Gesualdo

I have noticed many music history books mentions Don Carlo Gesualdo using"quarter tones",as they are usually called.Were these perhaps notated as enharmonic differences(Eb-D#)etc,suggesting 19tet as a reference?I have heard only one choral performance of his music on record which had a microtonal progression in the melody;the rest of the performance sounded very 12tet.

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MATS �LJARE
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Hi Mats.

>I have noticed many music history books mentions Don Carlo Gesualdo
>using"quarter tones",as they are usually called.Were these perhaps notated
>as enharmonic differences(Eb-D#)etc,

Yes.

>suggesting 19tet as a reference?

There seems to be no reason to suppose 19-tET -- our best guess as to what
meantone Gesualdo intended would probably be 1/4-comma meantone. In this
case, the enharmonic difference would be the diesis of 41 cents.

Paul!
What makes you think these enharmonic differences(Eb-D#) were to
sound on different notes and why do you think he would use meantone for
a capella choral music?

"Paul H. Erlich" wrote:

> Hi Mats.
>
> >I have noticed many music history books mentions Don Carlo Gesualdo
> >using"quarter tones",as they are usually called.Were these perhaps
> notated
> >as enharmonic differences(Eb-D#)etc,
>
> Yes.
>
> >suggesting 19tet as a reference?
>
> There seems to be no reason to suppose 19-tET -- our best guess as to
> what
> meantone Gesualdo intended would probably be 1/4-comma meantone. In
> this
> case, the enharmonic difference would be the diesis of 41 cents.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

> >I have noticed many music history books mentions Don Carlo Gesualdo > >using"quarter tones",as they are usually called.Were these perhaps
> notated >as enharmonic differences(Eb-D#)etc,
>
> Yes.
>
> >suggesting 19tet as a reference?
>
> There seems to be no reason to suppose 19-tET -- our best guess as to
> what
> meantone Gesualdo intended would probably be 1/4-comma meantone. In this
> case, the enharmonic difference would be the diesis of 41 cents.

Well,the obvious reason is that the chromatic tones and enharmonic differences(correct term?)are the same size in 19tet,so when combined it becomes a smoother melodic movement than 1/4.

-=-=-=-=-=-=-
MATS �LJARE
http://www.angelfire.com/mo/oljare
_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.

I wrote,

>> There seems to be no reason to suppose 19-tET -- our best guess as to
>> what
>> meantone Gesualdo intended would probably be 1/4-comma meantone. In this
>> case, the enharmonic difference would be the diesis of 41 cents.

Mats wrote,

>Well,the obvious reason is that the chromatic tones and enharmonic
>differences(correct term?)are the same size in 19tet,so when combined it
>becomes a smoother melodic movement than 1/4.

That could be one argument for it (though there would still be arguments
against it), but the crucial question is -- did Gesualdo actually write
"microchromatic" passages like C C# Db or C# Db D? My guess is that he
didn't -- his use of diesis ("enharmonic") shifts was quite different from
his use of chromatic semitones.

Hello, there, and in response to the discussion on Gesualdo, I might
offer a few general points.

First, I'm strongly inclined to agree with Paul Erlich that something
like 1/4-comma meantone may be the best guess for a fixed tuning
system that might fit Gesualdo's intonational concepts, albeit with
the caution that singers or performers of flexible-pitch instruments
both can and will inevitably deviate somewhat from any fixed tuning.
Thanks to Bill Alves also, for example, for duly emphasizing this
point.

Surveying 16th-century theorists, we find that they differ on the
issue of what intonation unaccompanied vocalists "naturally" tend
toward. Zarlino takes 5-limit just intonation (JI), as realized by
Ptolemy's syntonic diatonic, as the best theoretical model -- but with
some interesting comments that singers, unlike 5-limit JI keyboards,
seem to avoid "small intervals" such as the syntonic comma which
complicate life for players of such untempered keyboards.

This might suggest some kind of Vicentino/Erlich "adaptive JI" model
for 16th-century singers. In such a system, as in either the syntonic
diatonic or 1/4-comma meantone, the diesis defined by the difference
between three 5:4 major thirds and a 2:1 octave would be 128:125, or
about 41.06 cents.

While Fogliano and Zarlino take 5-limit JI as the vocal ideal, with
various forms of temperament much more practical for fixed keyboards
although JI arrangements are possible, Vicentino seems to accept
temperament as a pervasive quality of "modern" music, vocal or
instrumental. He thus identifies the common practice of the times
(1555) as "tempered and mixed music" or _musica participata e mista_,
referring both to the tempering or "blunting" of the fifth, and to
what he views as a mixture of the three Greek genera in usual as well
as experimental Renaissance music.

More specifically, Vicentino urges that his archicembalo be taken as a
standard by vocalists for judging intervals, including the more
difficult or unaccustomed diminished and augmented ones. Since the
context suggests he may be referring to his 31-note meantone cycle
rather than to his adaptive JI scheme, this suggests a viewpoint that
singers might well adapt a regular tuning as their standard.

In 1581, Vincenzo Galilei proposes that singers tend of themselves
toward an intonation somewhere between the 12-tone equal temperament
(12-tET) standard on the lute, and the 2/7-comma meantone temperament
which he prefers on the harpsichord (curiously following Zarlino, his
former teacher who became a rival in some empassioned
controversies). He holds that singers tend to make whole-tones the
same size, in contrast to the unequal 9:8 and 10:9 steps of classic
5-limit JI.

Given the intense rivalry between Zarlino and Galilei, it's
interesting that some kind of adaptive JI based more or less on
something like 1/4-comma meantone might fit some of the descriptions
of both theorists.

From this historical perspective, while it may be something of a moot
point exactly what ideal intonational model Gesualdo may have
followed, something like a 31-note meantone cycle (1/4-comma) with
room for adaptive JI adjustments by singers or other performers of
nonfixed-pitch instruments seems an attractive conjecture.

Let's clarify an important point: in 1/4-comma meantone or 31-tET,
there are two levels of fine inflection, which Vicentino describes as
the chromatic and enharmonic. Either system -- and a vocal adaptive
tuning based more or closely on either -- can be described for many
purposes in terms of units of 1/5-tone, or "fifthtones," each roughly
comparable to the meantone diesis of 128:125.

Chromatic progressions feature alterating steps of ~3/5-tone (the
diatonic semitone, ~117.11 cents in 1/4-comma) and ~2/5-tone (the
chromatic semitone, ~76.05 cents in 1/4-comma), the two steps adding
up to the "mean-tone" of ~193.16 cents, or half of a 5:4 third:

76 117
G -- G# -- A
|------------|
193

In the music of Vicentino -- but not Gesualdo, to my best and possibly
incomplete knowledge -- we additionally find "enharmonic" or direct
fifthtone progressions featuring the diesis of around 1/5-tone. In a
1/4-comma tuning, these dieses are slightly unequal, and which ones
are larger or smaller depends on the order of the tuning cycle. For
example, here's one possible fifthtone division of the same whole-tone
G-A, using a Vicentino-like notation with an asterisk (*) to represent
his dot above a note showing a pitch raised by a diesis:

41 35 41 41 35
G -- G* -- G# -- Ab -- Ab* -- A

While we could get into some interesting discussions about the tuning
of such "sliding of the voice" in fifthtones -- an ornament advocated
by Fabio Colonna in 1618 -- this seems to me a bit beyond the scope of
Gesualdo's music known to me, featuring direct chromaticism but not
enharmonic fifthtone passages.

For chromatic progressions, something like 1/4-comma meantone might
seem a bit "smoother" to me than 1/3-comma meantone or 19-tET; 5-limit
JI has the same diesis or difference between semitones as 1/4-comma,
if we take the whole-step G-A as a small whole-step at 10:9 (as in
Zarlino's scheme):

25:24 16:15
76 117 63 126 70.7 111.7
G -- G# -- A G -- G# -- A G -- G# ---- A
|------------| |------------| |------------|
193 193 182.4
10:9

1/4-comma 1/3-comma 5-JI

At least in a Renaissance/Manneristic kind of setting, I would say
that the difference between the 1/4-comma or 31-tET diesis and the
small semitone of 1/3-comma or 19-tET is one of kind rather than
degree.

While the smaller semitone of either system can serve as a variety of
cadential semitone -- and Vicentino uses this effect in some of his
altered cadences, in a manner advocated some 400 years later by Ivor
Darreg, by the way -- the fifthtone or diesis is of a different
order. It is "microtonal" in the modern sense of "too small to be
perceived as a usual scale step."

Indeed, Galilei, although often a radical theorist out to overthrow
the conventional techniques and rules of counterpoint a la Zarlino,
concludes that Vicentino's fifthtones are too small to suit the human
ear -- a complaint maybe echoed in some anti-microtonal doctrines of
the 20th century.

(In the very different intonational universe of neo-Gothic music, I
find that I routinely accept intervals on the order of 50-55 cents as
small semitones, either regular diatonic semitones as in 22-tET
(~54.55 cents), or special cadential ones as in a variety of tunings
with dieses of this order of size. To what degree the perception of an
interval as a discrete semitone step or "smaller than semitonal"
depends on its absolute size, and to what degree on the musical and
intonational context, is an intriguing question.)

As the 31-tone notations of Vicentino and Colonna illustrate, special
symbols would generally be required to indicate fifthtone
progressions, although the 20-note gamut of Gesualdo's madrigals
(Cb-B#) does include some possible diesis motions between accidentals
(e.g. Ab-G#, B#-C). I'm not sure if Gesualdo uses such _direct_
melodic motions.

However, a standard notation suffices to show the chromatic divisions
of either the 1/4-comma system (roughly 2/5-3/5 tone) or the 1/3-comma
or 19-tET system (1/3-2/3 tone) -- for example, G-G#-A.

While Gesualdo, to my best knowledge, doesn't use _direct_ fifthtone
progressions a la Vicentino and Colonna, there are passages in his
vocal music suggesting contrasts between notes or pitch levels a
fifthtone apart -- for example, a juxtaposition within a few measures
of B# and C, or vice versa.

In certain 20th-century writings, one encounters the assumption that
any move beyond a standard 12-note meantone gamut must imply some kind
of "equal temperament" -- implicitly meaning "12-tET," as opposed to
what I consider the likelier approximation of 31-tET.

While ascribing intonational ideals by association, like guilt by
association, can be a very risky practice, I might add that as
discussed in recent posts, Gesualdo's Neapolitan milieu of around 1600
showed enthusiasm for chromatic harpsichords of 19 notes (Gb-B#) in
1/4-comma meantone or the like, with some full 31-note keyboards also
(Stella, Colonna).

To say that a Neapolitan keyboard composer such as Trabaci is
evidently assuming 1/4-comma or something close is not necessarily to
say how Gesualdo's ensembles, very possibly combining human voices and
other flexible-pitch instruments with "semi-flexible" and fixed ones
(viols being a likely example of "semi-flexibility"), may have
negotiated his chromatic passages.

However, I do find it reasonable to conclude that the diesis, but not
the syntonic comma, seems a basic part of the intonational model as
applied to voices or most instruments -- the 12-tET lute serving as a
notable exception, where Eb and D# would be equivalent -- their
distinction "neutralized," to borrow a grammatical analogy.

In my view, in the Italian setting of around 1600, such an exception
may prove rather than negate the rule of diesis distinctions. It is
noteworthy that Vicenzo Galilei, despite his enthusiasm for 12-tET as
the most "perfect" tuning, finds it less than satisfactory on a
harpsichord as opposed to a lute, because of the more "vehement" sound
production on the former instrument (one is tempted to translate,
"because of the more prominent fifth partials").

The "neutralization" of the usual diesis on a 12-tET lute might be
analogous to the grammatical neutralization of tense in the first or
second person, or third person plural, of the English verb "set":

(1) I set the table at 5.
(2) You set out for the concert shortly after sunset.
(3) The stars of that constellation set shortly before dawn.

These sentences might express either the Simple Past tense ("I set the
table at 5 [yesterday]," a prospective Simple Present ("I set the
table at 5 this evening," spoken in the afternoon), or a kind of
generic or habitual Simple Present ("I set the table at 5 every day").
However, it would be impetuous, to say the least, for us to conclude
that English does not have morphological tense.

Having proposed a tentative conclusion that Gesualdo's music may
generally suggest 1/4-comma meantone, or some "adaptive JI" tuning for
flexible ensembles not too far from this, I would add that there is
certainly some room for variation.

For example, Mark Lindley has suggested that some Venetian keyboard
music (e.g. Andrea Gabrieli) in modes featuring a prevalent arithmetic
division of the fifth (e.g. the minor third below and major third
above, in Partchian terms "5-limit utonal sonorities") may ideally
favor Zarlino's (and Galilei's) 2/7-comma temperament. I'm not sure
what the effect would be for Gesualdo's music, but recall that Zarlino
may have described a 19-note keyboard based on 2/7-comma which could
cover the typical chromatic range of Gesualdo.

Most respectfully,

Margo Schulter
mschulter@value.net

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
[big snip]
> From this historical perspective, while it may be something of a
moot
> point exactly what ideal intonational model Gesualdo may have
> followed, something like a 31-note meantone cycle (1/4-comma) with
> room for adaptive JI adjustments by singers or other performers of
> nonfixed-pitch instruments seems an attractive conjecture.

While this comprehensive review was very nice (and I hope you'll
contribute with similar generosity to the FAQ we are about to
create), it might be worth mentioning a few more quantitative
facts . . . for example, the kind of adaptive JI you mentioned could
be thought of as based on 1/4-comma meantone but normally inflecting
each pitch either 3 cents (1/8 comma) higher or 3 cents lower,
depending on context . . . meanwhile, 2/7-comma meantone would
deviate from 1/4-comma meantone by about 3/4 of 1 cent (1/28 comma)
per fifth in the chain of fifths, so the tuning of the extreme notes
in a chain of 18 fifths (like Cb at one end, and E# at the other)
would differ by about 7 cents between the two systems, if both are
centered on a common D or A . . . this gives a sense of what level of
fineness we're talking about in making speculations about what tuning
singers may have used in the 16th century . . .

> In the music of Vicentino -- but not Gesualdo, to my best and
possibly
> incomplete knowledge -- we additionally find "enharmonic" or direct
> fifthtone progressions featuring the diesis of around 1/5-tone.

Actually, Gesualdo _did_ use direct enharmonic motions, as a glance
at Blackwood's book will reveal (if I recall correctly), and no doubt
this are the kind of motions that the original poster was inquiring
about when mentioning "quarter tones" in Gesualdo's music.

Thank you Margo and Paul for this possible intonation of Gesualdo. I
have to pose a few question and some observations.

First are there any recordings of unaccompanied choral music in
meantone.
Like is it even possible.

It seems that Gesualdo goes through more changes than anyone i can
think of. Sometimes he will, in a single phrase go through quite a few
different emotions, sometimes as a friend remarked, he will go through
all of them:)

If this is the case, just as 12 et will stand for more than one set of
ratios it seems Gesualdo's Music would need more that one form of
intonation depending on the emotional quality of micro parts of the
phrase. I do not think this is unique, but our musical ear and practice
far surpasses our rational explanation of what we are doing. For
instance, the intonation of cadences could (possibly does) differ than
the body of a phrase. Hence leading tones might have their own guiding
principles. I believe the concept of adaptive JI and extended reference
are two candles in this dark room. I think it would be a mistake to
think these are the only possibilities and expect theirs to come up with
more including yourselves. I can imagine certain parts of his music in
Pythagorean , others in Just without any trouble. It is no wonder that
so many of the recordings of his music is subjected to heavy vibrato
which is quite odd, considering you don't find this with his
contemporaries recordings. Knowing the intensity of his music and the
lack of assertiveness of meantone, I remain not quite convinced but more
informed as to your suggestions
knowing that dealing with intonation, surprises await behind every
corner that cause one to reevaluate what we assume.

All and all I rejoice in the fact of Gesualdo hearing in such
interesting way microtonality.

PERLICH@ACADIAN-ASSET.COM wrote:

> --- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
> [big snip]
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Margo:

> > In the music of Vicentino -- but not Gesualdo, to my best and
> possibly
> > incomplete knowledge -- we additionally find "enharmonic" or
direct
> > fifthtone progressions featuring the diesis of around 1/5-tone.

Did Vicentino write full pieces including such progressions?

Paul:

> Actually, Gesualdo _did_ use direct enharmonic motions, as a glance
> at Blackwood's book will reveal (if I recall correctly), and no
doubt
> this are the kind of motions that the original poster was inquiring
> about when mentioning "quarter tones" in Gesualdo's music.

I had to better part of an hour to scan through the complete works,
and get the library's photocopier to work. I couldn't find any such
examples. If you have the Blackwood book to glance at perhaps you
could say what pieces the examples are from?

I started on the last volume, thinking it would have the later music.
In fact, the first two volumes are the madrigals, so I should have
concentrated on them. I only found one example of a badly-spelt
third/sixth. And it turns out to be in an augmented triad. So
there's nothing at all to suggest an awareness of wider 9-limit
harmony.

There are some cases where a chromatic semitone is used melodically.
But they don't tend to be at cadences or anything like that. Usually
it's part of a chromatic run. It always fits (extended) 5-limit
tuning. I could find no examples of two chromatic or diatonic
semitones together, which would add up to a more interesting interval.

There are also examples of diminished octaves used harmonically, but
there's nothing special about them. Spelling of dissonances doesn't
really matter.

So, the whole thing looks like 12-note music with correct spellings.
That is, if you converted it all to 12 pitch classes, and then
converted it back to staff notation, minimising accidentals and
preserving 5-limit intervals, you'd get what you started with. Which
may mean the singers were thinking in terms of 12 pitch classes even
though the harpsichords were tuned more like a subset of 31. But
whatever, it's the way of thinking that led to 12-equal.

The Watkins book does say Gesualdo was unusual in being so strict in
his use of accidentals. So maybe some of his contemporaries were
letting the 7-flavour slip through.

A good idea for a research project (hint) might be to go through
harpsichord music that would have assumed meantone, and see if there's
any consistency to the use of bad spellings, or notes that would have
been outside the gamut.

Graham

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> Thank you Margo and Paul for this possible intonation of
Gesualdo. I
> have to pose a few question and some observations.
>
> First are there any recordings of unaccompanied choral music
in
> meantone.
> Like is it even possible.

I reiterate -- the distinction between meantone and, say,
Vicentino's adaptive JI system is too small to be meaningful
when applied to a capella vocal music -- both represent an
idealized point around which "authentic" Renaissance practice
will deviate more or less. What we can say with some
confidence is that neither 12-tET nor strict JI renditions would be
acceptable for this music.
>
> If this is the case, just as 12 et will stand for more than one set
of
> ratios it seems Gesualdo's Music would need more that one
form of
> intonation depending on the emotional quality of micro parts of
the
> phrase.

That's ironic -- you're saying 12-tET can stand for a lot of things
but meantone can't? I mean, I agree with you in principle, but you
could have picked a better example than 12-tET! Certainly, 20
notes of meantone or 30-some notes of Vicentino adaptive JI
can stand for a far greater (since they're unequal systems) range
of ratios than 12-tET. But yes, small vocal intonational inflections
for emotional purposes may have been part of the style, for all
we know.

> I believe the concept of adaptive JI and extended reference
> are two candles in this dark room. I think it would be a mistake
to
> think these are the only possibilities and expect theirs to come
up with
> more including yourselves.

"Theirs to come up with more including yourselves" -- what does
that mean?

> I can imagine certain parts of his music in
> Pythagorean , others in Just without any trouble.

Well it's quite another thing for us denizens of the 21st century, in
our little corner of tuning experimentation, to imaginatively try
things out in one tuning or another. However, even today, the vast
majority of trained singers are singing essentially in 12-tET,
accepting even its harsh major thirds (ignoring for now the tiny
distinction between 400 cents and Gerald Eskelin's still wider
"high third") as "normal". Similarly, singers in Gesualdo's day
may have been trained using meantone-tuned keyboards . . .
any documentation on this?

--- In tuning@y..., "Graham Breed" <graham@m...> wrote:

> I started on the last volume, thinking it would have the later
music.
> In fact, the first two volumes are the madrigals, so I should
have
> concentrated on them. I only found one example of a
badly-spelt
> third/sixth. And it turns out to be in an augmented triad. So
> there's nothing at all to suggest an awareness of wider 9-limit
> harmony.

Why would you expect to find any? The enharmonic slips that are
Gesualdo's "quarter-tones" have nothing to do with 9-limit
harmony . . .

> The Watkins book does say Gesualdo was unusual in being
so strict in
> his use of accidentals. So maybe some of his contemporaries
were
> letting the 7-flavour slip through.

Why would you think that? I really don't think there was any real
awareness of the 7-limit in those days, other than perhaps the
very stongest 7-limit sonority, the root-position otonal tetrad, in
the guise of the augmented sixth chord -- with melodic factors
dictating its resolution (aug. 6th expands outward to octave).

Paul Erlich wrote:
> --- In tuning@y..., "Graham Breed" <graham@m...> wrote:
>
> > I started on the last volume, thinking it would have the later
> music.
> > In fact, the first two volumes are the madrigals, so I should
> have
> > concentrated on them. I only found one example of a
> badly-spelt
> > third/sixth. And it turns out to be in an augmented triad. So
> > there's nothing at all to suggest an awareness of wider 9-limit
> > harmony.
>
> Why would you expect to find any?

I didn't expect anything. I was testing a hypothesis.

> The enharmonic slips that are
> Gesualdo's "quarter-tones" have nothing to do with 9-limit
> harmony . . .

So what do they have to do with? Nobody's yet given explanations,
examples or references (except to a book that's out of print).

> > The Watkins book does say Gesualdo was unusual in being
> so strict in
> > his use of accidentals. So maybe some of his contemporaries
> were
> > letting the 7-flavour slip through.
>
> Why would you think that?

Because the book said so. Gesualdo was praised in his day for getting
his accidentals right. That suggests other composers got them wrong,
which would usually give 9-limit harmony if played as written. Margo
also said once that notes were sometimes written that lay outside the
gamut, but again no examples.

> I really don't think there was any real
> awareness of the 7-limit in those days, other than perhaps the
> very stongest 7-limit sonority, the root-position otonal tetrad, in
> the guise of the augmented sixth chord -- with melodic factors
> dictating its resolution (aug. 6th expands outward to octave).

That's what I'm finding. Some theoreticians were aware of the
7-limit, but no composers. I haven't looked at augmented sixth
chords, though, so why would they suggest awareness of the 7-limit? I
didn't think they were used in important cadences.

The other hypothesis is that chromatic semitones were preferred in
cadences. This needn't suggest an awareness of the 9-limit, but would
give some of the same results. Augmented 6th chords resolving to
octaves would count the other way. If it's like

A# -> B
C -> B

then both parts are moving by diatonic semitones. Which suggests
diatonic semitones were preferred over chromatic ones. That agrees
with the quick survey I did of Gesualdo, in that he always has a good
reason for using chromatic semitones, and isn't more likely to do so
at important cadences.

Graham

I wrote,

>> The enharmonic slips that are
>> Gesualdo's "quarter-tones" have nothing to do with 9-limit
>> harmony . . .

Graham wrote,

>So what do they have to do with?

Slipping.

>>> letting the 7-flavour slip through.
>
>> Why would you think that?

>Because the book said so. Gesualdo was praised in his day for getting
>his accidentals right. That suggests other composers got them wrong,
>which would usually give 9-limit harmony if played as written.

Why would you assume that this was the intention? Remember, only a few
keyboards had enough split keys to express all the accidentals that Gesualdo
was using . . . so while 5-limit harmony would have been familiar, and
easily extendible to the extra accidentals Gesualdo was using by sensitive
singers, 9-limit harmony probably could not function as a similar "guide" to
the correct pitches.

>> I really don't think there was any real
>> awareness of the 7-limit in those days, other than perhaps the
>> very stongest 7-limit sonority, the root-position otonal tetrad, in
>> the guise of the augmented sixth chord -- with melodic factors
>> dictating its resolution (aug. 6th expands outward to octave).

>That's what I'm finding. Some theoreticians were aware of the
>7-limit, but no composers. I haven't looked at augmented sixth
>chords, though, so why would they suggest awareness of the 7-limit?

See below.

>diatonic semitones were preferred over chromatic ones.

Agreed.

>That agrees
>with the quick survey I did of Gesualdo, in that he always has a good
>reason for using chromatic semitones, and isn't more likely to do so
>at important cadences.

It seems that the augmented sixth chord was almost always played in root
position, which would suggest some affinity with the harmonic series which
it approximates almost perfectly. You don't find that many other resolutions
by contrary diatonic semitones into a consonant interval, except later the
diminished seventh to perfect fifth . . . I think Blackwood addresses this
issue in other ways too . . . I can't recall too well right now.

Though I haven't got the lineage down straight yet, Vicentino's student
(D'Este) was a generation earlier than the D'Este girl who became Gesualdo's
second wife. Gesualdo moved from Naples to Ferrara to be in the court of the
D'Este family and the Vicentino treasures are presumed to have been extant.

However, I do not think it made more than an impression of Gesualdo. It's
tiniest of tuning relationships were probably poorly mastered once Vicentino
had passed away. In other words it was probably out of tune when Gesualdo
looked upon it. He might have tried to tuned it for himself and then gotten
the ideas that Paul and Margo suspect. Kraig you might like this approach.

Since the first AFMM concert in 1981, there has been Gesualdo, but only one
piece, until I could get it right. It was done twice after that at ensuing
concerts. "Io Parto" is beautiful in its form and in its expression. The
tuning that always worked best for my instrumental transcriptions of the
Gesualdo madrigal was to produce pure just chords of major and minor and to
use voice leading to indicate a point for measurement, and to then anchor the
direction of the chord. There must be "odd" melodic intervals of a small
size created by this process, and maybe these are the "quartertones."

Johnny Reinhard

Johnny!
I would assume your approach is probably quite close to the practice
of the day.
Maybe i am wrong , but i know of no unaccompanied meantone choral
performances. Are there any?

Afmmjr@aol.com wrote:

> Since the first AFMM concert in 1981, there has been Gesualdo, but
> only one
> piece, until I could get it right. It was done twice after that at
> ensuing
> concerts. "Io Parto" is beautiful in its form and in its expression.
> The
> tuning that always worked best for my instrumental transcriptions of
> the
> Gesualdo madrigal was to produce pure just chords of major and minor
> and to
> use voice leading to indicate a point for measurement, and to then
> anchor the
> direction of the chord. There must be "odd" melodic intervals of a
> small
> size created by this process, and maybe these are the "quartertones."

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., PERLICH@A... wrote:

/tuning/topicId_18798.html#19003

> --- In tuning@y..., "Graham Breed" <graham@m...> wrote:
>
> > I started on the last volume, thinking it would have the later
> music.In fact, the first two volumes are the madrigals, so I should
> have concentrated on them. I only found one example of a
> badly-spelt third/sixth. And it turns out to be in an augmented
triad. So there's nothing at all to suggest an awareness of wider
9-limit harmony.
>

Although I know virtually nothing scholarly about this subject, I am
also a great lover of Gesualdo... Is it possible that the music of
his that you find in libraries is notated INCORRECTLY?? Is it
notated in 12-tET?? I'm under the assumption that, given the
references to his "correct use of accidentals" that perhaps he is
notating in some kind of meantone system, with non-equivalent
enharmonics, as we have been discussing. Is this true, and could the
printed editions STILL be incorrect. Just curious....

_______ _____ _____ _
Joseph Pehrson

Joseph, what Graham is saying below is that the Gesualdo scores he found
seem to have _absolutely correct spelling_ with respect to the meantone
notation in use at the time.

-----Original Message-----
From: jpehrson@rcn.com [mailto:jpehrson@rcn.com]
Sent: Monday, February 19, 2001 1:42 PM
To: tuning@yahoogroups.com
Subject: [tuning] Re: Gesualdo

--- In tuning@y..., PERLICH@A... wrote:

/tuning/topicId_18798.html#19003

> --- In tuning@y..., "Graham Breed" <graham@m...> wrote:
>
> > I started on the last volume, thinking it would have the later
> music.In fact, the first two volumes are the madrigals, so I should
> have concentrated on them. I only found one example of a
> badly-spelt third/sixth. And it turns out to be in an augmented
triad. So there's nothing at all to suggest an awareness of wider
9-limit harmony.
>

Although I know virtually nothing scholarly about this subject, I am
also a great lover of Gesualdo... Is it possible that the music of
his that you find in libraries is notated INCORRECTLY?? Is it
notated in 12-tET?? I'm under the assumption that, given the
references to his "correct use of accidentals" that perhaps he is
notating in some kind of meantone system, with non-equivalent
enharmonics, as we have been discussing. Is this true, and could the
printed editions STILL be incorrect. Just curious....

_______ _____ _____ _
Joseph Pehrson

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Johnny Reinhard wrote,

<<The tuning that always worked best for my instrumental
transcriptions of the Gesualdo madrigal was to produce pure just
chords of major and minor and to use voice leading to indicate a point
for measurement, and to then anchor the direction of the chord. There
must be "odd" melodic intervals of a small size created by this
process, and maybe these are the "quartertones.">>

The quartertone like diesis example Blackwood uses in his book is the
C-B-B# in the beginning of "Merc� grido piangendo".

Blackwood definitely sees Gesualdo's accidentals as idiomatically
meantone in nature, even "rigorously" so, with the exception being
that he frequently used more than twelve notes.

--Dan Stearns

Dan wrote,

>Blackwood definitely sees Gesualdo's accidentals as idiomatically
>meantone in nature, even "rigorously" so, with the exception being
>that he frequently used more than twelve notes.

I don't see how that constitutes an "exception"!

Paul H. Erlich wrote,

<<I don't see how that constitutes an "exception"!>>

Right, but Blackwood doesn't seem to be overly aware or clear about
this here... In fact he goes on to say that it shouldn't be surprising
that a composer of vocal music should find it unnecessary to "heed a
restriction associated solely with the limitations of keyboard
instruments."

--Dan Stearns

Sounds perfectly aware and clear to me! Unless you mean Blackwood may not
have been aware of the preponderance of split-key instruments in Gesualdo's
neighborhood?

-----Original Message-----
From: D.Stearns [mailto:STEARNS@CAPECOD.NET]
Sent: Monday, February 19, 2001 5:04 PM
To: tuning@yahoogroups.com
Subject: Re: [tuning] Re: Gesualdo

Paul H. Erlich wrote,

<<I don't see how that constitutes an "exception"!>>

Right, but Blackwood doesn't seem to be overly aware or clear about
this here... In fact he goes on to say that it shouldn't be surprising
that a composer of vocal music should find it unnecessary to "heed a
restriction associated solely with the limitations of keyboard
instruments."

--Dan Stearns

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Paul H. Erlich wrote,

<<Sounds perfectly aware and clear to me! Unless you mean Blackwood
may not have been aware of the preponderance of split-key instruments
in Gesualdo's neighborhood?>>

Right, or at the very least unclear about it. From what he wrote you
can't have it both ways -- "perfectly aware and clear" and yet unaware
that more than twelve notes was really no exception...

--Dan Stearns

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:

/tuning/topicId_18798.html#19017

> Joseph, what Graham is saying below is that the Gesualdo scores he
found seem to have _absolutely correct spelling_ with respect to the
meantone notation in use at the time.
>

Got it!... Thanks...

________ _____ _____ ___
Joseph Pehrson

Alas, I have not seen Easley Blackwood's book. However, whether or not
Easley sees idiomatic meantone usage or not means nothing regarding what
Gesualdo did. I remember when I did a radio show with Easley and he had just
finished his 24 etudes for synthesizer. When we spoke of 31tET, which I was
quite fond of, and using regularly with the Microtones band, it was beyond
his comprehension. He had stopped at 24tET and hadn't thought it necessary
to go much beyond it.

Now, realizing more of the importance of meantone and early music performance
practice is a good thing. However, the notation is likely different in
published versions of Gesualdo's music, all of Gesualdo is heard on
recordings in ET with vibrato. Only someone with perfect pitch would have
trouble negotiating a cappella ensemble singing, which drifts. There was no
concept of perfect pitch at this time.

Thinking an a cappella Renaissance chromaticist would be shackled to a
temperament is not likely, IMHO.\

Johnny Reinhard

LIst!
This seems like a little out of context. What are the other voices
doing and what happens afterward or is this a cadence. In 19 ET would
not B# be the same as C.

Again are there any recordings of choral music in meantone:)

"D.Stearns" wrote:

> The quartertone like diesis example Blackwood uses in his book is the
> C-B-B# in the beginning of "Merc� grido piangendo".

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Johnny Reinhard wrote,

>Only someone with perfect pitch would have
>trouble negotiating a cappella ensemble singing, which drifts. There was
no
>concept of perfect pitch at this time.

That's a very bold assertion! I'm sure Margo could respond with some
historical evidence. Besides, one doesn't need perfect pitch (I don't have
it) to be annoyed by drift!

Johnny, did you fully read Margo's post?

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

/tuning/topicId_18798.html#19032

> LIst!
> This seems like a little out of context. What are the other
voices doing and what happens afterward or is this a cadence. In 19 ET
would not B# be the same as C.
>

Kraig, it looks as though B# in 19-tET is 1137 cents if C is 1200...

_______ _____ ____ ___
Joseph Pehrson

In a message dated 2/19/01 2:35:03 PM Eastern Standard Time,
PERLICH@ACADIAN-ASSET.COM writes:

> Johnny, did you fully read Margo's post?

Paul, what are you hinting at?

Johnny

>> Johnny, did you fully read Margo's post?

>Paul, what are you hinting at?

Just wondering! If not, you might find it informative. That's all!

Johnny!
The best recording i have found (with the least vibrato) is
Gesualdo Sabato sancto. Philippe Herreweghe harmonia mundi hmc 901320

The ECM one is lifeless

As two people who have used 31 extensively for years, with its meantone
second, people would think we
would be in favor to the idea.

Afmmjr@aol.com wrote:

> However, the notation is likely different in
> published versions of Gesualdo's music, all of Gesualdo is heard on
> recordings in ET with vibrato.
>
> Thinking an a cappella Renaissance chromaticist would be shackled to a
>
> temperament is not likely, IMHO.\

>
>
> Johnny Reinhard
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

> Date: Mon, 19 Feb 2001 19:35:59 -0000
> From: jpehrson@rcn.com

> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> voices doing and what happens afterward or is this a cadence. In 19 ET
> would not B# be the same as C.

> Kraig, it looks as though B# in 19-tET is 1137 cents if C is 1200...

> _______ _____
> Joseph Pehrson

Sounds great, but I doubt it would be possible in reality for singers of
these pieces (not talking about 19-note keyboards etc).
Have you heard singers performing these in a way that it even comes
close to 19-ET?
Where would the singer get the reference pitch in 19-ET for a major
third or a fifth which is ca. 8 cents below pure. In "standard" meantone
it is all the time again the pure major third which can be used by
trained singers as reference in between.

kind regards
Ibo Ortgies

----------------------------------
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http://www.hum.gu.se/goart/ortgies/homepage.htm

GOArt (G�teborg Organ Art center) G�teborgs universitet
http://www.hum.gu.se/goart/w-1.htm
----------------------------------
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Support INZENSO

Ibo -- I don't think anyone's claiming Gesualdo meant for 19-tET to be used.
The point is, in a meantone or Vicentino adaptive JI system, B# is lower by
C, by an amount that could roughly be called a "quartertone". This whole
thread started because someone said they kept reading about "quartertones"
in Gesualdo's music -- no doubt this is what is meant.

Ibo Ortgies wrote:

> Sounds great, but I doubt it would be possible in reality for singers
> of
> these pieces (not talking about 19-note keyboards etc).
> Have you heard singers performing these in a way that it even comes
> close to 19-ET?

I agree and this is why i was asking about recordings. 19 has always
been very unacceptable to my ear.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Johnny Reinhard wrote:

> Thinking an a cappella Renaissance chromaticist would be shackled to a
> temperament is not likely, IMHO.\

Yes, but the interesting question is: did they unshackle themselves within
12 or 19 pitch classes? It seems to be 12, but most people see this is
too obvious to be worth stating.

Graham

--- In tuning@y..., Ibo Ortgies <ibo.ortgies@m...> wrote:

/tuning/topicId_18798.html#19054

>
> > voices doing and what happens afterward or is this a cadence. In
19 ET would not B# be the same as C.
>
> > Kraig, it looks as though B# in 19-tET is 1137 cents if C is
1200...
>
> > _______ _____
> > Joseph Pehrson
>
>
> Sounds great, but I doubt it would be possible in reality for
singers of these pieces (not talking about 19-note keyboards etc).
> Have you heard singers performing these in a way that it even comes
> close to 19-ET? Where would the singer get the reference pitch in
19-ET for a major third or a fifth which is ca. 8 cents below pure.
In
"standard" meantone it is all the time again the pure major third
which can be used by trained singers as reference in between.
>
> kind regards
> Ibo Ortgies
>

Thank you, Ibo, for your commentary and it looks as though you are
right. If I am understanding this list discussion, the probability
that Gesualdo used 1/4 comma meantone is much higher than that of his
using 19-tET (1/3 comma...)

_______ _____ _____ ___
Joseph Pehrson

Graham wrote,

>Yes, but the interesting question is: did they unshackle themselves within
>12 or 19 pitch classes? It seems to be 12, but most people see this is
>too obvious to be worth stating.

For Gesualdo it was clearly not 12 (and probably more than 19). Why else
would he write C-B-B#?

PERLICH@ACADIAN-ASSET.COM (Paul H. Erlich) wrote:

> Graham wrote,
>
> >Yes, but the interesting question is: did they unshackle themselves
> within >12 or 19 pitch classes? It seems to be 12, but most people see
> this is >too obvious to be worth stating.
>
> For Gesualdo it was clearly not 12 (and probably more than 19). Why else
> would he write C-B-B#?

I'll have to check the example. All of what I've seen so far is
consistent with 12. Some of the ideas people have come up with also
assume 12 pitch classes. If it was customary for singers to narrow
leading tones, why didn't composers write narrow leading tones into the
music?

Graham

Paul!
You might be completely right but i for one would like to know what
the other voices are doing and what happens next. If it is C# for me it
would change things

"Paul H. Erlich" wrote:

> For Gesualdo it was clearly not 12 (and probably more than 19). Why
> else
> would he write C-B-B#?

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

>"Paul H. Erlich" wrote:
>For Gesualdo it was clearly not 12 (and probably
>more than 19). Why else would he write C-B-B#?

Because enharmonic spelling can depend on vertical sonorities and
consistency as well. In the score of Io pur respiro that I have handy, he
obviously avoids augmented and diminished intervals when spelling vertical
sonorities. Thus he has an F in what we would call a D minor chord and an
E# 2 measures later in a C# major chord. That doesn't prove he was assuming
a >12/octave gamut. The only exception I see at a glance is a passing
augmented triad. In fact, if he had "misspelled" such chords it might be
clear evidence that he was NOT assuming enharmonic equivalence. Anyway, as
Margo has recalled, I have spoken before about the practical difficulties
of distinguishing tuning systems with the consistency of keyboard
instruments in choral performance.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Graham wrote,

>I'll have to check the example. All of what I've seen so far is
>consistent with 12. Some of the ideas people have come up with also
>assume 12 pitch classes.

I haven't seen any evidence for this point of view whatsoever.

I wrote,

>>For Gesualdo it was clearly not 12 (and probably
>>more than 19). Why else would he write C-B-B#?

Bill Alves wrote,

>Because enharmonic spelling can depend on vertical sonorities and
>consistency as well.

Bill, if you look at the example in question, there was no vertical
consideration that would have led to the spelling. The only possible reason
was to get a microtonal pitch shift.

>In the score of Io pur respiro that I have handy, he
>obviously avoids augmented and diminished intervals when spelling vertical
>sonorities....The only exception I see at a glance is a passing
>augmented triad.

Yes -- this agrees with what Graham (and Easley Blackwood) found.

>That doesn't prove he was assuming
>a >12/octave gamut.

No, but it doesn't prove he wasn't -- and in his time and day, if I'm
understanding Margo correctly, a closed 12-pitch system was _not_ how
musical notes were thought of.

Paul!
What if it was going to C#?
Like i said it is impossible to even talk about this without seeing
the context in which it occurred!

Also the possibly of drift maybe quite offensive to your own musical
language but could be symbolic to such a composer as Gesualdo. Maybe he
could not go back to where he was, like before his own traumatic event.

That he might of been exposed to a 19 tone harpsichord I find intriguing

"Paul H. Erlich" wrote:

> I wrote,
>
> >>For Gesualdo it was clearly not 12 (and probably
> >>more than 19). Why else would he write C-B-B#?
>
> Bill Alves wrote,
>
> >Because enharmonic spelling can depend on vertical sonorities and
> >consistency as well.
>
> Bill, if you look at the example in question, there was no vertical
> consideration that would have led to the spelling. The only possible
> reason
> was to get a microtonal pitch shift.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Kraig Grady wrote,

>What if it was going to C#?

What's the context?

>Like i said it is impossible to even talk about this without seeing the
context in which it occurred!

I saw the context -- it's published in Blackwood's book.

>Also the possibly of drift maybe quite offensive to your own musical
language but could be symbolic to such a composer as >Gesualdo. Maybe he
could not go back to where he was, like before his own traumatic event.

That could be a valid artistic interpretation of Gesualdo. But I wouldn't
call it a "historical" one . . . but who cares -- if you make good music,
that's all that matters.

Let me clarify my point of view on this, in case there's any confusion . . .
and in the hope of agreeing to disagree if our philosophies prove ultimately
incompatible.

I expect singers to sing melodic intervals fairly consistently (e.g., no
27:20 melodic fourths, etc.)
I expect singers to make slight tuning adjustments in order to yield JI in
vertical triads.
I expect singers to make slight tuning adjustments to counteract any overall
pitch drift, if they sense it occuring.

That's all! Now Vicentino's solution is a very precise way of acheving these
goals. But real singers singing in real time will of course be far less
precise -- more adjustment occuring here and less occuring there -- and may
not even acheive all the goals fully. Nevertheless, a tuning model which
ignores any of these goals will, in my opinion, deviate more severely and
noticeably from the efforts of a fine vocal ensemble than one that
incorporates all of them. So, if one were to, say, try to create a
synthesized version of a choral rendition of a Renaissance or early Baroque
piece, one could start with Vicentino's tuning, add small random errors,
throw in some slides and swoops, maybe a tiny bit of vibrato . . . and, if
one assumes that technology has progressed to the point where it can mimic
human singing realistically (perhaps someday it will), one should have a
realistic rendition . . .

Uh oh, I think I've just gotten myself in a lot of trouble by trying to get
out of it . . . well that's it for now . . .

Hello, there, and to join in on the dialogue while preparing to write
the second part of my main article, and also specifically to offer a
quick answer for now to a question from Bill Alves, please let me
offer a few interim remarks.

First, to Paul Erlich:

While maybe the language of my article may have been less clear to
others, you very correctly understood my point that as reported by
Palisca, Beneditti definitely was arguing that pitch drift made the
syntonic diatonic "not practicable, whether in instrements or voices."

As Palisca adds, "It is striking that in the very letter in which
Benedetti demonstrated the coincidence of vibrations in pitches
related as simple ratios, he proposed a system in which the
consonances deviate from these simplest ratios."

In leaving open the question of whether comma drifts might be
considered a vice and/or virtue, I was speaking for myself rather than
reporting the views of Benedetti or Palisca.

My purpose in discussing Benedetti, apart from the intrinsic interest
of the material, was to show that these issues were of interest to
16th-century theorists, and could, then as now, call forth different
views.

To Bill Alves:

Happily, your question regarding the two instrumental pieces of
Gesualdo, the _Canzona francese de Principe_ for keyboard, and the
four-part _Gagliarda_ which has often been interpreted as an ensemble
piece but could also be performed on keyboard (Glenn Watkins mentions
a recommendation of "viols or organ" as fitting this genre).

The Canzona is beautiful, and has lots of the ornamentation and
"fantastical" quality of keyboard music from this epoch around 1600.
Maybe most relevantly for this discussion, it has a 14-note range of
Eb-A#. Thus it could be played either on a 19-note (or larger)
chromatic harpsichord of Neapolitan vogue, or on a somewhat smaller
instrument with the appropriate split keys.

Watkins, as I'll discuss in the second part of my longer article,
suggests that the chromatic passages suggest an encounter with some
kind of archicembalo or the like -- there are ornaments producing
vertical diminished fourths and the like.

(Incidentally, Lasso's _Prophetiae Sibyllarum_ also has at least one
piece with a range of Eb-A#; this isn't to suggest that keyboards
participated in vocal performances of these pieces, nor to tie singers
to any fixed-pitch intonation, only to note an instance of this kind
of range.)

The Gagliarda, pretty much a typical texture of mostly note-against-
note with an engaging and stately quality, is Bb-A#, a 13-note range,
with a neat diagonal relationship at one point of D# in the highest
voice followed in the next sonority by Bb in the bass (with parallel
tenths between these parts descending a chromatic semitone, B3-D#4 to
Bb3-D4).

Again, if we assume a keyboard performance, or maybe an ensemble with
a keyboard as a "foundation" instrument (one manuscript has a "basso
continuo" identical to the lowest sounding voice of Gesualdo's piece),
either a 19-note or larger keyboard, or a smaller instrument with a
split Bb/A# key, would cover the range.

Of course, thanks for the fascinating item from the _New Grove_, which
confirms my own impression -- more in the coming post.

To Ibo Ortgies:

Thank you for bringing to this thread both your general erudition and
your special knowledge of keyboards with split keys or "subsemitones."
It's very pleasing how this discussion of Gesualdo is bringing out
more information on this general topic, including your most extensive
contributions here and on the World Wide Web.

To Johnny Reinhard:

First, thank you for advocating a position which I know is based on a
kind of performing experience which I cannot claim, not to mention a
far greater range of exposure to musics and intonations.

My own viewpoint would be that meantone -- or an adaptive intonation
for voices or other non-fixed-pitch instruments based more or less on
meantone steps adjusted to permit pure vertical concords -- is not so
much a "compromise" as an opportunity, for Vicentino or Gesualdo.

While there are many things I associate with Vicentino, "compromise"
isn't one of them, and the same goes for Gesualdo. The question
remains how their incredible musical statements can best be realized
in performance, and there we have lots of room for alternative
perspectives.

On some issues of theory and analysis, I'll address both your remarks
and those of Graham Breed.

To Johnny Reinhard and Graham Breed (and also again Paul Erlich):

There are various approaches not only to performing this music, but to
analyzing it. I find it natural that different people will apply their
own accustomed methods, ranging from 14th-century cadential theory to
16th-century concepts to 18th-19th century Roman numeral analysis to
Edward Lowinsky's "triadic atonality" (should we make that
"panmodality"?).

From a 16th-century viewpoint, I would say that the preference for a
major rather than minor third above the bass at significant points of
cadential repose -- or a harmonic rather than arithmetic division of
the fifth, with the major third below and minor third above (to use
Zarlino's terms, my own approach) -- is a general technique of the
era. Aaron documents it by remarks and examples in his _Toscanello_
and a treatise on the modes, and Vicentino and Zarlino make similar
points in the 1550's. Maybe the 18th century or later would call it a
_tierce de Picardie_ or "Picardy third" or the like, but in the 16th
century, starting around the epoch of Aaron, I'd call it mainly
"common practice."

Aside: one might wonder if a leaning in the late 15th and very early
16th century toward an Ab-C# meantone tuning (Ramos 1482 if we take
his keyboard tuning as in meantone, Schlick 1511) might reflect a
willingness to get along in E Phyrgian without a major third available
above the final. If we conclude in the traditional fashion on a fifth
and octave or the like, or accept a closing minor third (as might have
been the practice around 1500), then there's not necessarily a
problem. Once we lean toward the harmonic division as more conclusive,
as Aaron does in the 1520's, G# becomes a routine step (as in the
different context of later medieval practice), thus Eb-G# as the
standard range.

For 16th-century and early 17th-century music -- the "modern" side of
my usual era of orientation -- I would follow the theorists and, I
suspect, the composers, in looking at melody, two-voice progressions,
overall sonorities, and combined progressions.

My own training and inclination is to look at sonorities as
combinations of intervals, some of which Zarlino, for example,
compares in their different arrangements. The idea of "roots," as
opposed to intervals above the bass or between other parts, seems to
me mostly a later approach, although I recognize that Johannes Lippius
(1610, 1612) does describe a kind of inversion theory, with his
_basis_ comparable to the later "root" concept.

Just as some people's outlook on this music may be colored by
18th-century theory, mine may often be colored by 14th-century theory,
although the 16th century has its own character and logic despite our
sundry other associations, and I know that Gesualdo can't be reduced
to even the most inspired written theory any more than Wagner or
Schoenberg can -- or the earlier Perotin or Machaut or Landini, for
example.

For example, if I see a sonority of G3-B3-E4-B4, I might say (out of
context): "There's a major third and sixth above the bass which might
expand to the fifth and octave, while the major tenth between the
outer voices might move in parallel to arrive at F3-C4-F4-A4, another
complete harmonic division."

Here we have the traditional 14th-century element of M3-5 and M6-8,
still standard Renaissance progressions from "an imperfect concord to
the nearest perfect concord" (e.g. Ramos, Zarlino), plus the
16th-century element of 4:5:6 or 10:12:15 rather than 2:3:4 as the
complete stable sonority, so that the highest voice often moves to A4,
rather than to C5 in what is to me a "classic" 14th-century fashion.

Note that since Machaut's music was not evidently part of the
16th-century theoretical landscape, my medievalist associations could
be considered just as "anachronistic" as someone else's Rameauesque or
Wagnerian or Schoenbergian associations with this music.

While the medieval and Renaissance-Manneristic periods are in many
ways radically contrasting -- intonationally, to choose a most
relevant parameter -- they share what I might term a "combinative" or
"polydyadic" approach to verticality which for me is "natural,"
although to others it may be a less familiar outlook.

The idea of vertical sonorities progressing with the guidance of
two-voice resolutions, as some scholars of figured bass technique have
pointed out, is characteristic not only of medieval and Renaissance
technique, or of Manneristic technique in Gesualdo's age whether in
traditional polyphonic forms or in the new continuo-based genres, but
even in the German thoroughbass technique of around 1700 which served
as one grounding for Bach's music. By the end of the 17th century, of
course, major/minor tonality has become the increasingly prevailing
system, but some elements of the earlier 16th-17th century modal and
combinative approaches continue to exert a certain influence on
composers such as Bach, even as Rameau formulates a different
"chordal" point of view prevailing in the Classic-Romantic eras.

Since each of us approaches Gesualdo from the perspective of a
different conceptual map -- and cannot help doing so -- I mention some
of these considerations to suggest the value of multiple analyses
using whatever categories, notations, or methods we are each most at
home with. Theoretical sources from the 16th and early 17th centuries
can inform this process, but the diversity of viewpoints remains.

While our main focus is on intonation, it is difficult to discuss the
tuning of intervals or sonorities without naming them -- and revealing
something of our own maps and of ourselves.

Most respectfully,

Margo Schulter
mschulter@value.net

Hello, there, Bill Alves and Paul Erlich and everyone.

The idea of a 21-note chromatic system (seven diatonic notes plus
seven flats and seven sharps) seems very curious when applied to
Gesualdo or other composers of the 16th and early 17th centuries
practicing chromaticism or enharmonicism (the use of dieses or
fifthtones) in a meantone or meantone-like setting.

Glenn Watkins makes a statement similar to the one you quoted, Bill,
when he remarks that Gesualdo "extends the list of the sharps to the
complete complement of seven, though on the flat side, while he fails
to incorporate only the last flat (Fb), the fifth and sixth flats Gb
and Cb are rarely employed." See Watkins, _Gesualdo: The Man and His
Music_ (University of North Carolina Press, Chapel Hill, NC, 1973,
p. 195.

Maybe this concept of a 21-note chromatic set reflects some kind of
20th-century orientation, but from either a 16th-century perspective
or the viewpoint of general intonational structure, I would tend to
focus on two numbers: a "chromatic" set of 19 notes (e.g. Gb-B#), or
an "enharmonic" set of 31 notes, the complete cycle of Vicentino
(1555) or Colonna (1618).

In seeing why 19 or 31 notes are typical sizes for the special
chromatic or enharmonic keyboard instruments of this era, we might
focus on Ervin Wilson's concept of a "Moment of Symmetry" (MOS) in a
given kind of tuning system, here meantone with a dieses equal to
about 1/5-tone (i.e. a temperament at or near 1/4-comma with its pure
major thirds).

The typical _cembalo chromatico_ or "chromatic harpsichord" favored
around Naples in Gesualdo's epoch had 19 notes, typically tuned Gb-B#
(also the first 19 notes of Vicentino's archicembalo, making up his
lower manual, which thus in itself would be equivalent to such an
instrument).

This number of 19 defines a Moment of Symmetry or MOS, in which the
tuning system has only two sizes of adjacent steps: chromatic
semitones of 2/5-tone, and dieses of 1/5 tone. Here I'll use the
letters C for chromatic semitone, and D for diesis:

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

With an instrument tuned at or quite near to 1/4-comma, this MOS
leaves 12 chromatic semitones undivided into two diesis: one on either
side of each of the five notes D, E, G, A, and B, making ten; and one
immediately above each of the notes F and C, adding two more.

In the special case of 19-tone equal temperament (19-tET), described
and advocated by Guillaume Costeley in 1570, the diesis has a size
identical to that of the chromatic semitone, either being equal to
1/3-tone, so that this MOS defines a complete circulating system. The
1/3-comma temperament of Salinas (1577) with pure minor thirds
produces an almost identical circulating 19-note system.

For the instruments we are here considering, however, tempered at or
near 1/4-comma, the next MOS is at 31 notes, making the complete system
favored by Vicentino, with its property of virtual musical closure
demonstrated in 1618 by Colonna in his "example of circulation"
cadencing in turn on each of the 31 notes in the cycle of fifths.

Here there is only one basic type of adjacent interval, the diesis,
although in 1/4-comma meantone there is a slight difference in size
between a larger diesis or fifthtone at 128:125 (~41.06 cents) and a
smaller diesis of about 34.99 cents (very close to 50:49). In this
diagram, I show the 19-note "chromatic" set plus the additional
12-note set together making up a full 31-note enharmonic cycle, using
an asterisk (*) to represent Vicentino's dot above a note raised by a
diesis:

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

Thus it seems logical to me to speak of a 19-note chromatic set, or a
full 31-note enharmonic set; the idea of a "21-note chromatic set"
seems to me maybe a reflection of some viewpoint not especially
oriented toward either the keyboard instruments we are considering or
their tuning systems.

While the distinction between a 19-note chromatic set and a 31-note
enharmonic one seems natural, and fits the two kinds of keyboards
which especially typify this adventurous aspect of music in Gesualdo's
era (not to exclude smaller instruments with some split keys), the
motivation to move beyond the bounds of a 19-set might take on at
least three forms.

First, in the music of Vicentino and Colonna, there is the obvious
motivation of direct enharmonicism or "diesisism," with direct
fifthtone steps or altered progressions made possible by having two
keyboard ranks or manuals a fifthtone apart. Such a technique is
reflected in the special notations of Vicentino and Colonna to show
notes a fifthtone above or below usual steps in the 19-note gamut.

Secondly, in the vocal music of Gesualdo or in one piece for chromatic
harpsichord by Trabaci, there may be the desire to go slightly beyond
the usual 19-note gamut in order to effect a remote transposition or
to obtain sonorities with major or minor thirds in positions near the
edges of the gamut. For example, Gesualdo uses Cb (Vicentino's B*) in
one madrigal, while Trabaci writes D#-F##-A#, inviting the player of a
"common" chromatic harpsichord with only the usual 19 notes to
substitute D#-F#-A# (with the minor third).

Finally, as illustrated in Colonna's circulating piece, one might
desire to have a full 31-note system because of its musical closure.
Costeley's 19-note "thirdtone" system and the almost identical
1/3-comma system of Salinas also share this property, but arguably
with some compromise in euphony as compared with the 1/4-comma tuning
owing to the greater temperament of the fifth (~7.22 cents, or ~7.17
cents in the 1/3-comma tuning of Salinas), narrowing the major third
by the same amount.

Although it is possible to go beyond 19 notes for reasons other than
the exuberant enharmonicism of Vicentino or Colonna, nevertheless the
association of "chromatic" keyboards with a 19-note set, and of
"enharmonic" keyboards with a 31-note set, seems generally conducive
to the outlook of the tuning systems and music.

Most respectfully,

Margo Schulter
mschulter@value.net