Helmholtz–Ellis notation
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The Helmholtz–Ellis JI pitch notation (HEJI) is a musical 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
Below is a quick guide to the accidentals and commas used in Helmholtz–Ellis notation.
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 |
Harmonic | 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 | |||
5 | 5/4 | |||
7 | 7/4 | |||
9 | 9/8 | Default staff notation represents Pythagorean tuning | ||
11 | 11/8 | is not a half-sharp, as F is 7.1¢ flatter than F♯. | ||
13 | 13/8 | |||
15 | 15/8 | |||
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 | |||
21 | 21/16 | |||
23 | 23/16 | |||
25 | 25/16 | |||
27 | 27/16 | Default staff notation represents Pythagorean tuning | ||
29 | 29/16 | (todo) | Definition of the accidental is revised from 145/144 to 261/256 in the 2020 version by Plainsound Music Edition | |
31 | 31/16 | (todo) | Definition of the accidental is revised from 1024/1023 to 32/31 in the 2020 version by Plainsound Music Edition | |
33 | 33/32 | |||
35 | 35/32 | |||
37 | 37/32 | (todo) | (todo) | |
39 | 39/32 | |||
41 | 41/32 | (todo) | (todo) | |
43 | 43/32 | (todo) | (todo) | |
45 | 45/32 | |||
47 | 47/32 | (todo) | (todo) |
Helmholtz–Ellis glyphs
External links
- HEWM Notation (Helmholtz-Ellis-Wolf-Monzo) – Tonalsoft enyclopedia of microtonal music theory
- Plainsound Harmonic Space Calculator