User:TromboneBoi9/Generalized Dual-Fifth Notation: Difference between revisions

Line 1:

'''General dual-fifth notation''' (or ''GDF'' notation) is a system of notation that is designed for use with [[dual-fifth]] temperaments, intended for use with smaller dual-fifth [[EDO|EDOs]]. It can perhaps be considered a form of [[ups and downs notation]] since it uses the same nominals, symbols, and general principles, and when used for EDOs, it often materializes as a [[subset notation]].

The main goal of GDF notation is to describe intervals closer to what they actually "are," rather than notation systems like [[antidiatonic]] which make minor or neutral seconds look like major seconds.

==Overview==

The ~~idea~~ of GDF notation is to ~~maintain some semblance of a [[Chain-of-fifths notation|chain of fifths]] as used in other approachable~~ notation systems~~. To do this, it relies instead on the~~ [[~~9/8|major second~~]]~~, since a chain of 9/8 major seconds is the same as every other step in a chain of fifths~~ (~~assuming octave equivalence). Every remaining step in between is split to accommodate the dual fifths, with~~ the ~~major fifths notated as raised fifths (^5) and~~ minor ~~fifths notated as lowered fifths (v5). This ensures that there is no~~ fifth ~~that resembles a~~ ''perfect'' ~~fifth, as dual~~-~~fifth systems do not have them~~.

The main goal of GDF notation is to describe intervals closer to what they actually "are," rather than notation systems like [[antidiatonic]] (assigning the minor fifth to the ''perfect fifth'') which switches the minor-major duality.

That is to say, GDF relies on the logic that '''the major fifth and the minor fifth make a major ninth''' (major second when octave-reduced), or that <math>3^+ \cdot 3^- = 9</math>.

GDF notation does this by maintaining some fidelity to the [[Chain-of-fifths notation|chain of fifths]] as used in other approachable notation systems. To do so, it relies instead on the [[9/8|major second]], since a chain of 9/8 major seconds is the same as every other step in a chain of fifths (assuming octave equivalence). Every remaining step in between is split to accommodate the dual fifths, with the major fifths notated as raised fifths (^5) and minor fifths notated as lowered fifths (v5). This ensures that there is no fifth that resembles a ''perfect'' fifth, as dual-fifth systems do not have them.

<!-~~- For instance, [[23edo]]~~'~~s two~~ fifths ~~are 13\23 and 14\23, and its 9/4 approximation is 27\23; <math>13+14=27</math>, so 23edo will work~~. -->

That is to say, GDF relies on the logic that '''the major fifth and the minor fifth make a major ninth''' (major second when octave-reduced), or that <math>3^+ \cdot 3^- = 9</math>. This also means, unlike antidiatonic, neither of the major seconds generated from the off-fifths are treated as perfectly ''major'':

* Two major fifths make a doubly-raised second (^^M2).

* Two minor fifths make a doubly-lowered second (vvM2).

With split fifths, a chain of fifths would look something like this:

Line 35:

Line 38:

| vG&flat; || vA&flat; || vB&flat; || vC || vD || vE || vF&sharp;

|}

===Relation to ups and downs===

When using GDF notation with EDOs (especially small EDOs), it's usually the case that the GDF notation of <math>n</math>-edo is identical to the [[subset notation]] loaned from the [[ups and downs notation]] of <math>2n</math>-edo.

That being said, it should be noted that the symbols ''^'' and ''v'' used in GDF do '''not''' have the same meaning that they do in ups and downs notation (that is, an alteration of one [[arrow|edostep]]). In GDF, these symbols indicate alterations of a ''half''-edostep; full edosteps are indicated by ''^^'' and ''vv''.

It may help to trade the ''^'' and ''v'' symbols for something else, e.g. ''/'' and ''\'' (slash and backslash), so that ''^'' and ''v'' can keep their original meaning in ups and downs while the offset chains of seconds remain visually distinct. Just remember that ''/'' + ''/'' = ''^''.

==Tables==

~~For EDOs, it's usually the case that the GDF notation of <math>n</math>-edo is identical to the subset notation taken from <math>2n</math>-edo.~~

'''Please note''' that when GDF for EDOs, the symbols ''^'' and ''v'' do not represent single [[arrow|edosteps]] as they do in [[ups and downs notation]]. Instead, they refer to ''half''-edosteps; full edosteps are represented by ''^^'' and ''vv''.

===13edo===

GDF notation of [[13edo]] is identical to [[26edo]] subset notation.

{|class="wikitable"

! Steps !! Cents !! ~~Name(s)~~

! Steps !! Cents !! Names !! Alt. Names

|-

| 0 || 0.00 || C, vC&sharp;

| 0 || 0.00 || C, vC&sharp; ^C&flat; || C, \C&sharp;, /C&flat;

|-

| 1 || 92.31 || ^C&sharp;, vD&flat;

| 1 || 92.31 || ^^C, ^C&sharp;, vD&flat;, vvD || ^C, /C&sharp;, \D&flat;, vD

|-

| 2 || 184.62 || D, ^D&flat;

| 2 || 184.62 || D, ^D&flat;, vD&sharp; || D, /D&flat;, \D&sharp;

|-

| 3 || 276.92 || ^D&sharp;, vE&flat;

| 3 || 276.92 || ^^D, ^D&sharp;, vE&flat;, vvE || ^D, /D&sharp;, \E&flat;, vE

|-

| 4 || 369.23 || E, ^E&flat;

| 4 || 369.23 || E, ^E&flat; || E, /E&flat;

|-

| 5 || 461.54 || ^E&sharp;, vF

| 5 || 461.54 || vF, ^^E, vvF&sharp; || \F, ^E, vF&sharp;

|-

| 6 || 553.85 || F&sharp;, ^F

| 6 || 553.85 || ^F, F&sharp;, vG&flat; || /F, F&sharp;, \G&flat;

|-

| 7 || 646.15 || G&flat;, vG

| 7 || 646.15 || vG, G&flat;, ^^F&sharp;, vvG&sharp; || \G, G&flat;, ^F&sharp;, vG&flat;

|-

| 8 || 738.46 || G&sharp;, ^G

| 8 || 738.46 || ^G, G&sharp;, ^^G&flat;, vvA&flat; || /G, G&sharp;, ^G&flat;, vA&flat;

|-

| 9 || 830.77 || A&flat;, vA

| 9 || 830.77 || vA, A&flat;, ^^G&sharp;, vvA&sharp; || \A, A&flat;, ^G&sharp;, vA&sharp;

|-

| 10 || 923.08 || A&sharp;, ^A

| 10 || 923.08 || ^A, A&sharp; ^^A&flat;, vvB&flat; || /A, A&sharp;, ^A&flat;, vB&flat;

|-

| 11 || 1015.38 || B&flat;, vB

| 11 || 1015.38 || vB, B&flat;, ^^A&sharp; || \B, B&flat;, ^A&sharp;

|-

| 12 || 1107.69 || ^B, vC&flat;

| 12 || 1107.69 || ^B, ^^B&flat;, vC&flat; || /B, ^B&flat;, \C&flat;

|-

| 13 || 1200.00 || C, vC&sharp;

| 13 || 1200.00 || C, vC&sharp;, ^C&flat; || C, \C&sharp;, /C&flat;

|}

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GDF notation of [[18edo]] is identical to [[36edo]] subset notation.

{|class="wikitable"

! Steps !! Cents !! ~~Name(s)~~

! Steps !! Cents !! Names !! Alt. Names

|-

| 0 || 0.00 || C

| 0 || 0.00 || C || C

|-

| 1 || 66.67 || vC&sharp;, vD&flat;

| 1 || 66.67 || vC&sharp;, vD&flat;, ^^C || \C&sharp;, \D&flat;, ^C

|-

| 2 || 133.33 || ^C&sharp;, ^D&flat;

| 2 || 133.33 || ^C&sharp;, ^D&flat;, vvD || /C&sharp;, /D&flat;, vD

|-

| 3 || 200.00 || D

| 3 || 200.00 || D || D

|-

| 4 || 266.67 || vD&sharp;, vE&flat;

| 4 || 266.67 || vD&sharp;, vE&flat;, ^^D || \D&sharp;, \E&flat;, ^D

|-

| 5 || 333.33 || ^D&sharp;, ^E&flat;

| 5 || 333.33 || ^D&sharp;, ^E&flat;, vvE || /D&sharp;, /E&flat;, vE

|-

| 6 || 400.00 || E

| 6 || 400.00 || E || E

|-

| 7 || 466.67 || vF

| 7 || 466.67 || vF, ^^E || \F, ^E

|-

| 8 || 533.33 || ^F

| 8 || 533.33 || ^F, vvF&sharp;, vvG&flat; || /F, vF&sharp;, vG&flat;

|-

| 9 || 600.00 || F&sharp;, G&flat;

| 9 || 600.00 || F&sharp;, G&flat; || F&sharp;, G&flat;

|-

| 10 || 666.67 || vG

| 10 || 666.67 || vG, ^^F&sharp;, ^^G&flat; || \G, ^F&sharp;, ^G&flat;

|-

| 11 || 733.33 || ^G

| 11 || 733.33 || ^G, vvG&sharp;, vvA&flat; || /G, vG&sharp;, vA&flat;

|-

| 12 || 800.00 || G&sharp;, A&flat;

| 12 || 800.00 || G&sharp;, A&flat; || G&sharp;, A&flat;

|-

| 13 || 866.67 || vA

| 13 || 866.67 || vA, ^^G&sharp;, ^^A&flat; || \A, ^G&sharp;, ^A&flat;

|-

| 14 || 933.33 || ^A

| 14 || 933.33 || ^A, vvA&sharp;, vvB&flat; || /A, vA&sharp;, vB&flat;

|-

| 15 || 1000.00 || A&sharp;, B&flat;

| 15 || 1000.00 || A&sharp;, B&flat; || A&sharp;, B&flat;

|-

| 16 || 1066.67 || vB

| 16 || 1066.67 || vB, ^^A&sharp;, ^^B&flat; || \B, ^A&sharp;, ^B&flat;

|-

| 17 || 1133.33 || ^B

| 17 || 1133.33 || ^B, vvC || /B, vC

|-

| 18 || 1200.00 || C

| 18 || 1200.00 || C || C

|}

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GDF notation of [[23edo]] is identical to [[46edo]] subset notation.

{|class="wikitable"

! Steps !! Cents !! ~~Name(s)~~

! Steps !! Cents !! Names !! Alt. Names

|-

| 0 || 0.00 || C

| 0 || 0.00 || C || C

|-

| 1 || 52.17 || ^^C, vD&flat;

| 1 || 52.17 || ^^C, vD&flat; || ^C, \D&flat;

|-

| 2 || 104.35 || vC&sharp;, ^D&flat;

| 2 || 104.35 || vC&sharp;, ^D&flat; || \C&sharp;, /D&flat;

|-

| 3 || 156.52 || ^C&sharp;, vvD

| 3 || 156.52 || ^C&sharp;, vvD || /C&sharp;, vD

|-

| 4 || 208.70 || D

| 4 || 208.70 || D || D

|-

| 5 || 260.87 || ^^D, vE&flat;

| 5 || 260.87 || ^^D, vE&flat; || ^D, \E&flat;

|-

| 6 || 313.04 || vD&sharp;, ^E&flat;

| 6 || 313.04 || vD&sharp;, ^E&flat; || \D&sharp;, /E&flat;

|-

| 7 || 365.22 || ^D&sharp;, vvE

| 7 || 365.22 || ^D&sharp;, vvE || /D&sharp;, vE

|-

| 8 || 417.39 || E

| 8 || 417.39 || E || E

|-

| 9 || 469.57 || ^^E, vF

| 9 || 469.57 || ^^E, vF || ^E, \F

|-

| 10 || 521.74 || ^F, vvG&flat;

| 10 || 521.74 || ^F, vvG&flat; || /F, vG&flat;

|-

| 11 || 573.91 || vvF&sharp;, G&flat;

| 11 || 573.91 || vvF&sharp;, G&flat; || vF&sharp;, G&flat;

|-

| 12 || 626.09 || F&sharp;, ^^G&flat;

| 12 || 626.09 || F&sharp;, ^^G&flat; || F&sharp;, ^G&flat;

|-

| 13 || 678.26 || ^^F&sharp;, vG

| 13 || 678.26 || ^^F&sharp;, vG || ^F&sharp;, \G

|-

| 14 || 730.43 || ^G, vvA&flat;

| 14 || 730.43 || ^G, vvA&flat; || /G, vA&flat;

|-

| 15 || 782.61 || vvG&sharp;, A&flat;

| 15 || 782.61 || vvG&sharp;, A&flat; || vG&sharp;, A&flat;

|-

| 16 || 834.78 || G&sharp;, ^^A&flat;

| 16 || 834.78 || G&sharp;, ^^A&flat; || G&sharp;, ^A&flat;

|-

| 17 || 886.96 || ^^G&sharp;, vA

| 17 || 886.96 || ^^G&sharp;, vA || ^G&sharp;, \A

|-

| 18 || 939.13 || ^A, vvB&flat;

| 18 || 939.13 || ^A, vvB&flat; || /A, vB&flat;

|-

| 19 || 991.30 || B&flat;

| 19 || 991.30 || B&flat; || B&flat;

|-

| 20 || 1043.48 || ^^B&flat;, vC&flat;

| 20 || 1043.48 || ^^B&flat;, vC&flat; || ^B&flat;, \C&flat;

|-

| 21 || 1095.65 || vB, ^C&flat;

| 21 || 1095.65 || vB, ^C&flat; || \B, /C&flat;

|-

| 22 || 1147.83 || ^B

| 22 || 1147.83 || ^B, vvC || \B, vC

|-

| 23 || 1200.00 || C

| 23 || 1200.00 || C || C

|}

@@ Line 1: / Line 1: @@
 '''General dual-fifth notation''' (or ''GDF'' notation) is a system of notation that is designed for use with [[dual-fifth]] temperaments, intended for use with smaller dual-fifth [[EDO|EDOs]]. It can perhaps be considered a form of [[ups and downs notation]] since it uses the same nominals, symbols, and general principles, and when used for EDOs, it often materializes as a [[subset notation]].
-The main goal of GDF notation is to describe intervals closer to what they actually "are," rather than notation systems like [[antidiatonic]] which make minor or neutral seconds look like major seconds.
+==Overview==
-The idea of GDF notation is to maintain some semblance of a [[Chain-of-fifths notation|chain of fifths]] as used in other approachable notation systems. To do this, it relies instead on the [[9/8|major second]], since a chain of 9/8 major seconds is the same as every other step in a chain of fifths (assuming octave equivalence). Every remaining step in between is split to accommodate the dual fifths, with the major fifths notated as raised fifths (^5) and minor fifths notated as lowered fifths (v5). This ensures that there is no fifth that resembles a ''perfect'' fifth, as dual-fifth systems do not have them.
+The main goal of GDF notation is to describe intervals closer to what they actually "are," rather than notation systems like [[antidiatonic]] (assigning the minor fifth to the ''perfect fifth'') which switches the minor-major duality.
-That is to say, GDF relies on the logic that '''the major fifth and the minor fifth make a major ninth''' (major second when octave-reduced), or that <math>3^+ \cdot 3^- = 9</math>.
+GDF notation does this by maintaining some fidelity to the [[Chain-of-fifths notation|chain of fifths]] as used in other approachable notation systems. To do so, it relies instead on the [[9/8|major second]], since a chain of 9/8 major seconds is the same as every other step in a chain of fifths (assuming octave equivalence). Every remaining step in between is split to accommodate the dual fifths, with the major fifths notated as raised fifths (^5) and minor fifths notated as lowered fifths (v5). This ensures that there is no fifth that resembles a ''perfect'' fifth, as dual-fifth systems do not have them.
-<!-- For instance, [[23edo]]'s two fifths are 13\23 and 14\23, and its 9/4 approximation is 27\23; <math>13+14=27</math>, so 23edo will work. -->
+That is to say, GDF relies on the logic that '''the major fifth and the minor fifth make a major ninth''' (major second when octave-reduced), or that <math>3^+ \cdot 3^- = 9</math>. This also means, unlike antidiatonic, neither of the major seconds generated from the off-fifths are treated as perfectly ''major'':
+* Two major fifths make a doubly-raised second (^^M2).
+* Two minor fifths make a doubly-lowered second (vvM2).
 With split fifths, a chain of fifths would look something like this:
@@ Line 35: / Line 38: @@
 | vG&flat; || vA&flat; || vB&flat; || vC || vD || vE || vF&sharp;
 |}
+===Relation to ups and downs===
+When using GDF notation with EDOs (especially small EDOs), it's usually the case that the GDF notation of <math>n</math>-edo is identical to the [[subset notation]] loaned from the [[ups and downs notation]] of <math>2n</math>-edo.
+That being said, it should be noted that the symbols ''^'' and ''v'' used in GDF do '''not''' have the same meaning that they do in ups and downs notation (that is, an alteration of one [[arrow|edostep]]). In GDF, these symbols indicate alterations of a ''half''-edostep; full edosteps are indicated by ''^^'' and ''vv''.
+It may help to trade the ''^'' and ''v'' symbols for something else, e.g. ''/'' and ''\'' (slash and backslash), so that ''^'' and ''v'' can keep their original meaning in ups and downs while the offset chains of seconds remain visually distinct. Just remember that ''/'' + ''/'' = ''^''.
 ==Tables==
-For EDOs, it's usually the case that the GDF notation of <math>n</math>-edo is identical to the subset notation taken from <math>2n</math>-edo.
-'''Please note''' that when GDF for EDOs, the symbols ''^'' and ''v'' do not represent single [[arrow|edosteps]] as they do in [[ups and downs notation]]. Instead, they refer to ''half''-edosteps; full edosteps are represented by ''^^'' and ''vv''.
 ===13edo===
 GDF notation of [[13edo]] is identical to [[26edo]] subset notation.
 {|class="wikitable"
-! Steps !! Cents !! Name(s)
+! Steps !! Cents !! Names !! Alt. Names
 |-
-| 0 || 0.00 || C, vC&sharp;
+| 0 || 0.00 || C, vC&sharp; ^C&flat; || C, \C&sharp;, /C&flat;
 |-
-| 1 || 92.31 || ^C&sharp;, vD&flat;
+| 1 || 92.31 || ^^C, ^C&sharp;, vD&flat;, vvD || ^C, /C&sharp;, \D&flat;, vD
 |-
-| 2 || 184.62 || D, ^D&flat;
+| 2 || 184.62 || D, ^D&flat;, vD&sharp; || D, /D&flat;, \D&sharp;
 |-
-| 3 || 276.92 || ^D&sharp;, vE&flat;
+| 3 || 276.92 || ^^D, ^D&sharp;, vE&flat;, vvE || ^D, /D&sharp;, \E&flat;, vE
 |-
-| 4 || 369.23 || E, ^E&flat;
+| 4 || 369.23 || E, ^E&flat; || E, /E&flat;
 |-
-| 5 || 461.54 || ^E&sharp;, vF
+| 5 || 461.54 || vF, ^^E, vvF&sharp; || \F, ^E, vF&sharp;
 |-
-| 6 || 553.85 || F&sharp;, ^F
+| 6 || 553.85 || ^F, F&sharp;, vG&flat; || /F, F&sharp;, \G&flat;
 |-
-| 7 || 646.15 || G&flat;, vG
+| 7 || 646.15 || vG, G&flat;, ^^F&sharp;, vvG&sharp; || \G, G&flat;, ^F&sharp;, vG&flat;
 |-
-| 8 || 738.46 || G&sharp;, ^G
+| 8 || 738.46 || ^G, G&sharp;, ^^G&flat;, vvA&flat; || /G, G&sharp;, ^G&flat;, vA&flat;
 |-
-| 9 || 830.77 || A&flat;, vA
+| 9 || 830.77 || vA, A&flat;, ^^G&sharp;, vvA&sharp; || \A, A&flat;, ^G&sharp;, vA&sharp;
 |-
-| 10 || 923.08 || A&sharp;, ^A
+| 10 || 923.08 || ^A, A&sharp; ^^A&flat;, vvB&flat; || /A, A&sharp;, ^A&flat;, vB&flat;
 |-
-| 11 || 1015.38 || B&flat;, vB
+| 11 || 1015.38 || vB, B&flat;, ^^A&sharp; || \B, B&flat;, ^A&sharp;
 |-
-| 12 || 1107.69 || ^B, vC&flat;
+| 12 || 1107.69 || ^B, ^^B&flat;, vC&flat; || /B, ^B&flat;, \C&flat;
 |-
-| 13 || 1200.00 || C, vC&sharp;
+| 13 || 1200.00 || C, vC&sharp;, ^C&flat; || C, \C&sharp;, /C&flat;
 |}
@@ Line 78: / Line 86: @@
 GDF notation of [[18edo]] is identical to [[36edo]] subset notation.
 {|class="wikitable"
-! Steps !! Cents !! Name(s)
+! Steps !! Cents !! Names !! Alt. Names
 |-
-| 0 || 0.00 || C
+| 0 || 0.00 || C || C
 |-
-| 1 || 66.67 || vC&sharp;, vD&flat;
+| 1 || 66.67 || vC&sharp;, vD&flat;, ^^C || \C&sharp;, \D&flat;, ^C
 |-
-| 2 || 133.33 || ^C&sharp;, ^D&flat;
+| 2 || 133.33 || ^C&sharp;, ^D&flat;, vvD || /C&sharp;, /D&flat;, vD
 |-
-| 3 || 200.00 || D
+| 3 || 200.00 || D || D
 |-
-| 4 || 266.67 || vD&sharp;, vE&flat;
+| 4 || 266.67 || vD&sharp;, vE&flat;, ^^D || \D&sharp;, \E&flat;, ^D
 |-
-| 5 || 333.33 || ^D&sharp;, ^E&flat;
+| 5 || 333.33 || ^D&sharp;, ^E&flat;, vvE || /D&sharp;, /E&flat;, vE
 |-
-| 6 || 400.00 || E
+| 6 || 400.00 || E || E
 |-
-| 7 || 466.67 || vF
+| 7 || 466.67 || vF, ^^E || \F, ^E
 |-
-| 8 || 533.33 || ^F
+| 8 || 533.33 || ^F, vvF&sharp;, vvG&flat; || /F, vF&sharp;, vG&flat;
 |-
-| 9 || 600.00 || F&sharp;, G&flat;
+| 9 || 600.00 || F&sharp;, G&flat; || F&sharp;, G&flat;
 |-
-| 10 || 666.67 || vG
+| 10 || 666.67 || vG, ^^F&sharp;, ^^G&flat; || \G, ^F&sharp;, ^G&flat;
 |-
-| 11 || 733.33 || ^G
+| 11 || 733.33 || ^G, vvG&sharp;, vvA&flat; || /G, vG&sharp;, vA&flat;
 |-
-| 12 || 800.00 || G&sharp;, A&flat;
+| 12 || 800.00 || G&sharp;, A&flat; || G&sharp;, A&flat;
 |-
-| 13 || 866.67 || vA
+| 13 || 866.67 || vA, ^^G&sharp;, ^^A&flat; || \A, ^G&sharp;, ^A&flat;
 |-
-| 14 || 933.33 || ^A
+| 14 || 933.33 || ^A, vvA&sharp;, vvB&flat; || /A, vA&sharp;, vB&flat;
 |-
-| 15 || 1000.00 || A&sharp;, B&flat;
+| 15 || 1000.00 || A&sharp;, B&flat; || A&sharp;, B&flat;
 |-
-| 16 || 1066.67 || vB
+| 16 || 1066.67 || vB, ^^A&sharp;, ^^B&flat; || \B, ^A&sharp;, ^B&flat;
 |-
-| 17 || 1133.33 || ^B
+| 17 || 1133.33 || ^B, vvC || /B, vC
 |-
-| 18 || 1200.00 || C
+| 18 || 1200.00 || C || C
 |}
@@ Line 122: / Line 130: @@
 GDF notation of [[23edo]] is identical to [[46edo]] subset notation.
 {|class="wikitable"
-! Steps !! Cents !! Name(s)
+! Steps !! Cents !! Names !! Alt. Names
 |-
-| 0 || 0.00 || C
+| 0 || 0.00 || C || C
 |-
-| 1 || 52.17 || ^^C, vD&flat;
+| 1 || 52.17 || ^^C, vD&flat; || ^C, \D&flat;
 |-
-| 2 || 104.35 || vC&sharp;, ^D&flat;
+| 2 || 104.35 || vC&sharp;, ^D&flat; || \C&sharp;, /D&flat;
 |-
-| 3 || 156.52 || ^C&sharp;, vvD
+| 3 || 156.52 || ^C&sharp;, vvD || /C&sharp;, vD
 |-
-| 4 || 208.70 || D
+| 4 || 208.70 || D || D
 |-
-| 5 || 260.87 || ^^D, vE&flat;
+| 5 || 260.87 || ^^D, vE&flat; || ^D, \E&flat;
 |-
-| 6 || 313.04 || vD&sharp;, ^E&flat;
+| 6 || 313.04 || vD&sharp;, ^E&flat; || \D&sharp;, /E&flat;
 |-
-| 7 || 365.22 || ^D&sharp;, vvE
+| 7 || 365.22 || ^D&sharp;, vvE || /D&sharp;, vE
 |-
-| 8 || 417.39 || E
+| 8 || 417.39 || E || E
 |-
-| 9 || 469.57 || ^^E, vF
+| 9 || 469.57 || ^^E, vF || ^E, \F
 |-
-| 10 || 521.74 || ^F, vvG&flat;
+| 10 || 521.74 || ^F, vvG&flat; || /F, vG&flat;
 |-
-| 11 || 573.91 || vvF&sharp;, G&flat;
+| 11 || 573.91 || vvF&sharp;, G&flat; || vF&sharp;, G&flat;
 |-
-| 12 || 626.09 || F&sharp;, ^^G&flat;
+| 12 || 626.09 || F&sharp;, ^^G&flat; || F&sharp;, ^G&flat;
 |-
-| 13 || 678.26 || ^^F&sharp;, vG
+| 13 || 678.26 || ^^F&sharp;, vG || ^F&sharp;, \G
 |-
-| 14 || 730.43 || ^G, vvA&flat;
+| 14 || 730.43 || ^G, vvA&flat; || /G, vA&flat;
 |-
-| 15 || 782.61 || vvG&sharp;, A&flat;
+| 15 || 782.61 || vvG&sharp;, A&flat; || vG&sharp;, A&flat;
 |-
-| 16 || 834.78 || G&sharp;, ^^A&flat;
+| 16 || 834.78 || G&sharp;, ^^A&flat; || G&sharp;, ^A&flat;
 |-
-| 17 || 886.96 || ^^G&sharp;, vA
+| 17 || 886.96 || ^^G&sharp;, vA || ^G&sharp;, \A
 |-
-| 18 || 939.13 || ^A, vvB&flat;
+| 18 || 939.13 || ^A, vvB&flat; || /A, vB&flat;
 |-
-| 19 || 991.30 || B&flat;
+| 19 || 991.30 || B&flat; || B&flat;
 |-
-| 20 || 1043.48 || ^^B&flat;, vC&flat;
+| 20 || 1043.48 || ^^B&flat;, vC&flat; || ^B&flat;, \C&flat;
 |-
-| 21 || 1095.65 || vB, ^C&flat;
+| 21 || 1095.65 || vB, ^C&flat; || \B, /C&flat;
 |-
-| 22 || 1147.83 || ^B
+| 22 || 1147.83 || ^B, vvC || \B, vC
 |-
-| 23 || 1200.00 || C
+| 23 || 1200.00 || C || C
 |}