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Encyclopedia > 19 equal temperament

In music, 19 equal temperament, called 19-tet, 19-edo, or 19-et, is the scale derived by dividing the octave into 19 equally large steps. Each step represents a frequency ratio of 21/19, or 63.16 cents. The cent is a logarithmic unit of measure used for musical intervals. ...

Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley is said to have used it in his chanson Seigneur Dieu ta pitiƩ of 1558. In 1577 music theorist Francisco de Salinas in effect proposed it. Salinas discussed 1/3-comma meantone, in which the fifth is of size 694.786 cents; the fifth of 19-et is 694.737, which is only a twentieth of a cent flatter. Salinas suggested tuning nineteen tones to the octave to this tuning, which fails to close by less than a cent, so that his suggestion is effectively 19-et. In the nineteenth century mathematician and music theorist Wesley Woolhouse proposed it in mathematically exact terms, as a more practical alternative to meantone tunings he regarded as better, such as 50 equal temperament. Guillaume Costeley (ca. ...

Properties of 19 equal temperament

The most salient characteristic of 19-et is that it equates to the unison, or tempers out, the syntonic comma of 81/80. It is therefore a system of meantone temperament. It also tempers out the magic comma or small diesis, the interval 3125/3072, and therefore supports magic temperament, and the kleisma, the interval 15625/15552, and therefore supports hanson temperament. For none of these is 19-et close to an optimal tuning, however. The generating interval for meantone is a fifth, and the fifth of 19-et is flatter than ideal, a better choice being 31 equal temperament. The generating interval of magic is a major third, and again 19-et is flatter than ideal, a better choice being 41 equal temperament. The generating interval for hanson is the minor third, and the minor third of 19-et is only a seventh of a cent sharp. However, ideally the minor third should be sharper, and 53 equal temperament is a better choice. The syntonic comma, also known as the comma of Didymus or Ptolemaic comma, is a small interval between two musical notes, equal to the frequency ratio 81:80, or around 21. ... Meantone temperament is a system of musical tuning. ... In music, 53 equal temperament, called 53-tet, 53-edo, or 53-et, is the scale derived by dividing the octave into fifty-three equally large steps. ...

However, for all of these 19-et has the great advantage that it is practical to use on physical instruments, and many such instruments have been built. 19-et is in fact the second equal temperament, after 12-et which is able to deal with 5-limit music in a tolerable manner. It is less successful when it comes to the 7-limit, but at least still better than 12-et. Its most salient property in the 7-limit is that it tempers out the septimal diesis of 49/48, and hence equates the septimal minor third, 7/6, with the septimal whole tone of 8/7.

Musical examples

Foum by Jacob Barton short mp3 file

Prelude 1 for 19ET Piano by Jeff Harrington mp3 file

Prelude 2 for 19ET Piano by Jeff Harrington mp3 file

Prelude 3 for 19ET Piano by Jeff Harrington midi file

Juggler by Aaron Krister Johnson ogg file

External links

Bucht, Saku and Huovinen, Erkki, Perceived consonance of harmonic intervals in 19-tone equal temperament [gewi.uni-graz.at/~cim04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf]

Darreg, Ivor, A Case for Nineteen [1]

Howe, Hubert S. Jr., 19-Tone Theory and Applications [2]

Sethares, William A., Tunings for 19 Tone Equal Tempered Guitar, [3]



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