159edo/Notation

Accidentals in the 9/8 space. First sketch by Aura.

Accidentals in the 9/8 space. Reworked version.

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 chart 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
+6
+3
-3
-6

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 indicates a change by ca. 30 cents, this is larger than 64/63

Delta	Glyph
+8
+4
-4
-8

Darts

The dart glyph indicates a change by ca. 1 159edo step (ca. 7.5 cents), the dart has no traditional binding to a specific comma.

Delta	Glyph
+2
+1
-1
-2

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 reflect different intervals in Just Intonation.

Change in 1\159

Delta	Primary Glyph	Primary Glyph Name	Secondary Glyph	Secondary Glyph Name	Remarks
0		Natural
-1		Dart down			This is nothing more than a better version of the v marking from Ups and Downs Notation.
+1		Dart up			This is nothing more than a better version of the ^ marking from Ups and Downs Notation.
-2		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		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		Natural –Syntonic comma		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		Natural +Syntonic comma		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		Quarter flat +Syntonic comma, Demiflat +Syntonic comma		Septimal comma down	The primary glyph overall represents a lowering by 55/54.
+4		Quarter sharp –Syntonic comma, Demisharp –Syntonic comma		Septimal comma up	The primary glyph overall represents a raising by 55/54.
-5		Quarter flat with double dart up, Demiflat with double dart up
+5		Quarter sharp with double dart down, Demisharp with double dart down
-6		Quarter flat with dart up, Demiflat with dart up		Natural –2 Syntonic commas
+6		Quarter sharp with dart down, Demisharp with dart down		Natural +2 Syntonic commas
-7		Quarter flat, Demiflat			This glyph represents a lowering by 33/32, much like its identical Helmholtz-Ellis equivalent.
+7		Quarter sharp, Demisharp			This glyph represents a raising by 33/32, replacing its Helmholtz-Ellis equivalent on account of familiarity.
todo: 8..10
-11		Flat +Septimal comma
+11		Sharp –Septimal comma
-12		Flat +Syntonic comma
+12		Sharp –Syntonic comma
todo: 13, 14
-15		Flat
+15		Sharp
todo: 16, 17
-18		Flat –Syntonic comma
+18		Sharp +Syntonic comma
-19		Flat –Septimal comma
+19		Sharp +Septimal comma
todo: 20..26
-27		Double flat +Syntonic comma
+27		Double sharp –Syntonic comma
todo: 31, 32
-30		Double flat
+30		Double sharp