multiplication. I also show how Carrillo positioned his theories in relation to those of his international peers, particularly Arnold Schoenberg. Alongside many composer-theorists of the early twentieth century, Carrillo developed a conception of the atonal that was both technically systematic and deeply mythological. Understanding his ideas today contributes to an expanded history of early atonal music theory, beyond its habitual geographical boundaries.PEER REVIEWER: Gerry Lopez

This article investigates intervallic measurement and the tacit limitations engendered by a prevalent symmetrical perspective of measuring intervals. Various numerical and instrumental limitations and further detail of harmonic and melodic structures, such as Farey sequences, are illustrated. This approach distinguishes itself from a perspective of prime limits, explored by Harry Partch and others. A standardisation of ‘microtonal’ notation is not suggested; rather, the restrictions provided by any such standardisation are re-examined through an objective lens of ratios, to harness the generative potential of numbers. An orchestration-led approach to composition is described, where the tuning limitations of instruments are utilised for idiomatic composition. Tuning practices that ‘evade’ the octave are also discussed, including gamelan, mbira and three scales found by Wendy Carlos. The article concludes with a section on the construction of harmonic systems in the absence of instrumental influences.

From 1976, the works of the Venetian composer Luigi Nono (1924–90) are marked by a noticeable change in both his philosophical and his political outlook. What results is a decade (1980–9) of compositions that feature poetry in librettos, live electronics, the spatialization of sound and a prominent use of microtonal pitches. Together these create completely novel soundscapes that are noticeably different from his previous output. This article will examine a particular influence – the philosophy of Martin Heidegger – in the creation of the 1984 piece for large ensemble A Carlo Scarpa. The purpose of this is not only to allow for an insight into the music and structure of A Carlo Scarpa , but also to illuminate how philosophical and political ideas can be represented within the craft of composition, and the new paths of thinking that guided Nono’s artistic output during the 1980s.

In the musical cultures of the world, including the oral traditions of European peoples, a wide variety of musical scales have been and still are used. In contemporary Western music, growing awareness of other musical cultures, as well a certain saturation with the sounds of the 12-tone scale have led to experimentation with alternative scale systems. Applying a microtonal scale that divides the octave into 22 equal parts (22-EDO), this article discusses possible strategies for training musically educated Western adults. According to experiences from the research and teaching/learning process, the article introduces the music theoretical fundamentals of the 22-EDO scale, knowledge of which is an integral part of a potential training method, the creation of teaching materials and musical compositions. This knowledge was also the basis of my practice and performance at concerts in 2022 and 2023, and helps with the evaluation of the results based on direct experience and audio recordings. The analysis focuses on the online Gradus ad Parnassum course, which was initiated during the Covid-19 pandemic to teach microtonal singing.The findings indicate that the level of familiarity with the intervals (compared to those of the 12-tone scale) had a significant influence on learning outcomes, sometimes facilitating, but sometimes hindering, the process. Although the online format offered a number of advantages, such as connecting participants who would otherwise not have the opportunity to meet, it turned out that in-person training allowed for much faster progress due to the absence of physical distance and technical limitations.

This study investigates the role of extrinsic and intrinsic predictors in the perception of affect in mostly unfamiliar musical chords from the Bohlen-Pierce microtonal tuning system. Extrinsic predictors are derived, in part, from long-term statistical regularities in music; for example, the prevalence of a chord in a corpus of music that is relevant to a participant. Conversely, intrinsic predictors make no use of long-term statistical regularities in music; for example, psychoacoustic features inherent in the music, such as roughness. Two types of affect were measured for each chord: pleasantness/unpleasantness and happiness/sadness. We modelled the data with a number of novel and well-established intrinsic predictors, namely roughness, harmonicity, spectral entropy and average pitch height; and a single extrinsic predictor, 12-TET Dissimilarity, which was estimated by the chord's smallest distance to any 12-tone equally tempered chord. Musical sophistication was modelled as a potential moderator of the above predictors. Two experiments were conducted, each using slightly different tunings of the Bohlen-Pierce musical system: a just intonation version and an equal-tempered version. It was found that, across both tunings and across both affective responses, all the tested intrinsic features and 12-TET Dissimilarity have consistent influences in the expected direction. These results contrast with much current music perception research, which tends to assume the dominance of extrinsic over intrinsic predictors. This study highlights the importance of both intrinsic characteristics of the acoustic signal itself, as well as extrinsic factors, such as 12-TET Dissimilarity, on perception of affect in music.