Syntonic temperament
From Wikipedia, the free encyclopedia
The syntonic temperament[1] is a system of musical tuning in which the frequency ratio of each musical interval is a product of powers of an octave and a tempered perfect fifth, with the width of the tempered major third being equal to four tempered perfect fifths minus two octaves and the width of the tempered major second being equal to two tempered perfect fifths minus one octave (i.e., half the width of the major third).
The syntonic temperament is named after the syntonic comma, as that is the first comma tempered to unison in its comma sequence.
As shown in the fgure at right, the tonally-valid tuning range of the syntonic temperament includes a number of historically-important tunings, such as the currently-popular 12-tone equal division of the octave (12-edo tuning, also known as 12-tone “equal temperament”), the meantone tunings, and Pythagorean tuning.
From the center of the syntonic temperament’s tonally-valid tuning range, as the width of the tempered perfect fifth widens, the minor second narrows, eventually disappearing in 5-edo; as the width of the tempered perfect fifth narrows, the minor second widens, eventually equaling the major second in 7-edo.
The syntonic temperament is a regular temperament. Because it has two generators – the octave and tempered perfect fifth – it is a rank-2 regular temperament. Because one of its generators is the octave, the terminology of Erv Wilson would describe the syntonic temperament as a linear temperament.
[edit] Notes
- ^ Milne, A., Sethares, W.A. and Plamondon, J., Invariant Fingerings Across a Tuning Continuum, Computer Music Journal, Winter 2007, Vol. 31, No. 4, Pages 15-32.
