How useful is Vicentino's method?

I don't want to be a "Vicentino basher", but it strikes me that his
proposed methods have serious limitations. I speak of the twin circles
of 31-tET (or quarter-comma meantone) tuned 1/4 syntonic comma apart,
and subsets thereof, which Paul E and Margo have spoken about at length.

. Harmonically, how are chords like C,G,D or C,G,A to be constructed?
Each, ideally, requires a third set of notes because of the chain
of fifths implied by the chord. JI cannot be achieved here,
without increasing the number of available notes beyond 62.

. Common transitions such as C major -> A minor, with tied notes,
will require that at least one note that should be tied will have
to be dragged from one manual to the other in mid-stream. This is
not a good musical effect!

Of course, in the days before dynamic tuning, his proposals were about
as good as could reasonably be achieved, but by today's standards his
techniques would seem to be lacking.

Or perhaps I'm wrong? Does anyone have an actual sequence tuned by
the Vicentino method that we could compare to other tuning options?

JdL

John deLaubenfels wrote,

>Harmonically, how are chords like C,G,D or C,G,A to be constructed?
>Each, ideally, requires a third set of notes because of the chain
>of fifths implied by the chord. JI cannot be achieved here,
>without increasing the number of available notes beyond 62.

You'd leave one or more intervals in meantone. Remember, chords like C,D,G,A
or C,D,E,G,A or C,D,E,G,A,B sound better in meantone than JI anyway.

>Common transitions such as C major -> A minor, with tied notes,
>will require that at least one note that should be tied will have
>to be dragged from one manual to the other in mid-stream. This is
>not a good musical effect!

>Of course, in the days before dynamic tuning, his proposals were about
>as good as could reasonably be achieved, but by today's standards his
>techniques would seem to be lacking.

That is quite a double-standard! First you criticize the tuning for a
practical difficulty with the two keyboards, then you compare it to "dynamic
tuning" by which you presumably mean computer-controlled variable tuning for
each note. Imagine if you had to try to acheive the latter with the same
technology you find difficult for the former! It would be impossible!

Vicentino's second tuning should be taken as an adaptive JI solution that
can be acheived with a fairly small number of pitches. A fair comparison
might be with a section of the 5-limit JI lattice, perhaps even allowing
schismatic equivalency (i.e., Helmholtz's 24-tone quasi-JI system). For a
piece of music that stays within the traditional keys of pre-Bach music,
you'd need about 24 fixed pitches in either system. However, while both
systems would keep the vertical pain of triads to zero (with some vertical
pain in certain non-5-odd-limit chords), the Vicentino system would keep all
the horizontal retune motions below the audible threshold, while the strict
or schismatic JI systems would have frequent comma-sized retune motions.
Hence the Vicentino method is superior, for the number of fixed pitches
involved.

[I wrote:]
>>Harmonically, how are chords like C,G,D or C,G,A to be constructed?
>>Each, ideally, requires a third set of notes because of the chain
>>of fifths implied by the chord. JI cannot be achieved here,
>>without increasing the number of available notes beyond 62.

[Paul E wrote:]
>You'd leave one or more intervals in meantone. Remember, chords like
>C,D,G,A or C,D,E,G,A or C,D,E,G,A,B sound better in meantone than JI
>anyway.

Chords with exactly three notes in a chain of fifths can be tuned to JI,
so why not do it? Chords with four or more notes in chains of fifths
should tend toward meantone, we agree. But the former are probably much
more common than the latter, and there is no legitimate reason to
relegate them to meantone tuning with its flat fifths.

[JdL:]
>>Common transitions such as C major -> A minor, with tied notes,
>>will require that at least one note that should be tied will have
>>to be dragged from one manual to the other in mid-stream. This is
>>not a good musical effect!

>>Of course, in the days before dynamic tuning, his proposals were about
>>as good as could reasonably be achieved, but by today's standards his
>>techniques would seem to be lacking.

[Paul:]
>That is quite a double-standard! First you criticize the tuning for a
>practical difficulty with the two keyboards, then you compare it to
>"dynamic tuning" by which you presumably mean computer-controlled
>variable tuning for each note. Imagine if you had to try to acheive the
>latter with the same technology you find difficult for the former! It
>would be impossible!

Yes, and how does this make my statement a "double standard"?? I'm
simply saying that its usefulness has come and gone.

[Paul:]
>Vicentino's second tuning should be taken as an adaptive JI solution
>that can be acheived with a fairly small number of pitches. A fair
>comparison might be with a section of the 5-limit JI lattice, perhaps
>even allowing schismatic equivalency (i.e., Helmholtz's 24-tone
>quasi-JI system). For a piece of music that stays within the
>traditional keys of pre-Bach music, you'd need about 24 fixed pitches
>in either system. However, while both systems would keep the vertical
>pain of triads to zero (with some vertical pain in certain
>non-5-odd-limit chords), the Vicentino system would keep all the
>horizontal retune motions below the audible threshold, while the strict
>or schismatic JI systems would have frequent comma-sized retune
>motions. Hence the Vicentino method is superior, for the number of
>fixed pitches involved.

And what use does this have? You have to slide sounding notes to make
it work, so you're already in the electronic realm, so who cares how
many pitches you tune to, as long as tuning motion is acceptable?

JdL

John -- let's be clear. I'm not saying Vicentino's method has any benefits
over the methods you're currently using for making adaptively-tuned MIDI
files. At one point I noticed that Vicentino's method would have done better
than the results you were generating so I brought it up. However, since the
introduction of a COFT ground into your program (or perhaps ever earlier),
that is no longer true and your methods are superior.

However, if we are talking about _real instrumental performance_ and getting
vertical triads in JI, the number of fixed pitches/notation symbols is an
issue, and if the music is from the Renaissance, Baroque, or Classical
periods, Vicentino's method is substantially better than other methods which
have been proposed.

>Chords with exactly three notes in a chain of fifths can be tuned to JI,
>so why not do it? Chords with four or more notes in chains of fifths
>should tend toward meantone, we agree. But the former are probably much
>more common than the latter, and there is no legitimate reason to
>relegate them to meantone tuning with its flat fifths.

If you have a sus4 chord, C-F-G, making C-G a just fifth and C-F a meantone
fourth will sound ok, and this chord is a dissonance which resolves to a
5-odd-limit triad anyway in the repertoire in question.

>Yes, and how does this make my statement a "double standard"?? I'm
>simply saying that its usefulness has come and gone.

But you critique the practical difficulty of moving sustained notes from one
keyboard to the other. Such a critique, if extended to your methods, would
be devastating, wouldn't it?

>And what use does this have? You have to slide sounding notes to make
>it work, so you're already in the electronic realm,

Huh? What if you're writing a piece for strings and/or winds?

>so who cares how
>many pitches you tune to, as long as tuning motion is acceptable?

Again, in the electronic realm, Vicentino's method is no longer a contender
against your methods for adaptive tuning. That's not the context in which
Vicentino's method had been being brought up, though.

[Paul E. wrote:]
>John -- let's be clear. I'm not saying Vicentino's method has any
>benefits over the methods you're currently using for making
>adaptively-tuned MIDI files. At one point I noticed that Vicentino's
>method would have done better than the results you were generating so
>I brought it up. However, since the introduction of a COFT ground into
>your program (or perhaps ever earlier), that is no longer true and your
>methods are superior.

Hey, you're just trying to soften me up, right? ;->

[Paul:]
>However, if we are talking about _real instrumental performance_ and
>getting vertical triads in JI, the number of fixed pitches/notation
>symbols is an issue, and if the music is from the Renaissance, Baroque,
>or Classical periods, Vicentino's method is substantially better than
>other methods which have been proposed.

OK, but what real-life instruments are both flexible enough to
accommodate V's methods but not flexible enough to go a bit further?

[JdL:]
>>Chords with exactly three notes in a chain of fifths can be tuned to
>>JI, so why not do it? Chords with four or more notes in chains of
>>fifths should tend toward meantone, we agree. But the former are
>>probably much >more common than the latter, and there is no legitimate
>>reason to relegate them to meantone tuning with its flat fifths.

[Paul:]
>If you have a sus4 chord, C-F-G, making C-G a just fifth and C-F a
>meantone fourth will sound ok, and this chord is a dissonance which
>resolves to a 5-odd-limit triad anyway in the repertoire in question.

Well... it's not the end of the world, to be sure. But, to reiterate
a point that seems to irritate you, the context already makes it a
dissonance, and the tuning can still be just without disrupting that
(and, my ear definitely asks fourths and fifths to be closer than
meantone to just, whatever the context!!). Also, are you sure there
aren't other contexts where such chords might appear, where their
tuning should more urgently be just?

[JdL:]
>>Yes, and how does this make my statement a "double standard"?? I'm
>>simply saying that its usefulness has come and gone.

[Paul:]
>But you critique the practical difficulty of moving sustained notes
>from one keyboard to the other. Such a critique, if extended to your
>methods, would be devastating, wouldn't it?

My methods are only applicable to continuous variation of pitch.

[JdL:]
>>And what use does this have? You have to slide sounding notes to make
>>it work, so you're already in the electronic realm,

[Paul:]
>Huh? What if you're writing a piece for strings and/or winds?

OK, then they can go beyond Vicentino already.

[JdL:]
>>so who cares how
>>many pitches you tune to, as long as tuning motion is acceptable?

[Paul:]
>Again, in the electronic realm, Vicentino's method is no longer a
>contender against your methods for adaptive tuning. That's not the
>context in which Vicentino's method had been being brought up, though.

OK, fine. I guess you're acknowledging the point I was trying to make.
Hey, I can only hope I could have done a fifth as well as Vicentino if
I had lived when he lived! I'm just saying that, given the very useful
variability available from electronic instruments (AND, as you point
out, many acoustic instruments as well, with the noteable exception of
the piano!), his methods are of historical interest far more than of
practical applicability today.

JdL

>OK, but what real-life instruments are both flexible enough to
>accommodate V's methods but not flexible enough to go a bit further?

Say, a two-manual organ. Or a synth system which allows a limited tuning
table and doesn't support independent pitch bends for the voices.

>Well... it's not the end of the world, to be sure. But, to reiterate
>a point that seems to irritate you, the context already makes it a
>dissonance, and the tuning can still be just without disrupting that
>(and, my ear definitely asks fourths and fifths to be closer than
>meantone to just, whatever the context!!). Also, are you sure there
>aren't other contexts where such chords might appear, where their
>tuning should more urgently be just?

Only in Medieval or 20th century music.

>OK, fine. I guess you're acknowledging the point I was trying to make.
>Hey, I can only hope I could have done a fifth as well as Vicentino if
>I had lived when he lived! I'm just saying that, given the very useful
>variability available from electronic instruments (AND, as you point
>out, many acoustic instruments as well, with the noteable exception of
>the piano!), his methods are of historical interest far more than of
>practical applicability today.

To someone (and there are many still today) who is trying to render
common-practice music in strict JI, Vicentino's method can be of
_pedagogical_ utility.

[Paul E:]
>To someone (and there are many still today) who is trying to render
>common-practice music in strict JI, Vicentino's method can be of
>_pedagogical_ utility.

Hold on a sec: give me a definition, again, of "strict JI"? I remember
you correcting me when I used the term once, and my vague recollection
is/was that it is a very reSTRICTive term; I THOUGHT it meant "honoring"
commas among other things. Yes, no?

"_pedagogical_ utility." Well, what can I say? Is there any
correlation between that and actual enjoyment of music? Sorry, I'm
being cynical.

JdL

>Hold on a sec: give me a definition, again, of "strict JI"? I remember
>you correcting me when I used the term once, and my vague recollection
>is/was that it is a very reSTRICTive term; I THOUGHT it meant "honoring"
>commas among other things. Yes, no?

Strict JI means that all the pitches come from a connected portion of the JI
lattice. All melodic, as well as harmonic, intervals are JI.

>"_pedagogical_ utility." Well, what can I say? Is there any
>correlation between that and actual enjoyment of music?

Sure there is, if we're trying to win over practitioners of ET or strict JI.