Re: TD 656: New keyboard technologies and tuning arrays

Hello, there, and in Tuning Digest 656, Arthur W. Green wrote:

> While, I will try not step into this realm of unattractive cynicism
> for now, it is clear to me that whether or not Mr. Duringer's
> invention enables more sophisticated solo performance may be
> negligible at this time. The public will probably never view this
> invention as anything more than an oddity, as it is an unwaivering
> belief at the moment by the public that the synthesizer does not
> require the same kind of skill, prowess and stellar musicianship
> that a "real instrument played by a real musician does". Until this
> changes, I am not sure what can be said, since it seems to me the
> "problem" with electronic instruments isn't the instruments
> themselves.

Here I'm tempted to reply that in a medieval or Renaissance European
perspective, all instruments other than the human voice (the ideal)
are "artificial instruments" of different kinds.

In the 16th century, polyphonic instruments such as keyboards are also
known as "perfect instruments" -- that is, instruments capable in
themselves of supplying a "perfect" (or complete) harmony of three or
more voices and intervals at the same time.

Interestingly, in 1565, Tomas de Santa Maria's treatise on the art of
composition or improvisation for such instruments was written for
"keyboards, vihuela, harp, and other instruments capable of playing
three, four, or more voices."

From this perspective, a polyphonic electronic synthesizer is simply
another form of "perfect instrument." I tend to consider it a variant
on an organ or harpsichord.

Generally, playing medieval and Renaissance music on such an
instrument calls for the same kinds of musical decisions as using an
acoustical organ or harpsichord. For example, I ask myself, "Does this
sixth want to be made major before an octave -- and, if so, should I
use Eb or C#?" Whether one is playing on a period instrument or a
microtunable synthesizer, the answer might be different from
performance to performance, and depends on the performer.

This is also true for a more specialized question of the kind
especially appropriate for this Tuning List: "For this early
15th-century piece, should I play this interval in a 15-note
Pythagorean tuning as A-C# or A-Db?" While Ugolino of Orvieto tells us
that an "intelligent organist" can use a 17-note keyboard to realize
cadences more aptly, how one would use such a keyboard in the
stylistic ambience of this epoch remains an open question. It's an
area for imagination and the artist's taste.

What microtunable synthesizer technology does is to provide a more
accessible basis for such artistic judgment.

[On tunings with multiple manuals or "ranks" of keys]

> It would be nice perhaps to be able to figure out some "reliable"
> way to implement it in respect to each tuning by rank in respect to
> an adjacent ranks' tunings, rather then merely taking potshots in
> the manual mapping of the tuning of each rank in the synthesizer or
> the controller instrument. Perhaps, then it would seem so much less
> arbitrary in nature.

At the risk of being labelled a "7+5 chauvinist," I might suggest that
the topic of such keyboard designs also may have it's "x/y"
parameters. In the y-dimension, we have "generalizability," the idea
that each keyboard has the same intervals in the same arrangement.

In the x-dimension, we have "familiarity" -- or, more specifically,
familiarity for people used to a 12-note keyboard, and more
particularly yet one in the 7+5 arrangement which apparently came into
vogue sometime around the early to middle 14th century.

A "Xeno-Gothic" 24-note archicembalo with two identical Pythagorean
keyboards a Pythagorean comma apart, and likewise a 24-note meantone
archicembalo with two identical keyboards in 1/4-comma meantone a
diesis apart (128:125, or more generically a "fifthtone"), maximize
both advantages. Each keyboard in itself is ideally familiar --
especially to those of us used to Pythagorean or meantone tunings in
something like Eb-G# -- and the relationship between the two keyboards
is consistent and easy to grasp (at least for me).

Thus if we want both generalizability (symmetry between keyboards) and
familiarity (a familiar layout for each keyboard), then a "12 x 2"
array or 24 notes in all would seem an attractive choice.

From some people, of course, circularity is an important consideration
calling for larger arrays of notes: 53 for Pythagorean, or 31 for
1/4-comma meantone (real mathematical purists might insist on 31-tet
or 53-tet, evening out some variations in more remote intervals which
make a simple Pythagorean 53 or 1/4-comma meantone 31 actually a kind
of subtly unequal "well-temperament").

For the meantone situation, both historical precedent and certain
recent reports on this Tuning List about patent proposals lead me to
suspect that two 19-note keyboards might be a logical choice.

Of course, there would be two obvious applications for two such
keyboards tuned in unison: either a 19-tet system of the kind proposed
by Guillaume Costeley in 1570 (and endorsed in the 20th century by
such theorists as Joseph Yasser), or a 19-note set of 1/4-comma
meantone (or 31-tet if you prefer).

However, we could additionally use these keyboards to implement a
31-note meantone tuning. For a circulating 31-note meantone with
completely generalized keyboards (and a bit of redundancy), we can use
the 19 notes of the first manual plus 12 of the second, with the
others replicating some notes on the first manual, but maintaining the
consistent layout:

Db* Eb* Gb* Ab* Bb*
Db Eb F Gb Ab Bb C
C* D* E* F* G* A* B* C*
--------------------------------------------------------------------
Db Eb E# Gb Ab Bb B#
C# D# F# G# A#
C D E F G A B C

Note that in this tuning, both keyboards have an identical pattern:
major and minor semitones (about 3/5-tone and 2/5-tone respectively in
meantone 31) appear in the same places on either keyboard, and
corresponding notes on the two keyboards are always a diesis or
fifthtone apart.

Here I envision split keys on each keyboard for dividing the
whole-tones, e.g. C#/Db, with the front portion of the key giving C#
and the back Db (or whatever the user chooses to program, of course),
and a single small key between E and F or B and C.

> With the flexibility of MIDI and modern synthesizers, and of course
> the assignment of X/Y 'matrices' on the instrument itself, it seems
> to me that any sort of scheme can be left up the "performer". I
> rather like this idea, despite its lack of any sort available
> standard that I can recall.

This is a very important point, and one of the advantages of a
synthesizer: the hardware can permit many types of "software"
settings, with the performer free to choose between them.

> I will definitely agree that it is certainly not the first time this
> concept has been seen in practice. But, I do think with the level of
> technology we have today with electronic instruments, perhaps it
> might be wise to try this concept yet again, as I think it might be
> more promising this time around.

Certainly it should be more easily accessible. Now, as then,
overcoming psychological as well as technical barriers may be
important. We are told that many keyboardists of the late 16th century
were "frightened" by the multitude of keys on Vicentino's instrument,
and also can read the views of a theorist such as Vincenzo Galilei who
argued that intervals such as dieses or fifthtones were
"ill-proportioned" to the nature of the human ear!

One minor but not insignificant point might be the ergonomics of a
keyboard array. Using two 12-note controllers, I find that my main
problem can be in moving quickly from one manual to the other,
especially when using an organ-like sound and striving for legato. The
keyboards have to be at least around 3" apart vertically, a bit more
than the depth of each keyboard, and this is a bit of a "jump" for my
hands. I use a shelf permitting the upper manual to slide forward so
that it overlaps the lower one, a partial solution, but hardly an
ideal or comprehensive one.

Maybe a design deliberately combining two 12-note or 19-note keyboards
into a single package could emphasize making it easy to shift between
the keyboards, and also to play notes on different keyboards with the
fingers of one hand (something which a 16th-century observer remarks
is often called for on Vicentino's instrument).

Most appreciatively,

Margo Schulter
mschulter@value.net