Re: Vicentino's adaptive JI and 16th-century music

Hello, there, and in view of recent dialogue, I'd like strongly to
present my own view that Nicola Vicentino's "adaptive JI" scheme of
1555, apparently proposed independently by Paul Erlich, deserves to be
heard as an authentic Renaissance approach to Renaissance music.

First of all, I'd like to emphasize that to describe an intonational
scheme as "authentic" or "ideal" for a given period or style doesn't
mean that it is the _only_ artistic possibility for that era, let
alone for other eras of music it was obviously not intended to
address.

If John deLaubenfels comes up with an alternative and smoother scheme
for Renaissance music -- and as Paul has noted, he has already done
this for various periods -- then let's by all means use that as well.
Historical tunings deserve to be heard, and to be experimented with
and enlarged in derivative contexts (e.g. medieval Pythagorean in a
24-note Xeno-Gothic variation); but this doesn't mean that we have to
exclude everything else.

John, congratulating you for your impressive musical breakthroughs and
for the artistic as well as mathematical discernment needed along the
way, I'd emphasize that to champion historical tunings and methods is
not to discourage but rather to encourage innovations. It's
fascinating to be able say both, "Here's how Vicentino approaches
16th-century JI, as you'll hear in this performance"; and "Here's how
John deLaubenfels approaches it 445 years later." We can learn, and
grow, from both experiences.

The main point I would make about Vicentino's scheme is that it is a
_16th-century_ scheme of _5-limit_ adaptive JI, and should be viewed
artistically in that context. This isn't at all to exclude dialogue
where you (John and Paul) and others see how well it does or doesn't
fit other styles or periods; it might fit some 18th-century music, for
example, just as 1/4-comma meantone might fit some of Mozart very
nicely (using as many notes per octave as required).

Also, using Vicentino's method as a kind of "benchmark" for various
styles and periods -- can "adaptive tuning system X" do as well or
better? -- is fine.

What I'd like to emphasize is simply that this is a 16th-century
scheme for 16th-century music, which Vicentino himself described as
"mixed and tempered music."

If we focus on this primary setting and purpose of Vicentino's
adaptive JI system, we may be able to answer a number of questions and
maybe even to propose some "educated guesses" about what a performer
_might_ have done at the keyboard to handle certain "problem
situations." Of course, these "answers" and "guesses" are quite likely
to reflect my own viewpoints and biases; someone like Judith Conrad,
who plays (and _tunes_) actual historical instruments may have lots
more to say from a more informed perspective.

First of all, as Paul Erlich has observed, a sonority with two fifths
or fourths, or a fifth and a fourth, such as C-G-D or C-F-G, is an
independent concord in the Gothic and 20th-century eras of Western
European and related compositional styles (mildly unstable in some
Gothic styles, possibly stable in modern styles), but definitely a
dissonance in the 16th century, more specifically a suspension or the
like. Having one of those fifths or fourths tempered in the usual
meantone manner is no problem, in my view.

From experience (albeit on a synthesizer rather than a period organ or
harpsichord), however, I know that handling these sonorities with a
classic JI system like Zarlino's 15-note or 16-note octave _is_ a
problem, because in D-G-A one of those fifths or fourths is going to
be impure by a full syntonic comma! By all means give me a meantone
compromise in a 16th-century setting; in a medieval setting, where we
do want to maximize the consonance of these sonorities, Pythagorean
gives a very nice and pure 6:8:9.

How about C-G-A? As Thomas Morley (1597) tells us, taking "the fifth
and sixth together" is done mainly when "a discord is taken," and can
make "the best of closes" -- that is, it's a combination with tension
leading up to a cadence.

Again, G-A is not a 5-odd-limit interval, and Vicentino's system is
designed to get pure 5-odd-limit concords, not to optimize every
dissonant sonority also. Since C-G-A is a point of tension, having the
fifth in meantone, for example, shouldn't hurt and might possibly
underscore the musical action at this point.

How about a more serious practical problem: situations like the very
common 16th-century progression between two sonorities where the bass
moves by a third, e.g., in a MIDI-like notation with C4 as middle C:

F4 F4 G4 G4
C4 D4 E4 E4
A3 A3 C4 B3
F3 D3 or C3 E3

For a real-time performer as opposed to a player-harpsichord or MIDI
sequencer or the like, there's a solution I'd like to dare to mention:
now and then, revert to common meantone. In other words, Vicentino's
scheme could be used by an expert performer to get frequent and
beautiful adaptive JI, but not necessarily "perfect" adaptive JI.

The beauty of Vicentino's scheme, in my view, is that either manual has a
quite serviceable meantone tuning to "fall back on" at points where the
complexities of absolutely consistent adaptive JI might overwhelm the
player.

The first of 31-note-division tuning of Vicentino's archicembalo may also
support this kind of viewpoint. With his practical 36-note instrument,
having used 31 notes for the complete meantone cycle, he used the
remaining five as "comma keys" for pure fifths with the most frequently
used diatonic notes -- or, in his theoretical 38-note version, seven such
keys providing pure fifths for the usual diatonic notes.

What this says to me is that Vicentino was considering adaptive JI as a
beautiful effect even if it could only be used at _certain_ points in a
piece, just as a viol consort might tune many but not all sonorities with
just fifths and thirds. With the 31-note system, a pure sonority now and
then was considered worthwhile against a backdrop of meantone. With the
full adaptive JI system, maybe a meantone interval or sonority here and
there in a setting of more frequent vertical JI was likewise considered
fine.

Rather than speak of a departure from pure vertical JI as "pain,"
although this is certainly a graphic term, John, I might speak more
gently of "stress" or "tension." Either a minor third or fifth
tempered as in the common meantone of the 16th century, or a fifth a
syntonic comma narrow, is "impure" -- but there is a certain
difference here in the level of stress or tension.

From a likely Renaissance viewpoint, or at any rate my viewpoint as
someone who finds 1/4-comma meantone natural and beautiful for this
music, meantone on keyboards is the norm, and emulating Ptolemy's
syntonic diatonic on a keyboard an "extraordinary" effect. Vicentino
himself, in his writings, takes temperament as the norm and the "pure
fifth" tuning as a special effect.

In short, I suspect that an adept performer may in practice have mixed
much of the best (adaptive vertical JI) with some of the merely good
(normal meantone). With automated performance, of course, we can now
produce Vicentino's potential best: a beautiful system of vertical JI
for 16th-century music, nicely fitting its scheme of concord/discord.

In a radically different context, this is the approach I have taken
with a "multi-prime" neo-Gothic JI scheme combining pure fifths with
14:11 major thirds and the like. One 12-note keyboard I tune in this
scheme, the other in standard Pythagorean with pure fifths and fourths
in all the accustomed places. If in doubt, I can simply revert to
Pythagorean. Here the shift typically involves a comma of 896:891, a
bit less than 10 cents, with the shift in Vicentino's system typically
smaller (1/4 syntonic comma, ~5.38 cents).

With Vicentino's scheme, my main reaction is this: "Now that we have
the technology to pull this off by means of automated performance,
let's hear this great composer's extraordinary and ingenious
intonation applied to 16th-century music."

Just as Judith Conrad's performances on historical instruments don't
prevent others from using electronic ones for the same repertories, so
Vicentino's scheme doesn't prevent us from using others. However, it
would be very sad if performances on historical instruments stopped --
or if Vicentino's adaptive JI scheme weren't heard in all its wonder.

Most respectfully,

Margo Schulter
mschulter@value.net

Margo, thanks for your post. As always, I am most appreciative of your
combination of courtesy, candor, and scholarliness.

[Margo:]
>Hello, there, and in view of recent dialogue, I'd like strongly to
>present my own view that Nicola Vicentino's "adaptive JI" scheme of
>1555, apparently proposed independently by Paul Erlich, deserves to be
>heard as an authentic Renaissance approach to Renaissance music.

No argument, certainly! Where can one find an example, I wonder?

>First of all, I'd like to emphasize that to describe an intonational
>scheme as "authentic" or "ideal" for a given period or style doesn't
>mean that it is the _only_ artistic possibility for that era, let
>alone for other eras of music it was obviously not intended to
>address.

>If John deLaubenfels comes up with an alternative and smoother scheme
>for Renaissance music -- and as Paul has noted, he has already done
>this for various periods -- then let's by all means use that as well.
>Historical tunings deserve to be heard, and to be experimented with
>and enlarged in derivative contexts (e.g. medieval Pythagorean in a
>24-note Xeno-Gothic variation); but this doesn't mean that we have to
>exclude everything else.

Agreed, certainly.

>John, congratulating you for your impressive musical breakthroughs and
>for the artistic as well as mathematical discernment needed along the
>way, I'd emphasize that to champion historical tunings and methods is
>not to discourage but rather to encourage innovations. It's
>fascinating to be able say both, "Here's how Vicentino approaches
>16th-century JI, as you'll hear in this performance"; and "Here's how
>John deLaubenfels approaches it 445 years later." We can learn, and
>grow, from both experiences.

Would you be my press agent?

>The main point I would make about Vicentino's scheme is that it is a
>_16th-century_ scheme of _5-limit_ adaptive JI, and should be viewed
>artistically in that context. This isn't at all to exclude dialogue
>where you (John and Paul) and others see how well it does or doesn't
>fit other styles or periods; it might fit some 18th-century music, for
>example, just as 1/4-comma meantone might fit some of Mozart very
>nicely (using as many notes per octave as required).

What I am trying to sort out is this: how much of Vicentino's methods
are expressive of an ideal vision of 5-limit adaptive JI ideally suited
to the music of his day, and how much are concessions to the limitations
of his technologies? It's one of those questions that can never be
fully answered, and, as you know, I am also unabashed about mutating old
music in ways that please me, without necessarily being "authentic", but
the question is still of considerable interest.

>Also, using Vicentino's method as a kind of "benchmark" for various
>styles and periods -- can "adaptive tuning system X" do as well or
>better? -- is fine.

>What I'd like to emphasize is simply that this is a 16th-century
>scheme for 16th-century music, which Vicentino himself described as
>"mixed and tempered music."

>If we focus on this primary setting and purpose of Vicentino's
>adaptive JI system, we may be able to answer a number of questions and
>maybe even to propose some "educated guesses" about what a performer
>_might_ have done at the keyboard to handle certain "problem
>situations." Of course, these "answers" and "guesses" are quite likely
>to reflect my own viewpoints and biases; someone like Judith Conrad,
>who plays (and _tunes_) actual historical instruments may have lots
>more to say from a more informed perspective.

>First of all, as Paul Erlich has observed, a sonority with two fifths
>or fourths, or a fifth and a fourth, such as C-G-D or C-F-G, is an
>independent concord in the Gothic and 20th-century eras of Western
>European and related compositional styles (mildly unstable in some
>Gothic styles, possibly stable in modern styles), but definitely a
>dissonance in the 16th century, more specifically a suspension or the
>like. Having one of those fifths or fourths tempered in the usual
>meantone manner is no problem, in my view.

Well, I'm close to agreeing; it's not a make-or-break issue, but as I've
said, compromising the tuning of these chords is not, in my view,
necessary or beneficial.

>From experience (albeit on a synthesizer rather than a period organ or
>harpsichord), however, I know that handling these sonorities with a
>classic JI system like Zarlino's 15-note or 16-note octave _is_ a
>problem, because in D-G-A one of those fifths or fourths is going to
>be impure by a full syntonic comma! By all means give me a meantone
>compromise in a 16th-century setting; in a medieval setting, where we
>do want to maximize the consonance of these sonorities, Pythagorean
>gives a very nice and pure 6:8:9.

Love that pure 6:8:9!!

>How about C-G-A? As Thomas Morley (1597) tells us, taking "the fifth
>and sixth together" is done mainly when "a discord is taken," and can
>make "the best of closes" -- that is, it's a combination with tension
>leading up to a cadence.

>Again, G-A is not a 5-odd-limit interval, and Vicentino's system is
>designed to get pure 5-odd-limit concords, not to optimize every
>dissonant sonority also. Since C-G-A is a point of tension, having the
>fifth in meantone, for example, shouldn't hurt and might possibly
>underscore the musical action at this point.

Well... forgetting the major second G-A, we still have C-G and A-C to
worry about tuning. I'd rather get them closer to JI.

>How about a more serious practical problem: situations like the very
>common 16th-century progression between two sonorities where the bass
>moves by a third, e.g., in a MIDI-like notation with C4 as middle C:

>F4 F4 G4 G4
>C4 D4 E4 E4
>A3 A3 C4 B3
>F3 D3 or C3 E3

>For a real-time performer as opposed to a player-harpsichord or MIDI
>sequencer or the like, there's a solution I'd like to dare to mention:
>now and then, revert to common meantone. In other words, Vicentino's
>scheme could be used by an expert performer to get frequent and
>beautiful adaptive JI, but not necessarily "perfect" adaptive JI.

>The beauty of Vicentino's scheme, in my view, is that either manual has a
>quite serviceable meantone tuning to "fall back on" at points where the
>complexities of absolutely consistent adaptive JI might overwhelm the
>player.

Quite right, Margo. Where there is a "manual pump" going on in the
score, one can just remain in one manual till things calm down, then
restore examples of pure fifths as it becomes convenient.

>The first of 31-note-division tuning of Vicentino's archicembalo may also
>support this kind of viewpoint. With his practical 36-note instrument,
>having used 31 notes for the complete meantone cycle, he used the
>remaining five as "comma keys" for pure fifths with the most frequently
>used diatonic notes -- or, in his theoretical 38-note version, seven such
>keys providing pure fifths for the usual diatonic notes.

>What this says to me is that Vicentino was considering adaptive JI as a
>beautiful effect even if it could only be used at _certain_ points in a
>piece, just as a viol consort might tune many but not all sonorities with
>just fifths and thirds. With the 31-note system, a pure sonority now and
>then was considered worthwhile against a backdrop of meantone. With the
>full adaptive JI system, maybe a meantone interval or sonority here and
>there in a setting of more frequent vertical JI was likewise considered
>fine.

OK, point taken.

>Rather than speak of a departure from pure vertical JI as "pain,"
>although this is certainly a graphic term, John, I might speak more
>gently of "stress" or "tension." Either a minor third or fifth
>tempered as in the common meantone of the 16th century, or a fifth a
>syntonic comma narrow, is "impure" -- but there is a certain
>difference here in the level of stress or tension.

Well, to me the terms are virtually synonymous, but I'm open to a
different choice of words. Here, though, you seemingly seek to
differentiate the perception of deviation from JI. That, of course, is
more a matter of taste of individual ears than of choice of words.

>From a likely Renaissance viewpoint, or at any rate my viewpoint as
>someone who finds 1/4-comma meantone natural and beautiful for this
>music, meantone on keyboards is the norm, and emulating Ptolemy's
>syntonic diatonic on a keyboard an "extraordinary" effect. Vicentino
>himself, in his writings, takes temperament as the norm and the "pure
>fifth" tuning as a special effect.

OK...

>In short, I suspect that an adept performer may in practice have mixed
>much of the best (adaptive vertical JI) with some of the merely good
>(normal meantone). With automated performance, of course, we can now
>produce Vicentino's potential best: a beautiful system of vertical JI
>for 16th-century music, nicely fitting its scheme of concord/discord.

>In a radically different context, this is the approach I have taken
>with a "multi-prime" neo-Gothic JI scheme combining pure fifths with
>14:11 major thirds and the like. One 12-note keyboard I tune in this
>scheme, the other in standard Pythagorean with pure fifths and fourths
>in all the accustomed places. If in doubt, I can simply revert to
>Pythagorean. Here the shift typically involves a comma of 896:891, a
>bit less than 10 cents, with the shift in Vicentino's system typically
>smaller (1/4 syntonic comma, ~5.38 cents).

>With Vicentino's scheme, my main reaction is this: "Now that we have
>the technology to pull this off by means of automated performance,
>let's hear this great composer's extraordinary and ingenious
>intonation applied to 16th-century music."

But who is doing this? I want to hear it too! It's just that I barely
have time to pursue the course that makes the most sense to me, much
less an interesting historical vision and method.

>Just as Judith Conrad's performances on historical instruments don't
>prevent others from using electronic ones for the same repertories, so
>Vicentino's scheme doesn't prevent us from using others. However, it
>would be very sad if performances on historical instruments stopped --
>or if Vicentino's adaptive JI scheme weren't heard in all its wonder.

I hope it's clear that I very much agree! My basis for calling up its
alleged limitations is really all completely speculative in the absence
of actual examples of this tuning.

JdL