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Helmholtz–Ellis notation: Difference between revisions

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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>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-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;"
|+ 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]]
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| [[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-Ellis JI Pitch Notation (HEJI)].</ref>
| [[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>
|}
|}


{| class="wikitable sortable center-all left-5" style="margin: auto auto auto auto;"
{| class="wikitable sortable center-all left-6" 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
|-
|-
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| 1/1
| 1/1
| colspan="3" | [[File:HejiC.svg|48x48px]]
| colspan="3" | [[File:HejiC.svg|48x48px]]
| rowspan="3" | Default staff notation represents Pythagorean tuning
| rowspan="2" style="text-align: left"; | Default staff notation represents Pythagorean tuning
|-
|-
| 3
| 3
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| 9/8
| 9/8
| colspan="3" | [[File:HejiD.svg|48x48px]]
| colspan="3" | [[File:HejiD.svg|48x48px]]
| Default staff notation represents Pythagorean tuning
| style="text-align: left"; | Default staff notation represents Pythagorean tuning
|-
|-
| 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]]
| [[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|7.1¢]] flatter than F&#x266F;.
|-
|-
| 13
| 13
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| 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 in the 2020 version by Plainsound Music Edition
| style="text-align: left"; | Definition of the accidental is revised from 256/255 to 2187/2176 in the 2020 version by Plainsound Music Edition
|-
|-
| 19
| 19
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| 27/16
| 27/16
| colspan="3" | [[File:HejiA.svg|48x48px]]
| colspan="3" | [[File:HejiA.svg|48x48px]]
| Default staff notation represents Pythagorean tuning
| style="text-align: left"; | Default staff notation represents Pythagorean tuning
|-
|-
| 29
| 29
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| 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 in the 2020 version by Plainsound Music Edition
| style="text-align: left"; | Definition of the accidental is revised from 145/144 to 261/256 in the 2020 version by Plainsound Music Edition
|-
|-
| 31
| 31
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| 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 in the 2020 version by Plainsound Music Edition
| style="text-align: left"; | Definition of the accidental is revised from 1024/1023 to 32/31 in the 2020 version by Plainsound Music Edition
|-
|-
| 33
| 33
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| [[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]], in the update March 2025 of version 2022, [[File:HejiRaiseByOne47limitSixthtone.png|24x36px]] represents [[48/47]]
| In pre–March-2025 notation, [[File:HejiaccidentalCombiningRaise47Quartertone.svg|36x36px]] represents [[752/729]]; in the update March 2025 of version 2020, [[File:HejiRaiseByOne47limitSixthtone.png|24x36px]] represents [[48/47]].
|}
|}


== Helmholtz-Ellis glyphs ==
== Helmholtz–Ellis glyphs ==
<div style="margin: auto auto auto auto;">
<div style="margin: auto auto auto auto;">
<gallery>
<gallery>
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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:Heji51.svg | Combining raise by one 29-limit schisma (old)
File:Heji accidentalCombiningLower29LimitComma.svg | Combining lower by one 29-limit comma
File:Heji accidentalCombiningLower29LimitComma.svg | Combining lower by one 29-limit comma
File:HejiaccidentalCombiningRaise29LimitComma.svg | Combining raise by one 29-limit comma
File:HejiaccidentalCombiningRaise29LimitComma.svg | Combining raise by one 29-limit comma
File:HejiaccidentalCombiningLower31SchismaOld.svg | Combining lower by one 31-limit schisma (old)
File:HejiaccidentalCombiningRaise31SchismaOld.svg | Combining raise by one 31-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
Line 249: Line 245:
File:HejiaccidentalCombiningLower43Comma.svg | Combining lower by one 43-limit comma
File:HejiaccidentalCombiningLower43Comma.svg | Combining lower by one 43-limit comma
File:HejiaccidentalCombiningRaise43Comma.svg | Combining raise by one 43-limit comma
File:HejiaccidentalCombiningRaise43Comma.svg | Combining raise by one 43-limit comma
File:HejiaccidentalCombiningLower47Quartertone.svg | Combining lower by one 47-limit quartertone
File:HejiRaiseByOne47limitSixthtone.png | Raise by one 47-limit sixthtone (update 03.2025)
File:HejiaccidentalCombiningRaise47Quartertone.svg | Combining raise by one 47-limit quartertone
File:HejiLowerByOne47limitSixthtone.png | Lower by one 47-limit sixthtone (update 03.2025)
File:HejiRaiseByOne47limitSixthtone.png | Raise by one 47-limit Sixthtone (update 03.2025)
</gallery>
File:HejiLowerByOne47limitSixthtone.png | Lower by one 47-limit Sixthtone (update 03.2025)
</div>
</gallery></div>
 
=== Old/deprecated symbols ===
<div style="margin: auto auto auto auto;">
<gallery>
File:Heji50.svg | Combining lower by one 29-limit schisma (old)
File:Heji51.svg | Combining raise by one 29-limit schisma (old)
File:HejiaccidentalCombiningLower31SchismaOld.svg | Combining lower by one 31-limit schisma (old)
File:HejiaccidentalCombiningRaise31SchismaOld.svg | Combining raise by one 31-limit schisma (old)
File:HejiaccidentalCombiningLower47Quartertone.svg | Combining lower by one 47-limit quartertone (old)
File:HejiaccidentalCombiningRaise47Quartertone.svg | Combining raise by one 47-limit quartertone (old)
</gallery>
</div>


== External links ==
== External links ==
* [http://tonalsoft.com/enc/h/hewm.aspx HEWM Notation (Helmholtz-Ellis-Wolf-Monzo)] - 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]
* [https://w3c.github.io/smufl/latest/tables/extended-helmholtz-ellis-accidentals-just-intonation-supplement.html Glyphs in SMuFL]


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


== Notes ==
== Notes ==
Retrieved from "https://en.xen.wiki/w/Helmholtz–Ellis_notation"