Musical Temperaments - Equal Temperaments, Linear Temperaments, Meantone Temperament, Well Temperament, Quarter-Comma Meantone (Paperback)

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 36. Chapters: Equal temperaments, Linear temperaments, Meantone temperament, Well temperament, Quarter-comma meantone, Bohlen-Pierce scale, 53 equal temperament, 72 equal temperament, 31 equal temperament, 19 equal temperament, Dynamic tonality, Musical temperament, 34 equal temperament, Werckmeister temperament, Temperament ordinaire, 41 equal temperament, 22 equal temperament, 17 equal temperament, 15 equal temperament, Kirnberger temperament, Schismatic temperament, Syntonic temperament, Isomorphic keyboard, Septimal meantone temperament, Regular temperament, Young temperament, Arab tone system, Beta scale, Miracle temperament, Alpha scale, Magic temperament, Delta scale, Fluid tuning, Gamma scale. Excerpt: Quarter-comma meantone, or 1/4-comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. This method is a variant of Pythagorean tuning. The difference is that in this system the perfect fifth is flattened by one quarter of a syntonic comma, with respect to its just intonation used in Pythagorean tuning (frequency ratio 3:2). The purpose is to obtain justly intonated major thirds (an interval composed of 2 whole tones, with a frequency ratio equal to 5:4). It was described by Pietro Aron (also spelled Aaron), in his Toscanello de la Musica of 1523, by saying the major thirds should be tuned to be "sonorous and just, as united as possible." Later theorists Gioseffo Zarlino and Francisco de Salinas described the tuning with mathematical exactitude. In a meantone tuning, we have diatonic and chromatic semitones, with the diatonic semitone larger. In Pythagorean tuning, these correspond to the Pythagorean limma and the Pythagorean apotome, only now the apotome is larger. In any meantone or Pythagorean tuning, a whole tone is composed of two semitones of ea...