72-EDO Alterations

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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CopyCOPIED
xDegreexAlter.xCentsxSfx DexSfx Enxarrowxrhmxsimsxhessexsagxmsagxwysxgostzxgostcxbosxfernxhaba
000
11/1216 23irts
−1−1/12−16 23ertf
21/633 13ilxs
−2−1/6−33 13elxf
31/450ihqs
−3−1/4−50ehqf
31/450isehsaqf
−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
93/4150isisehssaqf
−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 symbols after Gould (U+E27A, U+E27B), half arrow symbols (hook) after Ezra Sims (U+E2A4, U+E2A1), Wilson plus/minus (U+E47B, U+E47C), 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), 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.

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), 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.

hesse — Hesse Notation

3 × 2 arrow symbols proposed by Horst-Peter Hesse (U+F606 - U+F60B), and Standard sharp / flat symbols (U+E260 - U+E264). They differentiate only marginally from the arrow symbols and are placed in the same way.

They are defined as “Optional glyphs” in the Ekmelos font since they are not included in SMuFL.

sag — Sagittal notation

12 × 2 Spartan Sagittal single-shaft and multi-shaft symbols (U+E302 … U+E335) after George D. Secor and David C. Keenan.

This is the "Pure Sagittal notation" in contrast to msag. It uses one distinct symbol for each degree up to the whole tone. For higher degree, two symbols are combined.

msag — Mixed Sagittal notation

3 × 2 Spartan Sagittal single-shaft symbols (U+E302 - U+E305, U+E30A, U+E30B), 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 Iwan 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 remaining degrees, two symbols are combined.

gostz — Gould / Stein / Zimmermann Notation

5 × 2 combined arrow symbols after Gould (U+E270 - U+E279), 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), completed with Wilson plus/minus (U+E47B, U+E47C), and Standard sharp / flat symbols (U+E260 - U+E264).

The notation uses the narrow variant of the reversed flat (U+E284, U+E285).

gostc — Gould / Stein / Couper Notation

Variant of gostz with the three-quarters-tone flat symbol after Mildred Couper (U+E489) (merger of mirrored flat symbols).

bos — Bosanquet commatic notation

One thru three comma symbols (sloping lines) after Robert H. M. Bosanquet (U+E479, U+E47A), 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), completed with Wilson plus/minus (U+E47B, U+E47C), and Standard sharp / flat symbols (U+E260 - U+E264).

haba — Hába notation

11 + 6 symbols after Alois Hába (U+F660 - U+F670), and Standard double-sharp / flat symbols (U+E263, U+E264).

The notation uses one distinct symbol for each degree ascending up to the whole tone and descending up to the semitone. For the remaining degrees, two symbols are combined.

Hába's symbols are defined as “Optional glyphs” in the Ekmelos font since they are not included in SMuFL.