Alterations in 24-EDO

The following table shows the alterations in the 24-tone equal-temperament system (24-EDO, quarter-tone system) up to the five-quarters-tone.

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<Degree<Alter.<Cents<Sfx De<Sfx En<go<stz<stc<stvt<arrow<sag<msag<arabic<persian<four
000  
11/450ihqs
−1−1/4−50ehqf
1   11/450isehsaqf 
1 −1−1/4−50esihfaqs 
21/2100iss
−2−1/2−100esf
33/4150isihtqs
−3−3/4−150esehtqf
1   33/4150isisehssaqf 
1 −3−3/4−150esesihffaqs 
41200isisss x
−4−1−200esesff
55/4250isisihfqs
−5−5/4−250esesehfqf
go – Gould Notation
5 × 2 combined arrow symbols after Gould (U+E270 - U+E279) for quarters-tones, and standard sharp / flat symbols (U+E260 - U+E264).
stz – Stein / Zimmermann Notation
Fractional sharp symbols and quarter-tone flat symbol after Richard Stein (U+E282 - U+E284) and three-quarters-tone flat symbol after Bernd A. Zimmerman (U+E285) (replacing Stein's “sesquiflat” symbol) for quarter-tones, and standard sharp / flat symbols (U+E260 - U+E264). Also known as Tartini / Couper notation.
Note: The notation uses the narrow shape of the reversed flat (U+E284, U+E285).
stc – Stein / Couper Notation
Variant of stz with the three-quarters-tone flat symbol after Mildred Couper (U+E489) (merger of mirrored flat symbols).
stvt – Stein / Van Blankenburg / Tartini Notation
Fractional sharp symbols after Richard Stein (U+E282, U+E283), quarter-tone flat symbol after Van Blankenburg (U+E488) (also known as “Tartini's hook”), three-quarters-tone flat symbol after Giuseppe Tartini (U+E487), and standard sharp / flat symbols (U+E260 - U+E264).
arrow – Arrow Notation
Arrow after Gould (U+E27A, U+E27B) for quarter-tones, and standard sharp / flat symbols (U+E260 - U+E264). All symbols are placed either alone or a standard symbol is combined with an arrow.
sag – Sagittal Notation
4 × 2 Spartan Sagittal single-shaft and multi-shaft symbols after George D. Secor and David C. Keenan (U+E30A ... U+E335). This is the "Pure Sagittal notation" in contrast to msag. It uses one distinct symbol for each degree up to the whole tone. For the five-quarters-tone degree, two symbols are combined.
msag – Mixed Sagittal Notation
1 × 2 Spartan Sagittal single-shaft symbols (U+E30A, U+E30B) for quarter-tones, standard sharp / flat symbols (U+E260 - U+E262, U+E264), and large double-sharp symbol (U+E47D). They are placed like arrow.
arabic – Arabic Notation
4 × 2 arabic symbols (U+ED30 - U+ED38). This notation uses its own natural sign (U+ED34 instead of U+E261).
persian – Persian Notation
Persian symbols Koron and Sori after Ali-Naghi Vaziri (probably) (U+E460, U+E461) for quarter-tones, and standard sharp / flat symbols (U+E260 - U+E264). They are placed like arrow.
four – Digit 4 Notation
sharp / flat symbols with digit 4 (U+E47E, U+E47F) for quarter-tones, and standard sharp / flat symbols (U+E260 - U+E264). They are placed like arrow.
  1. abcdIn most of the notation styles like go, stz and arrow, the one-quarter-tone and three-quarters-tone degrees have two distinct, enharmonically equivalent accidentals. Therefore, Ekmelily defines two note name suffixes each, e.g. qs and saqf (English) or ih and iseh (German). However, LilyPond does not support different accidentals for the same alteration. As a provisional solution, the combined note names (e.g. -saqf or -iseh) have slightly differing alterations and are therefore not suitable for transposition and MIDI output.