Alterations

The following table includes data of the alterations in the 72-tone equal-temperament system (72-EDO) up to the five-quarters-tone, i.e. 15 twelfth-tones up and down. The suffixes have been designed for the Note names in Ekmelily and ekmelib, based on the German and English names for semitones and quarter-tones that are already given in LilyPond. The Scheme symbols are defined in Ekmelily (internally used names for the alterations). The accidental symbols are shown for all predefined notation styles in Ekmelily version 1.7 or higher; but only the relevant symbols in the respective notation system. Ekmelily uses surrogate symbols for the remaining degrees (empty fields in the table). Unless otherwise stated, these are combinations with the Wilson plus/minus for sixth- and twelfth-tones.

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<Deg.Degree<Alter.Alteration, Inflection, Tone fraction<CentsCents tempered<Sfx deNote name suffix German<Sfx enNote name suffix English<Scheme SymbolScheme symbol for the alteration<arrowArrow notation 1<rhmRichter Herf / Maedel notation 2<simsSims notation 3<sagSagittal notation 4<msagMixed Sagittal notation 5<wysWyschnegradsky notation 6<goGould notation for quarter-tones 7<gosGould notation for sixth-tones 8<gostGould + Stein / Zimmermann notation 9<stzStein / Zimmermann notation 10<stcStein / Couper notation 11<stvtStein / Van Blankenburg / Tartini notation 12<bosBosanquet commatic notation 13<fourDigit 4 notation 14<fernFerneyhough notation 15
−15−5/4−250esesehfqfFIVE-Q-FLAT  
−14−7/6−233⅓eseselsxfSEVEN-SIXTH-FLAT       
−13−13/12−216⅔eseserttfTHIRTEEN-TWELFTH-FLAT        
−12−1−200esesffDOUBLE-FLAT 
−11−11/12−183⅓esesiretfELEVEN-TWELFTH-FLAT        
−10−5/6−166⅔esesilfxfFIVE-SIXTH-FLAT       
16−9−3/4−150esesihffaqsTHREE-Q-FLAT-EQUIV  
16−9−3/4−150esehtqfTHREE-Q-FLAT  
−8−2/3−133⅓eseltrfTWO-THIRD-FLAT      
−7−7/12−116⅔eserstfSEVEN-TWELFTH-FLAT        
−6−1/2−100esfFLAT 
−5−5/12−83⅓esirftfFIVE-TWELFTH-FLAT        
−4−1/3−66⅔esilrfTHIRD-FLAT      
16−3−1/4−50esihfaqsSEMI-FLAT-EQUIV  
16−3−1/4−50ehqfSEMI-FLAT   
−2−1/6−33⅓elxfSIXTH-FLAT       
−1−1/12−16⅔ertfTWELFTH-FLAT        
000  NATURAL
+1+1/12+16⅔irtsTWELFTH-SHARP        
+2+1/6+33⅓ilxsSIXTH-SHARP       
16+3+1/4+50ihqsSEMI-SHARP  
16+3+1/4+50isehsaqfSEMI-SHARP-EQUIV  
+4+1/3+66⅔iselrsTHIRD-SHARP      
+5+5/12+83⅓iserftsFIVE-TWELFTH-SHARP        
+6+1/2+100issSHARP 
+7+7/12+116⅔isirstsSEVEN-TWELFTH-SHARP        
+8+2/3+133⅓isiltrsTWO-THIRD-SHARP      
16+9+3/4+150isihtqsTHREE-Q-SHARP  
16+9+3/4+150isisehssaqfTHREE-Q-SHARP-EQUIV  
+10+5/6+166⅔isiselfxsFIVE-SIXTH-SHARP       
+11+11/12+183⅓isiseretsELEVEN-TWELFTH-SHARP        
+12+1+200isisssDOUBLE-SHARP 
+13+13/12+216⅔isisirttsTHIRTEEN-TWELFTH-SHARP        
+14+7/6+233⅓isisilsxsSEVEN-SIXTH-SHARP       
+15+5/4+250isisihfqsFIVE-Q-SHARP  
  1. arrow: Arrow after Gould for quarter-tones, half arrow (hook) after Ezra Sims for sixth-tones, and Wilson plus/minus for twelfth-tones. The latter are variants of the Bosanquet symbols after Ervin M. Wilson. The comma-up symbol has a vertical line resembling a plus sign. All symbols are placed either alone or in combination to the left of the traditional 12-EDO accidentals (sharp, flat). arrow is the default setting in Ekmelily.
  2. rhm: Three arrow symbols and their inversions for the degrees within a semitone introduced by Franz Richter Herf and Rolf Maedel. In Ekmelily, they are placed like arrow and not separately above the notes, as originally intended; see Notation.
  3. sims: Three arrow symbols and their inversions for the degrees within a semitone introduced by Ezra Sims. Also known as Maneri / Sims notation, due to the adoption of the accidentals by Joe Maneri of the Boston Microtonal Society. They are placed like arrow.
  4. sag: Spartan Sagittal single-shaft and multi-shaft accidentals by George D. Secor and David C. Keenan; see Sagittal. This is the "Pure Sagittal notation" in contrast to msag. It uses one distinct symbol for each degree up to the whole tone.
  5. msag: Mixed Sagittal notation: Three Spartan Sagittal single-shaft symbols and their inversions for the degrees within a semitone. They are placed like arrow.
  6. wys: Symbols after Ivan Wyschnegradsky. The notation uses one distinct symbol for each degree up to the whole tone.
  7. go: Combined arrow symbols after Gould for quarter-tones (24-EDO).
  8. gos: Combined arrow symbols after Gould, used here for sixth-tones (36-EDO). Ekmelily uses combinations with the Gould arrow as surrogates for quarter-tones.
  9. gost: Combined arrow symbols after Gould, used here for sixth-tones (36-EDO), and completed with the Stein / Zimmermann notation for quarter-tones.
  10. stz: Fractional sharp symbols and quarter-tone flat (reversed flat) symbol after Richard Stein, and three-quarters-tones flat symbol after Bernd Alois Zimmerman (replacing Stein's “sesquiflat” symbol) (24-EDO). Also known as Tartini / Couper notation. Ekmelily uses the narrower shape of the reversed flats.
  11. stc: Variant of stz with the three-quarters-tones flat symbol merging mirrored flat symbols after Mildred Couper.
  12. stvt: Fractional sharp symbols after Richard Stein, quarter-tone flat symbol after Van Blankenburg (also known as “Tartini's hook”), and three-quarters-tones flat symbol after Giuseppe Tartini.
  13. bos: Sloping lines for commatic alterations after Robert Holford Macdowall Bosanquet, used here for twelfth-, sixth-, and quarter-tones.
  14. four: Quarter-tone sharp and flat symbols with digit 4.
  15. fern: Third-tone and quarter-tone symbols (digit 3, 6, and 4 with arrow) after Brian Ferneyhough, completed with the Arrow notation.
  16. The one-quarter-tone and three-quarters-tones degrees have two distinct, enharmonically equivalent accidentals in some notation styles like arrow, rhm, and sims. Therefore, Ekmelily defines two note names each, e.g. cqs and csaqf (English) or cih and ciseh (German). However, LilyPond does not support different accidentals for the same alteration. As a provisional solution, the combined note names (e.g. csaqf or ciseh) and the corresponding …-EQUIV Scheme symbols have slightly differing alterations and are therefore not suitable for transposition and MIDI output.