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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]]. Based on [[chain-of-fifths notation]] with default staff notation representing [[Pythagorean tuning]], it adds a set of [[nominal-accidental chain|accidentals]] defined by [[formal comma]]s to reach 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]].
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== 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-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
* [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>[https://masa.plainsound.org/work.html#writing Marc Sabat : Music & Writings].</ref> 2004 version


== Quick reference ==
== Quick reference ==
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| [[43-limit|43]] || [[129/128]]
| [[43-limit|43]] || [[129/128]]
|-
|-
| [[47-limit|47]] || [[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>
| [[47-limit|47]] || [[48/47]]<ref group="note" name="v2025">In the recent March 2025 revision of HEJI, the 47 comma was changed 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>
|}
|}


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|-
|-
! rowspan="2" | Harmonic
! rowspan="2" | Harmonic
! rowspan="2" | Just Ratio
! rowspan="2" | [[Octave reduced]] ratio
! colspan="3" | Notation (assuming 1/1 is C)
! colspan="3" | Notation (assuming 1/1 is C)
! rowspan="2" | Comments
! rowspan="2" | Comments
|-
|-
! 2020 version (update 03.2025)
! New 2020 version<ref group="note" name="v2025"/>
! 2020 version
! Old 2020 version
! 2004 version
! 2004 version
|-
|-
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| 1/1
| 1/1
| colspan="3" | [[File:HejiC.svg|48x48px]]
| colspan="3" | [[File:HejiC.svg|48x48px]]
| rowspan="2" style="text-align: left"; | Default staff notation represents Pythagorean tuning
|  
|-
|-
| 3
| 3
| 3/2
| 3/2
| colspan="3" | [[File:HejiG.svg|48x48px]]
| colspan="3" | [[File:HejiG.svg|48x48px]]
|
|-
|-
| 5
| 5
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| 9/8
| 9/8
| colspan="3" | [[File:HejiD.svg|48x48px]]
| colspan="3" | [[File:HejiD.svg|48x48px]]
| style="text-align: left"; | Default staff notation represents Pythagorean tuning
| style="text-align: left"; |  
|-
|-
| 11
| 11
| 11/8
| 11/8
| colspan="3" | [[File:Heji41.svg|54x54px]][[File:HejiF.svg|48x48px]]
| colspan="3" | [[File:Heji41.svg|54x54px]][[File:HejiF.svg|48x48px]]
| style="text-align: left"; | [[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;.
| style="text-align: left"; | [[File:Heji41.svg|54x54px]] is ''not'' a half-sharp, as [[File:Heji41.svg|54x54px]][[File:Heji41.svg|54x54px]]F is [[243/242]] flatter than F♯.
|-
|-
| 13
| 13
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| 27/16
| 27/16
| colspan="3" | [[File:HejiA.svg|48x48px]]
| colspan="3" | [[File:HejiA.svg|48x48px]]
| style="text-align: left"; | Default staff notation represents Pythagorean tuning
|  
|-
|-
| 29
| 29
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== Notes ==
== Notes ==
<references />
<references group="note"/>
 
== References ==
<references/>


{{Navbox notation}}
{{Navbox notation}}
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