Helmholtz–Ellis notation: Difference between revisions

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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 [[Nominal-accidental chain|accidentals]] defined by formal commas for each [[prime harmonic]].
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 [[Nominal-accidental chain|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]].
Further accidentals were designed by [[richie]] for primes up to the [[89-limit]]; see [[richie's HEJI extensions]].


== Introductory materials ==
== Introductory materials ==
* [https://heji.plainsound.org/ 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
* [https://heji.plainsound.org/ 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
* [http://www.plainsound.org/pdfs/ji_notation.pdf Extended Helmholtz&ndash;Ellis JI Pitch Notation] by Marc Sabat and Wolfgang von Schweinitz from Plainsound Music Edition &ndash; deprecated<ref>See [https://masa.plainsound.org/work.html#writing Marc Sabat : Music & Writings]. </ref> 2004 version
* [http://www.plainsound.org/pdfs/ji_notation.pdf Extended Helmholtz-Ellis JI Pitch Notation] by Marc Sabat and Wolfgang von Schweinitz from Plainsound Music Edition - deprecated<ref>See [https://masa.plainsound.org/work.html#writing Marc Sabat : Music & Writings]. </ref> 2004 version


== Quick reference ==
== Quick reference ==
Below is a quick guide to the accidentals and commas used in Helmholtz&ndash;Ellis notation.
Below is a quick guide to the accidentals and commas used in Helmholtz-Ellis notation.


{| class="wikitable center-all" style="margin: auto auto auto auto;"
{| class="wikitable center-all" style="margin: auto auto auto auto;"
Line 39: Line 39:
| [[43-limit|43]] || [[129/128]]
| [[43-limit|43]] || [[129/128]]
|-
|-
| [[47-limit|47]] || [[752/729]], [[48/47]]<ref>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 [https://heji.plainsound.org The Helmholtz&ndash;Ellis JI Pitch Notation (HEJI)].</ref>
| [[47-limit|47]] || [[752/729]], [[48/47]]<ref>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 [https://heji.plainsound.org The Helmholtz-Ellis JI Pitch Notation (HEJI)].</ref>
|}<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;"
Line 97: Line 97:
| colspan="2" | [[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 in the 2020 version by Plainsound Music Edition
|-
|-
| 19
| 19
Line 128: Line 128:
| colspan="2" | [[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 in the 2020 version by Plainsound Music Edition
|-
|-
| 31
| 31
Line 134: Line 134:
| colspan="2" | [[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 in the 2020 version by Plainsound Music Edition
|-
|-
| 33
| 33
Line 183: Line 183:
|}
|}


{{Todo|inline=1|add images for March 2025 47-limit HEJI accidentals|show new notation for 47/32}}
== Helmholtz-Ellis glyphs ==
 
== Helmholtz&ndash;Ellis glyphs ==
<div style="margin: auto auto auto auto;">
<div style="margin: auto auto auto auto;">
<gallery>
<gallery>
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== External links ==
== External links ==
* [http://tonalsoft.com/enc/h/hewm.aspx HEWM Notation (Helmholtz-Ellis-Wolf-Monzo)] &ndash; Tonalsoft enyclopedia of microtonal music theory
* [http://tonalsoft.com/enc/h/hewm.aspx HEWM Notation (Helmholtz-Ellis-Wolf-Monzo)] - Tonalsoft enyclopedia of microtonal music theory
* [https://hejicalc.plainsound.org/ Plainsound Harmonic Space Calculator]
* [https://hejicalc.plainsound.org/ Plainsound Harmonic Space Calculator]
* [https://w3c.github.io/smufl/latest/tables/extended-helmholtz-ellis-accidentals-just-intonation-supplement.html/ Glyphs in smufl]


== See also ==
== See also ==

Revision as of 13:26, 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

Quick reference

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

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, 48/47[2]
Odd harmonics in the harmonic series
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

Helmholtz-Ellis glyphs

  • Double flat lowered by three syntonic commas
    Double flat lowered by three syntonic commas
  • Double flat lowered by two syntonic commas
    Double flat lowered by two syntonic commas
  • Double flat lowered by one syntonic comma
    Double flat lowered by one syntonic comma
  • Double flat
    Double flat
  • Double flat raised by one syntonic comma
    Double flat raised by one syntonic comma
  • Double flat raised by two syntonic commas
    Double flat raised by two syntonic commas
  • Double flat raised by three syntonic commas
    Double flat raised by three syntonic commas
  • Flat lowered by three syntonic commas
    Flat lowered by three syntonic commas
  • Flat lowered by two syntonic commas
    Flat lowered by two syntonic commas
  • Flat lowered by one syntonic comma
    Flat lowered by one syntonic comma
  • Flat
    Flat
  • Flat raised by one syntonic comma
    Flat raised by one syntonic comma
  • Flat raised by two syntonic commas
    Flat raised by two syntonic commas
  • Flat raised by three syntonic commas
    Flat raised by three syntonic commas
  • Natural lowered by three syntonic commas
    Natural lowered by three syntonic commas
  • Natural lowered by two syntonic commas
    Natural lowered by two syntonic commas
  • Natural lowered by one syntonic comma
    Natural lowered by one syntonic comma
  • Natural
    Natural
  • Natural raised by one syntonic comma
    Natural raised by one syntonic comma
  • Natural raised by two syntonic commas
    Natural raised by two syntonic commas
  • Natural raised by three syntonic commas
    Natural raised by three syntonic commas
  • Sharp lowered by three syntonic commas
    Sharp lowered by three syntonic commas
  • Sharp lowered by two syntonic commas
    Sharp lowered by two syntonic commas
  • Sharp lowered by one syntonic comma
    Sharp lowered by one syntonic comma
  • Sharp
    Sharp
  • Sharp raised by one syntonic comma
    Sharp raised by one syntonic comma
  • Sharp raised by two syntonic commas
    Sharp raised by two syntonic commas
  • Sharp raised by three syntonic commas
    Sharp raised by three syntonic commas
  • Double sharp lowered by three syntonic commas
    Double sharp lowered by three syntonic commas
  • Double sharp lowered by two syntonic commas
    Double sharp lowered by two syntonic commas
  • Double sharp lowered by one syntonic comma
    Double sharp lowered by one syntonic comma
  • Double sharp
    Double sharp
  • Double sharp raised by one syntonic comma
    Double sharp raised by one syntonic comma
  • Double sharp raised by two syntonic commas
    Double sharp raised by two syntonic commas
  • Double sharp raised by three syntonic commas
    Double sharp raised by three syntonic commas
  • Lower by two septimal commas
    Lower by two septimal commas
  • Lower by one septimal comma
    Lower by one septimal comma
  • Raise by one septimal comma
    Raise by one septimal comma
  • Raise by two septimal commas
    Raise by two septimal commas
  • Lower by one undecimal quartertone
    Lower by one undecimal quartertone
  • Raise by one undecimal quartertone
    Raise by one undecimal quartertone
  • Lower by one tridecimal third tone
    Lower by one tridecimal third tone
  • Raise by one tridecimal third tone
    Raise by one tridecimal third tone
  • Combining lower by one 17-limit schisma
    Combining lower by one 17-limit schisma
  • Combining raise by one 17-limit schisma
    Combining raise by one 17-limit schisma
  • Combining lower by one 19-limit schisma
    Combining lower by one 19-limit schisma
  • Combining raise by one 19-limit schisma
    Combining raise by one 19-limit schisma
  • Combining lower by one 23-limit comma
    Combining lower by one 23-limit comma
  • Combining raise by one 23-limit comma
    Combining raise by one 23-limit comma
  • Combining lower by one 29-limit schisma (old)
    Combining lower by one 29-limit schisma (old)
  • Combining raise by one 29-limit schisma (old)
    Combining raise by one 29-limit schisma (old)
  • Combining lower by one 29-limit comma
    Combining lower by one 29-limit comma
  • Combining raise by one 29-limit comma
    Combining raise by one 29-limit comma
  • Combining lower by one 31-limit schisma (old)
    Combining lower by one 31-limit schisma (old)
  • Combining raise by one 31-limit schisma (old)
    Combining raise by one 31-limit schisma (old)
  • Combining lower by one 31-limit quartertone
    Combining lower by one 31-limit quartertone
  • Combining raise by one 31-limit quartertone
    Combining raise by one 31-limit quartertone
  • Combining lower by one 37-limit quartertone
    Combining lower by one 37-limit quartertone
  • Combining raise by one 37-limit quartertone
    Combining raise by one 37-limit quartertone
  • Combining lower by one 41-limit comma
    Combining lower by one 41-limit comma
  • Combining raise by one 41-limit comma
    Combining raise by one 41-limit comma
  • Combining lower by one 43-limit comma
    Combining lower by one 43-limit comma
  • Combining raise by one 43-limit comma
    Combining raise by one 43-limit comma
  • Combining lower by one 47-limit quartertone
    Combining lower by one 47-limit quartertone
  • Combining raise by one 47-limit quartertone
    Combining raise by one 47-limit quartertone
  • Raise by one 47-limit Sixthtone (update 03.2025)
    Raise by one 47-limit Sixthtone (update 03.2025)
  • Lower by one 47-limit Sixthtone (update 03.2025)
    Lower by one 47-limit Sixthtone (update 03.2025)

External links

See also

Notes

  1. ↑ See Marc Sabat : Music & Writings.
  2. ↑ 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).


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