Helmholtz–Ellis notation: Difference between revisions

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== Quick reference ==
== Quick reference ==
Below is a quick guide to the accidentals and commas used in Helmholtz–Ellis notation.
Below is a quick guide to the accidentals and commas used in Helmholtz–Ellis notation.
{{Todo|inline=1|text=}}


{| class="wikitable center-all" style="margin: auto auto auto auto;"
{| class="wikitable center-all" style="margin: auto auto auto auto;"
|+ style="font-size: 105%;" | Formal commas
|+ style="font-size: 105%;" |Formal commas
|-
|-
! Prime !! Formal Comma
!Prime!!Formal Comma
|-
|-
| [[5-limit|5]] || [[81/80]]
|[[5-limit|5]]||[[81/80]]
|-
|-
| [[7-limit|7]] || [[64/63]]
|[[7-limit|7]]||[[64/63]]
|-
|-
| [[11-limit|11]] || [[33/32]]
|[[11-limit|11]]||[[33/32]]
|-
|-
| [[13-limit|13]] || [[27/26]]
|[[13-limit|13]]||[[27/26]]
|-
|-
| [[17-limit|17]] || [[2187/2176]]
|[[17-limit|17]]||[[2187/2176]]
|-
|-
| [[19-limit|19]] || [[513/512]]
|[[19-limit|19]]||[[513/512]]
|-
|-
| [[23-limit|23]] || [[736/729]]
|[[23-limit|23]]||[[736/729]]
|-
|-
| [[29-limit|29]] || [[261/256]]
|[[29-limit|29]]||[[261/256]]
|-
|-
| [[31-limit|31]] || [[32/31]]
|[[31-limit|31]]||[[32/31]]
|-
|-
| [[37-limit|37]] || [[37/36]]
|[[37-limit|37]]||[[37/36]]
|-
|-
| [[41-limit|41]] || [[82/81]]
|[[41-limit|41]]||[[82/81]]
|-
|-
| [[43-limit|43]] || [[129/128]]
|[[43-limit|43]]||[[129/128]]
|-
|-
| [[47-limit|47]] || [[752/729]]
|[[47-limit|47]]||[[752/729]]
|}<br />
|}<br />


{| class="wikitable sortable center-all left-5" style="margin: auto auto auto auto;"
{| class="wikitable sortable center-all left-5" style="margin: auto auto auto auto;"
|+ style="font-size: 105%;" | Odd harmonics in the harmonic series
|+ style="font-size: 105%;" |Odd harmonics in the harmonic series
|-
|-
! rowspan="2" | Harmonic
! rowspan="2" |Harmonic
! rowspan="2" | Just Ratio
! rowspan="2" |Just Ratio
! colspan="2" | Notation (assuming 1/1 is C)
! colspan="2" |Notation (assuming 1/1 is C)
! rowspan="2" | Comments
! rowspan="2" |Comments
|-
|-
! 2020 version
!2020 version
! 2004 version
!2004 version
|-
|-
| 1
|1
| 1/1
|1/1
| colspan="2" | [[File:HejiC.svg|48x48px]]
| colspan="2" |[[File:HejiC.svg|48x48px]]
| rowspan="2" | Default staff notation represents Pythagorean tuning
| rowspan="2" |Default staff notation represents Pythagorean tuning
|-
|-
| 3
|3
| 3/2
|3/2
| colspan="2" | [[File:HejiG.svg|48x48px]]
| colspan="2" |[[File:HejiG.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]]
|  
|
|-
|-
| 7
|7
| 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]]
|  
|
|-
|-
| 9
|9
| 9/8
|9/8
| colspan="2" | [[File:HejiD.svg|48x48px]]
| colspan="2" |[[File:HejiD.svg|48x48px]]
| Default staff notation represents Pythagorean tuning
|Default staff notation represents Pythagorean tuning
|-
|-
| 11
|11
| 11/8
|11/8
| colspan="2" | [[File:Heji41.svg|54x54px]][[File:HejiF.svg|48x48px]]
| colspan="2" |[[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&#x266F;.
|[[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&#x266F;.
|-
|-
| 13
| 13
| 13/8
|13/8
| colspan="2" | [[File:Heji42.svg|54x54px]][[File:HejiA.svg|48x48px]]
| colspan="2" |[[File:Heji42.svg|54x54px]][[File:HejiA.svg|48x48px]]
|  
|
|-
|-
| 15
|15
| 15/8
|15/8
| colspan="2" | [[File:Heji17.svg|54x54px]][[File:HejiB.svg|48x48px]]
| colspan="2" |[[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]]
|[[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
| 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]]
|  
|
|-
|-
| 21
|21
| 21/16
|21/16
| colspan="2" | [[File:Heji37.svg|54x54px]][[File:HejiF.svg|48x48px]]
| colspan="2" |[[File:Heji37.svg|54x54px]][[File:HejiF.svg|48x48px]]
|  
|
|-
|-
| 23
|23
| 23/16
| 23/16
| colspan="2" | [[File:Heji49.svg|54x54px]][[File:Heji25.svg|48x48px]][[File:HejiF.svg|48x48px]]
| colspan="2" |[[File:Heji49.svg|54x54px]][[File:Heji25.svg|48x48px]][[File:HejiF.svg|48x48px]]
|  
|
|-
|-
| 25
|25
| 25/16
|25/16
| colspan="2" | [[File:Heji23.svg|54x54px]][[File:HejiG.svg|48x48px]]
| colspan="2" |[[File:Heji23.svg|54x54px]][[File:HejiG.svg|48x48px]]
|  
|
|-
|-
| 27
| 27
| 27/16
|27/16
| colspan="2" | [[File:HejiA.svg|48x48px]]
| colspan="2" |[[File:HejiA.svg|48x48px]]
| Default staff notation represents Pythagorean tuning
|Default staff notation represents Pythagorean tuning
|-
|-
| 29
|29
| 29/16
|29/16
| (todo)
|[[File:HejiaccidentalCombiningRaise29LimitComma.svg|48x48px]][[File:Heji11.svg|48x48px]][[File:HejiB.svg|48x48px]]
| [[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
| 31/16
|31/16
| [[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
| 33/32
|33/32
| colspan="2" | [[File:Heji41.svg|54x54px]][[File:HejiC.svg|48x48px]]
| colspan="2" |[[File:Heji41.svg|54x54px]][[File:HejiC.svg|48x48px]]
|  
|
|-
|-
| 35
|35
| 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]]
|-
|-
| 37
|37
| 37/32
|37/32
| (todo)
|(todo)
| (todo)
|(todo)
|
|
|-
|-
| 39
|39
| 39/32
|39/32
| colspan="2" | [[File:Heji42.svg|54x54px]][[File:HejiE.svg|48x48px]]
| colspan="2" |[[File:Heji42.svg|54x54px]][[File:HejiE.svg|48x48px]]
|  
|
|-
|-
| 41
|41
| 41/32
|41/32
| (todo)
|(todo)
| (todo)
|(todo)
|
|
|-
|-
| 43
|43
| 43/32
| 43/32
| (todo)
|(todo)
| (todo)
|(todo)
|
|
|-
|-
| 45
|45
| 45/32
|45/32
| colspan="2" | [[File:Heji24.svg|54x54px]][[File:HejiF.svg|48x48px]]
| colspan="2" |[[File:Heji24.svg|54x54px]][[File:HejiF.svg|48x48px]]
|  
|
|-
|-
| 47
| 47
| 47/32
|47/32
| (todo)
| (todo)
| (todo)
| (todo)
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|}
|}


== Helmholtz&ndash;Ellis glyphs ==
==Helmholtz&ndash;Ellis glyphs==
{{Todo|update|inline=1|comment=Update the 29-limit comma.}}
<div style="margin: auto auto auto auto;">
<div style="margin: auto auto auto auto;">
<gallery>
y 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
Line 236: Line 235:
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></div>


== External links ==
<nowiki></gallery></nowiki></div>
* [http://tonalsoft.com/enc/h/hewm.aspx HEWM Notation (Helmholtz-Ellis-Wolf-Monzo)] &ndash; Tonalsoft enyclopedia of microtonal music theory
 
* [https://hejicalc.plainsound.org/ Plainsound Harmonic Space Calculator]
==External links==
*[http://tonalsoft.com/enc/h/hewm.aspx HEWM Notation (Helmholtz-Ellis-Wolf-Monzo)] &ndas
 
==External links ==
*[http://tonalsoft.com/enc/h/hewm.aspx HEWM Notation (Helmholtz-Ellis-Wolf-Monzo)] &ndash; Tonalsoft enyclopedia of microtonal music theory
*[https://hejicalc.plainsound.org/ Plainsound Harmonic Space Calculator]


== See also ==
==See also==
* [[Color notation]]
*[[Color notation]]
* [[Functional Just System]] (FJS)
*[[Functional Just System]] (FJS)
* [[Ben Johnston's notation]]
*[[Ben Johnston's notation]]
* [[:Category:SVG]]
*[[:Category:SVG]]


== Notes ==
==Notes==
<references />
<references />


Revision as of 07:58, 4 March 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

Quick reference

Below is a quick guide to the accidentals and commas used in Helmholtz–Ellis notation.

Todo:
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 in the harmonic series
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 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

y three syntonic commas File:Heji2.svg | Double flat lowered by two syntonic commas File:Heji3.svg | Double flat lowered by one syntonic comma File:Heji4.svg | Double flat File:Heji5.svg | Double flat raised by one syntonic comma File:Heji6.svg | Double flat raised by two syntonic commas File:Heji7.svg | Double flat raised by three syntonic commas File:Heji8.svg | Flat lowered by three syntonic commas File:Heji9.svg | Flat lowered by two syntonic commas File:Heji10.svg | Flat lowered by one syntonic comma File:Heji11.svg | Flat File:Heji12.svg | Flat raised by one syntonic comma File:Heji13.svg | Flat raised by two syntonic commas File:Heji14.svg | Flat raised by three syntonic commas File:Heji15.svg | Natural lowered by three syntonic commas File:Heji16.svg | Natural lowered by two syntonic commas File:Heji17.svg | Natural lowered by one syntonic comma File:Heji18.svg | Natural File:Heji19.svg | Natural raised by one syntonic comma File:Heji20.svg | Natural raised by two syntonic commas File:Heji21.svg | Natural raised by three syntonic commas File:Heji22.svg | Sharp lowered by three syntonic commas File:Heji23.svg | Sharp lowered by two syntonic commas File:Heji24.svg | Sharp lowered by one syntonic comma File:Heji25.svg | Sharp File:Heji26.svg | Sharp raised by one syntonic comma File:Heji27.svg | Sharp raised by two syntonic commas File:Heji28.svg | Sharp raised 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:Heji31.svg | Double sharp lowered by one syntonic comma File:Heji32.svg | Double sharp File:Heji33.svg | Double sharp raised by one syntonic comma File:Heji34.svg | Double sharp raised by two syntonic commas File:Heji35.svg | Double sharp raised by three syntonic commas File:Heji36.svg | Lower by two septimal commas File:Heji37.svg | Lower by one septimal comma File:Heji38.svg | Raise by one septimal comma File:Heji39.svg | Raise by two septimal commas File:Heji40.svg | Lower by one undecimal quartertone File:Heji41.svg | Raise by one undecimal quartertone File:Heji42.svg | Lower 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:Heji45.svg | Combining raise by one 17-limit schisma File:Heji46.svg | Combining lower 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:Heji49.svg | Combining raise by one 23-limit comma File:Heji50.svg | Combining lower 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:Heji53.svg | Combining raise by one 31-limit quartertone

</gallery>

External links

External links

See also

Notes

  1. ↑ See Marc Sabat : Music & Writings.


View • Talk • EditMusical notation
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Just intonation Functional Just System • Ben Johnston's notation (Johnston–Copper notation) • Helmholtz–Ellis notation • Color notation
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Temperaments Chain-of-fifths notation • Stein–Zimmermann–Gould notation • Ups and downs notation • 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.
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