Harmonytimbre's Structures in the Works of Vladimir Tarnopolski: On the Problem of Harmonic Analysis of New Music

Композиторская техника Владимира Тарнопольского основывается на создании индивидуальных детализированных звуковысотных структур, которые трактуются как единые звучности. Композитор называет такие структуры «гармониетембрами». Можно не только рассматривать их с точки зрения тембровой краски, но и анализировать их звуковысотную структуру, преобразование которой происходит по законам гармонии. В статье проанализирована гармоническая сторона гармониетембровых структур в музыке Тарнопольского на примере сочинений разных лет: «Кассандра» (1991), «Маятник Фуко» (2004), «Be@thoven. Invokation» (2017). В результате анализа выявлены основные приемы работы с гармониетембрами и сформулированы закономерности построения звуковысотных структур в музыке Тарнопольского. Vladimir Tarnopolski's compositional technique is based on the individual detailed pitch structures, which are interpreted as a one sound. The composer calls such structures “harmonytimbres.” We can consider them not only from the point of view of timbre character, but also analyze their pitch structure, which develops according to the laws of harmony. The article is devoted to the harmonic side of harmonytimbre's structures in Tarnopolski's music on the example of his works from different years: “Cassandra” (1991), “Foucault's Pendulum” (2004), “Be@thoven. Invokation” (2017). As a result of the analysis, the main methods of working with harmonytimbres are identified and the regularities of constructing pitch structures in Tarnopolski's music are formulated.

Probe Tone Paradigm Reveals Less Differentiated Tonal Hierarchy in Rock Music

Krumhansl and Kessler’s (1982) pioneering experiments on tonal hierarchies in Western music have long been considered the gold standard for researchers interested in the mental representation of musical pitch structure. The current experiment used the probe tone technique to investigate the tonal hierarchy in classical and rock music. As predicted, the observed profiles for these two styles were structurally similar, reflecting a shared underlying Western tonal structure. Most interestingly, however, the rock profile was significantly less differentiated than the classical profile, reflecting theoretical work that describes pitch organization in rock music as more permissive and less hierarchical than in classical music. This line of research contradicts the idea that music from the common-practice era is representative of all Western musics, and challenges music cognition researchers to explore style-appropriate stimuli and models of pitch structure for their experiments.

A Transformational Approach to Gesture in Shō Performance

Through an analysis of contemporary shō performance practice, this article explores the relationship between instrumental gesture and modal theory in contemporary gagaku. I demonstrate that the idiosyncratic arrangement of the pipes on the shō is closely related to the pitch structure and tonal function of the aitake pitch clusters. My analysis synthesizes two approaches. First, I adopt David Lewin’s (1987) transformational attitude to conceptualize the aitake not as static musical objects but as processes of motion enacted by the te-utsuri—standardized fingering movements for shifting between two aitake. Second, I treat the aitake as sonic byproducts of a performer's instrumental gestures to examine how the aitake are related to one another kinesthetically, and whether these relationships correlate with the pitch structures of the aitake. I argue that relatedness between aitake is determined by the parsimony of te-utsuri. The most parsimonious movements can be enacted between four aitake: bō, kotsu, ichi and otsu. These aitake are identical to the clusters that accompany the fundamental tones of five of the six modes: Ichikotsu-chō, Hyōjō, Taishiki-chō, Oshiki-chō and Banshiki-chō. These findings demonstrate that the pipes of the shō, while seemingly arranged in no discernable order, prioritize parsimonious te-utsuri between each of the aitake accompanying the fundamental modal degrees. An analysis of the pitch structure of aitake through the lens of te-utsuri reveals a striking correlation between gestural parsimony and tonal function.

What Do Signatures Signify?

At the beginning of the seventeenth century English composers used only a handful of keys: they combined five keynotes (G, A, C, D, and F) with the three signatures documented in English solmization theory (♮,♭, and♭♭). By the end of the century English theorists described eighteen keys—all of the modern major and minor keys with up to four signature accidentals. But the route from eight to eighteen keys was not straightforward. This article traces this route by examining how the function of signature flats and sharps changed in seventeenth-century England. At the beginning of the century signature flats and sharps were clefs, mere notational symbols that provided a shorthand for the probable pitches in a composition. As a result, English musicians used adjacent keys (i.e., ♮-D and -D), which were distinct, well-formed versions of a broader category of D minor. In the middle of the century, composers and theorists used ad hoc and asymmetrical strategies ♭ to create new keys. Composers explored new flat keys through the process of signature creep, while theorists devised new sharp keys when they identified the parallel key relationship. Finally, theoretical interventions at the end of the century “fixed” keys into our modern system but obscured the varied pitch structure that still animated musical practice. The messy, flexible circumstances in which keys arose complicate several assumptions about modern key; this evidence challenges notions of transpositional equivalence and reveals that different kinds of keys may be built on different conceptual foundations.

Pitch Syntax as an Evolutionary Prelingual Innovation

Pitch syntax is an important part of musical syntax. It is a complex hierarchical system that involves generative production and perception based on pitch. Because hierarchical systems are also present in language grammar, the processing of a pitch hierarchy is predominantly explained by the activity of cognitive mechanisms that are not solely specific to music. However, in contrast to the processing of language grammar, which is mainly cognitive in nature, the processing of pitch syntax includes subtle emotional sensations that are often described in terms of tension and resolution or instability and stability. This difference suggests that the very nature of pitch syntax may be evolutionarily older than grammar in language, and has served another adaptive function. The aim of this paper is to indicate that the recognition of pitch structure may be a separate ability, rather than merely being part of general syntactic processing. It is also proposed that pitch syntax has evolved as a specific tool for social bonding in which subtle emotions of tension and resolution are indications of mutual trust. From this perspective, it is considered that musical pitch started to act as a medium of communication by the means of spectral synchronization between the brains of hominins. Pitch syntax facilitated spectral synchronization between performers of a well-established, enduring, communal ritual and in this way increased social cohesion. This process led to the evolution of new cortico-subcortical pathways that enabled the implicit learning of pitch hierarchy and the intuitive use of pitch structure in music before language, as we know it now, began.

Automatic acoustic analyses quantify variation in pitch structure within and between human music, speech, and bird song

Scientists studying music and evolution often discuss similarities and differences between music, language, and bird song, but few studies have simultaneously compared these three domains quantitatively. To enable such com-parison, here we demonstrate several methods of cross-cultural/cross-species comparison of pitch structures in audio recordings. We utilized a small subset of 9 record-ings of human music, human speech, and bird song se-lected to maximize variation within and between these three domains. We extend previous automated analyses of scale structure and propose new methods for quantifying pitch discreteness and melodic interval structure, compar-ing automated analyses against human subjective ratings. Our quantitative analyses confirm that both human music and bird song can vary greatly along a continuum from pieces/songs with very discrete pitches and clear scale structure to those without. However, even the most “mu-sical” examples of speech showed minimal levels of dis-crete pitches or precise scales. On the other hand, all samples including human speech tended to use small in-tervals, consistent with the “motor constraint hypothesis”. Our analyses suggest that our methods can be used to ob-jectively perform meaningful cross-cultural and cross-species analysis of pitch structure from audio recordings, particularly after using our new pitch discreteness algo-rithm to screen and remove recordings that do not contain discrete pitches. We also identify areas in need of future development such as automated note segmentation and automated scale degree identification.

Probe Tone Paradigm Reveals Less Differentiated Tonal Hierarchy in Rock Music

Krumhansl & Kessler’s (1982) pioneering experiments on tonal hierarchies in Western music have long been considered the gold standard for researchers interested in the mental representation of musical pitch structure. The current experiment used the probe tone technique to investigate the tonal hierarchy in classical and rock music. As predicted, the observed profiles for these two styles were structurally similar, reflecting a shared underlying Western tonal structure. Most interestingly, however, the rock profile was significantly less differentiated than the classical profile, reflecting theoretical work that describes pitch organization in rock music as more permissive and less hierarchical than in classical music. These results contradict the assumption that music from the common-practice era is representative of all Western musics, and challenges music cognition researchers to be more thoughtful when choosing stimuli and models of pitch structure for their experiments.

Activation in the right inferior parietal lobule reflects the representation of musical structure beyond simple pitch discrimination

Pitch discrimination tasks typically engage the superior temporal gyrus and the right inferior frontal gyrus. It is currently unclear whether these regions are equally involved in the processing of incongruous notes in melodies, which requires the representation of musical structure (tonality) in addition to pitch discrimination. To this aim, 14 participants completed two tasks while undergoing functional magnetic resonance imaging, one in which they had to identify a pitch change in a series of non-melodic repeating tones and a second in which they had to identify an incongruous note in a tonal melody. In both tasks, the deviants activated the right superior temporal gyrus. A contrast between deviants in the melodic task and deviants in the non-melodic task (melodic > non-melodic) revealed additional activity in the right inferior parietal lobule. Activation in the inferior parietal lobule likely represents processes related to the maintenance of tonal pitch structure in working memory during pitch discrimination.

Random feedback makes listeners tone-deaf

The mental representation of pitch structure (tonal knowledge) is a core component of musical experience and is learned implicitly through exposure to music. One theory of congenital amusia (tone deafness) posits that conscious access to tonal knowledge is disrupted, leading to a severe deficit of music cognition. We tested this idea by providing random performance feedback to neurotypical listeners while they listened to melodies for tonal incongruities and had their electrical brain activity monitored. The introduction of random feedback was associated with a reduction of accuracy and confidence, and a suppression of the late positive brain response usually elicited by conscious detection of a tonal violation. These effects mirror the behavioural and neurophysiological profile of amusia. In contrast, random feedback was associated with an increase in the amplitude of the early right anterior negativity, possibly due to heightened attention to the experimental task. This successful simulation of amusia in a normal brain highlights the key role of feedback in learning, and thereby provides a new avenue for the rehabilitation of learning disorders.