Re: Microtuning hardware -- Tunings I have known

Hello, there, and here's some information about the synthesizer and
related equipment I use both for more or less standard European
historical tunings (mostly medieval Pythagorean and Renaissance/
Manneristic meantone), a very experimental historical tuning
(Vicentino), and some Xeno-Gothic and 17-tone equal temperament
(17-tet) offshoots:

-- Yamaha TX-802 synthesizer with cartridge to store custom tunings
-- Two MIDI controller keyboards (MK-4902), 4 octaves (49 notes)
-- MIDI Solutions Merger (MIDI-Merge box to merge two keyboards)

A somewhat "lower tech" and very functional as well as pleasing
adjunct is a wooden keyboard stand designed by my best friend to hold
the two keyboards in comfortable playing position. She came up with a
sliding shelf for the upper manual which permits it to be adjusted to
taste for playing, and to be moved back in order to change settings on
the lower manual (for example the choice of MIDI channel).

Having answered the basic survey question about hardware, maybe I
should at this point explain that the rest of my remarks concern the
kinds of music and tunings for which I use this system.

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1. Conventional medieval/Renaissance music and "split keys"
-----------------------------------------------------------

For conventional medieval and Renaissance music, the built-in
Pythagorean and 1/4-comma meantone tunings of the TX-802 cover the
territory very nicely for me. In a standard 12-note tuning, what I am
playing in effect is a usual two-manual organ or harpsichord, often
with contrasting registrations for the two manuals (which can add to
the contrapuntal interest).

For somewhat more experimental music, the "part-tuning" feature makes
it easy to set up what I might call "virtual split-key" tunings with
from 13 to about 16 notes per octave.

In these "split-key" tunings, I use the part-tuning feature in
conjunction with the very nice option for transposing the built-in
Pythagorean and meantone tunings to any desired position for the
"Wolf" fifth or fourth. By setting the lower manual to a meantone
tuning in Eb-G#, for example, and the upper manual to the same tuning
in F-A#, I can perform the Prologue from the _Prophetiae Sibyllarum_
of Orlando di Lasso. In effect, the two manuals provide split keys for
Eb/D# and Bb/A#, the other notes remaining in unison.

Similarly, for some early 15th-century music, I've found it very
interesting to use a Pythagorean tuning with one manual in Eb-G# and
the other in G-Bb -- permitting a choice of G#/Ab, C#/Db, and F#/Gb
to produce, for example, either a regular Pythagorean third such as
E-G# in a cadential resolution to D-A, or a smooth diminished fourth
E-Ab in a prolonged noncadential sonority.

Managing these virtual split-key arrangements may take a bit of
planned choreography at the keyboard in playing a piece, but permits
enjoying the potential of 13-16 notes per octave while getting the
benefits of an instrument with two contrasting manuals.

(Psychologically, 17 notes seems a point of transition, because all
accidentals including Bb/A# will be different on the two keyboards --
Bb representing an integral note in the medieval/Renaissance gamut, in
contrast to the other accidentals which are regarded as "devised"
additions or _musica ficta_.)

For the intonationally fastidious, one minor glitch of relying on
these built-in transpositions is that a given note (e.g. F) may vary
by one tuning unit (1/1024 octave or ~1.17 cents) in different
transpositions. Thus certain unisons or octaves between notes on the
two manuals may be off by 1.17 cents. One tuning expert has expressed
the view that even a 1-cent error can definitely change the quality of
a unison or octave, although another has commented to me that for most
timbres, it might not be a big issue. I haven't noticed anything
glaring so far when using these convenient transpositions, which might
say something about my taste (or choice or registrations).

Another Renaissance tuning I'm experimenting with is a 15-note scheme
in 5-limit just intonation based on a keyboard described by Zarlino
and discussed by Karol Berger. This is rather like the split-key
schemes I describe above, except of course for the complications of
having two flavors of D, Bb, and F# a syntonic comma (81:80, ~21.51
cents) apart, and needing to keep track of which flavor is needed for
a given sonority in a piece. For simple vocal pieces, where the
keyboard choreography is not too impractical, this tuning is (now
as then) a fascinating realization of pure ensemble intonation on a
fixed-pitch instrument.

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2. Xenharmonics, Renaissance (Vicentino) and Neo-Gothic
-------------------------------------------------------

Moving into clearly xenharmonic Renaissance territory, I use custom
tuning tables to define two varieties of 24-note meantone for
Renaissance fifthtone music of the kind composed and advocated by
Vicentino. In my "standard" 24-note archicembalo tuning, the lower
manual is in a usual Eb-G# meantone, and the upper manual has a custom
tuning a diesis of 128:125 (~41.06 cents) higher, or Eb*-Ab as I
notate this (using a * to show a note raised by a diesis).

The second tuning is the same, except that the second manual has D# in
place of Eb* -- slightly asymmetrical (Bb*-Ab plus D#), but
conveniently leaving the standard manual in a usual Eb-G#. I have
still to set up a third tuning required by one of Vicentino's pieces:
Ab-C#/Ab*-Db. Maybe writing this article will encourage me to complete
this task.

While these 24-note tunings are actually subsets of Vicentino's full
36-note archicembalo, another 24-note tuning is a modern offshoot of
Gothic music: Xeno-Gothic, with two 12-note Pythagorean tunings a
Pythagorean comma apart (531441:524288, ~23.46 cents). To set this, I
place the first manual in standard Pythagorean, Eb-G#, and the second
manual in a custom tuning identical to this but a comma higher (very
nicely approximated as 20 tuning units, or 20/1024 octave).

Just as Vicentino's archicembalo gives the usual intervals of
Renaissance music plus some intriguing "proximates" (e.g. "proximate
minor thirds" near 11:9, a diesis wider than the usual ones), so a
Xeno-Gothic archicembalo gives usual medieval Pythagorean intervals
plus "proximates" a comma wider than smaller.

As in Vicentino's "Xeno-Renaissance" system (as I might call it), so
in this "Xeno-Gothic" system, the "proximate" intervals can supplement
the usual ones in melodic progressions and in vertical sonorities.

A different kind of "Neo-Gothic" tuning I am exploring is 17-tone
equal temperament, or 17-tet, set up with custom tuning tables placing
the diatonic keys of both manuals in unison, but either mapping the
"standard" medieval/Renaissance accidentals Eb-G# to one keyboard and
the other five accidentals to the other, or mapping flats to one
keyboard and sharps to the other.

For Gothic music, 17-tet tends to sound like an exaggerated
Pythagorean -- exaggerated enough to make it a kind of xenharmonic
realization, "different" and intriguing. Timbre can definitely shade
this effect, with Yahama's built-in "PuffPipes" voice (A56), a bit
like a portative organ, having a really pleasant effect for some
14th-century styles.

This is a quick survey of "tunings I have known," and maybe will put
the hardware in a musical context.

Most respectfully,

Margo Schulter
mschulter@value.net