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 ?
Peter Frampton has been a loyal customer of AxCent Tuning Systems and its predecessor company TransPerformance, producers of benchmark self tuning guitar systems.
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.
First, earlier, more flexible tuning systems are based on natural acoustics that sound good to humans.
Serious misunderstandings mar the discussion of Ramos's tuning system (not "the centerpiece of his treatise") and his criticism of Guido's hexachord theory (she misapprehends the concept of "mutation"), Aaron's "quattro modi da gli antichi" (which have as little to do with Boethius's modi as with Aretino's: Aaron is discussing mensural modes, and the "antichi" are fifteenth-century authors), and Vicentino's revival of the Greek genera in modern music (tetrachords were not viewed as "simple, four-note modules that could be easily interchanged and replaced by modules from another genus when a given altered note was needed," thus "offering a solution to the technical problems of accidentals in music composition").
Contract Awarded For Multiple ECOMAXA Combustion Tuning Systems And Combustion Dynamics Monitoring Systems (CDMS) For A 7FA Fleet Of Gas Turbines
After a brief survey of the use of alternative tuning systems in twentieth-century music, Chalmers begins his elucidation and expansion of tetrachordal theories with the arithmetic approach of Pythagoras and Ptolemy, in which intervals are expressed as numerical ratios, or as harmonic divisions - 1/2, 1/3, 1/4, and so on - of a string, and the complementary approach of Aristoxenus and his followers, who thought of musical intervals as spatial distances divisible into parts in the same way that a line can be divided with a ruler (and much as on a piano keyboard, where equal intervals span constant distances).
Zenith holds key patents used in tuning systems in essentially all cable-compatible TVs and VCRs on the U.