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. Ben Johnston created a system of notation for pieces in just intonation where the unmarked C, F, and G major chords are just major chords (4:5:6) and accidentals create just tuning in other keys. Between 2000 and 2003, Wolfgang von Schweinitz and Marc Sabat developed the Extended Helmholtz-Ellis Just Intonation (JI) pitch notation, a modern adaptation and extension of the notation principles first used by Hermann von Helmholtz, Arthur von Oettingen, and Alexander John Ellis that some other musicians use for notating extended just intonation. History of notation of accidentals The three principal symbols indicating whether a note should be raised or lowered in pitch are derived from variations of the small letter b: the sharp () and natural () signs from the square "b quadratum", and the flat sign () from the round "b rotundum" b. The different kinds of B were eventually written differently, so as to distinguish them in music theory treatises and in notation. The flat sign derives from a round b that signified the soft hexachord, hexachordum molle, particularly the presence of B. The name of the flat sign in French is bémol from medieval French bé mol, which in modern French is bé mou ("soft b"). The natural sign and the sharp sign derive from variations of a square b that signified the hard hexachord, hexachordum durum, where the note in question is B. The name of the natural sign in French is bécarre from medieval French bé quarre, which in modern French is