Microtonal Notation

1. Pitch Notation
• Historical Pitch (Ellis 1880)
• Concert pitch {WP}
  
• A 440 (pitch standard) {WP}
• American standard pitch notation (ASPN) {WP}
• Helmholtz pitch notation {WP}
2. Chain of Fifths Notation {XW}
• Chain of fifths {XW}
• Nominal-accidental chain {XW}
• Nominals
• Accidentals
• Enharmonics
3. Just Intonation (JI) Notation
   
• 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 and Schweinitz, Extended Helmholtz-Ellis JI (HEJI2) Pitch Notation, v2020 {Plainsound.org}
  
• See also:
  
• HEJI2.otf font {Plainsound.org}
  
• Sabat and Schweinitz, The Extended Helmholtz-Ellis JI Pitch Notation {Plainsound.org}
• Web apps:
• Nicholson, Johnston Notation to Helmholtz-Ellis Converter {Plainsound.org}
• Nicholson, Sabat and Rawicki, Plainsound Harmonic Space Calculator {Plainsound.org; About}
4. 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
5. Quarter Tones
   
• See 24-edo {WP; XW}
• See also: 24-edo notation {XW}
  
6. 1/5 Tones
• See 31 equal temperament {WP; XW}
• See also: 31-edo notation {XW}
  
7. Other Systems
• Blackwood notation (Blackwood 1985}
• Color notation {XW}
• Functional Just System (FJS) {XW}
• Giedraitis, Ups and Downs Notation {XW}
• Helmholtz/Ellis/Wolf/Monzo notation (HEWM) notation {Tonalsoft}, Gann 2019, pp. 123-124
• Maneri-Sims Notation, see 72-tet {WP}
• Secor and Kennan, Sagittal notation {Sagittal.org} {XW} (Secor and Keenan 2006}
• Sagittal: A Microtonal Notation System {Sagittal.org}
• Periodic Table of Small EDOs {Sagittal.org}
8. 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

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. {GB}

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}

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

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://marsbat.space/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. Plainsound Music Edition. Available online at: <https://marsbat.space/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/>.

Updated: December 4, 2025