Topic
Microtonal music
About: Microtonal music is a research topic. Over the lifetime, 133 publications have been published within this topic receiving 1017 citations. The topic is also known as: microtonalism & microtonality.
Papers published on a yearly basis
Papers
TL;DR: This paper argues for another way of assessing the resources of a pitch system, one that is independent of ratio concerns and that considers the individual intervals as transformations forming a mathematical group.
Abstract: It is well-known that most of the musical instruments of the orchestra are constrained to produce 12 distinct pitch classes or categories per octave This makes it rather easy to realize music based on a 12-fold octave division with such instruments but next to impossible to realize a piece of music based on any other pitch system With the advent of the computer, the possibilities of exploring alternative microtonal systems of octave division broaden considerably In the face of seemingly boundless freedom of choice, what is needed is a basis for selection that will tell us which systems offer the greatest resources and will thereby be the most likely to reward our exploration In fact, there is a deeper question than this, and that is the question of how one might appropriately describe the resources of a pitch system To be sure, the ultimate resources of a pitch system are some function of its intervals, the primitive pairwise relations between pitches So the question really boils down to one of how to conceive of intervals The commonly accepted answer is that the canonical definition of an interval is to be couched in terms of a frequency ratio, moreover a ratio of powers of small integers, a mathematical object of the form 23"q5r , with p, q, r ranging over positive and negative integers The resources of an equal-tempered n-fold pitch system of octave division are then a function of the "goodness-of-fit" between the equal log-frequency grid of the system and some set of ratios (Mandelbaum 1961; Stoney 1970; von Hoerner 1974; 1976) Certain ratios may be set aside as special in the sense that it is particularly important to approximate them closely, for example, 2-13' (p5) or 2-251 (M3) In this paper I shall argue for another way of assessing the resources of a pitch system, one that is independent of ratio concerns and that considers the individual intervals as transformations forming a mathematical group Every equal-tempered system of n-fold octave division, as well as every system of n ratios that can be approximated by an equal-tempered system, possesses the structure of the so-called cyclic group of order n, Ci We will examine the structure of C12 and see that it possesses rather special properties that make the sets we call diatonic scales possible Our first major result will thus be that diatonic scales may be profitably represented in terms of C12, without recourse to ratios Inquiring into the specific nature of C12 that supports such pitch sets will suggest a method of generalization that yields a new family of microtonal systems Unlike the goodness-of-fit approach, which leads to systems of size 9, 31, and 41 tones, our group-theoretic concerns will suggest systems of octave division based on 20, 30, and 42 tones Further, it will be possible to specify diatonic scale "analogs" in each of these systems and to say Computer Music Journal, Vol 4, No 4, Winter 1980, 0148-9267/80/ 040066-19 $0400/0 C 1980 Massachusetts Institute of Technology
218 citations
Book•
1 Jan 1974
TL;DR: Among the few truly experimental composers in our cultural history, Partch's life (19011974) and music embody most completely the quintessential American rootlessness, isolation, pre-civilized cult of experience, and dichotomy of practical invention and transcendental visions as discussed by the authors.
Abstract: Among the few truly experimental composers in our cultural history, Harry Partch's life (19011974) and music embody most completely the quintessential American rootlessness, isolation, pre-civilized cult of experience, and dichotomy of practical invention and transcendental visions. Having lived mostly in the remote deserts of Arizona and New Mexico with no access to formal training, Partch naturally created theatrical ritualistic works incorporating Indian chants, Japanese kabuki and Noh, Polynesian microtones, Balinese gamelan, Greek tragedy, dance, mime, and sardonic commentary on Hollywood and commercial pop music of modern civilization. First published in 1949, Genesis of a Music is the manifesto of Partch's radical compositional practice and instruments (which owe nothing to the 300-year-old European tradition of Western music. ) He contrasts Abstract and Corporeal music, proclaiming the latter as the vital, emotionally tactile form derived from the spoken word (like Greek, Chinese, Arabic, and Indian musics) and surveys the history of world music at length from this perspective. Parts II, III, and IV explain Partch's theories of scales, intonation, and instrument construction with copious acoustical and mathematical documentation. Anyone with a musically creative attitude, whether or not familiar with traditional music theory, will find this book revelatory.
85 citations
1 Jan 2003
TL;DR: In this paper, a 21st-century approach to music composition using the latest results from mathematical music theory and musical acoustics is presented, based on generalizations of the well-known properties of our familiar 12tone scales.
Abstract: Richard Plotkin Department of Music University of Chicago Chicago, IL 60637 rplotkin@uchicago.edu Developments in music theory, musical acoustics, and psychoacoustics over the last 15 to 20 years have resulted in a single structural basis that provides common ground for analysis of musical systems that include non-standardlnon-octavesystems, microtonal systems, and systems that use unusual tunings common in non-western music. These developments make it likely that a confluence of understanding in musical acoustics, psychoacoustics, and music synthesis is about to take place. This common structural basis will lead to generalized rules of composition, unheard of since the classic work Treatise On Harmony by Rameau (1722), based on generalizations of the well-known properties of our familiar 12tone scales. Indeed, some of these generalizations have already been articulated. As participants in various aspects of this work for the past 14 years [1-7], we are in a unique position to collect, assess, and distill the important contributions to this, truly, multidisciplinary field. It is our purpose, in this paper, to articulate a 21st century approach to music composition using the latest results from mathematical music theory and musical acoustics. In our presentation we will produce audio and visual examples applying these techniques.
62 citations
TL;DR: The greater portion of this article outlines the history of microtonal keyboards, with a view towards establishing the most useful design principles, and how these principles can be adopted for synthesizer control.
Abstract: As real-time computer music performance systems become more widespread, the question of controller design becomes increasingly pertinent. The flexibility of pitch afforded by computer technology suggests the use of new input devices optimized for playing in arbitrary tuning systems. In particular, keyboards are well-suited for polyphonic playing, and there is a legacy of historical microtonal keyboards that can serve as models for controller design. Several motivations for using a microtonal keyboard in computer music can be discerned. The obvious use is for live performance-microtonal music no longer needs to be primarily restricted to tape music on the one hand and to the musiciancraftsman who constructs special acoustic instruments on the other. An equally compelling motivation drives the composer of microtonal music. The real-time aural feedback provided by such a device can open the door to experimentation with many tuning systems whose harmonic resources might otherwise remain untapped. A flexible device for real-time pitch control could also be of use in psychoacoustic research. The greater portion of this article outlines the history of microtonal keyboards, with a view towards establishing the most useful design principles. The final section considers how these principles can be adopted for synthesizer control. A programmable keyboard is particularly useful, allowing a variety of tuning systems and key layouts; software written by the author for such a purpose is described. With such a device, different keyboard layouts can be used to match the tuning system and the nature of the musician's usage, as will be explained. History and Principles of Microtonal Keyboards
45 citations
TL;DR: 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, contrast with much current music perception research, which tends to assume the dominance of extrinsic over intrinsic predictors.
Abstract: 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.
43 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2020 | 7 |
| 2019 | 9 |
| 2018 | 7 |
| 2017 | 8 |
| 2016 | 6 |