Helmholtz–Ellis notation: Difference between revisions

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→Helmholtz–Ellis glyphs: update the gallery of Heji glyphs with more new glyphs and expand with some old glyphs
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| [[File:HejiaccidentalCombiningRaise29LimitComma.svg|48x48px]][[File:Heji11.svg|54x54px]][[File:HejiB.svg|48x48px]]
| [[File:Heji51.svg|48x48px]][[File:Heji12.svg|48x48px]][[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<br />in the 2020 version by Plainsound Music Edition
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|-
| 31
| 31
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| [[File:Heji52.svg|48x48px]][[File:HejiC.svg|48x48px]]
| [[File:Heji52.svg|54x54px]][[File:HejiC.svg|48x48px]]
| (todo)
| [[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<br />in the 2020 version by Plainsound Music Edition
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| 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]]
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| colspan="2" | [[File:HejiaccidentalCombiningRaise37Quartertone.svg|48x48px]][[File:HejiD.svg|48x48px]]
| (todo)
|  
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|-
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| colspan="2" | [[File:Heji42.svg|54x54px]][[File:HejiE.svg|48x48px]]
| [[File:Heji42.svg|54x54px]][[File:HejiE.svg|48x48px]]
| (todo)
|  
|  
|-
|-
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| [[File:HejiaccidentalCombiningRaise41Comma.svg|48x48px]][[File:HejiE.svg|48x48px]]
| (todo)
| (todo)
| (todo)
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| [[File:HejiaccidentalCombiningRaise43Comma.svg|48x48px]][[File:HejiF.svg|48x48px]]
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| (todo)
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| [[File:HejiaccidentalCombiningRaise47Quartertone.svg|48x48px]][[File:Heji25.svg|54x54px]][[File:HejiF.svg|48x48px]]
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Revision as of 11:03, 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.

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 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 (todo)
41 41/32 (todo)
43 43/32 (todo)
45 45/32
47 47/32 (todo)

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

External links

See also

Notes

  1. ↑ See Marc Sabat : Music & Writings.


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