Harpejji: Difference between revisions

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The Harpejji (see [https://en.wikipedia.org/wiki/Harpejji Wikipedia]) is a tapping stringed instrument which is a physically constrained to be an [[isomorphic keyboard]]. It is a successor to the StarrBoard which was created by [[John Starrett]].

The '''Harpejji''' (see [https://en.wikipedia.org/wiki/Harpejji Wikipedia]) is a tapping stringed instrument which is a physically constrained to be an [[isomorphic keyboard]]. It is a successor to the StarrBoard which was created by [[John Starrett]].

The standard layout for a Harpejji is like this, with the open strings tuned in whole tones of 12edo, so that the seventh string is an octave above the first.

Line 9:

C D E F# G# Bb c d e f# g# bb

~~However,~~ the ~~same general idea for a~~ layout ~~can also be applied to any chain~~-~~of-fifths EDO,~~ and ~~the only difference is what shape the unisons take on the fretboard. (For a rank~~-~~2 chain~~-of-~~fifths tuning which is not an EDO, there will be no unisons on different strings).~~

Note that the diatonic scale appears in two different shapes in this layout: an up-and-to-the-right shape:

For example, a 19edo Harpejji layout might look like this:

c' d'

f g a b

c d e

F G A B

C D E

and also a down-and-to-the-right shape, which is less compact:

E

F G A B

c d e

f g a b

The same general idea for a layout can also be applied to any chain-of-fifths EDO, but only one of these diatonic scale shapes will be preserved. Also, the shapes that unisons between different strings take will be different. (For a rank-2 chain-of-fifths tuning which is not an EDO, there will be no unisons on different strings at all.)

For example, a 19edo Harpejji layout (based on preserving the up-and-to-the-right shape of the diatonic scale) might look like this:

F G A B c# d# e# gb ab bb c' d'

Line 21:

Line 36:

To interpret this, keep in mind that C-D is 3 steps of 19edo, E-F is 2 steps, and # and b modify pitches by 1 step. Thus there is a consistent spacing of 3 steps between adjacent strings (columns), and adjacent frets (rows) are 2 steps apart. (In contrast to 12edo, G#-Ab is not a unison but E#-Fb is.)

As you can see, the (meantone) diatonic scale has exactly the same shape on the fretboard, and the main difference compared to the 12edo layout is that unisons are no longer a knights-move away on adjacent strings (2 up and 1 left). Instead, in 19edo the unisons are 3 up and 2 left.

As you can see, the up-and-to-the-right (meantone) diatonic scale has exactly the same shape on the fretboard, and the main difference compared to the 12edo layout is that unisons are no longer a knights-move away on adjacent strings (2 up and 1 left). Instead, in 19edo the unisons are 3 up and 2 left. This means the down-and-to-the-right shape doesn't work the same way anymore, since from E you have to skip over E# to get to F.

An alternative layout for 19edo, based on preserving the down-and-to-the-right shape of the diatonic scale, looks like this:

Eb F G A B c# d# f# gb ab bb c'

D# E# Gb Ab Bb c d e f# g# a# cb

D E F# G# A# cb db eb f g a b

Db Eb F G A B c# d# e# gb ab bb

C# D# E# Gb Ab Bb c d e f# g# a#

C D E F# G# A# cb db eb f g a

Cb Db Eb F G A B c# d# e# gb ab

While the previous 19edo layout had successive frets spaced at a distance of 2 19edo steps from each other, this layout instead has every 19edo step as its own fret. This could be a disadvantage in that the spaces between frets might become too small for the fingers in the high register.

==Neutral third generator (split fifth)==

In [[neutral third scales]], the chromatic semitone is split in half. Unfortunately there is no good way to do this while preserving the up-and-to-the-right diatonic scale shape, but it's simple with the down-and-to-the-right diatonic scale shape. Using notation where ^ = (1/2)# and v = (1/2)b, the result looks like this:

C D E F# G# A# B# cx

Cv Dv Ev F^ G^ A^ B^ c#^

Cb Db Eb F G A B c# d# e# fx

Fv Gv Av Bv c^ d^ e^ f#^

Fb Gb Ab Bb c d e f# g#

cv dv ev f^ g^

cb db eb f g

One drawback of this is the frets would be quite close together, for example in 31edo they would be only one 31edo step.

In a particular EDO, of course, there will be enharmonic equivalences, so there will be unisons between different strings. For example, 17edo is perhaps the simplest reasonable one which has a neutral third (sorry, 10edo!):

D^ F G A B dv ev f^ g^ a^ c' d'

D E Gv Av Bv c^ d^ f g a b dv'

Dv Ev F^ G^ A^ c d e gv av bv c^'

C^ D^ F G A B dv ev f^ g^ a^ c'

C D E Gv Av Bv c^ d^ f g a b

Cv Dv Ev F^ G^ A^ c d e gv av bv

Because of the particularly simple enharmonic relationships in 17edo, the up-and-to-the-right shape of the diatonic scale is restored in this one (because E^ = F).

The version of this one for 24edo happens to be exactly the same as the standard 12edo layout with a new fret in between each pair of 24edo ones.

D E F# G# Bb c d e f# g# bb

Dv Ev F^ G^ A^ B^ dv ev f^ g^ a^

Db Eb F G A B c# eb f g a

C^ D^ Fv Gv Av Bv c^ d^ e^ gv av

C D E F# Ab Bb c d e f# g#

Cv Dv Ev F^ G^ A^ cv dv ev f^ g^

An alternative layout to the above (for any neutral thirds tuning) preserves neither shape of the diatonic scale but uses a new one where E-F and B-C wrap back to the left. It has the advantage of having frets that are a neutral second apart, which is actually even wider than in the standard 12edo Harpejji:

db eb f g a b

cv dv ev f^ g^ a^

Gb Ab Bb c d e f# g#

Fv Gv Av Bv c^ d^ e^ f#^

Eb F G A B c# d# e#

Dv Ev F^ G^ A^ B^ c#^

C D E F# G# A# B#

The 24edo version of that looks like this:

A B c# eb f g a b c#'

G^ A^ B^ dv ev f^ g^ a^ b^ dv'

F# G# Bb c d e f# g# bb c' d'

Fv Gv Av Bv c^ d^ e^ gv av bv c^'

Eb F G A B c# eb f g a b

Dv Ev F^ G^ A^ B^ dv ev f^ g^ a^

C D E F# Ab Bb c d e f# g#

In this case the frets of a single string turn out to be exactly 8edo.

[[Category:Instruments]]

@@ Line 1: / Line 1: @@
-The Harpejji (see [https://en.wikipedia.org/wiki/Harpejji Wikipedia]) is a tapping stringed instrument which is a physically constrained to be an [[isomorphic keyboard]]. It is a successor to the StarrBoard which was created by [[John Starrett]].
+The '''Harpejji''' (see [https://en.wikipedia.org/wiki/Harpejji Wikipedia]) is a tapping stringed instrument which is a physically constrained to be an [[isomorphic keyboard]]. It is a successor to the StarrBoard which was created by [[John Starrett]].
 The standard layout for a Harpejji is like this, with the open strings tuned in whole tones of 12edo, so that the seventh string is an octave above the first.
@@ Line 9: / Line 9: @@
   C  D  E  F# G# Bb c  d  e  f# g# bb
-However, the same general idea for a layout can also be applied to any chain-of-fifths EDO, and the only difference is what shape the unisons take on the fretboard. (For a rank-2 chain-of-fifths tuning which is not an EDO, there will be no unisons on different strings).
+Note that the diatonic scale appears in two different shapes in this layout: an up-and-to-the-right shape:
-For example, a 19edo Harpejji layout might look like this:
+                               c' d'
+                      f  g  a  b
+                c  d  e
+       F  G  A  B
+ C  D  E
+and also a down-and-to-the-right shape, which is less compact:
+ E
+    F  G  A  B
+                c  d  e
+                         f  g  a  b
+The same general idea for a layout can also be applied to any chain-of-fifths EDO, but only one of these diatonic scale shapes will be preserved. Also, the shapes that unisons between different strings take will be different. (For a rank-2 chain-of-fifths tuning which is not an EDO, there will be no unisons on different strings at all.)
+For example, a 19edo Harpejji layout (based on preserving the up-and-to-the-right shape of the diatonic scale) might look like this:
   F  G  A  B  c# d# e# gb ab bb c' d'
@@ Line 21: / Line 36: @@
 To interpret this, keep in mind that C-D is 3 steps of 19edo, E-F is 2 steps, and # and b modify pitches by 1 step. Thus there is a consistent spacing of 3 steps between adjacent strings (columns), and adjacent frets (rows) are 2 steps apart. (In contrast to 12edo, G#-Ab is not a unison but E#-Fb is.)
-As you can see, the (meantone) diatonic scale has exactly the same shape on the fretboard, and the main difference compared to the 12edo layout is that unisons are no longer a knights-move away on adjacent strings (2 up and 1 left). Instead, in 19edo the unisons are 3 up and 2 left.
+As you can see, the up-and-to-the-right (meantone) diatonic scale has exactly the same shape on the fretboard, and the main difference compared to the 12edo layout is that unisons are no longer a knights-move away on adjacent strings (2 up and 1 left). Instead, in 19edo the unisons are 3 up and 2 left. This means the down-and-to-the-right shape doesn't work the same way anymore, since from E you have to skip over E# to get to F.
+An alternative layout for 19edo, based on preserving the down-and-to-the-right shape of the diatonic scale, looks like this:
+ Eb F  G  A  B  c# d# f# gb ab bb c'
+ D# E# Gb Ab Bb c  d  e  f# g# a# cb
+ D  E  F# G# A# cb db eb f  g  a  b
+ Db Eb F  G  A  B  c# d# e# gb ab bb
+ C# D# E# Gb Ab Bb c  d  e  f# g# a#
+ C  D  E  F# G# A# cb db eb f  g  a
+ Cb Db Eb F  G  A  B  c# d# e# gb ab
+While the previous 19edo layout had successive frets spaced at a distance of 2 19edo steps from each other, this layout instead has every 19edo step as its own fret. This could be a disadvantage in that the spaces between frets might become too small for the fingers in the high register.
+==Neutral third generator (split fifth)==
+In [[neutral third scales]], the chromatic semitone is split in half. Unfortunately there is no good way to do this while preserving the up-and-to-the-right diatonic scale shape, but it's simple with the down-and-to-the-right diatonic scale shape. Using notation where ^ = (1/2)# and v = (1/2)b, the result looks like this:
+ C  D  E  F# G# A# B# cx
+ Cv Dv Ev F^ G^ A^ B^ c#^
+ Cb Db Eb F  G  A  B  c# d# e# fx
+          Fv Gv Av Bv c^ d^ e^ f#^
+          Fb Gb Ab Bb c  d  e  f# g#
+                      cv dv ev f^ g^
+                      cb db eb f  g
+One drawback of this is the frets would be quite close together, for example in 31edo they would be only one 31edo step.
+In a particular EDO, of course, there will be enharmonic equivalences, so there will be unisons between different strings. For example, 17edo is perhaps the simplest reasonable one which has a neutral third (sorry, 10edo!):
+ D^ F  G  A  B  dv ev f^ g^ a^ c' d'
+ D  E  Gv Av Bv c^ d^ f  g  a  b  dv'
+ Dv Ev F^ G^ A^ c  d  e  gv av bv c^'
+ C^ D^ F  G  A  B  dv ev f^ g^ a^ c'
+ C  D  E  Gv Av Bv c^ d^ f  g  a  b
+ Cv Dv Ev F^ G^ A^ c  d  e  gv av bv
+Because of the particularly simple enharmonic relationships in 17edo, the up-and-to-the-right shape of the diatonic scale is restored in this one (because E^ = F).
+The version of this one for 24edo happens to be exactly the same as the standard 12edo layout with a new fret in between each pair of 24edo ones.
+ D  E  F# G# Bb c  d  e  f# g# bb
+ Dv Ev F^ G^ A^ B^ dv ev f^ g^ a^
+ Db Eb F  G  A  B  c# eb f  g  a
+ C^ D^ Fv Gv Av Bv c^ d^ e^ gv av
+ C  D  E  F# Ab Bb c  d  e  f# g#
+ Cv Dv Ev F^ G^ A^ cv dv ev f^ g^
+An alternative layout to the above (for any neutral thirds tuning) preserves neither shape of the diatonic scale but uses a new one where E-F and B-C wrap back to the left. It has the advantage of having frets that are a neutral second apart, which is actually even wider than in the standard 12edo Harpejji:
+       db eb f  g  a  b
+       cv dv ev f^ g^ a^
+ Gb Ab Bb c  d  e  f# g#
+ Fv Gv Av Bv c^ d^ e^ f#^
+ Eb F  G  A  B  c# d# e#
+ Dv Ev F^ G^ A^ B^ c#^
+ C  D  E  F# G# A# B#
+The 24edo version of that looks like this:
+ A  B  c# eb f  g  a  b  c#'
+ G^ A^ B^ dv ev f^ g^ a^ b^ dv'
+ F# G# Bb c  d  e  f# g# bb c' d'
+ Fv Gv Av Bv c^ d^ e^ gv av bv c^'
+ Eb F  G  A  B  c# eb f  g  a  b
+ Dv Ev F^ G^ A^ B^ dv ev f^ g^ a^
+ C  D  E  F# Ab Bb c  d  e  f# g#
+In this case the frets of a single string turn out to be exactly 8edo.
+[[Category:Instruments]]