Three-octave meantone keyboard layout

Here's a useful keyboard layout that uses a standard 61-note keyboard. It
can be used for meantone scales or other kinds of scales with up to 24
notes per octave. The fingering is the same in each octave, although only
three of the black notes are available in all three octaves.

Place the naturals and five flats (12 notes per octave) on the white keys.
Then use the black keys for sharps and double sharps. Here's what an
"ideal" octave would look like, although on a real keyboard, 3-4 of the
black keys are missing in each octave.

C# Cx D# Dx E# F# Fx G# Gx A# Ax B#
C Db D Eb E F Gb G Ab A Bb B C

Note that C#, F#, and G# are available in all three octaves. B# is only
available in the lower octave, Fx in the middle octave, and the others only
in two of the three octaves. Of course, you can start the scale on any
pitch and transpose the whole scale up or down if you need more sharps or
more flats for a particular piece. You can also put different combinations
of sharps and flats on the white keys, but this arrangement happens to work
out well and is probably easier to remember.

I'm sure someone must have thought of this before, since it seems so
obvious in hindsight, but I don't remember seeing it.

I'm also considering a similar layout for 15-note scales, but the obvious
choice (putting Blackwood's decatonic scale on the white keys) leaves more
gaps in the scale than necessary.

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Herman Miller wrote:

> Here's a useful keyboard layout that uses a standard 61-note keyboard.
> It
> can be used for meantone scales or other kinds of scales with up to 24
> notes per octave. The fingering is the same in each octave, although
> only
> three of the black notes are available in all three octaves.
>
> Place the naturals and five flats (12 notes per octave) on the white
> keys.
> Then use the black keys for sharps and double sharps.

So this means 21 notes to the octave?

> I'm sure someone must have thought of this before, since it seems so
> obvious in hindsight, but I don't remember seeing it.

Well, I thought of the thing here a while back:

http://x31eq.com/schv12.htm

which is a similar idea, but centered on the black notes, and for schismic
tuning. It's even more obvious, but I have yet to hear of any previous
discovery. Although there are also logical mappings for equal
temperaments out there.

Later on, I thought of tuning the black notes to 12-equal and having the
white notes as either quarter or sixth tones. In fact, I got as far as
tuning this up, but haven't done much with it.

One advantage of these mappings is that they can each be programmed as a
12 note non-octave scale. What's the smallest interval over which your
scale repeats?

Graham

On Thu, 1 Jun 2000 23:23 +0100 (BST), graham@microtonal.co.uk wrote:

>Herman Miller wrote:
>
>> Place the naturals and five flats (12 notes per octave) on the white
>> keys.
>> Then use the black keys for sharps and double sharps.
>
>So this means 21 notes to the octave?

Only the lower octave has 21 notes; the other two have 20. The exact
distribution works out like this:

x x x x x x x x x / x x x x x x x x | x x x x x x x x
o o o o o o o o o o o o / o o o o o o o o o o o o | o o o o o o o o o o o o

Cx Dx Gx Ax Dx Fx Ax Cx Gx
C# E#F# G# B# C# D# F# G# A# C# D# E#F# G# A#
C D E F G A B C D E F G A B C D E F G A B
Db Eb Gb Ab Bb Db Eb Gb Ab Bb Db Eb Gb Ab Bb

>One advantage of these mappings is that they can each be programmed as a
>12 note non-octave scale. What's the smallest interval over which your
>scale repeats?

12 notes, which conveniently is a perfect fifth. (Note the big gap between
D and Eb in the lower octave.) For the specific case of 31-TET, it might be
possible to find a scale mapping that repeats at the neutral third (half a
perfect fifth) or the diminished third (1/3 of a perfect fifth), in cases
where that might be useful

Of course, I didn't notice this symmetry until I'd already programmed in
the scale the hard way, one note at a time on the DX7II control panel.
--
see my music page ---> ---<http://www.io.com/~hmiller/music/music.html>--
h i l r i . o "If all Printers were determin'd not to print any
m l e @ o c m thing till they were sure it would offend no body,
(Herman Miller) there would be very little printed." -Ben Franklin