159edo/Notation
The 159edo-notation system proposed by Aura modifies the Helmholtz-Ellis notation in such a way that undecimal quartertones play a central role alongside the traditional accidentals. It should be noted that most of the symbols listed on this page derive their functions from JI, though the dart symbols in particular have the potential to see usage in later versions of Ups and Downs notation.
Available base glyphs
Quartertones and Syntonic commas
As in HEJI, classic accidentals and arrows for syntonic commas are combined. Beyond HEJI, quartertone accidentals are also used, being combined with syntonic comma arrows in the same way.
| -30 | -22 | -15 | -7 | 0 | +7 | +15 | +22 | +30 | |
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| +6 | 
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| +3 | 
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| -3 | 
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| -6 | 
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Septimal commas and darts
Glyphs for septimal commas or darts are alternatively used: they are not combined in this system.
Septimal commas
The septimal comma glyph traditionally indicates a change by 64/63, and thus, in this particular system, it is bound to the equivalent step size, which is around 30 cents- slightly larger than normal.
| Delta | Glyph |
|---|---|
| +8 | 
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| +4 | 
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| -4 | 
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| -8 | 
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Darts
The dart glyph in this system indicates a change by a single 159edo step (around 7.5 cents). As the dart has no traditional binding to a specific comma, it can also be used for other EDOs to indicate a single step in their corresponding notation systems.
| Delta | Glyph |
|---|---|
| +2 | 
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| +1 | 
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| -1 | 
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| -2 | 
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Combined accidentals
The following table (under construction) shows the symbols and describes their function. The terms in the glyph name sections reflect absolute displacements, - means down, + means up. Furthermore, symbols with multiple names will have both names sharing the same cell. The choice between the primary and secondary glyphs for any given step is often determined both by absolute TE error and by harmonic and melodic context for any given score, particularly as the primary and secondary glyphs usually reflect different intervals in Just Intonation.
The table illustrates modification of a given tone by accidentals up to 30 steps of 159edo. The just whole tone (9/8) interval is mapped to 27 steps of 159 edo (or 9 steps of 53edo). The corresponding interval is (27*1200/159=) 203.77 cents (0.2 cents flat).
| Delta | Primary Glyph | Primary Glyph Name | Secondary Glyph | Secondary Glyph Name | Remarks |
|---|---|---|---|---|---|
| 0 |
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Natural | |||
| -1 |
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Dart down | This is nothing more than a better version of the v marking from Ups and Downs Notation.
| ||
| +1 |
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Dart up | This is nothing more than a better version of the ^ marking from Ups and Downs Notation.
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| -2 |
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Double dart down | This is two darts down fused into a single glyph for a more compact representation of vv from Ups and Downs Notation.
| ||
| +2 |
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Double dart up | This is two darts up fused into a single glyph for a more compact representation of ^^ from Ups and Downs Notation.
| ||
| -3 |
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Natural –Syntonic comma |
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Quarter flat +Septimal comma, Demiflat +Septimal comma | The intervals represented by the primary and secondary glyphs for this step differ by 385/384 in Just Intonation. |
| +3 |
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Natural +Syntonic comma |
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Quarter sharp –Septimal comma, Demisharp –Septimal comma | The intervals represented by the primary and secondary glyphs for this step differ by 385/384 in Just Intonation. |
| -4 |
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Quarter flat +Syntonic comma, Demiflat +Syntonic comma |
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Septimal comma down | The primary glyph overall represents a lowering by 55/54. |
| +4 |
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Quarter sharp –Syntonic comma, Demisharp –Syntonic comma |
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Septimal comma up | The primary glyph overall represents a raising by 55/54. |
| -5 |
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Quarter flat with double dart up, Demiflat with double dart up | |||
| +5 |
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Quarter sharp with double dart down, Demisharp with double dart down | |||
| -6 |
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Quarter flat with dart up, Demiflat with dart up |
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Natural –2 Syntonic commas | |
| +6 |
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Quarter sharp with dart down, Demisharp with dart down |
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Natural +2 Syntonic commas | |
| -7 |
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Quarter flat, Demiflat | This glyph represents a lowering by 33/32, much like its identical Helmholtz-Ellis equivalent. | ||
| +7 |
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Quarter sharp, Demisharp | This glyph represents a raising by 33/32, replacing its Helmholtz-Ellis equivalent on account of familiarity. | ||
| -8 |
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Quarter flat, Demiflat with Dart down |
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2 Septimal commas down | |
| +8 |
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Quarter sharp, Demisharp with Dart up |
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2 Septimal commas up | |
| -9 |
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Quarter flat with double dart down, Demiflat with double dart down |
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Flat +2 Syntonic commas | |
| +9 |
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Quarter sharp with double dart up, Demisharp with double dart up |
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Sharp –2 Syntonic commas | |
| -10 |
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Quarter flat –Syntonic comma, Demiflat –Syntonic comma | |||
| +10 |
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Quarter sharp +Syntonic comma, Demisharp +Syntonic comma | |||
| -11 |
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Flat +Septimal comma | |||
| +11 |
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Sharp –Septimal comma | |||
| -12 |
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Flat +Syntonic comma | |||
| +12 |
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Sharp –Syntonic comma | |||
| todo: 13, 14 | |||||
| -15 |
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Flat | |||
| +15 |
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Sharp | |||
| todo: 16, 17 | |||||
| -18 |
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Flat –Syntonic comma | |||
| +18 |
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Sharp +Syntonic comma | |||
| -19 |
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Flat –Septimal comma | |||
| +19 |
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Sharp +Septimal comma | |||
| todo: 20..26 | |||||
| -27 |
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Double flat +Syntonic comma | |||
| +27 |
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Double sharp –Syntonic comma | |||
| todo: 28, 29 | |||||
| -30 |
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Double flat | |||
| +30 |
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Double sharp | |||