Helmholtz–Ellis notation
The Helmholtz-Ellis JI pitch notation (HEJI) is a notation system for just intonation intervals up to the 47-limit. It consists of a set of accidentals defined by formal commas for each prime harmonic.
Further accidentals were designed by richie for primes up to the 89-limit; see richie's HEJI extensions.
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[1] 2004 version
Quick reference
Formal commas
| Prime | Formal Comma |
|---|---|
| 5 | 81/80 |
| 7 | 64/63 |
| 11 | 33/32 |
| 13 | 27/26 |
| 17 | 2187/2176 |
| 19 | 513/512 |
| 23 | 736/729 |
| 29 | 261/256 |
| 31 | 32/31 |
| 37 | 37/36 |
| 41 | 82/81 |
| 43 | 129/128 |
| 47 | 752/729 |
Prime harmonics
| Prime | Just Ratio | Notation (assuming 1/1 is C) | Comments | |
|---|---|---|---|---|
| 2020 version | 2004 version | |||
| 1 | 1/1 | 
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|
Default staff notation represents Pythagorean tuning |
| 3 | 3/2 | 
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Default staff notation represents Pythagorean tuning |
| 5 | 5/4 |  
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| 7 | 7/4 |   
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| 11 | 11/8 |  
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| 13 | 13/8 |  
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| 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 | 
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| 23 | 23/16 | 
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| 29 | 29/16 | (todo) | 
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Definition of the accidental is revised from 145/144 to 261/256 in the 2020 version by Plainsound Music Edition |
| 31 | 31/16 | 
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(todo) | Definition of the accidental is revised from 1024/1023 to 32/31 in the 2020 version by Plainsound Music Edition |
| 37 | 37/32 | (todo) | (todo) | |
| 41 | 41/32 | (todo) | (todo) | |
| 43 | 43/32 | (todo) | (todo) | |
| 47 | 47/32 | (todo) | (todo) | |
Helmholtz-Ellis glyphs
|
Todo: update
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 (old) -
Combining raise by one 29-limit schisma (old) -
Combining lower by one 31-limit quartertone -
Combining raise by one 31-limit quartertone
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