Yahoo Tuning Groups Ultimate Backup tuning Re: Modality, Tonality, Transpositions, and Tunings (1 of 2)

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Modality, Tonality, Transpositions, and Tunings
Gorzanis (1567), Cima (1606), and Bach (1722)
Part I of II
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Hello, everyone, and my special thanks to Bill Alves for raising a
question with some fascinating implications for the study of how
tunings and the musical styles they realize may interact. Therefore I
very warmly dedicate what follows to this scholar and composer.

The question is basically this: why is it that while Bach writes
keyboard pieces in C# major in his _Well-Tempered Clavier_ of 1722
(WTC for short), no one was writing such pieces a century earlier?

The obvious answer, as Bill Alves notes, is that while one certainly
could have played such pieces on an appropriately retuned meantone
keyboard in 1622, no one kept keyboards in such a tuning.

Interestingly, however, the composer and organist Giovanni Paolo Cima
(c. 1570-?, fl. 1622) in his _Partitio de Ricercari & Canzoni Alla
Francese_ (1606), does include a brief keyboard piece given first in a
usual D Dorian, and then with the final transposed to each of the
other 11 steps of an ascending scale, with instructions before each
example for retuning the necessary notes.[1]

Thus in the early 17th century, at least one keyboard composer did
write in C# Dorian. However, such pieces involving the transposition
of usual progressions to remote steps of a 12-note chromatic scale
seem the exception rather than the rule in 1606 or 1622, as opposed to
Bach's epoch a century later.

Here I would suggest that in approaching the musical question raised
by Bill Alves about pieces written in "C# major," we focus not only on
the matter of a transposition to C#, but on the _major_ part of the
question: the distinction between the fluid and flexible modality of
the late 16th and early 17th centuries and the major/minor tonality of
Bach's era.

For convenience, borrowing a useful term proposed by recent authors, I
use the term Manneristic Era for the period of around 1540-1640, or
roughly Rore-Monteverdi.[2] This era, in my view, is synonymous with
the practice of late tertian modality, with many chromatic and
sometimes enharmonic adornments.

From an intonational viewpoint, this period includes the 19-note and
31-note circulating keyboards of Vicentino (1555), Costeley (1570),
and Colonna (1618), as well as the 19-note _Cembali chromatici_ or
chromatic harpsichords popular in Neapolitan circles around 1600.[3]

Given this wealth of adventurous intonations and compositions, one
might ask: "Why is there no modal equivalent of Bach's WTC from the
Manneristic Era?"

---------------------------------------------------------
1. The Equally-Tempered Lute: The "48" of Gorzanis (1567)
---------------------------------------------------------

Interestingly, there _is_ such an equivalent -- but for lute rather
than keyboard. By 1567, Giacomo Gorzanis (c. 1530-c.1575-1579) had
composed a collection of 48 lute dances: each step of the 12-note
chromatic scale serves as a final for four dances. Among each of these
sets of four dances, there is an interesting contrast: two are in
modes belonging to Zarlino's family with a major third above the final
(Lydian, Mixolydian, Ionian), and two in modes belonging to his family
with a minor third above the final (Dorian, Phrygian, Aeolian).[4]

For this lute collection, unlike Cima's demonstration of keyboard
transposition about 40 years later, no retuning is required -- because
by around 1545, the standard lute tuning had evidently become 12-tone
equal temperament (12-tet), in which all semitones are equal. Unlike
Bach's WTC, very likely to have been played in 1722 on a clavier in
some unequal well-temperament, the 48-piece cycle of Gorzanis in 1567
is indeed a very practical celebration of 12-tet.

The adoption of 12-tet for the lute by the mid-16th century can be
seen as a union of fretting symmetry and Sethareanism.[5] From the
viewpoint of a player realizing a polyphonic composition or
improvisation, having equal semitones much simplified the problems of
fretting across strings. From a Setharean perspective, the timbre of
the lute strings (as opposed to those of the harpsichord) "softened"
the wide major thirds which resulted from the metrics of a tuning
dividing the octave into 12 equal semitones.

While the theories of William Sethares concerning timbre and
consonance were still some four centuries in the future, Vincenzo
Galilei in his _Dialogue on Ancient and Modern Music_ (1581) and
_Fronimo_ (1584) articulated both factors favoring 12-tet: equal
semitones are extremely convenient for the lutenist, while the strings
soften the effect of the resulting thirds.[6]

Given a closed and freely transposible system of 12 notes, the
Gorzanis collection of 1567 was one logical development -- just as
Bach's collection was a celebration of the transpositions made
possible by the well-temperaments of Werckmeister and his colleagues.

Thus a lutenist of the Manneristic Era enjoyed the flexibility of a
system of 12 modes each freely transposible to 12 steps.

For a 12-note keyboard, however, as Cima's examples demonstrate, such
free transpositions would require extensive retuning -- a situation
unlike that of the world of Werckmeister and Bach. What might be the
reasons behind this difference?

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2. The domesticated Wolves that didn't bark
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In surveying the keyboard tunings of the Manneristic Era, we note that
there seemed little interest in circulating tunings with _12_ notes
per octave.

Circulating tunings indeed there were, but in 19 notes (Costeley) or
in 31 (Vicentino, Colonna). These tunings attained closure (or virtual
closure, if the 31-note schemes are realized in 1/4-comma meantone) by
expansion of the musical universe beyond the usual 12 notes. In
addition to making possible transpositions of the 12 modes to any of
the 19 or 31 steps, these schemes open new universes of expressive
resources: the enharmonic fifthtones of Vicentino and Colonna, or the
thirdtones of Costeley.

Other and more common arrangements, while leaving the tuning open,
permitted many extraordinary chromatic effects and transpositions of
the kind practiced in the madrigals of Gesualdo. The chromatic
harpsichords popular in Naples around 1600 offered a 19-note range of
Gb-B#, accommodating all of this Prince's madrigals, with the
exception of one occurrence of Cb. Less ambitious instruments with a
few split keys or _subsemitonia_ -- e.g. G#/Ab, Eb/D#, and Bb/A# --
would permit the performance of such experimental music as Lasso's
_Prophetiae Sibyllarum_.

What these different keyboard instruments and tuning systems share is
the use of more than 12 notes in meantone, a temperament optimizing
the vertical thirds and sixths which serve as the prime concords in
this music.

The approach of expanding a usual 12-note meantone tuning opens the
way to new transpositions and expressive possibilities while retaining
the uniformly smooth and blending qualities of thirds and sixths
across (or around) the gamut. True, Costeley's 19-tet tuning (almost
identical to 1/3-comma with pure minor thirds) makes some notable
compromises in order to achieve closure in only 19 notes; but still,
it keeps a rather high level of tertian euphony.

By comparison, the development of a circulating keyboard tuning with
only 12 notes involves, in a tertian style like that of the
Manneristic period, serious compromises in the intonation of thirds
and sixths. The laws of mathematics demand that the average size of
major thirds (and diminished fourths) in such a scheme must be 400
cents, or about 13.69 cents larger than a pure 5:4 (~386.31 cents).

To have adopted such a scheme for the harpsichord, in contrast to the
lute with its softening Setharean qualities, would have been to
entertain a barking of domesticated Wolves -- intervals which,
although not as dramatically far from 5:4 as a meantone diminished
fourth (32:25 or ~427.37 cents in 1/4-comma), would have very tangibly
deviated from the sonorous meantone ideal.

We might therefore say that a 12-note well-temperament for keyboard
represents, to borrow a phrase of Sherlock Holmes, "the domesticated
Wolves that didn't bark."

In noting this intonational clue, we should not neglect the various
approaches to remote transpositions which were practiced by composers
and discussed by theorists. These approaches illustrate different
solutions either repositioning or expanding the chain of optimized
meantone sonority rather than compromising it.

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2.1. Cima's 12 transpositions
-----------------------------

In showing how a 12-note meantone keyboard can be retuned to transpose
a piece in the Dorian mode on D to each of the other 11 steps of a
chromatic scale, Cima has in mind "the convenience of singers in their
_concerti_."[7] While earlier authors such as Zarlino and Morley had
mentioned an organist's need at times to transpose in order to
accommodate singers, Cima seeks to generalize the practice to "any
tone and interval of our Instrument."[8]

Interestingly, in notating the transposed versions, Cima does not
follow the usual accidental spellings, but uses unchanged the
spellings of the black keys in the standard Eb-G# tuning. Thus his
spelling for the notes of the Dorian mode with a final of C# is as
follows (here I use C4 for middle C, with higher numbers showing
higher octaves)[9]:

C#4 Eb4 E4 F#4 G#4 B[b]4 B4 C#5

This notation identifies the 12 keys of the instrument by fixed names,
however they are retuned for a given transposition. In the case of
this C# transposition, the retuning instructions are as follows, a
"diesis" here meaning simply a sharp:

"Tune f fa ut a major third higher than the diesis of
c sol fa ut [C# -- i.e., C#-E#]. b fa b mi b molle
[Bb] at a major third with the diesis of f fa ut
[F# -- i.e. F#-A#]. c sol fa ut at a major third
with the diesis of g sol re ut [G# -- i.e. G#-B#].
e la mi b molle [Eb] at a major third with b fa b mi
quadro [B -- i.e. B-D#]."[10]

In other words, to provide the regular notes of C# Dorian plus some
routine accidental inflections, the three standard sharps of the Eb-G#
tuning must be supplemented by four others supplied by this retuning.
Using conventional notation, the basic scale is thus:

C#4 D#4 E4 F#4 G#4 A#4 B4 C#5

In addition to these regular notes of the mode, we also need B# for
subsemitonal approaches at cadences to the final C#, and E# for a
concordant and conclusive major third (or tenth) above the final in
the closing sonority C#4-G#4-C#5-E#5. Here Cima notates the highest
note as F5, and indeed it is played by pressing a retuned F key.

Cima remarks that such retunings map the instrument so that "no one
but you will know how to play it," and his notation based on fixed
names for the instrument's keys regardless of the relocation of major
and minor semitones may reinforce this impression.[11]

As the composer notes, his method is designed to solve the problem of
transposing for singers on a 12-note instrument, rather than possibly
combining arbitrary transpositions in a single piece. In 1606,
however, there were instruments available which could play Cima's
complete set of transpositions without any need for retuning.

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2.2. Gesualdo, Doni, and the chromatic harpsichord
--------------------------------------------------

While Gesualdo's madrigals are of course intended primarily for
voices freed from the constraints of any fixed intonation, one
fascinating passage analyzed by the early 17th-century theorist
Giovanni Battista Doni as an instance of modal transposition
illustrates the kind of music which the Neapolitan chromatic
harpsichord could negotiate with its Gb-B# compass.

In his landmark study of Gesualdo, Glenn Watkins notes this passage
from the madrigal _Merce` grido piangendo_ (Book V, 1611). At the
words _Morro`, morro` dunque tacendo_, the voices move through a
series of sonorities beginning with

A#4 C#4
F#4 G#4
C#4 E#4
F#3 C#4

Doni analyzes this passage as representing, in Watkins's words, "a
transposition from C Lydian to C# Lydian" -- the Lydian mode, in
Doni's neo-Classic naming scheme, meaning the C mode, or Ionian in the
usual system.[12]

Such a passage could be played without problem on a Neapolitan
chromatic harpsichord with its 19-note compass in 1/4-comma meantone,
as well as on the circulating 31-note keyboards of Vicentino and
Colonna, or the 19-tet keyboard of Costeley.

---------------------------------------
2.3. Colonna's 31-note circumnavigation
---------------------------------------

While I am not aware of any cycle of pieces from the Manneristic Era
with finals on all 31 steps of Vicentino's archicembalo or Colonna's
Sambuca Lincea, the latter composer did include in his treatise of
1618 an "example of circulation" demonstrating the free transpositions
available on such an instrument.

Starting and concluding with a sonority on C -- thus making the mode
in effect Ionian -- Colonna's piece moves through cadences in a chain
of fifths down or fourths up visiting each of the 31 steps.[13]

For Colonna, such "circulation" was only one aspect of the instrument
and its tuning system, with counterpoint after the ancient Greek
genera and expressive fifthtone passages as other main attractions.

However, it is interesting that the first known European keyboard
piece to illustrate a circulating temperament should (to my best
knowledge) be based on a circumnavigation not in 12 fifths, but in 31.

(To be continued)

Most respectfully,

Margo Schulter
mschulter@value.net

Re: Modality, Tonality, Transpositions, and Tunings (1 of 2)

🔗M. Schulter <mschulter@xxxxx.xxxx>

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