Helmholtz–Ellis notation: Difference between revisions
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| Line 47: | Line 47: | ||
! rowspan="2" | Harmonic | ! rowspan="2" | Harmonic | ||
! rowspan="2" | Just Ratio | ! rowspan="2" | Just Ratio | ||
! colspan=" | ! colspan="3" | Notation (assuming 1/1 is C) | ||
! rowspan="2" | Comments | ! rowspan="2" | Comments | ||
|- | |- | ||
! 2020 version (update 03.2025) | |||
! 2020 version | ! 2020 version | ||
! 2004 version | ! 2004 version | ||
| Line 55: | Line 56: | ||
| 1 | | 1 | ||
| 1/1 | | 1/1 | ||
| colspan=" | | colspan="3" | [[File:HejiC.svg|48x48px]] | ||
| rowspan=" | | rowspan="3" | Default staff notation represents Pythagorean tuning | ||
|- | |- | ||
| 3 | | 3 | ||
| 3/2 | | 3/2 | ||
| colspan=" | | colspan="3" | [[File:HejiG.svg|48x48px]] | ||
|- | |- | ||
| 5 | | 5 | ||
| 5/4 | | 5/4 | ||
| colspan=" | | colspan="3" | [[File:Heji17.svg|54x54px]][[File:HejiE.svg|48x48px]] | ||
| | | | ||
|- | |- | ||
| 7 | | 7 | ||
| 7/4 | | 7/4 | ||
| colspan=" | | colspan="3" | [[File:Heji37.svg|54x54px]][[File:Heji11.svg|54x54px]][[File:HejiB.svg|48x48px]] | ||
| | | | ||
|- | |- | ||
| 9 | | 9 | ||
| 9/8 | | 9/8 | ||
| colspan=" | | colspan="3" | [[File:HejiD.svg|48x48px]] | ||
| Default staff notation represents Pythagorean tuning | | Default staff notation represents Pythagorean tuning | ||
|- | |- | ||
| 11 | | 11 | ||
| 11/8 | | 11/8 | ||
| colspan=" | | colspan="3" | [[File:Heji41.svg|54x54px]][[File:HejiF.svg|48x48px]] | ||
| [[File:Heji41.svg|54x54px]] is ''not'' a half-sharp, as [[File:Heji41.svg|54x54px]][[File:Heji41.svg|54x54px]]F is [[243/242|7.1¢]] flatter than F♯. | | [[File:Heji41.svg|54x54px]] is ''not'' a half-sharp, as [[File:Heji41.svg|54x54px]][[File:Heji41.svg|54x54px]]F is [[243/242|7.1¢]] flatter than F♯. | ||
|- | |- | ||
| 13 | | 13 | ||
| 13/8 | | 13/8 | ||
| colspan=" | | colspan="3" | [[File:Heji42.svg|54x54px]][[File:HejiA.svg|48x48px]] | ||
| | | | ||
|- | |- | ||
| 15 | | 15 | ||
| 15/8 | | 15/8 | ||
| colspan=" | | colspan="3" | [[File:Heji17.svg|54x54px]][[File:HejiB.svg|48x48px]] | ||
| | | | ||
|- | |- | ||
| 17 | | 17 | ||
| 17/16 | | 17/16 | ||
| [[File:Heji44.svg|54x54px]][[File:Heji25.svg|54x54px]][[File:HejiC.svg|48x48px]] | | colspan="2" | [[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]] | ||
| 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 100: | Line 101: | ||
| 19 | | 19 | ||
| 19/16 | | 19/16 | ||
| colspan=" | | colspan="3" | [[File:Heji47.svg|54x54px]][[File:Heji11.svg|54x54px]][[File:HejiE.svg|48x48px]] | ||
| | | | ||
|- | |- | ||
| 21 | | 21 | ||
| 21/16 | | 21/16 | ||
| colspan=" | | colspan="3" | [[File:Heji37.svg|54x54px]][[File:HejiF.svg|48x48px]] | ||
| | | | ||
|- | |- | ||
| 23 | | 23 | ||
| 23/16 | | 23/16 | ||
| colspan=" | | colspan="3" | [[File:Heji49.svg|54x54px]][[File:Heji25.svg|48x48px]][[File:HejiF.svg|48x48px]] | ||
| | | | ||
|- | |- | ||
| 25 | | 25 | ||
| 25/16 | | 25/16 | ||
| colspan=" | | colspan="3" | [[File:Heji23.svg|54x54px]][[File:HejiG.svg|48x48px]] | ||
| | | | ||
|- | |- | ||
| 27 | | 27 | ||
| 27/16 | | 27/16 | ||
| colspan=" | | colspan="3" | [[File:HejiA.svg|48x48px]] | ||
| Default staff notation represents Pythagorean tuning | | Default staff notation represents Pythagorean tuning | ||
|- | |- | ||
| 29 | | 29 | ||
| 29/16 | | 29/16 | ||
| [[File:HejiaccidentalCombiningRaise29LimitComma.svg|48x48px]][[File:Heji11.svg|54x54px]][[File:HejiB.svg|48x48px]] | | colspan="2" | [[File:HejiaccidentalCombiningRaise29LimitComma.svg|48x48px]][[File:Heji11.svg|54x54px]][[File:HejiB.svg|48x48px]] | ||
| [[File:Heji51.svg|54x54px]][[File:Heji12.svg|54x54px]][[File:HejiB.svg|48x48px]] | | [[File:Heji51.svg|54x54px]][[File:Heji12.svg|54x54px]][[File:HejiB.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 | ||
| Line 131: | Line 132: | ||
| 31 | | 31 | ||
| 31/16 | | 31/16 | ||
| [[File:Heji52.svg|54x54px]][[File:HejiC.svg|48x48px]] | | colspan="2" | [[File:Heji52.svg|54x54px]][[File:HejiC.svg|48x48px]] | ||
| [[File:HejiaccidentalCombiningLower31SchismaOld.svg|48x48px]][[File:Heji40.svg|54x54px]][[File:HejiC.svg|48x48px]] | | [[File:HejiaccidentalCombiningLower31SchismaOld.svg|48x48px]][[File:Heji40.svg|54x54px]][[File:HejiC.svg|48x48px]] | ||
| 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 137: | Line 138: | ||
| 33 | | 33 | ||
| 33/32 | | 33/32 | ||
| colspan=" | | colspan="3" | [[File:Heji41.svg|54x54px]][[File:HejiC.svg|48x48px]] | ||
| | | | ||
|- | |- | ||
| 35 | | 35 | ||
| 35/32 | | 35/32 | ||
| colspan=" | | colspan="3" | [[File:Heji37.svg|54x54px]][[File:Heji17.svg|54x54px]][[File:HejiD.svg|48x48px]] | ||
| | | | ||
|- | |- | ||
| 37 | | 37 | ||
| 37/32 | | 37/32 | ||
| [[File:HejiaccidentalCombiningRaise37Quartertone.svg|48x48px]][[File:HejiD.svg|48x48px]] | | colspan="2" | [[File:HejiaccidentalCombiningRaise37Quartertone.svg|48x48px]][[File:HejiD.svg|48x48px]] | ||
| | | - | ||
| | | | ||
|- | |- | ||
| 39 | | 39 | ||
| 39/32 | | 39/32 | ||
| [[File:Heji42.svg|54x54px]][[File:HejiE.svg|48x48px]] | | colspan="2" | [[File:Heji42.svg|54x54px]][[File:HejiE.svg|48x48px]] | ||
| | | - | ||
| | | | ||
|- | |- | ||
| 41 | | 41 | ||
| 41/32 | | 41/32 | ||
| [[File:HejiaccidentalCombiningRaise41Comma.svg|48x48px]][[File:HejiE.svg|48x48px]] | | colspan="2" | [[File:HejiaccidentalCombiningRaise41Comma.svg|48x48px]][[File:HejiE.svg|48x48px]] | ||
| | | - | ||
| | | | ||
|- | |- | ||
| 43 | | 43 | ||
| 43/32 | | 43/32 | ||
| [[File:HejiaccidentalCombiningRaise43Comma.svg|48x48px]][[File:HejiF.svg|48x48px]] | | colspan="2" | [[File:HejiaccidentalCombiningRaise43Comma.svg|48x48px]][[File:HejiF.svg|48x48px]] | ||
| | | - | ||
| | | | ||
|- | |- | ||
| 45 | | 45 | ||
| 45/32 | | 45/32 | ||
| colspan=" | | colspan="3" | [[File:Heji24.svg|54x54px]][[File:HejiF.svg|48x48px]] | ||
| | | | ||
|- | |- | ||
| 47 | | 47 | ||
| 47/32 | | 47/32 | ||
| [[File:HejiLowerByOne47limitSixthtone.png|24x36px]][[File:HejiG.svg|48x48px]] | |||
| [[File:HejiaccidentalCombiningRaise47Quartertone.svg|48x48px]][[File:Heji25.svg|54x54px]][[File:HejiF.svg|48x48px]] | | [[File:HejiaccidentalCombiningRaise47Quartertone.svg|48x48px]][[File:Heji25.svg|54x54px]][[File:HejiF.svg|48x48px]] | ||
| | | - | ||
| Pre-March 2025 notation, where [[File:HejiaccidentalCombiningRaise47Quartertone.svg|48x48px]] represents [[752/729]] | | Pre-March 2025 notation, where [[File:HejiaccidentalCombiningRaise47Quartertone.svg|48x48px]] represents [[752/729]], in the update March 2025 of version 2022, [[File:HejiRaiseByOne47limitSixthtone.png|24x36px]] represents [[48/47]] | ||
|} | |} | ||
| Line 251: | Line 253: | ||
File:HejiaccidentalCombiningLower47Quartertone.svg | Combining lower by one 47-limit quartertone | File:HejiaccidentalCombiningLower47Quartertone.svg | Combining lower by one 47-limit quartertone | ||
File:HejiaccidentalCombiningRaise47Quartertone.svg | Combining raise by one 47-limit quartertone | File:HejiaccidentalCombiningRaise47Quartertone.svg | Combining raise by one 47-limit quartertone | ||
File:HejiRaiseByOne47limitSixthtone.png | Raise by one 47-limit Sixthtone (update 03.2025) | |||
File:HejiLowerByOne47limitSixthtone.png | Lower by one 47-limit Sixthtone (update 03.2025) | |||
</gallery></div> | </gallery></div> | ||
Revision as of 13:18, 20 June 2025
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, 48/47[2] |
| Harmonic | Just Ratio | Notation (assuming 1/1 is C) | Comments | ||
|---|---|---|---|---|---|
| 2020 version (update 03.2025) | 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 | 
|
|
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 | |
| 33 | 33/32 |
|
|||
| 35 | 35/32 |
|
|||
| 37 | 37/32 | 
|
- | ||
| 39 | 39/32 |
|
- | ||
| 41 | 41/32 | 
|
- | ||
| 43 | 43/32 | 
|
- | ||
| 45 | 45/32 | 
|
|||
| 47 | 47/32 | 
|
|
- | Pre-March 2025 notation, where represents 752/729, in the update March 2025 of version 2022,  represents 48/47
|
|
Todo: add images for March 2025 47-limit HEJI accidentals , show new notation for 47/32 |
Helmholtz–Ellis glyphs
-
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 29-limit comma -
Combining raise by one 29-limit comma -
Combining lower by one 31-limit schisma (old) -
Combining raise by one 31-limit schisma (old) -
Combining lower by one 31-limit quartertone -
Combining raise by one 31-limit quartertone -
Combining lower by one 37-limit quartertone -
Combining raise by one 37-limit quartertone -
Combining lower by one 41-limit comma -
Combining raise by one 41-limit comma -
Combining lower by one 43-limit comma -
Combining raise by one 43-limit comma -
Combining lower by one 47-limit quartertone -
Combining raise by one 47-limit quartertone -
Raise by one 47-limit Sixthtone (update 03.2025) -
Lower by one 47-limit Sixthtone (update 03.2025)
External links
- HEWM Notation (Helmholtz-Ellis-Wolf-Monzo) – Tonalsoft enyclopedia of microtonal music theory
- Plainsound Harmonic Space Calculator
See also
Notes
- ↑ See Marc Sabat : Music & Writings.
- ↑ The recent March 2025 revision of HEJI changed the 47 comma from 752/729 to 48/47, which has yet to gain popular support. See The Helmholtz–Ellis JI Pitch Notation (HEJI).
| View • Talk • EditMusical notation | |
|---|---|
| Universal | Sagittal notation |
| Just intonation | Functional Just System • Ben Johnston's notation (Johnston–Copper notation) • Helmholtz–Ellis notation • Color notation |
| MOS scales | Diamond-mos notation • KISS notation (Quasi-diatonic MOS notation) |
| Temperaments | Circle-of-fifths notation • Ups and downs notation (alternative symbols) • Syntonic–rastmic subchroma notation • Extended meantone notation • Fractional sharp notation |
See musical notation for a longer list of systems by category. See Category:Notation for the most complete, comprehensive list, but not sorted by category. | |