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 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.

Microtonality

2018 ◽  
Author(s):  
Gayle Young
Keyword(s):  
Nineteenth Century ◽  
Twelve Tone ◽  
Equal Temperament

Microtonality refers to any use of pitch that departs from twelve equally-spaced tones per octave (twelve-tone equal temperament), the standard tuning established in Europe since the nineteenth century. This tuning has come to dominate music internationally through the widespread use of mass-produced instruments with standard tunings, such as electronic keyboards.

In-between Painting and Music—or, Thinking with Paul Klee and Anton Webern

2013 ◽  
Vol 43 (3) ◽  
pp. 419-442
Author(s):  
Marcia Sá Cavalcante Schuback
Keyword(s):  
Present Article ◽  
General Purpose ◽  
Anton Webern ◽  
Main Question ◽  
Musical Structure ◽  
Twelve Tone ◽  
Paul Klee ◽  
Starting Point

Abstract The present article discusses the relation between painting and music in the work by Paul Klee, bringing it into conversation with the music by Anton Webern. It assumes, as a starting point, that the main question is not about relating painting and music but rather about the relation between moving towards painting and moving towards music, hence the relation between forming forces and not between formed forms. Since for Klee the musical structure of the pictorial is understood as “active linear polyphony,” the article develops this notion in conversation with Webern’s thoughts on the polyphonic structure of twelve-tone music. The general purpose of the article is to determine what kind of thoughts emerge from the in-between of painting and music.

Slaves from the Windward Coast

1980 ◽  
Vol 21 (1) ◽  
pp. 17-34 ◽  
Author(s):  
Adam Jones ◽  
Marion Johnson
Keyword(s):  
Nineteenth Century ◽  
Seventeenth Century ◽  
Sierra Leone ◽  
Ivory Coast ◽  
Great Distance ◽  
Gold Coast ◽  
Oral Traditions ◽  
Large Numbers

The ‘Windward Coast’ between Cape Mount and Assini (modern Liberia and Ivory Coast) is credited by Curtin with the export of very large numbers of slaves in the late seventeenth century and most of the eighteenth, but with hardly any in the nineteenth. It is suggested here that the actual figures for the earlier period are much lower, many of those slaves attributed to this stretch of coast in the English trade having come from the region Curtin calls ‘Sierra Leone’, while a large proportion of those carried in French ships came from the Gold Coast or beyond. In the nineteenth century, slave trading continued on the coast between Cape Mount and New Sestos until 1840. More work is needed on available sources. The figures are far too uncertain to be used for a chronological underpinning of oral traditions of peoples a great distance inland.

A System for Tuning Instruments Using Recorded Music Instead of Theory-Based Frequency Presets

2012 ◽  
Vol 36 (3) ◽  
pp. 43-56 ◽  
Author(s):  
Barış Bozkurt
Keyword(s):  
Visual Feedback ◽  
Musical Instrument ◽  
Oral Traditions ◽  
Audio Feedback ◽  
Twelve Tone ◽  
Musical Scale ◽  
Scale Theory ◽  
Tuning Method ◽  
Fundamental Frequencies ◽  
Master Musician

Musical instrument tuners are devices that help musicians to adjust their instruments such that the played notes have the desired fundamental frequencies. In a conventional tuner, the reference tuning frequencies are preset, where the presets are obtained from tuning (musical scale) theory, such as twelve-tone equal temperament, or are user-specified temperaments. For many kinds of music in oral traditions, especially nonwestern music, widely accepted theoretical presets for tuning frequencies are not available because of the use of non-standard tunings. For such contexts, the “reference” is a master musician or a recording of a master musician. In this article, a tuning method and technology are presented that help the musician to tune the instrument according to a given (user-provided) recording. The method makes use of simultaneous audio and visual feedback during the tuning process, in which novel approaches are used for both modalities. For audio feedback, loopable stable frames, obtained automatically from the recording, are looped and played continuously. For visual feedback, a superimposed plot of the auto-difference functions is displayed instead of the conventional tuner's approach of detecting frequencies and displaying the amount of frequency difference between the input and the reference.

The Frontier States of Western Yorubaland, 1600–1889. By BIODUN ADEDIRAN. Ibadan: Institut Français de Recherche en Afrique, 1994. Pp. x + 248. No price given (ISBN 978-2015-25-3).

1997 ◽  
Vol 38 (1) ◽  
pp. 123-177
Author(s):  
PAUL E. LOVEJOY
Keyword(s):  
African Diaspora ◽  
Oral Traditions ◽  
Large Numbers ◽  
History Of

The identification of the various sub-groups of the Yoruba offers a challenge to historians, particularly since large numbers of Yoruba-speaking people were deported into the African diaspora. In this contribution to Yoruba historiography, Adediran analyses the history of the western Yoruba sub-groups, especially those resident in République du Benin and also in Togo. This study expands upon Adediran's Ph.D. thesis (Awolowo University, 1980) and is based on oral traditions and archival materials, as well as an excellent grasp of the published literature.

Cytoplasmic Granules in Lymphocytes from Rats Dosed with SK&F 14336-D

1971 ◽  
Vol 29 ◽  
pp. 556-557
Author(s):  
T. G. Merrill ◽  
B. J. Payne ◽  
A. J. Tousimis
Keyword(s):  
Lipid Storage ◽  
Pokeweed Mitogen ◽  
Electron Microscopic ◽  
Cytoplasmic Granules ◽  
Storage Diseases ◽  
Tay Sachs Disease ◽  
Large Numbers ◽  
Microscopic Studies ◽  
Neurovisceral Lipidosis

Rats given SK&F 14336-D (9-[3-Dimethylamino propyl]-2-chloroacridane), a tranquilizing drug, developed an increased number of vacuolated lymphocytes as observed by light microscopy. Vacuoles in peripheral blood of rats and humans apparently are rare and are not usually reported in differential counts. Transforming agents such as phytohemagglutinin and pokeweed mitogen induce similar vacuoles in in vitro cultures of lymphocytes. These vacuoles have also been reported in some of the lipid-storage diseases of humans such as amaurotic familial idiocy, familial neurovisceral lipidosis, lipomucopolysaccharidosis and sphingomyelinosis. Electron microscopic studies of Tay-Sachs' disease and of chloroquine treated swine have demonstrated large numbers of “membranous cytoplasmic granules” in the cytoplasm of neurons, in addition to lymphocytes. The present study was undertaken with the purpose of characterizing the membranous inclusions and developing an experimental animal model which may be used for the study of lipid storage diseases.

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