Helmholtz–Ellis notation

Introductory materials

• The Helmholtz-Ellis JI Pitch Notation (HEJI) by Marc Sabat and Thomas Nicholson from Plainsound Music Edition – 2020 version with revised symbols for primes up to 47 entirely based on alterations of Pythagorean notes
• Extended Helmholtz-Ellis JI Pitch Notation by Marc Sabat and Wolfgang von Schweinitz from Plainsound Music Edition – deprecated 2004 version

Helmholtz-Ellis glyphs

Todo: update the 29-limit comma.

• 
  Double flat lowered by three syntonic commas
• 
  Double flat lowered by two syntonic commas
• 
  Double flat lowered by one syntonic comma
• 
  Double flat
• 
  Double flat raised by one syntonic comma
• 
  Double flat raised by two syntonic commas
• 
  Double flat raised by three syntonic commas
• 
  Flat lowered by three syntonic commas
• 
  Flat lowered by two syntonic commas
• 
  Flat lowered by one syntonic comma
• 
  Flat
• 
  Flat raised by one syntonic comma
• 
  Flat raised by two syntonic commas
• 
  Flat raised by three syntonic commas
• 
  Natural lowered by three syntonic commas
• 
  Natural lowered by two syntonic commas
• 
  Natural lowered by one syntonic comma
• 
  Natural
• 
  Natural raised by one syntonic comma
• 
  Natural raised by two syntonic commas
• 
  Natural raised by three syntonic commas
• 
  Sharp lowered by three syntonic commas
• 
  Sharp lowered by two syntonic commas
• 
  Sharp lowered by one syntonic comma
• 
  Sharp
• 
  Sharp raised by one syntonic comma
• 
  Sharp raised by two syntonic commas
• 
  Sharp raised by three syntonic commas
• 
  Double sharp lowered by three syntonic commas
• 
  Double sharp lowered by two syntonic commas
• 
  Double sharp lowered by one syntonic comma
• 
  Double sharp
• 
  Double sharp raised by one syntonic comma
• 
  Double sharp raised by two syntonic commas
• 
  Double sharp raised by three syntonic commas
• 
  Lower by two septimal commas
• 
  Lower by one septimal comma
• 
  Raise by one septimal comma
• 
  Raise by two septimal commas
• 
  Lower by one undecimal quartertone
• 
  Raise by one undecimal quartertone
• 
  Lower by one tridecimal third tone
• 
  Raise by one tridecimal third tone
• 
  Combining lower by one 17-limit schisma
• 
  Combining raise by one 17-limit schisma
• 
  Combining lower by one 19-limit schisma
• 
  Combining raise by one 19-limit schisma
• 
  Combining lower by one 23-limit comma
• 
  Combining raise by one 23-limit comma
• 
  Combining lower by one 29-limit schisma
• 
  Combining raise by one 29-limit schisma
• 
  Combining lower by one 31-limit quartertone
• 
  Combining raise by one 31-limit quartertone

Quick reference

Formal commas

• 81/80
• 64/63
• 33/32
• 27/26
• 2187/2176
• 513/512
• 736/729
• 261/256
• 32/31

Prime harmonics

Prime	Just Ratio	Notation (assuming 1/1 is C)		Comments
		2020 version	2004 version
1	1/1			Default staff notation represents Pythagorean tuning
3	3/2			Default staff notation represents Pythagorean tuning
5	5/4
7	7/4
11	11/8
13	13/8
17	17/16			Definition of the accidental is revised from 256/255 to 2187/2176 in the 2020 version by Plainsound Music Edition
19	19/16
23	23/16
29	29/16			Definition of the accidental is revised from 145/144 to 261/256 in the 2020 version by Plainsound Music Edition
31	31/16			Definition of the accidental is revised from 1024/1023 to 32/31 in the 2020 version by Plainsound Music Edition

External links

• HEWM Notation (Helmholtz-Ellis-Wolf-Monzo) – Tonalsoft enyclopedia of microtonal music theory
• Plainsound Harmonic Space Calculator

See also

• Functional Just System (FJS) – a logical notation system for the entirety of just intonation
• Ben Johnston's notation
• Other notation systems: http://lumma.org/music/theory/notation/