In the 19th and early 20th centuries, when Turkish musicians switched from their traditional notation systems—which were not staff-based—to the European staff-based system, they refined the European accidental system so they could notate Turkish scales that use intervals smaller than a tempered semitone. There are several such systems, which vary as to how they divide the octave they presuppose or the graphical shape of the accidentals. The most widely used system (created by Rauf Yekta Bey) uses a system of four sharps (roughly +25 cents, +75 cents, +125 cents and +175 cents) and four flats (roughly −25 cents, −75 cents, −125 cents and −175 cents), none of which correspond to the tempered sharp and flat. They presuppose a Pythagorean division of the octave taking the Pythagorean comma (about an eighth of the tempered tone, actually closer to 24 cents, defined as the difference between seven octaves and 12 just-intonation fifths) as the basic interval. The Turkish systems have also been adopted by some Arab musicians.
