159edo/Notation: Difference between revisions

Line 571:

=== Advantages and disadvantages ===

Among the advantages of this system is the fact that it keeps the traditional naturals, sharps, flats, double sharps and double flats, and assigns them to values based on 3-limit JI, resulting in this system having some level of familiarity for musicians from a traditional background. However, the disadvantages of this system are that this system relies on too many glyphs, a number of which need to be deciphered, and furthermore, the arrangement of combined and simple accidentals- as well as arrangement of the quartertone accidentals- is counterintuitive.

Among the advantages of this system is the fact that it keeps the traditional naturals, sharps, flats, double sharps and double flats, and assigns them to values based on 3-limit JI, resulting in this system having some level of familiarity for musicians from a traditional background. However, the disadvantages of this system are that this system relies on too many glyphs, a number of which need to be deciphered, and furthermore, the arrangement of combined and simple accidentals- as well as arrangement of the quartertone accidentals- is counterintuitive. In addition, a demisharp is approximately a half-sharp, yet here it is called a quarter-sharp, a break with well-established microtonal convention. Finally, two demisharps do not add up to a sharp as one would expect.

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

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

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

According to this system, 159edo would be notated with a combination of ups/downs 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. Double-~~darts~~ are called dup and dud. Triple-~~darts~~ are trup and trud. Double-slants are dublift and dubdrop.

According to this system, 159edo would be notated with a combination of ups/downs 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. Double-arrows are called dup and dud. Triple-arrows are trup and trud. Double-slants are dublift and dubdrop.

<tt>

Line 606:

14 \# dropsharp

15 # sharp

</tt>

Line 612:

Line 613:

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 ^^^^^^^.

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

The spectrum of qualities looks like this:

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\\m (dubdrop minor)

-1 \m dropminor

0 m minor

1 /m liftminor

2 ^\m updrop minor

//m (dublift minor)

3 ^m upminor

4 ^/m uplift minor

5 v\~ ~~downdropmid~~

5 ^^\m dupdrop minor

6 ~~v~ downmid~~

^//m (up dublift minor)

7 v/~ ~~downliftmid~~

6 ^^m dupminor

8 ^\~ ~~updropmid~~

vvvM (trudmajor)

9 ^~ ~~upmid~~

7 ^^/m duplift minor

10 ^/~ ~~upliftmid~~

vvv/M (trudlift major)

11 v\M downdrop major

8 ^^^\m trupdrop minor

12 vM downmajor

^^//m (dup dublift minor)

13 v/M downlift major

vv\M duddrop major

9 ^^^m trupminor

vvM dudmajor

10 ^^^/m truplift minor

vv/M dudlift major

v\\M (down dubdrop major)

11 v\M downdrop major

12 vM downmajor

13 v/M downlift major

\\M (dubdrop major)

14 \M dropmajor

15 M major

16 /M liftmajor

17 ^\M updrop major

//M (dublift major)

18 ^M upmajor

19 ^/M uplift major

20 ^^\M dupdrop major

21 ^^M dupmajor (same as dudminor of the next higher degree)

</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

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)^^/11 = C down-9 downdrop-7 duplift-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.

This system uses both arrows 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.

=== Advantages and disadvantages ===

===Advantages and disadvantages===

~~Among the advantages~~ of this ~~system~~ is ~~the fact~~ that it keeps the traditional naturals, sharps, flats, double sharps and double flats, and assigns them to values based on 3-limit JI~~, resulting in~~ this ~~system having~~ some level of familiarity for musicians from a traditional background, while being simpler and more intuitive than the first system. ~~However, among the disadvantages of this~~ system ~~are~~ the ~~lack of quartertone accidentals,~~ and, ~~the need for~~ a prior understanding [[53edo]], which ~~is often not the most straightforward~~ to ~~begin with in terms of notation~~, as noted by [https://en.wikipedia.org/wiki/53_equal_temperament#Notation Wikipedia's article on 53edo]. The net effect of these two disadvantages is that this system is likely to be less accessible to many microtonal musicians due to many beginners in particular being more likely to have experience with the more straightforward [[24edo]].

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. It assumes a prior understanding of [[53edo]], which could be a disadvantage if one comes to 159edo directly, without first exploring 53.

[[Category:159edo]]

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[[Category:159edo notation| ]]

== Sagittal notation ==

== Sagittal notation==

The following table shows [[sagittal notation]] accidentals in one apotome for 159edo.

{| class="wikitable center-all"

! Steps

!Steps

| 0

|0

| 1

|1

| 2

|2

| 3

|3

| 4

|4

| 5

|5

| 6

|6

| 7

|7

| 8

|8

| 9

|9

| 10

|10

| 11

| 12

|12

| 13

|13

| 14

|14

| 15

|-

! Accidental

!Accidental

| [[File:Sagittal natural.png]]

|[[File:Sagittal natural.png]]

| [[File:Sagittal nai.png]]

|[[File:Sagittal nai.png]]

| [[File:Sagittal sanai.png]]

|[[File:Sagittal sanai.png]]

| [[File:Sagittal pai.png]]

|[[File:Sagittal pai.png]]

| [[File:Sagittal tai.png]]

|[[File:Sagittal tai.png]]

| [[File:Sagittal janai.png]]

|[[File:Sagittal janai.png]]

| [[File:Sagittal phai.png]]

|[[File:Sagittal phai.png]]

| [[File:Sagittal pakai.png]]

|[[File:Sagittal pakai.png]]

| [[File:Sagittal jatai.png]]

|[[File:Sagittal jatai.png]]

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

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

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

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

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

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

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

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

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

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

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

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

| [[File:Sagittal sharp.png]]

|[[File:Sagittal sharp.png]]

|}

=== Advantages and disadvantages ===

===Advantages and disadvantages ===

The advantages and disadvantages are largely the same as those of Sagittal notation in general.

== Syntonic-Rastmic Subchroma notation ==

==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]].

Line 732:

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14 #\ raflat sharp

15 # sharp

</tt>

=== Advantages and disadvantages ===

===Advantages and disadvantages ===

By striking a good balance between the number of accidentals and their semantic consistency, Syntonic-Rastmic Subchroma notation manages to address the weaknesses of both Ups and Downs notation and Sagittal notation, and, as it's derived from Neutral Circle-of-Fifths notation- the de facto standard foundation for notation in 24edo- it is more easily accessible to microtonal musicians at the beginner level, all while retaining Helmholtz-Ellis notation's advantage of fixing the key notation problems that have plagued 53edo itself by means of accounting for the 2.3.5.11 subgroup in general and the syntonic comma specifically.

[[Category:Todo:expand]]

@@ Line 571: / Line 571: @@
 === Advantages and disadvantages ===
-Among the advantages of this system is the fact that it keeps the traditional naturals, sharps, flats, double sharps and double flats, and assigns them to values based on 3-limit JI, resulting in this system having some level of familiarity for musicians from a traditional background.  However, the disadvantages of this system are that this system relies on too many glyphs, a number of which need to be deciphered, and furthermore, the arrangement of combined and simple accidentals- as well as arrangement of the quartertone accidentals- is counterintuitive.
+Among the advantages of this system is the fact that it keeps the traditional naturals, sharps, flats, double sharps and double flats, and assigns them to values based on 3-limit JI, resulting in this system having some level of familiarity for musicians from a traditional background.  However, the disadvantages of this system are that this system relies on too many glyphs, a number of which need to be deciphered, and furthermore, the arrangement of combined and simple accidentals- as well as arrangement of the quartertone accidentals- is counterintuitive. In addition, a demisharp is approximately a half-sharp, yet here it is called a quarter-sharp, a break with well-established microtonal convention. Finally, two demisharps do not add up to a sharp as one would expect.
 == Ups-and-Downs-based notation ==
-Another system proposed by [[User:TallKite|TallKite]] involves simpler notation, with as few extra accidental pairs as possible.  One could do with only one extra pair, only ups and downs (that is, darts), but one would need at least septuple ups, and in practice octuple or more, rendering such a system impractical. As a result, this system has two extra pairs of accidentals.
+Another system proposed by [[User:TallKite|TallKite]] involves simpler notation, with as few extra accidental pairs as possible.  One could do with only one extra pair, only ups and downs (that is, arrows), but one would need at least septuple ups, and in practice octuple or more, rendering such a system impractical. As a result, this system has two extra pairs of accidentals.
-According to this system, 159edo would be notated with a combination of ups/downs 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. Double-darts are called dup and dud. Triple-darts are trup and trud. Double-slants are dublift and dubdrop.
+According to this system, 159edo would be notated with a combination of ups/downs 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. Double-arrows are called dup and dud. Triple-arrows are trup and trud. Double-slants are dublift and dubdrop.
 <tt>
@@ Line 606: / Line 606: @@
 \#	dropsharp
 #	sharp
 </tt>
@@ Line 612: / Line 613: @@
 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 ^^^^^^^.
+Instead of ^^^ one could put an actual numeral 3 right on the score, like ^3. If someone actually used just arrows and no slants, they would really need to write ^7 and not ^^^^^^^.
 The spectrum of qualities looks like this:
@@ Line 623: / Line 624: @@
      \\m  (dubdrop minor)
   -1 \m    dropminor
-m	 minor
+m	  minor
-/m 	 liftminor
+/m    liftminor
-^\m	 updrop minor
+^\m	  updrop minor
      //m  (dublift minor)
-^m 	 upminor
+^m 	  upminor
-^/m	 uplift minor
+^/m	  uplift minor
-v\~	 downdropmid
+^^\m  dupdrop minor
-v~	 downmid
+    ^//m (up dublift minor)
-v/~	 downliftmid
+^^m   dupminor
-^\~	 updropmid
+    vvvM (trudmajor)
-^~	 upmid
+^^/m  duplift minor
-^/~	 upliftmid
+   vvv/M (trudlift major)
-v\M	 downdrop major
+^^^\m trupdrop minor
-vM	 downmajor
+   ^^//m (dup dublift minor)
-v/M	 downlift major
+    vv\M  duddrop major
+^^^m  trupminor
+   vvM	  dudmajor
+^^^/m truplift minor
+    vv/M  dudlift major
+    v\\M (down dubdrop major)
+v\M	  downdrop major
+vM	  downmajor
+v/M   downlift major
      \\M  (dubdrop major)
-\M	 dropmajor
+\M	  dropmajor
-M	 major
+M	  major
-/M 	 liftmajor
+/M 	  liftmajor
-^\M	 updrop major
+^\M	  updrop major
      //M  (dublift major)
-^M	 upmajor
+^M	  upmajor
-^/M	 uplift major
+^/M	  uplift major
 ^^\M  dupdrop major
 ^^M   dupmajor (same as dudminor of the next higher degree)
 </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
+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)^^/11 = C down-9 downdrop-7 duplift-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.
+This system uses both arrows 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.
-=== Advantages and disadvantages ===
+===Advantages and disadvantages===
-Among the advantages of this system is the fact that it keeps the traditional naturals, sharps, flats, double sharps and double flats, and assigns them to values based on 3-limit JI, resulting in this system having some level of familiarity for musicians from a traditional background, while being simpler and more intuitive than the first system.  However, among the disadvantages of this system are the lack of quartertone accidentals, and, the need for a prior understanding [[53edo]], which is often not the most straightforward to begin with in terms of notation, as noted by [https://en.wikipedia.org/wiki/53_equal_temperament#Notation Wikipedia's article on 53edo].  The net effect of these two disadvantages is that this system is likely to be less accessible to many microtonal musicians due to many beginners in particular being more likely to have experience with the more straightforward [[24edo]].
+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. It assumes a prior understanding of [[53edo]], which could be a disadvantage if one comes to 159edo directly, without first exploring 53.
 [[Category:159edo]]
@@ Line 662: / Line 672: @@
 [[Category:159edo notation| ]] <!-- main article -->
-== Sagittal notation ==
+== Sagittal notation==
 The following table shows [[sagittal notation]] accidentals in one apotome for 159edo.
 {| class="wikitable center-all"
-! Steps
+!Steps
-| 0
+|0
-| 1
+|1
-| 2
+|2
-| 3
+|3
-| 4
+|4
-| 5
+|5
-| 6
+|6
-| 7
+|7
-| 8
+|8
-| 9
+|9
-| 10
+|10
 | 11
-| 12
+|12
-| 13
+|13
-| 14
+|14
 | 15
 |-
-! Accidental
+!Accidental
-| [[File:Sagittal natural.png]]
+|[[File:Sagittal natural.png]]
-| [[File:Sagittal nai.png]]
+|[[File:Sagittal nai.png]]
-| [[File:Sagittal sanai.png]]
+|[[File:Sagittal sanai.png]]
-| [[File:Sagittal pai.png]]
+|[[File:Sagittal pai.png]]
-| [[File:Sagittal tai.png]]
+|[[File:Sagittal tai.png]]
-| [[File:Sagittal janai.png]]
+|[[File:Sagittal janai.png]]
-| [[File:Sagittal phai.png]]
+|[[File:Sagittal phai.png]]
-| [[File:Sagittal pakai.png]]
+|[[File:Sagittal pakai.png]]
-| [[File:Sagittal jatai.png]]
+|[[File:Sagittal jatai.png]]
-| [[File:Sagittal sharp phao.png]]
+|[[File:Sagittal sharp phao.png]]
-| [[File:Sagittal sharp janao.png]]
+|[[File:Sagittal sharp janao.png]]
-| [[File:Sagittal sharp tao.png]]
+|[[File:Sagittal sharp tao.png]]
-| [[File:Sagittal sharp pao.png]]
+|[[File:Sagittal sharp pao.png]]
-| [[File:Sagittal sharp sanao.png]]
+|[[File:Sagittal sharp sanao.png]]
-| [[File:Sagittal sharp nao.png]]
+|[[File:Sagittal sharp nao.png]]
-| [[File:Sagittal sharp.png]]
+|[[File:Sagittal sharp.png]]
 |}
-=== Advantages and disadvantages ===
+===Advantages and disadvantages ===
 The advantages and disadvantages are largely the same as those of Sagittal notation in general.
-== Syntonic-Rastmic Subchroma notation ==
+==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]].
@@ Line 732: / Line 743: @@
 #\	 raflat sharp
 #	 sharp
 </tt>
-=== Advantages and disadvantages ===
+===Advantages and disadvantages ===
 By striking a good balance between the number of accidentals and their semantic consistency, Syntonic-Rastmic Subchroma notation manages to address the weaknesses of both Ups and Downs notation and Sagittal notation, and, as it's derived from Neutral Circle-of-Fifths notation- the de facto standard foundation for notation in 24edo- it is more easily accessible to microtonal musicians at the beginner level, all while retaining Helmholtz-Ellis notation's advantage of fixing the key notation problems that have plagued 53edo itself by means of accounting for the 2.3.5.11 subgroup in general and the syntonic comma specifically.
 [[Category:Todo:expand]]