Re: John Bull piece (Cb-E#) and intonation

Hello, there, and this is a response to some recent posts by Paul
Erlich and Dale C. Carr on the hexachord fantasia by John Bull. More
generally, this thread raises the issues of possible intonational
solutions for Elizabethan and Jacobean virginals music using
accidentals outside the most usual meantone range of Eb-G#.

Since shorter articles often tend to invite easier feedback, I'll try
to keep my comments here reasonably concise, with the explicit
intention of inviting lots of feedback, questions, and further
dialogue.

First of all, Paul asked whether the "Wolf fifth" G#-Eb ever gets used
in Renaissance and Manneristic music (say 1420-1640). Here I would
reply that the indicated use of such impure fifths or fourths is to my
best knowledge confined in this period to a few pieces for an
"enharmonic" keyboard such as Vicentino's archicembalo (1555) or
Colonna's Sambuca Lincea (1618) dividing the whole-tone into five
parts. While Vicentino himself generally prefers to avoid such
imperfect fifths or fourths both in theory and known practice, they do
occur in an anonymous Portuguese keyboard piece brought to our
attention here by Johnny Reinhart, and also in some examples by
Colonna.

In contrast, the use of regularly spelled fifths and other intervals
outside the most common 12-note range of Eb-G# occurs from at least
the later 14th century on (e.g. Ab-Eb). For example, the famous
_Fumeux fume_ of Solage uses a 15-note range of Gb-G# (although this
is not a keyboard piece), and in the early 15th century Prosdocimus of
Beldemandis and Ugolino of Orvieto endorse a 17-note range of Gb-A#.

Here it should be emphasized that while Eb-G# is indeed the most usual
range in medieval and Renaissance compositions, theorists such as
Ramos (1482) and Schlick (1511) actually prefer Ab to G# in a 12-note
tuning.

Ramos thus prefers Ab-C# for a 12-note keyboard, although he adds that
some musicians like to support both sides of the G#/Ab question by
adding a split key providing both accidentals; this happens in
practice on the Lucca organ of the 1480's with Ab/G# and Eb/D#.

Schlick, as I mentioned in an earlier post, prefers a kind of 12-note
kludge in which a single lever provides a reasonably tolerable Ab or a
marginally acceptable G# for use in quick running passages.

Pieces calling for intervals outside the most common 12-note meantone
range Eb-G# might be placed in three general categories:

(1) Pieces fitting within a 12-note chain of fifths
other than Eb-G#: e.g. Ab-C# or Bb-D#. For such
pieces, retuning an accidental or two on a
12-note meantone instrument should solve the
problem.

(2) Pieces calling for around 13-15 notes per
octave, e.g. using both Ab/G#, Eb/D#, or
Bb/A#. Here an instrument with two or
three split keys can solve the problem;
and an approximation of well-temperament
such as Schlick's might also be a possible
solution in some cases.

(3) Pieces calling for more extended keyboards,
for example a "chromatic harpsichord" with
19 notes or an archicembalso with 31 notes --
or, possibly, some thorough well-temperament
scheme.

Of course, these are rough and very general categories, and pieces may
have some interesting nuances.

First of all, Dale's remarks may reflect a view also expressed in some
modern editions of virginals music that the use of notes outside a usual
meantone range may suggest some kind of well-temperament. I certainly
wouldn't venture to exclude this possibility, although Mark Lindley, for
example, concludes that a keyboard of more than 12 notes is the more
probable and preferable solution.

One possible piece of evidence is provided by Thomas Morley (1597),
who in a discussion of the diatonic, chromatic, and enharmonic genera
notes that on the virginals G# could not serve as the equivalent of
Ab, since the former note would be more than 1/8-tone lower than the
latter. He mentions a kind of virginals called "chromatica," which are
actually "half enharmonica" -- that is, likely, which have an
enharmonic diesis between such alternative accidentals as G#/Ab or
Eb/D#. Such a passage suggests to me that such instruments might have
been known in England as well as on the Continent of Europe.

In the case of Bull's piece, I thank Dale for his very important
correction to my remark about the piece using "five flats and five
sharps." In fact, as Dale points out, it uses Cb as well as E#.

If I am correct in reading the overall range as Cb-E#, then two kinds
of solutions involving an extended keyboard in 19-note meantone are
possible. Quite seriously, I would warn that I cannot guarantee that
in reading a transcription I might not have overlooked an odd
accidental somewhere, so I welcome corrections on this point.

On a 19-note keyboard tuned in a temperament at or near 1/4-comma
(pure major thirds), one could simply alter the usual range of Gb-B#
by retuning the B# key up a diesis (128:125 or ~41.06 cents in this
temperament) to Cb. This is the same kind of solution as retuning a
12-note instrument from Eb-G# to Ab-C# or Bb-D# if a piece requires
it.

On a 19-tet keyboard like that described by Costeley (1570), there
would be no problem, because in this tuning B#=Cb (and likewise
E#=Fb). However, Lindley for example suggests that English music of
this era may lean to a temperament of somewhat _less_ than 1/4-comma,
say about 1/5-comma, which produces a "sprightly" effect with some
virginals music -- as opposed to a full 1/3-comma.

On a 31-note keyboard such as that of Vicentino or Colonna, of course,
Cb would be included, so again there would be no problem.

Curiously, Lindley's hypothesis of an English penchant for
temperaments of around 1/5-comma raises the possibility of a 12-note
compromise scheme such as Schlick's. Possibly Dowland's scheme of
well-temperament for a lute might be relevant, although two cautions
could be in line.

First, Vincenzo Galilei draws a distinction between the harpsichord
and lute which could be relevant for well-tempered schemes as well as
12-tet: he finds that 12-tet, although fine for the lute and ideally
symmetrical, is less "supportable" on a harpsichord with its different
string materials and plucking action. In modern terms, the fifth
partial is more prominent on an instrument such as harpsichord (or
organ). Thus a scheme such as 12-tet, or a well-temperament with
prominent thirds near Pythagorean, might be routine for a lute (where
12-tet is the standard tuning by around 1545) but questionable for
keyboard instruments.

Secondly, Schlick's scheme is designed to permit a marginal use of G#
in ornamental cadential passages; Lindley suggests an interpretation
of this scheme in which Ab-C is comparable to 12-tet and E-G# to
Pythagorean. Schlick's comments suggest that Pythagorean or
near-Pythagorean thirds were not regarded as very satisfactory for
sustained sonorities, although the judgment of Werckmeister's era
might be more tolerant.

A final note on meantone tunings: Bull's piece may serve as an
illustration of how retuning an odd accidental can solve the problem
of making a composition fit on a _relatively_ "small" keyboard. Thus
while the piece seems outside the usual 19-note Neapolitan "chromatic
harpsichord" range of Gb-B#, retuning B# to Cb permits things to "fit"
nicely.

Vicentino's known examples in the enharmonic genus (with fifthtone
intervals) may also illustrate this point. While Vicentino's
archicembalo has 31 notes, I was pleased to find any one of his
examples can fit on a keyboard with "only" 24 notes per octave, very
convenient when using two regular 12-note synthesizer keyboards.

How one sorts out all these possibilities may be in part a matter of
viewpoint. Thus modern writers who favor 12-tet or some unequal
12-note well-temperament may take virginals music as a step in this
direction; those who favor meantone tunings of more than 12 notes per
octave may prefer a solution of this kind. Morley at least suggests
that "chromatic" virginals like the 19-note harpsichords of Naples
were known to English readers.

While Bull's piece is an especially adventurous one, it might be
interesting to see how many virginals pieces require both Ab/G# or
Eb/D#, and how many using notes outside Eb-G# might fit within an
alternative 12-note tuning (e.g. Ab-C# or Bb-D#). Such an
investigation, while it might not point to a definitive answer, might
help us in better assessing the intonation question.

Most respectfully,

Margo Schulter
mschulter@value.net