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'''Richie's HEJI extensions''' are a set of 9 pairs of accidentals, designed by [[richie]], that extend [[ | '''Richie's HEJI extensions''' are a set of 9 pairs of accidentals, designed by [[richie]], that extend [[Helmholtz–Ellis notation]]'s accidentals from the [[47-limit]] to the [[89-limit]]. These allow the [[Musical notation|notation]] of [[just intonation]] intervals with much higher prime factors, which are encountered relatively often with some approaches to JI such as [[primodality]] and music making use of [[isoharmonic chords]]. | ||
These accidentals are available as an OpenType font (see [[File:HEJI fonts.zip]]) | These accidentals are available as an OpenType font (see [[File:HEJI fonts.zip]]) | ||
The harmonic series scales from the gallery below are also available as a Dorico template (see [[File:Harmonic Series Scales.zip]]). | The harmonic series scales from the gallery below are also available as a Dorico template (see [[File:Harmonic Series Scales.zip]]). | ||
{| class="wikitable" | |||
|+ | |||
!descending | |||
!ascending | |||
!prime | |||
!ratio | |||
!otonal alteration (±) | |||
!cent deviation | |||
|- | |||
|[[File:53o.png|center|66x66px|alt=]] | |||
|[[File:53u.png|center|66x66px|alt=]] | |||
|53 | |||
|53/54 | |||
| - | |||
|32.4 | |||
|- | |||
|[[File:59o.png|center|71x71px|alt=]] | |||
|[[File:59u.png|center|71x71px|alt=]] | |||
|59 | |||
|236/243 | |||
| - | |||
|50.6 | |||
|- | |||
|[[File:61o.png|center|48x48px|alt=]] | |||
|[[File:61otonal.png|center|48x48px|alt=]] | |||
|61 | |||
|244/243 | |||
| + | |||
|7.1 | |||
|- | |||
|[[File:67o hejiex copy.jpg|center|46x46px|alt=]] | |||
|[[File:67u hejiex copy.jpg|center|46x46px|alt=]] | |||
|67 | |||
|2144/2187 | |||
| - | |||
|34.4 | |||
|- | |||
|[[File:71o heji extension.png|center|52x52px|alt=]] | |||
|[[File:71u heji extension.png|center|52x52px|alt=]] | |||
|71 | |||
|71/72 | |||
| - | |||
|24.2 | |||
|- | |||
|[[File:73u extension 2022.png|center|alt=|51x51px]] | |||
|[[File:73o.png.png|center|alt=|51x51px]] | |||
|73 | |||
|73/72 | |||
| + | |||
|23.9 | |||
|- | |||
|[[File:79o.png|center|60x60px|alt=]] | |||
|[[File:79u.png|center|60x60px|alt=]] | |||
|79 | |||
|79/81 | |||
| - | |||
|43.3 | |||
|- | |||
|[[File:83o extension 2022.png|center|alt=|66x66px]] | |||
|[[File:83u extension 2022.png|center|alt=|62x62px]] | |||
|83 | |||
|249/256 | |||
| - | |||
|48.0 | |||
|- | |||
|[[File:89o heji extension.png|center|61x61px|alt=]] | |||
|[[File:89u heji extension.png|center|61x61px|alt=]] | |||
|89 | |||
|712/729 | |||
| - | |||
|40.9 | |||
|} | |||
== Gallery == | == Gallery == | ||
<gallery> | <gallery> | ||
File: | File:Harmonic Series Scales - 001.jpg|[[Harmonic series]] scales from 26:52 to 34:68 | ||
File:Harmonic Series Scales - 002.jpg|Harmonic series scales from 36:72 to 48:96 | |||
File: | |||
</gallery> | </gallery> | ||
== External links == | |||
* [http://notation.richiegreene.com/ notation.richiegreene.com] | |||
[[Category:Notation]] | [[Category:Notation]] | ||
[[Category: | [[Category:Helmholtz–Ellis notation]] | ||
Latest revision as of 02:12, 16 May 2026
Richie's HEJI extensions are a set of 9 pairs of accidentals, designed by richie, that extend Helmholtz–Ellis notation's accidentals from the 47-limit to the 89-limit. These allow the notation of just intonation intervals with much higher prime factors, which are encountered relatively often with some approaches to JI such as primodality and music making use of isoharmonic chords.
These accidentals are available as an OpenType font (see File:HEJI fonts.zip)
The harmonic series scales from the gallery below are also available as a Dorico template (see File:Harmonic Series Scales.zip).
| descending | ascending | prime | ratio | otonal alteration (±) | cent deviation |
|---|---|---|---|---|---|
 |
 |
53 | 53/54 | - | 32.4 |
 |
 |
59 | 236/243 | - | 50.6 |
 |
 |
61 | 244/243 | + | 7.1 |
 |
 |
67 | 2144/2187 | - | 34.4 |
 |
 |
71 | 71/72 | - | 24.2 |
 |
 |
73 | 73/72 | + | 23.9 |
 |
 |
79 | 79/81 | - | 43.3 |
 |
 |
83 | 249/256 | - | 48.0 |
 |
 |
89 | 712/729 | - | 40.9 |
Gallery
-
Harmonic series scales from 26:52 to 34:68 -
Harmonic series scales from 36:72 to 48:96
