159edo/Notation: Difference between revisions

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[[File:159edo-accidentals.png|320px|thumb|Accidentals in the [[9/8]] space. Reworked version.]]

== Helmholtz-Ellis-based notation ==

The [[159edo]]-notation system proposed by [[User:Aura|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]]. In addition, it should be noted that accidentals are not just modifiers for single notes, but signs that indicate the change of both the tonal and modal base, and can thus appear in key signatures.

== Available base glyphs ==

=== Available base glyphs ===

=== Quartertones and Syntonic commas ===

==== 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. Furthermore, just as in classic notation.

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=== Septimal commas and darts ===

==== Septimal commas and darts ====

Glyphs for septimal commas and darts are also used, but are generally not combined with each other except in certain musical contexts such as modulation. That said, if this system were to be extended to the 13-limit, the septimal comma glyphs would likely be combined with the 13-limit glyphs due to both 7-limit and 13-limit intervals having close connections to trientones (one third tones).

~~==== 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.

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| [[File:Heji36.svg|48x48px]]

|}

~~==== 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.

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== Combined accidentals ==

=== Combined accidentals ===

The following table illustrates modification of a given tone by accidentals up to 30 steps of 159edo. The terms in the glyph name sections reflect absolute displacements, <code>–</code> means down, <code>+</code> 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. For reference, the just whole tone interval, [[9/8]], is mapped to 27 steps of 159 edo (or 9 steps of [[53edo]]) which is (27*1200/159=) 203.77 cents (0.2 cents flat).

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== Ups-and-Downs-based notation ==

Another system proposed by [[User:TallKite|TallKite]] involves simpler notation, with as few extra accidental pairs as possible. While one could do single-pair, only ups and downs (or darts as you say), but one would need at least septuple ups, and in practice octuple or more, rendering such a system impractical, so as a result, this system has two extra pairs of accidentals.

According to this system, 159edo would be notated with with a combination of ups/downs (that is, darts) and lifts/drops. The latter (referred to as "slants" here) are written / and \. The ups and downs are used as in 53edo, so one up is 3 edosteps. One lift is 1 edostep.

<tt>

0 natural

1 / lift

2 ^\ updrop

// (double-lift)

3 ^ up

4 ^/ uplift

5 ^^\ double-updrop

^// (up double-lift)

6 ^^ double-up

vvv# triple-downsharp

7 ^^/ double-uplift

vvv/# triple-down liftsharp

8 ^^^\ triple-updrop

^^// (double-up double-lift)

vv\# double-down dropsharp

9 ^^^ triple-up

vv# double-downsharp

10 ^^^/ triple-up lift

vv/# double-down liftsharp

v\\# (down double-drop sharp)

11 v\# downdrop sharp

12 v# downsharp

13 v/# downlift sharp

\\# (double-drop sharp)

14 \# dropsharp

15 # sharp

</tt>

Notes flatter than natural can be deduced by symmetry, i.e. C \C v/C vC v\C etc. Notes beyond sharp just run through the same list, but adding "sharp":

sharp, liftsharp, updrop sharp (or double-lift sharp), upsharp, uplift sharp...

going to double-sharp eventually.

Instead of ^^^ one could put an actual numeral 3 right on the score, like ^3. If someone actually used just darts and no slants, they would really need to write ^7 and not ^^^^^^^.

The spectrum of qualities looks like this:

<tt>

0 m minor

1 /m liftminor

2 ^\m updrop minor

3 ^m upminor

4 ^/m uplift minor

5 v\~ downdropmid

6 v~ downmid

7 v/~ downliftmid

8 ^\~ updropmid

9 ^~ upmid

10 ^/~ upliftmid

11 v\M downdrop major

12 vM downmajor

13 v/M downlift major

14 \M dropmajor

15 M major

16 /M liftmajor

17 ^\M updrop major

18 ^M upmajor

19 ^/M uplift major

etc.

</tt>

Thus 4:5:6:7:9:11 = P1 vM3 P5 v\m7 M9 v/~11 = C vE G v\Bb D ^^/F = Cv9(v\7)v/~11 = C down-9 downdrop-7 downlift-mid-11

This system uses both darts and slants for larger EDOs only when the EDO is multi-ring- that is, the circle of 5ths doesn't include every note- and each ring requires ups and downs. For example 205edo is 5 rings of 41edo, but 124edo is not 4 rings of 31edo. The lifts and drops label the rings. In 159edo, there's a lift ring, a drop ring, and a plain ring. The lift ring is also a double-drop ring, and the drop ring is also a double-lift ring.

[[Category:159edo]]

@@ Line 2: / Line 2: @@
 [[File:159edo-accidentals.png|320px|thumb|Accidentals in the [[9/8]] space. Reworked version.]]
+== Helmholtz-Ellis-based notation ==
 The [[159edo]]-notation system proposed by [[User:Aura|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]].  In addition, it should be noted that accidentals are not just modifiers for single notes, but signs that indicate the change of both the tonal and modal base, and can thus appear in key signatures.
-== Available base glyphs ==
+=== Available base glyphs ===
-=== Quartertones and Syntonic commas ===
+==== 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.  Furthermore, just as in classic notation.
@@ Line 81: / Line 83: @@
 |}
-=== Septimal commas and darts ===
+==== Septimal commas and darts ====
 Glyphs for septimal commas and darts are also used, but are generally not combined with each other except in certain musical contexts such as modulation.  That said, if this system were to be extended to the 13-limit, the septimal comma glyphs would likely be combined with the 13-limit glyphs due to both 7-limit and 13-limit intervals having close connections to trientones (one third tones).
-==== 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.
@@ Line 105: / Line 105: @@
 | [[File:Heji36.svg|48x48px]]
 |}
-==== 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.
@@ Line 127: / Line 125: @@
 |}
-== Combined accidentals ==
+=== Combined accidentals ===
 The following table illustrates modification of a given tone by accidentals up to 30 steps of 159edo. The terms in the glyph name sections reflect absolute displacements, <code>–</code> means down, <code>+</code> 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.  For reference, the just whole tone interval, [[9/8]], is mapped to 27 steps of 159 edo (or 9 steps of [[53edo]]) which is (27*1200/159=) 203.77 cents (0.2 cents flat).
@@ Line 570: / Line 568: @@
 |-
 |}
+== Ups-and-Downs-based notation ==
+Another system proposed by [[User:TallKite|TallKite]] involves simpler notation, with as few extra accidental pairs as possible.  While one could do single-pair, only ups and downs (or darts as you say), but one would need at least septuple ups, and in practice octuple or more, rendering such a system impractical, so as a result, this system has two extra pairs of accidentals.
+According to this system, 159edo would be notated with with a combination of ups/downs (that is, darts) and lifts/drops. The latter (referred to as "slants" here) are written / and \. The ups and downs are used as in 53edo, so one up is 3 edosteps. One lift is 1 edostep.
+<tt>
+	natural
+/ 	lift
+^\ 	updrop
+   // 	(double-lift)
+^ 	up
+^/ 	uplift
+^^\ 	double-updrop
+   ^// 	(up double-lift)
+^^ 	double-up
+   vvv#	triple-downsharp
+^^/	double-uplift
+   vvv/# triple-down liftsharp
+^^^\	triple-updrop
+   ^^//	(double-up double-lift)
+   vv\#	double-down dropsharp
+^^^	triple-up
+   vv#	double-downsharp
+^^^/ triple-up lift
+    vv/# double-down liftsharp
+    v\\# (down double-drop sharp)
+v\#	downdrop sharp
+v#	downsharp
+v/#	downlift sharp
+    \\#	(double-drop sharp)
+\#	dropsharp
+#	sharp
+</tt>
+Notes flatter than natural can be deduced by symmetry, i.e. C \C v/C vC v\C etc. Notes beyond sharp just run through the same list, but adding "sharp":
+sharp, liftsharp, updrop sharp (or double-lift sharp), upsharp, uplift sharp...
+going to double-sharp eventually.
+Instead of ^^^ one could put an actual numeral 3 right on the score, like ^3. If someone actually used just darts and no slants, they would really need to write ^7 and not ^^^^^^^.
+The spectrum of qualities looks like this:
+<tt>
+  m	minor
+  /m 	liftminor
+  ^\m	updrop minor
+  ^m 	upminor
+  ^/m	uplift minor
+  v\~	downdropmid
+  v~	downmid
+  v/~	downliftmid
+  ^\~	updropmid
+  ^~	upmid
+^/~	upliftmid
+v\M	downdrop major
+vM	downmajor
+v/M	downlift major
+\M	dropmajor
+M	major
+/M 	liftmajor
+^\M	updrop major
+^M	upmajor
+^/M	uplift major
+ etc.
+</tt>
+Thus 4:5:6:7:9:11 = P1 vM3 P5 v\m7 M9 v/~11 = C vE G v\Bb D ^^/F = Cv9(v\7)v/~11 = C down-9 downdrop-7 downlift-mid-11
+This system uses both darts and slants for larger EDOs only when the EDO is multi-ring- that is, the circle of 5ths doesn't include every note- and each ring requires ups and downs. For example 205edo is 5 rings of 41edo, but 124edo is not 4 rings of 31edo. The lifts and drops label the rings. In 159edo, there's a lift ring, a drop ring, and a plain ring. The lift ring is also a double-drop ring, and the drop ring is also a double-lift ring.
 [[Category:159edo]]