Microtonal Notation

1. Pitch Notation
   
• American standard pitch notation (ASPN) {WP}, C4 is middle C
• C4 is middle C
  
• Helmholtz pitch notation {WP}
• c' is middle C
• A440 (pitch standard) {WP}
• History of pitch standards in Western music {WP} (see Ellis 1880; Haynes 2002; Rotam 2017)
• See also: Concert pitch {WP}
2. Chain of Fifths {XW}
• Chain of fifths {XW}
• Nominal-accidental chain {XW}
• Nominals
• Accidentals
• Enharmonics
3. Mictrotonal Music Notation {XW}
   • Types of notation
   • Intended for just intonation
   • Intended for MOS scales and any temperaments containing them
   • Intended for equal temperaments
     
   • Intended for both equal and unequal temperaments
4. Just Intonation (JI) {XW}
   
• Johnston Notation {XW}
• Gann, How to Use Ben Johnston's Just Intonation Notation {KyleGann.com} (Gann 2019, pp. 118-122)
  
• Helmholtz-Ellis Notation {XW} (Gann 2019, pp. 123-124)
• Sabat, An informal introduction to the Helmholtz-Ellis Accidentals {Plainsound}
  
• Sabat and Schweinitz, The Extended Helmholtz-Ellis JI Pitch Notation {Plainsound} (Sabat and Schweinitz 2005)
• LEGEND: Extended Helmholtz-Ellis JI (HEJI2) Pitch Notation, v6.2024 {Plainsound}
  
• HEJI2.otf font {Plainsound}
• Software:
• Nicholson, Johnston Notation to Helmholtz-Ellis Converter {Plainsound}
• Nicholson, Sabat and Rawicki, Plainsound Harmonic Space Calculator {Plainsound; About}
• JI Array Notation {XW}, Gann 2019, pp. 157-158
• Prime Factorization Theorem {WP}
• 5-limit intervals; e.g.,
• 3/2 = 2^-1 x 3¹ x 5⁰ is: -1, 1, 0
• 5/4 = 2^-2 x 3⁰ x 5¹ is: -2, 0, 1
• 81/80 = 2^-4 x 3⁴ x 5^-1 is: -4, 4, -1
• 7-limit intervals; e.g.,
• 7/4 = 2^-2 x 3⁰ x 5⁰ x 7¹ is: -2, 0, 0, 1
• 8/7 = 2³ x 3⁰ x 5⁰ x 7^-1 is: 3, 0, 0, -1
• 11-limit; e.g.,
• 11/8 = 2^-3 x 3⁰ x 5⁰ x 7⁰ x 11¹ is: -3, 0, 0, 0, 1
• 12/11 = 2² x 3¹ x 5⁰ x 7⁰ x 11^-1 is: 2, 1, 0, 0, -1
• Giedraitis, Color notation {XW}
5. EDOs {XW}
   Intro.: Sabat, Welcome {Ableton}; Introducton to EDO tunings {Ableton}
   
• Closely approximate certain consonant intervals (small-number ratios): 12, 19, 31, 41, 43, 53, 55, 72
• Do not include a consonant perfect fifth: 5-edo, 7-edo, 11-edo, 13-edo, 35-edo
  
• 12-edo
• 12-edo {WP; XW}
  
• 19-edo
• 19-edo {WP; XW; Listen: Ableton}
  
• 22-edo
• 22-edo {WP; XW; Listen: Ableton}
  
• 24-edo, 1/4 tones
• 24-edo {WP; XW; Listen: Ableton}
• 24-edo notation {XW}
  
• 31-edo, 1/5 tones
• 31-edo {WP; XW; Listen: Ableton}
  
• 31-edo notation {XW}
• 36-edo, 1/6 tones
• 36-edo notation {XW; Listen: Ableton}
• JI-intervals approx.: WP
• 41-edo
• 41-edo {WP; XW; Listen: Ableton; Lumatone: YouTube}
  
• 43-edo
• 43-edo {WP; XW; Listen: Ableton}
• JI-intervals approx.: WP
  
• 53-edo
• 53-edo {WP; XW; Listen: Ableton; Lumatone: YouTube}
  
• 72-edo, 1/12 Tones
• 72-edo notation {WP; XW; TonalSoft; Listen: Ableton}
  
• Maneri-Sims Notation {WP}
  
6. Saggital Notation
   Intro.: Blumeyer, Sagittal: The Universal Microtonal Notation System {YouTube}
   
• Kennan and Secor, Sagittal notation {XW; ME} (Secor and Keenan 2006}
• A Microtonal Notation System {Sagittal.org}
• Periodic Table of Small EDOs {Sagittal.org}
7. Other
   
• Blackwood notation (Blackwood 1985)
• Bohlen-Pierce Tuning {Listen: Ableton}
  
• Functional Just System (FJS) {XW}
• Yacavone, Custom FJS Explorer {Yacavone.net}
• Giedraitis, Ups and Downs Notation {XW}
• Helmholtz/Ellis/Wolf/Monzo HEWM notation {Tonalsoft}, Gann 2019, pp. 123-124
• Lumma, Close to Common-Practice {Lumma.org}
  
8. Notation Converters
• Yacovone, Xen-Calc {Yacovone.net}
• Nicholson, Johnston Notation to Helmholtz-Ellis Converter {Plainsound.org}
9. Notation Programs {WP}
• Dorico
• Sabat, Microtonal Notation in Dorico (August 28, 2018) {ScoringNotes}
• Nicholson, Microtonal Playback in Dorico (September 4, 2018) {ScoringNotes}
• MuseScore
• Microtonal plug-ins {XW}
• Sibelius
• Robert Puff, Sibelius Quick Tip : Quarter-tone playback {Of Note}

See also: Xenharmonic Wiki, Musical Notation {XW}

LEGEND
HFF - Huygens-Fokker Foundation
Tonalsoft - Monzo, Tonalsoft Encyclopedia
WP - Wikipedia
XW - Xenharmonic Wiki

Composers

Microtonality – https://en.wikipedia.org/wiki/Microtonality

Microtonal Composers – https://en.wikipedia.org/wiki/Category:Microtonal_composers

Scores

Incipitsify – https://www.youtube.com/@incipitsify

Links

Huygens-Fokker Foundation: Centre for Microtonal Music, Microtonality – https://huygens-fokker.org/en/microtonality/

Sabat, Music & Writings – https://masa.plainsound.org/

Rothman, ScoringNotes – https://www.scoringnotes.com

Xenharmonic Wiki, Music Notation – https://en.xen.wiki/w/Musical_notation

References

Blackwood, Easley. 2014/1985. The Structure of Recognizable Diatonic Tunings. Princeton NJ: Princeton University Press. {TCL}

Ellis, A.J. 1880. "The History of Musical Pitch." Nature 21: 550–554. {Nature}

Gann, Kyle. 2019. The Arithmetic of Listening: Tuning Theory and History for the Impractical Musician. Urbana, IL: University of Illinois Press. {GB; U. of Illinois Press; Full text: TCL; Audio Examples}

Giedraitis, Kite. 2016. Alternative Tunings: Theory, Notation and Practice. Available online at: <https://www.tallkite.com/words.html>.

Griffiths, Paul, Mark Lindley and Ioannis Zannos. "Microtone." Grove Music Online. {Grove}

Haynes, Bruce. 2002. A History of Performing Pitch: The Story of 'A'. New York: Bloomsbury. {GB}

Narushima, Terumi. 2019. Microtonality and the Tuning Systems of Erv Wilson. New York: Routledge. {GB; Full text: TCL}

Nicholson, Thomas and Marc Sabat. 2018. Fundamental Principles of Just Intonation and Microtonal Composition. Available online at: <https://masa.plainsound.org/pdfs/JI.pdf>.

Read, Gardner. 1990. 20th-Century Microtonal Notation. New York: Bloomsbury. {Bloomsbury}

Rotem, Elam. 2017. "Historical Pitch." Early Music Sources (2017). Available online at: <https://www.earlymusicsources.com/youtube/historical-pitch>.

Secor, George D. and David C. Keenan. 2006. "Sagittal: A Microtonal Notation System." Xenharmonikon 18 (2006). Available online at: <https://sagittal.org/sagittal.pdf>.

Sabat, Marc and Wolfgang von Schweinitz. 2004. The Extended Helmholtz-Ellis JI Pitch Notation, translated by  Plainsound Music Edition. Available online at: <https://masa.plainsound.org/pdfs/notation.pdf>.

Skinner, Miles L. 2006. Toward a Quarter-Tone Syntax. Selected Analyses of Works by Toward a Quarter-Tone Syntax: Selected Analyses of Works by Blackwood, Hába, Ives, and Wyschnegradsky. PhD Dissertation, University of Buffalo. Available online at: <https://www.tierceron.com/diss/>.

Tenney, James. 1983. "John Cage and the Theory of Harmony." Soundings 13, edited by Peter Garland. Available online at: <https://www.plainsound.org/pdfs/JC&ToH.pdf>.

Updated: January 19, 2026