159edo/Notation: Difference between revisions

== Helmholtz–Ellis-based notation ==

The first [[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, with mainstream quartertone accidentals being used to represent them.  This is because undecimal quartertones are actually useful in modulation to keys that are not on the same circle of fifths while being simultaneously within an unnoticeable comma's distance from the quartertone of [[24edo]], which many musicians outside the microtonal community proper have at least a passing familiarity with.  It should be noted that most of the symbols listed in this section derive their functions from JI.  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.

==== Quartertones and syntonic commas ====

! −30

! −22

! −15

! −7

! −3

! −6

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).

| −4

| −8

| −1

| −2

|+ style="font-size: 105%;" | Change in 1\159

| −1

| This is nothing more than a better version of the <code>v</code> marking from Ups and downs notation.

| This is nothing more than a better version of the <code>^</code> marking from Ups and downs notation.

| −2

| This is two darts down fused into a single glyph for a more compact representation of <code>vv</code> from Ups and downs notation.

| This is two darts up fused into a single glyph for a more compact representation of <code>^^</code> from Ups and downs notation.

| −3

| −4

| −5

| −6

| −7

| −8

| −9

| −10

| −11

| −12

| −13

| −14

| −15

| −16

| −17

| −18

| −19

| −20

| −21

| −22

| −23

| −24

| −25

| −26

| −27

| −28

| −29

| −30

== Ups-and-downs-based notation ==

* 7\159 = ^^> = dupquip or vvv<# = trudquidsharp

Notes flatter than natural can be deduced by symmetry, i.e. C vC vvC vvvC ^<C <C etc. Notes beyond sharp just run through the same list, but adding "sharp": sharp, upsharp, dupsharp, quupsharp, quipsharp... going to double-sharp eventually.

* −6 = v<m = downquidminor (same as upquipmajor of the next lower degree)

* 21 = ^>M = upquipmajor (same as downquidminor of the next higher degree)

Thus 4:5:6:7:9:11 = P1 vvvM3 P5 ^<m7 M9 ^^>11 = C vvvE G ^<Bb D ^^>F = Cvvv9(^<7)^^>11 = C trud-9 quud-7 dupquip-11

Alternatively, drops and lifts can be added to 53edo ups and downs notation to avoid large multiples of ups and downs and to keep the size of an up and a down more consistent with smaller edos.

* 1\159 = / = lift

* 2\159 = \^ = drop-up

* 3\159 = ^ = up

* 4\159 = /^ = lift-up

* 5\159 = \^^ = drop-dup

* 6\159 = ^^ = dup

* 7\159 = /^^ = lift-dup

* 8\159 = \vv# = drop-dudsharp

* 9\159 = vv# = dudsharp

* 10\159 = /vv# = lift-dudsharp

* 11\159 = \v# = drop-downsharp

* 12\159 = v# = downsharp

* 13\159 = /v# = lift-downsharp

* 14\159 = \# = drop-sharp

* 15\159 = # = sharp

The spectrum of qualities for this style looks like this:

* -6 = vvm = dudminor (same as dupmajor of the next lower degree)

* -1 = \m = drop-minor

* 1 = /m = lift-minor

* 4 = /^m = lift-upminor

* 5 = \^^m = drop-dupminor = \vvvM = drop-trudmajor

* 10 = /^^^m = lift-trupminor = /vvM = lift-dudmajor

* 11 = \vM = drop-downmajor

* 13 = /vM = lift-downmajor

* 14 = \M = drop-major

* 17 = \^M = drop-upmajor

* 19 = /^M = lift-upmajor

=== Advantages and disadvantages ===

One advantage of this notation is that it keeps the traditional naturals, sharps, flats, double sharps and double flats, and assigns them to values based on 3-limit JI. Thus this notation has some level of familiarity for musicians from a traditional background, while being simpler and more intuitive than the first system. This system avoids half-sharps and half-flats because the sharp and the flat are each 15 edosteps. 15 is an odd number, so there are strictly speaking no half-sharps in 159edo.

== Sagittal notation ==

! Steps

| 0

| 1

| 2

| 3

| 4

| 5

| 6

| 7

| 8

| 9

| 10

| 12

| 13

| 14

! Accidental

| [[File:Sagittal natural.png]]

| [[File:Sagittal nai.png]]

| [[File:Sagittal sanai.png]]

| [[File:Sagittal pai.png]]

| [[File:Sagittal tai.png]]

| [[File:Sagittal janai.png]]

| [[File:Sagittal phai.png]]

| [[File:Sagittal pakai.png]]

| [[File:Sagittal jatai.png]]

| [[File:Sagittal sharp phao.png]]

| [[File:Sagittal sharp janao.png]]

| [[File:Sagittal sharp tao.png]]

| [[File:Sagittal sharp pao.png]]

| [[File:Sagittal sharp sanao.png]]

| [[File:Sagittal sharp nao.png]]

| [[File:Sagittal sharp.png]]

=== Advantages and disadvantages ===

== Syntonic–rastmic subchroma notation ==

The [[Talk:159edo notation #My Second Idea for a Notation System|second 159edo-notation system]] proposed by Aura eventually blossomed into [[syntonic–rastmic subchroma notation]], an expansion of [[neutral circle-of-fifths notation]] which turns out to be powerful enough to cover systems such as [[311edo]].

=== Advantages and disadvantages ===

{{Navbox notation}}