Alterations in 72-EDO

The following table shows the alterations in the 72-tone equal-temperament system (72-EDO, twelfth-tone system, Ekmelic system) up to the five-quarters-tone, i.e. 15 twelfth-tone degrees.

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xDegreexAlter.xCentsxSfx DexSfx Enxarrowxrhmxsimsxsagxmsagxwysxgostxbosxfern
000  
11/1216 23irts
−1−1/12−16 23ertf
21/633 13ilxs
−2−1/6−33 13elxf
31/450ihqs
−3−1/4−50ehqf
1   31/450isehsaqf  
1 −3−1/4−50esihfaqs  
41/366 23iselrs
−4−1/3−66 23esilrf
55/1283 13iserfts
−5−5/12−83 13esirftf
61/2100iss
−6−1/2−100esf
77/12116 23isirsts
−7−7/12−116 23eserstf
82/3133 13isiltrs
−8−2/3−133 13eseltrf
93/4150isihtqs
−9−3/4−150esehtqf
1   93/4150isisehssaqf  
1 −9−3/4−150esesihffaqs  
105/6166 23isiselfxs
−10−5/6−166 23esesilfxf
1111/12183 13isiserets
−11−11/12−183 13esesiretf
121200isisss x
−12−1−200esesff
1313/12216 23isisirtts
−13−13/12−216 23eseserttf
147/6233 13isisilsxs
−14−7/6−233 13eseselsxf
155/4250isisihfqs
−15−5/4−250esesehfqf
arrow – Arrow notation
Arrow after Gould (U+E27A, U+E27B) for quarter-tones, half arrow (hook) after Ezra Sims (U+E2A4, U+E2A1) for sixth-tones, Wilson plus/minus (U+E47B, U+E47C) 2 for twelfth-tones, and standard sharp / flat symbols (U+E260 - U+E264). All symbols are placed either alone or a standard symbol is combined with one of the other symbols.
rhm – Richter Herf / Maedel notation
3 × 2 arrow symbols after Franz Richter Herf and Rolf Maedel (U+F600 - U+F605) for the degrees within the semitone, and standard sharp / flat symbols (U+E260 - U+E264). They are placed like arrow. The arrow symbols were originally placed separately above the notes; see Notation. But this is not supported by Ekmelily and ekmelib.
Note: The arrow symbols are defined as “Optional glyphs” in the Ekmelos Font since they are not included in SMuFL.
sims – Sims notation
3 × 2 arrow symbols after Ezra Sims (U+E2A0 - U+E2A5) for the degrees within the semitone, and standard sharp / flat symbols (U+E260 - U+E264). They are placed like arrow. Also known as Maneri / Sims notation, due to the adoption of the accidentals by Joe Maneri of the Boston Microtonal Society.
sag – Sagittal notation
12 × 2 Spartan Sagittal single-shaft and multi-shaft symbols after George D. Secor and David C. Keenan (U+E302 ... 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 degrees up to the five-quarters-tone, two symbols are combined.
msag – Mixed Sagittal notation
3 × 2 Spartan Sagittal single-shaft symbols (U+E302 - U+E305, U+E30A, U+E30B) for the degrees within the semitone, standard sharp / flat symbols (U+E260 - U+E262, U+E264), and large double-sharp symbol (U+E47D). They are placed like arrow.
wys – Wyschnegradsky notation
11 × 2 symbols after Ivan Wyschnegradsky (U+E420 - U+E435), and standard double-sharp / flat symbols (U+E263, U+E264). The notation uses one distinct symbol for each degree up to the whole tone. For the degrees up to the five-quarters-tone, two symbols are combined.
gost – Gould + Stein / Zimmermann notation
5 × 2 combined arrow symbols after Gould (U+E270 - U+E279) for sixth-tones, 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) for quarter-tones, completed with Wilson plus/minus (U+E47B, U+E47C) 2 for twelfth-tones, and standard sharp / flat symbols (U+E260 - U+E264).
Note: The notation uses the narrow shape of the reversed flat (U+E284, U+E285).
bos – Bosanquet commatic notation
One thru three comma symbols (sloping lines) after Robert H. M. Bosanquet (U+E479, U+E47A) for the degrees within the semitone, and standard sharp / flat symbols (U+E260 - U+E264). They are placed like arrow.
fern – Ferneyhough notation
3 × 2 combined digit-arrow symbols after Brian Ferneyhough (U+E48A - U+E48F) for third- and quarter-tones, completed with Wilson plus/minus (U+E47B, U+E47C) 2 for twelfth-tones, and standard sharp / flat symbols (U+E260 - U+E264).
  1. abcdIn most of the notation styles like arrow, rhm, and sims, 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.
  2. abcWilson Plus and Minus are variants of the Bosanquet symbols after Ervin M. Wilson. The comma-up symbol has a vertical line resembling a plus sign.