Generalized and regularized keyboards

Hello, everyone, and I'd like briefly to comment on this keyboard
discussion, which has made me take a look at some of Erv Wilson's
articles, by the way.

Especially in MMM, I should try to concentrate on practical experience
that might offer some feedback or perspective. Also, I should
acknowledge my lack of experience with generalized keyboards -- as
opposed to regularized 24-note Halberstadt pairs (two conventional
12-note keyboards at some distance apart, with the same pattern of
steps and intervals on each keyboard).

First, I shouldn't let my own lack of experience stop me from
affirming that while it might not be "indispensable" to everyone's
music making, a generalized keyboard has very obvious advantages which
I'd consider indeed essential to many of the large tuning sets used
and discussed by people like George Secor, Erv Wilson, and so forth.
The question isn't whether someone could get along without this tool,
but whether it is indeed a valuable improvement -- which it is.

Secondly, I suspect that I am able to get along reasonably well with a
regularized keyboard -- interestingly, with irregular as well as
regular tunings -- because of certain constraints or parameters which
a generalized keyboard user might well call simply limitations.

Reading a fascinating article by Bosanquet himself, and a letter by
Wilson (available at <http://www.anaphoria.com> in the Wilson
archives) suggests to me that a situation where a generalized keyboard
might be especially helpful is in dealing with systems and uses where
one seeks to combine pure or near-pure ratios of 3 and 5, for example,
using intervals derived from long chains of fifths or involving comma
distinctions.

In contrast, if I'm looking to built a texture based on ratios of 3
and 5, I'm likely to use a meantone (regular or modified); and if I'm
using a positive tuning (fifths wider than 700 cents), it likely means
that I regard larger major thirds from a chain of four fifths as
desired intervals. Thus a Halberstadt arrangement is reasonably
serviceable, at least comparatively so -- although I suspect that
George wouldn't be shy about pointing out the advantages of a
generalized keyboard for something like his 17-WT as well!

One possible hypothesis might be that the 24-note regularized keyboard
might be less impractical if the following question could be answered
yes: "Would you be happy tuning a 'usual' 12-note chain of fifths for
this system? -- 'usual' implying that the tuning might be regular or
irregular."

For my favorite 24-note systems, the answer is generally an
enthusiastic "Yes!" -- indeed, I started using some of these as
12-note tunings and then discovered all the extra intervals and
sonorities I could enjoy by adding another 12 notes at some convenient
distance from the first 12.

However, someone interested in combining ratios of 3 and 5 (not to
exclude others) in some implementation or variation on 41-EDO or
46-EDO might not be as enthusiastic as I am about major thirds at
ratios like 19:15 or 14:11 -- at least while they seek, as I do in
meantone, to produce textures which consistently use 5:4 thirds.
This could explain why a generalized keyboard would be especially
valuable in such a situation, historically a focus for Helmholtz/Ellis
and Bosanquet as well, for example, Wilson at least in some of his
correspondence -- but I don't want to imply that it wouldn't have
advantages for other situations also.

The advantage of a dual-Halberstadt solution is maybe more easy
availability of 12-note MIDI controllers than technical virtue; and it
calls for developing fluent bimanualism, or the art of playing with
one hand on two keyboards. I must admit that for fast polyphonic
passages, I tend to favor notes within a single 12-note set.

Ergonomically, the main problem I'm aware of is the vertical distance
between two manuals, required by the thickness of the keyboards and
the shelf to hold the upper one (although that is quite compact).
Moving between diatonic notes on the lower keyboard and accidentals
on the upper keyboard is the most difficult situation. For some
situations, maybe I should consider reversing the relation of the two
keybaords so that the higher one is physically lower, if this means
that more accidentals for a given piece occur on that keyboard rather
than the physically upper one.

Anyway, I have every reason to consider the generalized keyboard a
very valuable improvement, while emphasizing that other solutions may
be practical to a greater or lesser extent depending on the musical
context and also the approach to performance.

Peace and love,

Margo