Microtonal Notation
Composers of microtonal music have developed a number of notations for indicating the various pitches outside of standard notation. One such system for notating quarter tones, used by the Czech Alois Hába and other composers, is shown on the right.
In the 19th and beginning 20th century, when Turkish musicians switched from their traditional notation systems — which were not staff-based — to the European staff-based system, they created a refinement to the European accidental system in order to be able to notate Turkish scales which make use of intervals smaller than the tempered semitone. There are several such systems which vary as to the division of the octave they presuppose or merely the graphical shape of the accidentals. The most widely used system (created by Rauf Yekta Bey) uses a system of 4 sharps (roughly +25 cents, +75 cents, +125 cents and +175 cents) and 4 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 8th of the tempered tone, actually closer to 24 cents, defined as the difference between 7 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 are used to create just tuning in other keys. Between 2000 and 2003, Wolfgang von Schweinitz and Marc Sabat developed The Extended Helmholtz-Ellis 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 which is rapidly becoming adopted by musicians working in extended Just Intonation (for more details, see the Wikipedia article on Just Intonation).
Read more about this topic: Accidental (music)