scholarly journals On the Geometric Realisation of Equal Tempered Music

2019 ◽  
Vol 18 (3) ◽  
pp. 53-75
Author(s):  
Robert Linton Tavis Ashton-Bell
Keyword(s):  
Music Theory ◽  
Harmonic Series ◽  
Musical Structure ◽  
Musical Harmony ◽  
Abstract Thought ◽  
Musical Structures ◽  
Equal Temperament ◽  
Whole Number ◽  
Simon Stevin ◽  
Tools And Techniques

Since the time of Pythagoras (c.550BC), mathematicians interested in music have asked, “What governs the whole number ratios that emerge from derivations of the harmonic series?” Simon Stevin (1548-1620) devised a mathematical underlay (where a semitone equals 21/12) that gave rise to the equal temperament tuning system we still use today. Beyond this, the structure of formalised musical orderings have eluded many of us. Music theorists use the tools and techniques of their trade to peer into the higher-order musical structures that underpin musical harmony. These methods of investigating music theory and harmony are difficult to learn (and teach), as complex abstract thought is required to imagine the components of a phenomenon that cannot be seen. This paper outlines a method to understanding the mathematical underpinnings of the equal tempered tuning system. Using this method, musical structure can be quantitatively modelled as a series of harmonic elements at each pulse of musical time.

A Psychocultural Theory of Musical Interval

2018 ◽  
Vol 35 (4) ◽  
pp. 475-501 ◽  
Author(s):  
Richard Parncutt ◽  
Graham Hair
Keyword(s):  
Oral Traditions ◽  
Harmonic Series ◽  
Musical Structure ◽  
Twelve Tone ◽  
Musical Thought ◽  
Brain Mechanism ◽  
Large Numbers ◽  
Equal Temperament ◽  
Voiced Speech ◽  
Structure Perception

The Pythagoreans linked musical intervals with integer ratios, cosmic order, and the human soul. The empirical approach of Aristoxenus, based on real musicians making real music, was neglected. Today, many music scholars and researchers still conceptualize intervals as ratios. We argue that this idea is fundamentally incorrect and present convergent evidence against it. There is no internally consistent “Just” scale: a 6th scale degree that is 5:3 above the 1st is not a perfect 5th (3:2) above the 2nd (9:8). Pythagorean tuning solves this problem, but creates another: ratios of psychologically implausible large numbers. Performers do not switch between two ratios of one interval (e.g., 5:4 and 81:64 for the major third), modern studies of performance intonation show no consistent preferences for specific ratios, and no known brain mechanism is sensitive to ratios in musical contexts. Moreover, physical frequency and perceived pitch are not the same. Rameau and Helmholtz derived musical intervals from the harmonic series, which is audible in everyday sounds including voiced speech; but those intervals, like musical intervals, are perceived categorically. Musical intervals and scales, although they depend in part on acoustic factors, are primarily psychocultural entities—not mathematical or physical. Intervals are historically and culturally variable distances that are learned from oral traditions. There is no perfect tuning for any interval; even octaves are stretched relative to 2:1. Twelve-tone equal temperament is not intrinsically better or worse than Just or Pythagorean. Ratio theory is an important chapter in the history Western musical thought, but it is inconsistent with a modern evidence-based understanding of musical structure, perception and cognition.

scholarly journals A Vigilance Explanation of Musical Chills? Effects of Loudness and Brightness Manipulations

2020 ◽  
Vol 3 ◽  
pp. 205920432091565
Author(s):  
Scott Bannister
Keyword(s):  
Emotional Experience ◽  
Spectral Brightness ◽  
Musical Structure ◽  
Low Level ◽  
Complex Interactions ◽  
Musical Structures ◽  
Study Participants ◽  
And Control ◽  
Auditory Looming ◽  
Control Piece

Recent research has suggested that low-level psychoacoustic parameters such as loudness and spectral brightness are correlated with musical chills, a subjective emotional experience accompanied by goosebumps, shivers, and tingling sensations. These relationships may be explained by a vigilance theory of chills, through the process of auditory looming; however, these correlations or theories have never been causally tested. In the current study, participants ( N = 40) listened to five variations (original, low loudness, high loudness, low brightness, high brightness) of an experimental and control piece of chills music, characterized by a crescendo and guitar solo respectively; this qualitative distinction was made based on whether the underlying musical structure of the pieces was or was not capable of engaging auditory looming processes. It was predicted that increases in loudness would result in increased chills frequency across participants, indicated by button presses; brightness was included as an exploratory parameter. Results show that for the experimental piece, increases in loudness resulted in significantly more frequent chills experiences, and increases in brightness significantly reduced the frequency of chills, whereas no effects were found for the control piece. Findings are discussed in terms of vigilance and social bonding theories of chills, and the complex interactions between low-level psychoacoustic properties and higher-level musical structures.

scholarly journals Relating Musical Structure and Content to Aesthetic Response: A Model and Analysis of Beethoven's Piano Sonata Op. 110

2005 ◽  
Vol 130 (1) ◽  
pp. 74-118 ◽  
Author(s):  
Adam Ockelford
Keyword(s):  
Music Theory ◽  
Musical Structure ◽  
Aesthetic Response ◽  
Piano Sonata ◽  
Music Psychology ◽  
The Core ◽  
Physical Context ◽  
Musical Event ◽  
New Framework

AbstractA model is presented which aims to show how, for listeners familiar with a given style, aesthetic response to music may be related to its ‘structure’ (as defined in relation to ‘zygonic’ theory) and ‘content’ (the particular perceived qualities of sound that pertain to a given musical event). The model combines recent empirical findings from music psychology with other approaches adapted from music theory and philosophy. Intramusical considerations, which form the core of the model, are positioned within a broader socio-cultural, cognitive and physical context. The new framework is used to inform an analysis of Beethoven's Piano Sonata op.110, which examines in particular the notions of teleology in music and narrative metaphor.

Functional Ambiguity in Musical Structures

1983 ◽  
Vol 1 (1) ◽  
pp. 3-27 ◽  
Author(s):  
William Thomson
Keyword(s):  
General Theory ◽  
Final Section ◽  
Limited Attention ◽  
Musical Structure ◽  
The Past ◽  
Extensive Analysis ◽  
Musical Structures ◽  
Definition Of

This paper first establishes a definition of ambiguity and its significance to art and to perception in general. Its understanding is framed within a hierarchical conception of musical structure most similar to that of Leonard B. Meyer (1956,1973). Following (1) an illustrative survey of occurrences of intentional ambiguity found in the standard music repertory, and (2) a discussion of the limited attention paid by music theorists to ambiguity in the past, a general theory of musical ambiguity's causes is developed. The paper's final section consists of an extensive analysis of functional ambiguity as a principal expressive vehicle in Chopin's Mazurka, Opus 17, No. 4.

scholarly journals C, F-sharp and E-flat: The tragic, the sublime and the oppressed (with C-sharp as Nemesis): Reflections on Eine kleine Trauermusik by Milan Mihajlović

New Sound ◽  
2019 ◽  
pp. 131-160
Author(s):  
Miloš Zatkalik
Keyword(s):  
Harmonic Series ◽  
Piano Concerto ◽  
The Unconscious ◽  
Pitch Organization ◽  
The Sublime ◽  
Musical Structures ◽  
Pitch Structure ◽  
Psychoanalytic Perspective ◽  
Unconscious Mind

In the present paper, I will discuss tonal centers and referential sonorities in the composition Eine kleine Trauermusik (1992) by one of the leading Serbian composers Milan Mihajlović. Even though its pitch structure may appear rather straightforward with its octatonic scale and the primary tonal center in C, and with referential (quasi-tonic) chords derived from the harmonic series, I intend to highlight intricate narrative trajectories and dramatic conflicts between various tonal centers (treated as actors/characters). These narratives can be related to certain archetypal plots, with the conclusion that there exists ambiguity between the tragic and the ironic archetype. On a higher plane, similar conflict/interplay/ambiguity exists between different principles of pitch organization, i.e. the octatonic and functionally tonal. The unresolved ambiguities and simultaneity of conflicting interpretations are examined from the psychoanalytic perspective, which postulates isomorphism between musical structures and processes and the processes unfolding in the unconscious mind. Finally, the effect of these narratives, especially the overwhelming impact induced by the excerpt from Mozart's piano concerto is linked with the idea of sublime as conceived by Kant, but also including other approaches (Burke, Lyotard etc.).

scholarly journals Topology of Networks in Generalized Musical Spaces

2020 ◽  
Vol 30 ◽  
pp. 38-43
Author(s):  
Marco Buongiorno Nardelli
Keyword(s):  
Network Analysis ◽  
Music Theory ◽  
Network Topology ◽  
Contemporary Music ◽  
Human Perception ◽  
Compositional Process ◽  
Topology Analysis ◽  
Musical Structures ◽  
Compositional Design ◽  
Emergent Behaviors

The abstraction of musical structures as mathematical objects in a geometrical space is one of the major accomplishments of contemporary music theory. The author generalizes the concept of musical spaces as networks and derives compositional design principles via network topology analysis. This approach provides a framework for analysis and quantification of similarity of musical objects and structures and suggests a way to relate such measures to human perception of different musical entities. Finally, network analysis provides alternative ways of interpreting the compositional process by quantifying emergent behaviors with well-established statistical mechanics. Interpreting the latter as probabilistic randomness in the network, the author develops novel compositional design frameworks.

Music Theory's Other Nature: Reflections on Gaia, Humans, and Music in the Anthropocene

2021 ◽  
Vol 45 (1) ◽  
pp. 7-22
Author(s):  
Alexander Rehding
Keyword(s):  
Music Theory ◽  
Symphony Orchestra ◽  
Actor Network Theory ◽  
Traditional Music ◽  
Harmonic Series ◽  
Test Case ◽  
Gaia Hypothesis ◽  
Novel Approach ◽  
Relationship Of ◽  
The Relationship

The new historical paradigm ushered in by the Anthropocene offers a timely and urgent opportunity to rethink the relationship of humans and nature. Bruno Latour's take on the Gaia hypothesis, which rejects the traditional subject/object divide, shows how the human can be inscribed into the work of music theory. This turn toward Latour's Actor-Network Theory, which erases the categorical difference between human and nonhuman agents, now dressed up in cosmic garb under the banner of the Gaia hypothesis, appears to be distant from traditional music-theoretical concerns, but the connection is in fact less far-fetched than it seems. J. G. Kastner's music theory, taking its cue from the sound of the Aeolian harp, serves as a test case here: the Aeolian harp, played by wind directly, had long served as a Romantic image of the superhuman forces of nature, but Kastner argues that the Aeolian network only becomes complete in human ears. By unraveling the various instances and agencies of Kastner's theory, this article charts a novel approach to music and sound that sidesteps the conceptual problems in which the nineteenth-century mainstream habitually gets entangled. Kastner's work is based on a fundamental crisis in the conception of sound, after the invention of the mechanical siren (1819) tore down any certainties about the categorical distinction between noise and musical sound. Seeking to rebuild the understanding of sound from the ground up, Kastner leaves no stone unturned, from the obsolete Pythagorean tradition of musica mundana to travelers’ reports about curious sonic environmental phenomena from distant parts of the world. Where the old mechanistic paradigm was built on a “physical music” (and a static “sound of nature” based on the harmonic series), Kastner proposes a new “chemical music” that is based on the dynamic, ever-changing sonority of the Aeolian harp. This chemical music does not (yet) exist, but Kastner gives us some clues about its features, especially in his transcription/simulation of the sound of the Aeolian harp scored for double symphony orchestra. Kastner's “chemical music” finally closes the music-theoretical network that he builds around his new conception of the supernatural sound of the Aeolian harp and its human and nonhuman agents.

scholarly journals Analysing change in music therapy interactions of children with communication difficulties

2016 ◽  
Vol 371 (1693) ◽  
pp. 20150374 ◽  
Author(s):  
Neta Spiro ◽  
Tommi Himberg
Keyword(s):  
Music Therapy ◽  
Reliability And Validity ◽  
Rhythmic Activity ◽  
General Level ◽  
Small Scale ◽  
Musical Structure ◽  
Video Recordings ◽  
Musical Structures ◽  
Behavioural Characteristics ◽  
Therapy Sessions

Music therapy has been found to improve communicative behaviours and joint attention in children with autism, but it is unclear what in the music therapy sessions drives those changes. We developed an annotation protocol and tools to accumulate large datasets of music therapy, for analysis of interaction dynamics. Analysis of video recordings of improvisational music therapy sessions focused on simple, unambiguous individual and shared behaviours: movement and facing behaviours, rhythmic activity and musical structures and the relationships between them. To test the feasibility of the protocol, early and late sessions of five client–therapist pairs were annotated and analysed to track changes in behaviours. To assess the reliability and validity of the protocol, inter-rater reliability of the annotation tiers was calculated, and the therapists provided feedback about the relevance of the analyses and results. This small-scale study suggests that there are both similarities and differences in the profiles of client–therapist sessions. For example, all therapists faced the clients most of the time, while the clients did not face back so often. Conversely, only two pairs had an increase in regular pulse from early to late sessions. More broadly, similarity across pairs at a general level is complemented by variation in the details. This perhaps goes some way to reconciling client- and context-specificity on one hand and generalizability on the other. Behavioural characteristics seem to influence each other. For instance, shared rhythmic pulse alternated with mutual facing and the occurrence of shared pulse was found to relate to the musical structure. These observations point towards a framework for looking at change in music therapy that focuses on networks of variables or broader categories. The results suggest that even when starting with simple behaviours, we can trace aspects of interaction and change in music therapy, which are seen as relevant by therapists.

scholarly journals Musical Structure as Narrative in Rock

2011 ◽  
Vol 8 (1) ◽  
Author(s):  
John Fernando Encarnacao
Keyword(s):  
Rock Music ◽  
Basic Structure ◽  
Art Music ◽  
Musical Structure ◽  
Western Art ◽  
Musical Structures ◽  
Starting Point ◽  
Alternative Approaches ◽  
Sense Of Home ◽  
Quest Narrative

In an attempt to take a fresh look at the analysis of form in rock music, this paper uses Susan McClary’s (2000) idea of ‘quest narrative’ in Western art music as a starting point. While much pop and rock adheres to the basic structure of the establishment of a home territory, episodes or adventures away, and then a return, my study suggests three categories of rock music form that provide alternatives to common combinations of verses, choruses and bridges through which the quest narrative is delivered. Labyrinth forms present more than the usual number of sections to confound our sense of ‘home’, and consequently of ‘quest’. Single-cell forms use repetition to suggest either a kind of stasis or to disrupt our expectations of beginning, middle and end. Immersive forms blur sectional divisions and invite more sensual and participatory responses to the recorded text. With regard to all of these alternative approaches to structure, Judy Lochhead’s (1992) concept of ‘forming’ is called upon to underline rock music forms that unfold as process, rather than map received formal constructs. Central to the argument are a couple of crucial definitions. Following Theodore Gracyk (1996), it is not songs, as such, but particular recordings that constitute rock music texts. Additionally, narrative is understood not in (direct) relation to the lyrics of a song, nor in terms of artists’ biographies or the trajectories of musical styles, but considered in terms of musical structure. It is hoped that this outline of non-narrative musical structures in rock may have applications not only to other types of music, but to other time-based art forms.

scholarly journals Types and Applications of P3,0 Seventh-Chord Transformations in Late Nineteenth-Century Music

2016 ◽  
Vol 22 (2) ◽  
Author(s):  
Samuel Reenan ◽  
Richard Bass
Keyword(s):  
Nineteenth Century ◽  
Music Theory ◽  
The Other ◽  
Late Nineteenth Century ◽  
Voice Leading ◽  
Musical Structure ◽  
Tristan Und Isolde ◽  
Richard Strauss ◽  
Late Nineteenth

The expression P3,0refers to one class of parsimonious voice-leading transformations between seventh chords introduced in a 1998 article by Jack Douthett and Peter Steinbach as Pm,n(Journal of Music Theory42 (2): 241–63). In addition to tones that may be held in common, the subscripts indicate the number of voices that move by half step (m) or whole step (n) in connecting one seventh chord to the next. P3,0designates a transformation in which one of the chord members is held in common while each of the other three moves by half step. P3,0transformations produce some of the most striking chromatic harmonic progressions in the late Romantic repertoire. This study focuses on aspects of P3,0transformations that include 1) their place in the broader context of neo-Riemannian voice-leading transformations; 2) their properties and a specific means of notating all possible P3,0types; 3) explications of how the various types are integrated within late nineteenth-century harmonic practice and interact with traditional tonal harmony; and 4) analytic applications that demonstrate how P3,0transformations operate within and contribute to musical structure, including the opening of the Prelude to Wagner’sTristan und Isolde, and a complete song (“Ruhe, meine Seele!” op. 27 no. 1) by Richard Strauss.

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