Richie's HEJI extensions: Difference between revisions
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!cent deviation | !cent deviation | ||
|- | |- | ||
|[[File:53o.png|center| | |[[File:53o.png|center|66x66px|alt=]] | ||
|[[File:53u.png|center| | |[[File:53u.png|center|66x66px|alt=]] | ||
|53 | |53 | ||
|53/54 | |53/54 | ||
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|32.4 | |32.4 | ||
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|[[File:59o.png|center| | |[[File:59o.png|center|71x71px|alt=]] | ||
|[[File:59u.png|center| | |[[File:59u.png|center|71x71px|alt=]] | ||
|59 | |59 | ||
|236/243 | |236/243 | ||
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|50.6 | |50.6 | ||
|- | |- | ||
|[[File:61o.png|center| | |[[File:61o.png|center|48x48px|alt=]] | ||
|[[File:61otonal.png|center| | |[[File:61otonal.png|center|48x48px|alt=]] | ||
|61 | |61 | ||
|244/243 | |244/243 | ||
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|7.1 | |7.1 | ||
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|[[File:67o hejiex copy.jpg|center| | |[[File:67o hejiex copy.jpg|center|46x46px|alt=]] | ||
|[[File:67u hejiex copy.jpg|center| | |[[File:67u hejiex copy.jpg|center|46x46px|alt=]] | ||
|67 | |67 | ||
|2144/2187 | |2144/2187 | ||
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|34.4 | |34.4 | ||
|- | |- | ||
|[[File:71o heji extension.png|center| | |[[File:71o heji extension.png|center|52x52px|alt=]] | ||
|[[File:71u heji extension.png|center| | |[[File:71u heji extension.png|center|52x52px|alt=]] | ||
|71 | |71 | ||
|71/72 | |71/72 | ||
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|24.2 | |24.2 | ||
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|[[File:73u extension 2022.png|center|alt=| | |[[File:73u extension 2022.png|center|alt=|51x51px]] | ||
|[[File:73o.png.png|center|alt=| | |[[File:73o.png.png|center|alt=|51x51px]] | ||
|73 | |73 | ||
|73/72 | |73/72 | ||
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|23.9 | |23.9 | ||
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|[[File:79o.png|center| | |[[File:79o.png|center|60x60px|alt=]] | ||
|[[File:79u.png|center| | |[[File:79u.png|center|60x60px|alt=]] | ||
|79 | |79 | ||
|79/81 | |79/81 | ||
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|43.3 | |43.3 | ||
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|[[File:83o extension 2022.png|center|alt=| | |[[File:83o extension 2022.png|center|alt=|66x66px]] | ||
|[[File:83u extension 2022.png|center|alt=| | |[[File:83u extension 2022.png|center|alt=|62x62px]] | ||
|83 | |83 | ||
|249/256 | |249/256 | ||
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|48.0 | |48.0 | ||
|- | |- | ||
|[[File:89o heji extension.png|center| | |[[File:89o heji extension.png|center|61x61px|alt=]] | ||
|[[File:89u heji extension.png|center| | |[[File:89u heji extension.png|center|61x61px|alt=]] | ||
|89 | |89 | ||
|712/729 | |712/729 | ||
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== 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> | ||
[[Category:Notation]] | [[Category:Notation]] | ||
[[Category:Helmholtz–Ellis notation]] | [[Category:Helmholtz–Ellis notation]] | ||
Revision as of 00:10, 26 January 2025
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.
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
