tuning systems

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tuning systems,

methods for assigning pitches to the twelve Western pitch names that constitute the octave. The term usually refers to this procedure in the tuning of keyboard instruments. The need for a tuning system hinges on the conflict of pitch relationships in the natural overtone series and the exigencies of musical compositional systems, specifically those utilizing the familiar diatonic scale. Chronologically, the conflict occurred in the early Renaissance when composers had an increasing desire to modulate from one key to another. Implicit in the concept of modulation is the condition of identity of intervals between corresponding scale degrees in different modes or keys. A keyboard instrument tuned to a function of any natural interval except the octave will not satisfy that condition. The Pythagorean system, derived from a scale supposedly invented by PythagorasPythagoras
, c.582–c.507 B.C., pre-Socratic Greek philosopher, founder of the Pythagorean school. He migrated from his native Samos to Crotona and established a secret religious society or order similar to, and possibly influenced by, the earlier Orphic cult.
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 (c.550 B.C.), was generated by acoustically perfect fifths. It exhibited an audible difference between the interval of a semitone and the interval resulting from the subtraction of the semitone from the whole tone. The mean-tone system generated the scale with fifths just flat enough to eliminate this difference, producing a scale containing acoustically perfect thirds. Discrepancy between chromatic notes (semitones) rendered this system unsuitable for successive modulations. Equal temperament tuning, which replaced mean-tone tuning in the 18th cent. and is universally accepted for Western music today, partitions the octave into twelve equal semitones. All intervals except the octave are acoustically out of tune, but by a tolerable degree, making complex modulations and atonality possible.
References in periodicals archive ?
Many writings remained in manuscript during his lifetime: a treatise on counterpoint (edited by Frieder Rempp in 1980) and various discourses on the use of dissonances, the enharmonic genus, the unison, forms of the octave, and the tuning systems of Pythagoras, Aristoxenus, and Ptolemy (edited and translated by Claude V.
The suggestion to produce a practice tape to facilitate learning pieces in an unfamiliar tuning system is undoubtedly on the mark, as is the one for composers to use instruments with fixed tuning to create a pitch environment into which the string player can fit intuitively.
The idea of a pure interval (one that can be derived from the harmonic series) underlies a number of White's observations concerning tuning systems, but the potential of this idea as an agent of synthesis - by means of a more universal concept of consonance or dissonance - is not explored.
First, earlier, more flexible tuning systems are based on natural acoustics that sound good to humans.
Kyle Gann demystifies Young's sound universe with an extended analysis of the various tuning systems Young used from his early notated works (such as Trio for Strings), through the improvisational works with the Theatre of Eternal Music and specific works such as The Four Dreams of China, The Well-Tuned Piano (1964-present), and Chronos Kristalla (1990).
The endless debates about tuning systems, the problem of the mathematical basis of music, the question of Greek modes and their relation to ecclesiastical modes, the attempt to revive the fabled effects of Greek music in modern practice, the relation of music to poetics, the conflict between theory and practice, especially with regard to the categorization of consonances: all these subjects and more exercised generations of writers, often to an exceedingly acrimonious degree.