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.
{| class="wikitable center-all" style="margin: auto auto auto auto;"
{| class="wikitable center-all" style="margin: auto auto auto auto;"
|+ style="font-size: 110%;" | Formal commas
|+ style="font-size: 105%;" | Formal commas
! Prime
! Prime !! Formal Comma
! Formal Comma
|-
|-
| [[5-limit|5]]
| [[5-limit|5]] || [[81/80]]
| [[81/80]]
|-
|-
| [[7-limit|7]]
| [[7-limit|7]] || [[64/63]]
| [[64/63]]
|-
|-
| [[11-limit|11]]
| [[11-limit|11]] || [[33/32]]
| [[33/32]]
|-
|-
| [[13-limit|13]]
| [[13-limit|13]] || [[27/26]]
| [[27/26]]
|-
|-
| [[17-limit|17]]
| [[17-limit|17]] || [[2187/2176]]
| [[2187/2176]]
|-
|-
| [[19-limit|19]]
| [[19-limit|19]] || [[513/512]]
| [[513/512]]
|-
|-
| [[23-limit|23]]
| [[23-limit|23]] || [[736/729]]
| [[736/729]]
|-
|-
| [[29-limit|29]]
| [[29-limit|29]] || [[261/256]]
| [[261/256]]
|-
|-
| [[31-limit|31]]
| [[31-limit|31]] || [[32/31]]
| [[32/31]]
|-
|-
| [[37-limit|37]]
| [[37-limit|37]] || [[37/36]]
| [[37/36]]
|-
|-
| [[41-limit|41]]
| [[41-limit|41]] || [[82/81]]
| [[82/81]]
|-
|-
| [[43-limit|43]]
| [[43-limit|43]] || [[129/128]]
| [[129/128]]
|-
|-
| [[47-limit|47]]
| [[47-limit|47]] || [[752/729]]
| [[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: 110%;" | 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

Revision as of 11:50, 30 July 2024

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
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 (todo) 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

Todo: update

Update the 29-limit comma.

  • 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 31-limit quartertone
    Combining lower by one 31-limit quartertone
  • Combining raise by one 31-limit quartertone
    Combining raise by one 31-limit quartertone

External links

See also

Notes

  1. ↑ See Marc Sabat : Music & Writings.
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