In music, 17 equal temperament is the tempered scale derived by dividing the octave into 17 equal steps (equal frequency ratios). Each step represents a frequency ratio of 17√2, or 70.6 cents. 17-ET is the tuning of the regular diatonic tuning in which the tempered perfect fifth is equal to 705.88 cents, as shown in Figure 1 (look for the label "17-TET").

History and use

Alexander J. Ellis refers to a tuning of seventeen tones based on perfect fourths and fifths as the Arabic scale. In the thirteenth century, Middle-Eastern musician Safi al-Din Urmawi developed a theoretical system of seventeen tones to describe Arabic and Persian music, although the tones were not equally spaced. This 17-tone system remained the primary theoretical system until the development of the quarter tone scale.

Notation

Easley Blackwood Jr. created a notation system where sharps and flats raised/lowered 2 steps. This yields the chromatic scale: Quarter tone sharps and flats can also be used, yielding the following chromatic scale:

Interval size

Below are some intervals in 17 compared to just. ! interval name ! size (steps) ! size (cents) ! audio ! just ratio ! just (cents) ! audio ! error

[I–IV–V–I chord progression in 17.

[[File:Simple_I-IV-V-I_isomorphic_17-TET.mid]] Whereas in 12, B♮ is 11 steps, in 17, B♮ is 16 steps. | upload.wikimedia.org/wikipedia/commons/a/a0/Simple///I-IV-V-I///isomorphic///17-TET.png]

Relation to 34 EDO

17 is where every other step in the 34 scale is included, and the others are not accessible. Conversely 34 is a subset of 17.

Sources