Helmholtz–Ellis notation: Difference between revisions
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== Quick reference == | == Quick reference == | ||
{| class="wikitable center-all" style="margin: auto auto auto auto;" | |||
{| class="wikitable center-all" | |+ style="font-size: 110%;" | Formal commas | ||
! Prime | ! Prime | ||
! Formal Comma | ! Formal Comma | ||
| Line 51: | Line 51: | ||
| [[47-limit|47]] | | [[47-limit|47]] | ||
| [[752/729]] | | [[752/729]] | ||
|} | |}<br /> | ||
{| class="wikitable sortable center-all left-5" style="margin: auto auto auto auto;" | |||
{| class="wikitable sortable center-all left-5" | |+ style="font-size: 110%;" | Odd harmonics in the harmonic series | ||
! rowspan="2" | Harmonic | ! rowspan="2" | Harmonic | ||
! rowspan="2" | Just Ratio | ! rowspan="2" | Just Ratio | ||
| Line 106: | Line 106: | ||
| [[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]] | ||
| 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 | ||
|- | |- | ||
| 19 | | 19 | ||
| Line 137: | Line 137: | ||
| (todo) | | (todo) | ||
| [[File:Heji51.svg|48x48px]][[File:Heji12.svg|48x48px]][[File:HejiB.svg|48x48px]] | | [[File:Heji51.svg|48x48px]][[File:Heji12.svg|48x48px]][[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 | ||
|- | |- | ||
| 31 | | 31 | ||
| Line 143: | Line 143: | ||
| [[File:Heji52.svg|48x48px]][[File:HejiC.svg|48x48px]] | | [[File:Heji52.svg|48x48px]][[File:HejiC.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 | ||
|- | |- | ||
| 33 | | 33 | ||
| Line 189: | Line 189: | ||
|} | |} | ||
== Helmholtz | == Helmholtz–Ellis glyphs == | ||
{{Todo|update|inline=1|comment=Update the 29-limit comma. }} | {{Todo|update|inline=1|comment=Update the 29-limit comma. }} | ||
<gallery> | <gallery> | ||
File:Heji1.svg|Double flat lowered by three syntonic commas | File:Heji1.svg | Double flat lowered by three syntonic commas | ||
File:Heji2.svg|Double flat lowered by two syntonic commas | File:Heji2.svg | Double flat lowered by two syntonic commas | ||
File:Heji3.svg|Double flat lowered by one syntonic comma | File:Heji3.svg | Double flat lowered by one syntonic comma | ||
File:Heji4.svg|Double flat | File:Heji4.svg | Double flat | ||
File:Heji5.svg|Double flat raised by one syntonic comma | File:Heji5.svg | Double flat raised by one syntonic comma | ||
File:Heji6.svg|Double flat raised by two syntonic commas | File:Heji6.svg | Double flat raised by two syntonic commas | ||
File:Heji7.svg|Double flat raised by three syntonic commas | File:Heji7.svg | Double flat raised by three syntonic commas | ||
File:Heji8.svg|Flat lowered by three syntonic commas | File:Heji8.svg | Flat lowered by three syntonic commas | ||
File:Heji9.svg|Flat lowered by two syntonic commas | File:Heji9.svg | Flat lowered by two syntonic commas | ||
File:Heji10.svg|Flat lowered by one syntonic comma | File:Heji10.svg | Flat lowered by one syntonic comma | ||
File:Heji11.svg|Flat | File:Heji11.svg | Flat | ||
File:Heji12.svg|Flat raised by one syntonic comma | File:Heji12.svg | Flat raised by one syntonic comma | ||
File:Heji13.svg|Flat raised by two syntonic commas | File:Heji13.svg | Flat raised by two syntonic commas | ||
File:Heji14.svg|Flat raised by three syntonic commas | File:Heji14.svg | Flat raised by three syntonic commas | ||
File:Heji15.svg|Natural lowered by three syntonic commas | File:Heji15.svg | Natural lowered by three syntonic commas | ||
File:Heji16.svg|Natural lowered by two syntonic commas | File:Heji16.svg | Natural lowered by two syntonic commas | ||
File:Heji17.svg|Natural lowered by one syntonic comma | File:Heji17.svg | Natural lowered by one syntonic comma | ||
File:Heji18.svg|Natural | File:Heji18.svg | Natural | ||
File:Heji19.svg|Natural raised by one syntonic comma | File:Heji19.svg | Natural raised by one syntonic comma | ||
File:Heji20.svg|Natural raised by two syntonic commas | File:Heji20.svg | Natural raised by two syntonic commas | ||
File:Heji21.svg|Natural raised by three syntonic commas | File:Heji21.svg | Natural raised by three syntonic commas | ||
File:Heji22.svg|Sharp lowered by three syntonic commas | File:Heji22.svg | Sharp lowered by three syntonic commas | ||
File:Heji23.svg|Sharp lowered by two syntonic commas | File:Heji23.svg | Sharp lowered by two syntonic commas | ||
File:Heji24.svg|Sharp lowered by one syntonic comma | File:Heji24.svg | Sharp lowered by one syntonic comma | ||
File:Heji25.svg|Sharp | File:Heji25.svg | Sharp | ||
File:Heji26.svg|Sharp raised by one syntonic comma | File:Heji26.svg | Sharp raised by one syntonic comma | ||
File:Heji27.svg|Sharp raised by two syntonic commas | File:Heji27.svg | Sharp raised by two syntonic commas | ||
File:Heji28.svg|Sharp raised by three syntonic commas | File:Heji28.svg | Sharp raised by three syntonic commas | ||
File:Heji29.svg|Double sharp lowered by three syntonic commas | File:Heji29.svg | Double sharp lowered by three syntonic commas | ||
File:Heji30.svg|Double sharp lowered by two syntonic commas | File:Heji30.svg | Double sharp lowered by two syntonic commas | ||
File:Heji31.svg|Double sharp lowered by one syntonic comma | File:Heji31.svg | Double sharp lowered by one syntonic comma | ||
File:Heji32.svg|Double sharp | File:Heji32.svg | Double sharp | ||
File:Heji33.svg|Double sharp raised by one syntonic comma | File:Heji33.svg | Double sharp raised by one syntonic comma | ||
File:Heji34.svg|Double sharp raised by two syntonic commas | File:Heji34.svg | Double sharp raised by two syntonic commas | ||
File:Heji35.svg|Double sharp raised by three syntonic commas | File:Heji35.svg | Double sharp raised by three syntonic commas | ||
File:Heji36.svg|Lower by two septimal commas | File:Heji36.svg | Lower by two septimal commas | ||
File:Heji37.svg|Lower by one septimal comma | File:Heji37.svg | Lower by one septimal comma | ||
File:Heji38.svg|Raise by one septimal comma | File:Heji38.svg | Raise by one septimal comma | ||
File:Heji39.svg|Raise by two septimal commas | File:Heji39.svg | Raise by two septimal commas | ||
File:Heji40.svg|Lower by one undecimal quartertone | File:Heji40.svg | Lower by one undecimal quartertone | ||
File:Heji41.svg|Raise by one undecimal quartertone | File:Heji41.svg | Raise by one undecimal quartertone | ||
File:Heji42.svg|Lower by one tridecimal third tone | File:Heji42.svg | Lower by one tridecimal third tone | ||
File:Heji43.svg|Raise by one tridecimal third tone | File:Heji43.svg | Raise by one tridecimal third tone | ||
File:Heji44.svg|Combining lower by one 17-limit schisma | File:Heji44.svg | Combining lower by one 17-limit schisma | ||
File:Heji45.svg|Combining raise by one 17-limit schisma | File:Heji45.svg | Combining raise by one 17-limit schisma | ||
File:Heji46.svg|Combining lower by one 19-limit schisma | File:Heji46.svg | Combining lower by one 19-limit schisma | ||
File:Heji47.svg|Combining raise by one 19-limit schisma | File:Heji47.svg | Combining raise by one 19-limit schisma | ||
File:Heji48.svg|Combining lower by one 23-limit comma | File:Heji48.svg | Combining lower by one 23-limit comma | ||
File:Heji49.svg|Combining raise by one 23-limit comma | File:Heji49.svg | Combining raise by one 23-limit comma | ||
File:Heji50.svg|Combining lower by one 29-limit schisma (old) | File:Heji50.svg | Combining lower by one 29-limit schisma (old) | ||
File:Heji51.svg|Combining raise by one 29-limit schisma (old) | File:Heji51.svg | Combining raise by one 29-limit schisma (old) | ||
File:Heji52.svg|Combining lower by one 31-limit quartertone | File:Heji52.svg | Combining lower by one 31-limit quartertone | ||
File:Heji53.svg|Combining raise by one 31-limit quartertone | File:Heji53.svg | Combining raise by one 31-limit quartertone | ||
</gallery> | </gallery> | ||
| Line 256: | Line 256: | ||
== Notes == | == Notes == | ||
<references/> | <references /> | ||
[[Category:Helmholtz–Ellis notation| ]] <!-- Main article --> | [[Category:Helmholtz–Ellis notation| ]] <!-- Main article --> | ||
[[Category:Notation]] | [[Category:Notation]] | ||
[[Category:Just intonation]] | [[Category:Just intonation]] | ||
Revision as of 18:15, 22 May 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
| 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 |  
|
||
| 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
|
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