Archicembalo in meantone 24: Renaissance fifthtone music (3 of 4)

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An archicembalo in 24-note meantone:
Renaissance fifthtone music on two 12-note keyboards
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(Part III of IV)

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4. Historical issues: "tunability" and chirality
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Like the larger archicembalo of Vicentino and Sambuca Lincea of
Colonna (Section 2), a 24-note archicembalo for fifthtone music raises
interesting issues regarding an "historically appropriate" or
"authentic" tuning.[25]

We might divide the tuning question into two basic parts. First,
should we use 1/4-comma meantone with its subtly unequal fifthtones,
or 31-tet? Here the arguments may be mostly the same for a 24-note
instrument as for the complete 31-note or larger keyboards of
Vicentino and Colonna.

Secondly, if we choose a 1/4-comma tuning, the question of chirality
(Section 3) arises: which enharmonic notes should be tuned as flats or
sharps? Here a 24-note tuning may invite a simpler answer than a
31-note tuning, where arbitrary convention, the nature of the music to
be played, and intriguing questions of intonational aesthetics may all
play a part.[26]

As to the first or general question, the beauty of 1/4-comma tuning is
that it happily approximates a division by equal fifthtones[27] while
fitting the advice of both Vicentino and Colonna that the usual notes
on their instruments are tuned "as on ordinary keyboards," serving as
a foundation for the rest of the tuning.

Vicentino tells us that the 12 notes of his first two ranks (see
Section 2) are tuned as on usual instruments, with the fifths
"somewhat blunted, as the good masters do it."[28] Colonna similarly
states that his ranks of basic diatonic notes, sharps (+2/5-tone), and
flats (+3/5-tone) are tuned as on "common chromatic harpsichords"
(_Cembali Chromatici communi_) of 19 notes, the remaining enharmonic
ranks then being accorded with these.[29] This latter remark may
reflect the popularity of such 19-note keyboards among Neapolitan
musicians around 1600.

As a well-documented 16th-century temperament quite practical to tune
by ear, 1/4-comma meantone with its pure major thirds would seem to
fit these descriptions better than a precise 31-tet division. In 1523,
Pietro Aaron directs that at least one major third (C-E) be tuned
"sonorous and just, as blending as possible," while Zarlino (1571) and
Salinas (1577) define the 1/4-comma tuning in systematic and
mathematical terms. While Zarlino calls this "a new temperament,"
Salinas claims that he was regarded as its inventor during his
youthful stay in Rome, where he arrived in 1538.[30]

In practice, the 1/4-comma tuning approximates Vicentino's or
Colonna's model of apparently equal fifthtones much as the Earth
approximates, but does not precisely conform to, the shape of a
sphere. When carried to 31 notes, the result is a circulating
temperament of the kind described by these authors, albeit with subtle
asymmetries -- quite possibly overshadowed by those resulting from the
vagaries of the tuning process itself.[31]

If we do choose a 1/4-comma meantone, then the second question of
chirality arises. Here both the tuning process itself and the intended
repertory may influence the decision. Curiously, the use of "authentic
historical approaches" might lead to a different tuning of certain
notes on a 24-note instrument than on Vicentino's, for example.

With our 24-note instrument intended mainly for the Renaissance
fifthtone compositions of Vicentino and Bernard, or for new music in
similar styles, tuning all enharmonic notes at the flat end of the
chain is an obvious choice.

From an "historical tunability" perspective, this approach seems the
natural one because it tunes all 24 notes as a single chain of fifths
(Eb*-G#). One might say: "Simply place the first manual in a usual
Eb-G# tuning with pure major thirds, and then, starting at Eb, carry
the tuning an additional 12 fifths down on the second manual."

One could carry out the tuning of the second manual as a series of
pure major thirds: first Ab-C, Db-F, and Gb-C; then the remaining
enharmonic notes, B*(Cb)-Eb, E*(Fb)-Ab, A*(Bbb)-Db, etc.

Musically, this tuning provides usual meantone major and minor thirds
for all regularly spelled sonorities within its range; and tuning all
enharmonic notes as flats also has this advantage in the Ab-C#/Ab*-Db
or Bb-D#/Bb*-Eb ranges called for by Vicentino's fifthtone pieces.

While this flat-end tuning seems the natural one for our 24-note
archicembalo, it yields some intervals differing from those in a
1/4-comma realization of Vicentino's scheme, which generally places
enharmonic notes on the sharp end of the chain. Specifically,
proximate minor thirds will vary, as in this variety of cadential
flourish discussed in Section 1 where the outer voices stand at the
fifth while the middle voice ascends from minor to major third:

Vicentino: Eb* = D##
--------------------
G3
(386.31) (351.32) (310.26)
Eb3 -- +34.99 -- Eb*3=D## -- +41.06 -- E3
(310.26) SF (345.25) LF (386.31)
C3

24-note: Eb* = Fbb
------------------
G3
(386.31) (345.25) (310.26)
Eb3 -- +41.06 -- Eb*3=Fbb -- +34.99 -- E3
(310.26) LF (351.32) SF (386.31)
C3

In Vicentino's sharp-end tuning, the middle voice moves by a small
fifthtone followed by a large fifthtone (SF-LF), while our flat-end
tuning has the converse sequence -- and also a converse arrangement
of the slightly unequal proximate minor thirds in the second sonority.
Note that the smaller of these thirds, ~345.25 cents, is closer to
Vicentino's approximate ratio of 11:9 (~347.41 cents); the larger,
~351.32 cents, is almost identical to a pure 49:40 (~351.34 cents).

While matching Vicentino's chirality might seem ideally "authentic,"
on a 24-note instrument it would involve the unlikely procedure of two
disconnected chains of fifths: Cb(B*)-G# and D##(Eb*)-D###(E*). Tuning
along a single chain of fifths, Eb*-G#, seems far more in keeping with
16th-century procedures such as Vicentino's: natural variations may be
more authentic than absolute uniformity.

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5. Meantone ranges, retuning, and transposition
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As discussed in Section 1, our 24-note archicembalo fits the musical
requirements of 16th-century fifthtone compositions by Vicentino and
Bertrand fitting into a "dual meantone" gamut such as Eb-G#/Eb*-Ab.

Fortunately, each of Vicentino's and Bertrand's pieces fit into such a
24-note range. Possibly not quite so fortunately, different pieces use
different 24-note ranges: Eb-G#/Eb*-Ab, Ab-C#/Ab*-Db, or Bb-D#/Bb*-Eb.

This situation is closely analogous to the more usual predicament of
using a 12-note meantone keyboard to play Renaissance pieces having
different 12-note ranges (Eb-G#, Ab-C#, Bb-D#). The obvious solution
is to retune between pieces, choosing the versions of G#/Ab and Eb/D#
needed for a specific piece.

This same solution is the obvious one for our 24-note archicembalo,
with a few complications added by the factor of _two_ keyboards.
Linking our three 24-note ranges to specific pieces of Vicentino and
Bertrand may make issues more concrete.

Since Eb-G# enjoys a status as the usual 12-note range in Renaissance
theory and practice, it seems natural to regard an Eb-G#/Eb*-Ab tuning
as "standard." This tuning fits Bertrand's single known enharmonic
chanson _Ie suis tellement amoureux_ (1578), and also Vicentino's
example in his treatise of 1555 giving the opening of his madrigal
_Soav'e dolc'ardore_[32]:

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

Vicentino's first part of his madrigal _Dolce mio ben_ from the same
treatise, and also some of his four-voice examples of enharmonic
cadences, may be accommodated with an Ab-C#/Ab*-Db tuning[33]:

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

This tuning, like the standard one, invites a perfectly symmetrical
arrangement of the two keyboards. In this respect, our third tuning
presents a bit of a dilemma.

Vicentino's complete Latin secular motet _Musica prisca caput_, and
also his first part of the madrigal _Madonna, il poco dolce_, call for
a Bb-D#/Ab*-Db tuning[34]. Mapping this to another purely symmetrical
arrangement, we would have:

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

While this mapping is quite practice, it presents the curious
situation where D# appears as a "usual" note on the lower keyboard,
and Eb as an "unusual" note on the upper keyboard. If we wish to
follow the convention of treating Eb as usual and D# as unusual, as on
Vicentino's keyboard, then a slight break in symmetry is required:

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

For a harpsichord, one advantage of this arrangement is that it makes
it possible to move from Eb-G#/Eb*-Ab to Bb-D#/Bb*-Eb by retuning only
a single note per octave: changing Eb* on the upper manual to D# at
the opposite extreme of the 24-note chain of fifths. On a digital
instrument where the retuning is accomplished by tables, the choice
may be more of a matter of pure taste.

If retuning between pieces is inconvenient or impractical, then an
alternative would be to transpose where necessary into our standard
range of Eb-G#/Eb*-Ab. Pieces calling for a range of Ab-C#/Ab*-Db
could be transposed up a fifth or down a fourth, and pieces calling
for Bb-D#/Bb*-Eb likewise transposed up a fourth or down a fifth.

Most respectfully,

Margo Schulter
mschulter@value.net