Helmholtz–Ellis notation: Difference between revisions
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| Line 54: | Line 54: | ||
=== Odd harmonics === | === Odd harmonics === | ||
{| class="wikitable sortable center-all | {| class="wikitable sortable center-all" | ||
! rowspan="2" | Harmonic | ! rowspan="2" | Harmonic | ||
! rowspan="2" | Just Ratio | ! rowspan="2" | Just Ratio | ||
! colspan="2" | Notation | ! colspan="2" | Notation with C as root | ||
! colspan="2" | Notation with A as root | |||
! rowspan="2" | Comments | ! rowspan="2" | Comments | ||
|- | |- | ||
! 2020 version | |||
! 2004 version | |||
! 2020 version | ! 2020 version | ||
! 2004 version | ! 2004 version | ||
| Line 66: | Line 69: | ||
| 1/1 | | 1/1 | ||
| colspan="2" | [[File:HejiC.svg|48x48px]] | | colspan="2" | [[File:HejiC.svg|48x48px]] | ||
| colspan="2" | [[File:HejiA.svg|48x48px]] | |||
| rowspan="2" | Default staff notation represents Pythagorean tuning | | rowspan="2" | Default staff notation represents Pythagorean tuning | ||
|- | |- | ||
| Line 71: | Line 75: | ||
| 3/2 | | 3/2 | ||
| colspan="2" | [[File:HejiG.svg|48x48px]] | | colspan="2" | [[File:HejiG.svg|48x48px]] | ||
| colspan="2" | [[File:HejiE.svg|48x48px]] | |||
|- | |- | ||
| 5 | | 5 | ||
| 5/4 | | 5/4 | ||
| colspan="2" | [[File:Heji17.svg|54x54px]][[File:HejiE.svg|48x48px]] | | colspan="2" | [[File:Heji17.svg|54x54px]][[File:HejiE.svg|48x48px]] | ||
| colspan="2" | [[File:Heji24.svg|54x54px]][[File:HejiC.svg|48x48px]] | |||
| | | | ||
|- | |- | ||
| Line 80: | Line 86: | ||
| 7/4 | | 7/4 | ||
| colspan="2" | [[File:Heji37.svg|54x54px]][[File:Heji11.svg|54x54px]][[File:HejiB.svg|48x48px]] | | colspan="2" | [[File:Heji37.svg|54x54px]][[File:Heji11.svg|54x54px]][[File:HejiB.svg|48x48px]] | ||
| colspan="2" | [[File:Heji37.svg|54x54px]][[File:HejiG.svg|48x48px]] | |||
| | | | ||
|- | |- | ||
| Line 85: | Line 92: | ||
| 9/8 | | 9/8 | ||
| colspan="2" | [[File:HejiD.svg|48x48px]] | | colspan="2" | [[File:HejiD.svg|48x48px]] | ||
| colspan="2" | [[File:HejiB.svg|48x48px]] | |||
| Default staff notation represents Pythagorean tuning | | Default staff notation represents Pythagorean tuning | ||
|- | |- | ||
| Line 90: | Line 98: | ||
| 11/8 | | 11/8 | ||
| colspan="2" | [[File:Heji41.svg|54x54px]][[File:HejiF.svg|48x48px]] | | colspan="2" | [[File:Heji41.svg|54x54px]][[File:HejiF.svg|48x48px]] | ||
| colspan="2" | [[File:Heji41.svg|54x54px]][[File:HejiD.svg|48x48px]] | |||
| | | | ||
|- | |- | ||
| Line 95: | Line 104: | ||
| 13/8 | | 13/8 | ||
| colspan="2" | [[File:Heji42.svg|54x54px]][[File:HejiA.svg|48x48px]] | | colspan="2" | [[File:Heji42.svg|54x54px]][[File:HejiA.svg|48x48px]] | ||
| colspan="2" | [[File:Heji42.svg|54x54px]][[File:Heji25.svg|54x54px]][[File:HejiF.svg|48x48px]] | |||
| | | | ||
|- | |- | ||
| Line 100: | Line 110: | ||
| 15/8 | | 15/8 | ||
| colspan="2" | [[File:Heji17.svg|54x54px]][[File:HejiB.svg|48x48px]] | | colspan="2" | [[File:Heji17.svg|54x54px]][[File:HejiB.svg|48x48px]] | ||
| colspan="2" | [[File:Heji24.svg|54x54px]][[File:HejiG.svg|48x48px]] | |||
| | | | ||
|- | |- | ||
| Line 106: | Line 117: | ||
| [[File:Heji44.svg|54x54px]][[File:Heji25.svg|54x54px]][[File:HejiC.svg|48x48px]] | | [[File:Heji44.svg|54x54px]][[File:Heji25.svg|54x54px]][[File:HejiC.svg|48x48px]] | ||
| [[File:Heji44.svg|54x54px]][[File:Heji12.svg|54x54px]][[File:HejiD.svg|48x48px]] | | [[File:Heji44.svg|54x54px]][[File:Heji12.svg|54x54px]][[File:HejiD.svg|48x48px]] | ||
| [[File:Heji44.svg|54x54px]][[File:Heji25.svg|54x54px]][[File:HejiA.svg|48x48px]] | |||
| [[File:Heji44.svg|54x54px]][[File:Heji12.svg|54x54px]][[File:HejiB.svg|48x48px]] | |||
| Definition of the accidental is revised from 256/255 to 2187/2176<br>in the 2020 version by Plainsound Music Edition | | Definition of the accidental is revised from 256/255 to 2187/2176<br>in the 2020 version by Plainsound Music Edition | ||
|- | |- | ||
| Line 111: | Line 124: | ||
| 19/16 | | 19/16 | ||
| colspan="2" | [[File:Heji47.svg|54x54px]][[File:Heji11.svg|54x54px]][[File:HejiE.svg|48x48px]] | | colspan="2" | [[File:Heji47.svg|54x54px]][[File:Heji11.svg|54x54px]][[File:HejiE.svg|48x48px]] | ||
| colspan="2" | [[File:Heji47.svg|54x54px]][[File:HejiC.svg|48x48px]] | |||
| | | | ||
|- | |- | ||
| Line 116: | Line 130: | ||
| 21/16 | | 21/16 | ||
| colspan="2" | [[File:Heji37.svg|54x54px]][[File:HejiF.svg|48x48px]] | | colspan="2" | [[File:Heji37.svg|54x54px]][[File:HejiF.svg|48x48px]] | ||
| colspan="2" | [[File:Heji37.svg|54x54px]][[File:HejiD.svg|48x48px]] | |||
| | | | ||
|- | |- | ||
| 23 | | 23 | ||
| 23/16 | | 23/16 | ||
| colspan="2" | [[File:Heji49.svg|54x54px]][[File:Heji25.svg|48x48px]][[File: | | colspan="2" | [[File:Heji49.svg|54x54px]][[File:Heji25.svg|54x54px]][[File:HejiF.svg|48x48px]] | ||
| colspan="2" | [[File:Heji49.svg|54x54px]][[File:Heji25.svg|54x54px]][[File:HejiD.svg|48x48px]] | |||
| | | | ||
|- | |- | ||
| Line 126: | Line 142: | ||
| 25/16 | | 25/16 | ||
| colspan="2" | [[File:Heji23.svg|54x54px]][[File:HejiG.svg|48x48px]] | | colspan="2" | [[File:Heji23.svg|54x54px]][[File:HejiG.svg|48x48px]] | ||
| colspan="2" | [[File:Heji23.svg|54x54px]][[File:HejiE.svg|48x48px]] | |||
| | | | ||
|- | |- | ||
| Line 131: | Line 148: | ||
| 27/16 | | 27/16 | ||
| colspan="2" | [[File:HejiA.svg|48x48px]] | | colspan="2" | [[File:HejiA.svg|48x48px]] | ||
| colspan="2" | [[File:Heji25.svg|54x54px]][[File:HejiF.svg|48x48px]] | |||
| Default staff notation represents Pythagorean tuning | | Default staff notation represents Pythagorean tuning | ||
|- | |- | ||
| Line 136: | Line 154: | ||
| 29/16 | | 29/16 | ||
| (todo) | | (todo) | ||
| [[File:Heji51.svg| | | [[File:Heji51.svg|54x54px]][[File:Heji12.svg|54x54px]][[File:HejiB.svg|48x48px]] | ||
| (todo) | |||
| [[File:Heji51.svg|54x54px]][[File:Heji19.svg|54x54px]][[File:HejiG.svg|48x48px]] | |||
| Definition of the accidental is revised from 145/144 to 261/256<br>in the 2020 version by Plainsound Music Edition | | Definition of the accidental is revised from 145/144 to 261/256<br>in the 2020 version by Plainsound Music Edition | ||
|- | |- | ||
| 31 | | 31 | ||
| 31/16 | | 31/16 | ||
| [[File:Heji52.svg|48x48px]][[File: | | [[File:Heji52.svg|54x54px]][[File:HejiC.svg|48x48px]] | ||
| (todo) | |||
| [[File:Heji52.svg|54x54px]][[File:HejiA.svg|48x48px]] | |||
| (todo) | | (todo) | ||
| Definition of the accidental is revised from 1024/1023 to 32/31<br>in the 2020 version by Plainsound Music Edition | | Definition of the accidental is revised from 1024/1023 to 32/31<br>in the 2020 version by Plainsound Music Edition | ||
| Line 148: | Line 170: | ||
| 33/32 | | 33/32 | ||
| colspan="2" | [[File:Heji41.svg|54x54px]][[File:HejiC.svg|48x48px]] | | colspan="2" | [[File:Heji41.svg|54x54px]][[File:HejiC.svg|48x48px]] | ||
| colspan="2" | [[File:Heji41.svg|54x54px]][[File:HejiA.svg|48x48px]] | |||
| | | | ||
|- | |- | ||
| Line 153: | Line 176: | ||
| 35/32 | | 35/32 | ||
| colspan="2" | [[File:Heji37.svg|54x54px]][[File:Heji17.svg|54x54px]][[File:HejiD.svg|48x48px]] | | colspan="2" | [[File:Heji37.svg|54x54px]][[File:Heji17.svg|54x54px]][[File:HejiD.svg|48x48px]] | ||
| colspan="2" | [[File:Heji37.svg|54x54px]][[File:Heji17.svg|54x54px]][[File:HejiB.svg|48x48px]] | |||
|- | |- | ||
| 37 | | 37 | ||
| 37/32 | | 37/32 | ||
| (todo) | |||
| (todo) | |||
| (todo) | | (todo) | ||
| (todo) | | (todo) | ||
| Line 163: | Line 189: | ||
| 39/32 | | 39/32 | ||
| colspan="2" | [[File:Heji42.svg|54x54px]][[File:HejiE.svg|48x48px]] | | colspan="2" | [[File:Heji42.svg|54x54px]][[File:HejiE.svg|48x48px]] | ||
| colspan="2" | [[File:Heji42.svg|54x54px]][[File:Heji25.svg|54x54px]][[File:HejiC.svg|48x48px]] | |||
| | | | ||
|- | |- | ||
| 41 | | 41 | ||
| 41/32 | | 41/32 | ||
| (todo) | |||
| (todo) | |||
| (todo) | | (todo) | ||
| (todo) | | (todo) | ||
| Line 173: | Line 202: | ||
| 43 | | 43 | ||
| 43/32 | | 43/32 | ||
| (todo) | |||
| (todo) | |||
| (todo) | | (todo) | ||
| (todo) | | (todo) | ||
| Line 180: | Line 211: | ||
| 45/32 | | 45/32 | ||
| colspan="2" | [[File:Heji24.svg|54x54px]][[File:HejiF.svg|48x48px]] | | colspan="2" | [[File:Heji24.svg|54x54px]][[File:HejiF.svg|48x48px]] | ||
| colspan="2" | [[File:Heji24.svg|54x54px]][[File:HejiD.svg|48x48px]] | |||
| | | | ||
|- | |- | ||
| 47 | | 47 | ||
| 47/32 | | 47/32 | ||
| (todo) | |||
| (todo) | |||
| (todo) | | (todo) | ||
| (todo) | | (todo) | ||
Revision as of 23:23, 22 March 2024
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
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 |
Odd harmonics
| Harmonic | Just Ratio | Notation with C as root | Notation with A as root | Comments | ||
|---|---|---|---|---|---|---|
| 2020 version | 2004 version | 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 |  
|
|
|||
| 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) | 
|
(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) |
|
(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) | (todo) | (todo) | |
| 39 | 39/32 |
|
|
|||
| 41 | 41/32 | (todo) | (todo) | (todo) | (todo) | |
| 43 | 43/32 | (todo) | (todo) | (todo) | (todo) | |
| 45 | 45/32 |
|
|
|||
| 47 | 47/32 | (todo) | (todo) | (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