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.

scholarly journals Revising the musical equal temperament

2016 ◽  
Vol 38 (1) ◽  
Author(s):  
Haye Hinrichsen
Keyword(s):  
Nineteenth Century ◽  
Frequency Ratio ◽  
Western Music ◽  
Equal Temperament ◽  
Frequency Ratios ◽  
High Degree

Western music is predominantly based on the equal temperament with a constant semitone frequency ratio of 21/12. Although this temperament has been in use since the nineteenth century and in spite of its high degree of symmetry, various musicians have repeatedly expressed their discomfort with the harmonicity of certain intervals. Recently it was suggested that this problem can be overcome by introducing a modified temperament with a constant but slightly increased frequency ratio. In this paper we confirm this conjecture quantitatively. Using entropy as a measure for harmonicity, we show numerically that the harmonic optimum is in fact obtained for frequency ratios slightly larger than 21/12. This suggests that the equal temperament should be replaced by a harmonized stretched temperament as a new standard.

Literature, Music, and Science in Nineteenth Century Russian Culture: Prince Odoyevskiy’s Quest for a Natural Enharmonic Scale

2002 ◽  
Vol 15 (2) ◽  
pp. 183-207 ◽  
Author(s):  
Dimitri Bayuk
Keyword(s):  
Nineteenth Century ◽  
Short Stories ◽  
Musical Instrument ◽  
Experimental Science ◽  
Musical Culture ◽  
Musical Scale ◽  
Russian Music ◽  
Positive Science ◽  
Equal Temperament ◽  
And Mathematics

ArgumentAn attempt to understand and analyze a unique nineteenth-century musical instrument – the enharmonic piano from the collection of the Glinka Museum of Russian Musical Culture in Moscow – directs a historian towards Prince Vladimir Odoyevskiy’s efforts to construct a special musical scale corresponding to the indigenous tradition of Russian music. Known today mostly as an author of Romantic short stories, Odoyevskiy was also an amateur scientist and musician, a follower of Schelling’s Naturphilosophie, and a mystic. He tried to design his new musical scale and instruments on the basis of experimental science and mathematics. Odoyevskiy’s life-long search for a synthesis of literature, music, positive science, and spirituality demonstrates how the adaptation and appropriation of European arts preceded and paved the way towards the appropriation of European sciences among the educated élite in nineteenth-century Russia. The tensions inherent in the process led to Odoyevskiy’s nationalist rebellion against the European musical standard, the equal temperament. His call for a different musical scale remained largely ignored in the nineteenth century, until the topic was raised anew by twentieth-century composers and musicians.

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.

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