17 equal temperament



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 $\sqrt{2|17}$, 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:
 * C, D♭, C♯, D, E♭, D♯, E, F, G♭, F♯, G, A♭, G♯, A, B♭, A♯, B, C

Quarter tone sharps and flats can also be used, yielding the following chromatic scale:
 * C, C/D♭, C♯/D, D, D/E♭, D♯/E, E, F, F/G♭, F♯/G, G, G/A♭, G♯/A, A, A/B♭, A♯/B, B, C

Interval size
Below are some intervals in 17-EDO compared to just.

Relation to 34-ET
17-ET is where every other step in the 34-ET scale is included, and the others are not accessible. Conversely 34-ET is a subdivision of 17-ET.