Helmholtz–Ellis notation: Difference between revisions

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'''Helmholtz-Ellis notation''' is a [[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 [[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]].
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=== Formal commas ===
=== Formal commas ===
{| class="wikitable center-all"
{| class="wikitable center-all"
|+Formal commas below 32-limit
! Prime
! Prime
! Formal Comma
! Formal Comma
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| [[31-limit|31]]
| [[31-limit|31]]
| [[32/31]]
| [[32/31]]
|-
| [[37-limit|37]]
| [[37/36]]
|-
| [[41-limit|41]]
| [[82/81]]
|-
| [[43-limit|43]]
| [[129/128]]
|-
| [[47-limit|47]]
| [[752/729]]
|}
|}


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| (todo)
| (todo)
| 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
|-
| 37
| 37/32
| (todo)
| (todo)
|
|-
| 41
| 41/32
| (todo)
| (todo)
|
|-
| 43
| 43/32
| (todo)
| (todo)
|
|-
| 47
| 47/32
| (todo)
| (todo)
|
|}
|}


== Helmholtz-Ellis glyphs ==
== Helmholtz-Ellis glyphs ==

Revision as of 07:50, 3 January 2023

The Helmholtz-Ellis JI pitch notation (HEJI) is a 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

  1. ↑ See Marc Sabat : Music & Writings.

Quick reference

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

Prime harmonics

Prime 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 Default staff notation represents Pythagorean tuning
5 5/4
7 7/4
11 11/8
13 13/8
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
23 23/16
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
37 37/32 (todo) (todo)
41 41/32 (todo) (todo)
43 43/32 (todo) (todo)
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

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