Musical tuning system with 17 pitches equally-spaced on a logarithmic scale
In music, 17 equal temperament is the temperedscale 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.[2] 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.[citation needed]
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.
Major chord on C in 17 equal temperament: all notes within 37 cents of just intonation (rather than 14 for 12 equal temperament)