Richie's HEJI extensions: Difference between revisions
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'''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]]. | '''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]]) | ||
| Line 13: | Line 13: | ||
!cent deviation | !cent deviation | ||
|- | |- | ||
| | |[[File:53o.png|center|66x66px|alt=]] | ||
| | |[[File:53u.png|center|66x66px|alt=]] | ||
|53 | |53 | ||
|53/54 | |53/54 | ||
| Line 20: | Line 20: | ||
|32.4 | |32.4 | ||
|- | |- | ||
| | |[[File:59o.png|center|71x71px|alt=]] | ||
| | |[[File:59u.png|center|71x71px|alt=]] | ||
|59 | |59 | ||
|236/243 | |236/243 | ||
| Line 27: | Line 27: | ||
|50.6 | |50.6 | ||
|- | |- | ||
| | |[[File:61o.png|center|48x48px|alt=]] | ||
| | |[[File:61otonal.png|center|48x48px|alt=]] | ||
|61 | |61 | ||
|244/243 | |244/243 | ||
| Line 34: | Line 34: | ||
|7.1 | |7.1 | ||
|- | |- | ||
|[[File:67o | |[[File:67o hejiex copy.jpg|center|46x46px|alt=]] | ||
|[[File:67u | |[[File:67u hejiex copy.jpg|center|46x46px|alt=]] | ||
|67 | |67 | ||
|2144/2187 | |2144/2187 | ||
| Line 41: | Line 41: | ||
|34.4 | |34.4 | ||
|- | |- | ||
| | |[[File:71o heji extension.png|center|52x52px|alt=]] | ||
| | |[[File:71u heji extension.png|center|52x52px|alt=]] | ||
|71 | |71 | ||
|71/72 | |71/72 | ||
| Line 48: | Line 48: | ||
|24.2 | |24.2 | ||
|- | |- | ||
|[[File:73u extension 2022.png|center]] | |[[File:73u extension 2022.png|center|alt=|51x51px]] | ||
|[[File:73o.png.png|center]] | |[[File:73o.png.png|center|alt=|51x51px]] | ||
|73 | |73 | ||
|73/72 | |73/72 | ||
| Line 55: | Line 55: | ||
|23.9 | |23.9 | ||
|- | |- | ||
| | |[[File:79o.png|center|60x60px|alt=]] | ||
| | |[[File:79u.png|center|60x60px|alt=]] | ||
|79 | |79 | ||
|79/81 | |79/81 | ||
| Line 62: | Line 62: | ||
|43.3 | |43.3 | ||
|- | |- | ||
|[[File:83o extension 2022.png|center]] | |[[File:83o extension 2022.png|center|alt=|66x66px]] | ||
|[[File:83u extension 2022.png|center]] | |[[File:83u extension 2022.png|center|alt=|62x62px]] | ||
|83 | |83 | ||
|249/256 | |249/256 | ||
| Line 69: | Line 69: | ||
|48.0 | |48.0 | ||
|- | |- | ||
| | |[[File:89o heji extension.png|center|61x61px|alt=]] | ||
| | |[[File:89u heji extension.png|center|61x61px|alt=]] | ||
|89 | |89 | ||
|712/729 | |712/729 | ||
| Line 79: | Line 79: | ||
== 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:Helmholtz–Ellis notation]] | [[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
