Helmholtz–Ellis notation

Helmholtz-Ellis glyphs

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

Harmonic primes

Prime	Just (ratio)	Helmholtz-Ellis notation assuming 1/1 is C	Comments
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
19	19/16
23	23/16
29	29/16
31	31/16

External links

HEWM Notation (Helmholtz-Ellis-Wolf-Monzo) - Tonalsoft enyclopedia of microtonal music theory

von Schweinitz - Extended Helmholtz-Ellis JI Pitch Notation

Plainsound Harmonic Space Calculat

See also

The Functional Just System (FJS) is a logical notation system for the entirety of just intonation (JI) which is both more coherent and more succinct than both Helmholtz-Ellis notation and Ben Johnston notation. https://misotanni.github.io/fjs/en/index.html

Other notation systems: http://lumma.org/music/theory/notation/