Re: 7-limit thinking

The exchange was...

>
> > 7-limit thinking has been absolutely fundamental since Monteverdi,
> > IMHO.
>
> We will have to agree to disagree, then.
>

I'm with Paul (and my ears) on this one. If someone can come up with
performance practice materials from Monteverdi's time saying that "the
subdominant must be properly lowered to provide the full sweetness of
the resolution" or some such then I won't buy that they did it. Just
because we have access to musics now which DO use the 4:5:6:7 chord doesn't
mean that we can impose it on musics then.

Note that materials regarding the flattenning of the leading tone during
the meantone era (in contradiction to performance practices today) are
available (Mozart), so we can rightly believe that meantone was not just
the talk of theoriticians at the time. Find Monteverdis performance
note saying that the 4:3 subdominant (which was certainly known then,
had to be "bruised slightly" to properly express the music of the "thirds
revolution. Why were black keys split and not white keys? (Augmented six
!= dominant seven).

But I'm in full agreement regarding Paganini and Liszt!

(Yeah, its sort of sacrelige to continue with these discussions at
times like these, then again, the only non-war talk on the news
is the economics news which, despite being what this is all about,
is still bit on the disqusting side...)

Bob Valentine

[Gene wrote:]
>>>7-limit thinking has been absolutely fundamental since Monteverdi,
>>>IMHO.

[Paul E wrote:]
>>We will have to agree to disagree, then.

[Bob Valentine:]
>I'm with Paul (and my ears) on this one. If someone can come up with
>performance practice materials from Monteverdi's time saying that "the
>subdominant must be properly lowered to provide the full sweetness of
>the resolution" or some such then I won't buy that they did it.

Am I understanding you correctly, as saying that to your ears, 7-limit
tunings don't work for Monteverdi's music, and that you would reject
them even if they turned out to be the practice of the time? If so, I
have no objection, since this is strictly a matter of taste, and we are
always free to second-guess the practices of past masters, even as we
celebrate their achievements.

>Just
>because we have access to musics now which DO use the 4:5:6:7 chord
>doesn't mean that we can impose it on musics then.

Again I am not sure exactly what you are asserting here. We cannot
change historical fact, to be sure (though we are free to doubt
something which is _presented_ as historical fact), but we certainly
can impose any tuning at all on any music at all.

>(Yeah, its sort of sacrelige to continue with these discussions at
>times like these, then again, the only non-war talk on the news
>is the economics news which, despite being what this is all about,
>is still bit on the disqusting side...)

I think it would be wrong to put music aside at any time. To do so
would be to succumb to the wishes of those who would harm us. Of course
what has happened touches each of us at every moment of the day, but if
anything it is all the _more_ vital to keep beauty in our lives.

JdL

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

> Again I am not sure exactly what you are asserting here. We cannot
> change historical fact, to be sure (though we are free to doubt
> something which is _presented_ as historical fact), but we certainly
> can impose any tuning at all on any music at all.

It's done all the time, as I pointed out before. If Glenn Gould can
sit down and hum along to Bach on his Steinway then it seems absurd
to cavil at retuning V7, so long as it works. To say composers
*wanted* it sharp makes no sense, since they didn't have a choice and
therefore did not choose to make it sharp. To say they wrote their
music with it sharp is certainly true, and may very well effect the
result of any retuning. The only way to decide is to try it and see
if it sounds good.

> >(Yeah, its sort of sacrelige to continue with these discussions at
> >times like these, then again, the only non-war talk on the news
> >is the economics news which, despite being what this is all about,
> >is still bit on the disqusting side...)

> I think it would be wrong to put music aside at any time.

I find thinking about anything which gets that horrible picture of
the airplane hitting the WTC out of my mind is excellent, and I am
sorry even to bring it up.

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:

> I'm with Paul (and my ears) on this one. If someone can come up
with
> performance practice materials from Monteverdi's time saying
that "the
> subdominant must be properly lowered to provide the full sweetness
of
> the resolution" or some such then I won't buy that they did it.

Why don't people sing Dunstaple and Dufay in a Pythagorean scale? The
music doesn't come with a book of instructions, telling you how
sharp to make the third, and people deduce performence practice from
the nature of the music itself, not from the writings of contemporary
theorists. If we have _a capella_ music using the V7, how do we know
how sharp to sing it--in fact, how sharp is it actually sung? I
suspect the choir director has a lot to do with that.

Just
> because we have access to musics now which DO use the 4:5:6:7 chord
doesn't
> mean that we can impose it on musics then.

Just because we have 12-et now doesn't mean we can impose it on
musics then--except that we do. How do you know how something 300
years ago was sung? Where is the evidence people *wanted* the seventh
degree sharp?

> Note that materials regarding the flattenning of the leading tone
during
> the meantone era (in contradiction to performance practices today)
are
> available (Mozart), so we can rightly believe that meantone was not
just
> the talk of theoriticians at the time.

Keyboard music in particular *must* use a fixed scale; I don't think
you can use it as the touchstone of all practice, however.

Why were black keys split and not white keys? (Augmented six
> != dominant seven).

It was easier? A keyboard with split white keys in 19-et would have
made sense, but would be harder to conceptualize. I don't think you
can conlude anything about the 7-limit from this, because it would
have made a lot more sense in the 5-limit.

--- In tuning@y..., Robert C Valentine <
BVAL@I...> wrote:
>
> The exchange was...
>
> >
> > > 7-limit thinking has been absolutely fundamental since Monteverdi,
> > > IMHO.
> >
> > We will have to agree to disagree, then.
> >
>
> I'm with Paul (and my ears) on this one. If someone can come up with
> performance practice materials from Monteverdi's time saying that "the
> subdominant must be properly lowered to provide the full sweetness of
> the resolution" or some such then I won't buy that they did it. Just
> because we have access to musics now which DO use the 4:5:6:7 chord doesn't
> mean that we can impose it on musics then.
>
> Note that materials regarding the flattenning of the leading tone during
> the meantone era (in contradiction to performance practices today) are
> available (Mozart), so we can rightly believe that meantone was not just
> the talk of theoriticians at the time. Find Monteverdis performance
> note saying that the 4:3 subdominant (which was certainly known then,
> had to be "bruised slightly" to properly express the music of the "thirds
> revolution. Why were black keys split and not white keys? (Augmented six
> != dominant seven).

Thanks, Robert, for your support. Where are
Margo Schulter and Mark Nowitzky?

>
JdL said :
>
> Am I understanding you correctly, as saying that to your ears, 7-limit
> tunings don't work for Monteverdi's music, and that you would reject
> them even if they turned out to be the practice of the time? If so, I
> have no objection, since this is strictly a matter of taste, and we are
> always free to second-guess the practices of past masters, even as we
> celebrate their achievements.

Everyone is free to tune things as they wish. Howver, if I decide to
perform Monteverdi in 23-tet AND imply that it is historically accurate,
then that merits a challenge.

In listenning to coral groups singing common practice music, I have not
heard in a common practice cadential passage, the resolution of the
fourth of the tonic moving from 4/3 -> 21/16 -> 5/4 (anymore than I
hear 10/9 -> 9/8 -> 1/1). Okay, maybe we lost these things via the
development of fixed pitch instruments being our reference. But if
I am going to believe that they took place in the past, then find the
contemporarious (?!) performance notes describing it. (We do have such
notes describing splitting the tone, resisting the sharpenning of the
leading tone etc indicating that the meantone practice was in fact a
practice and not a theory).

Again, we are free to do whatever we want with tuning, and if it
continues to make the music speak anew to our ears, thats even
better.

Gene (or another Bob) said

>
> Why don't people sing Dunstaple and Dufay in a Pythagorean scale?

Some do! Some of them claim historical accuracy in doing so.

> The
> music doesn't come with a book of instructions, telling you how
> sharp to make the third, and people deduce performence practice from
> the nature of the music itself, not from the writings of contemporary
> theorists. If we have _a capella_ music using the V7, how do we know
> how sharp to sing it--in fact, how sharp is it actually sung? I
> suspect the choir director has a lot to do with that.
>

Okay, perhaps I misunderstood. There is no reason not to perform
music in any tuning one wants. However, to make claims of historical
acccuracy, one should have performance notes from the time that
support that viewpoint. Singing a V7 with a 21/16 replacing the 4/3
has melodic implications that would have been written about. This is
a larger "wobble" than that of 10/9 vs 9/8, and there was tons
of writing about THAT.

> Just
> > because we have access to musics now which DO use the 4:5:6:7 chord
> doesn't
> > mean that we can impose it on musics then.
>
> Just because we have 12-et now doesn't mean we can impose it on
> musics then--except that we do. How do you know how something 300
> years ago was sung? Where is the evidence people *wanted* the seventh
> degree sharp?

The evidence is that until you produce something that shows that F
was supposed to move during the cadential passages, then there is no
reason to think that it was supposed to. I referred to split-key
keyboards for that reason, they were supposed to address other notes
that were 'broken' in 5 limit harmony. C was a very popular key. They
seemed to feel no more need for a split F as they needed a split D,
and theorists and performance practitioners didn't even seem to mention
it, unlike the problems with D.

>
> > Note that materials regarding the flattenning of the leading tone
> during
> > the meantone era (in contradiction to performance practices today)
> are
> > available (Mozart), so we can rightly believe that meantone was not
> just
> > the talk of theoriticians at the time.
>
> Keyboard music in particular *must* use a fixed scale; I don't think
> you can use it as the touchstone of all practice, however.
>

Mozart was referring to violin practice.

> Why were black keys split and not white keys? (Augmented six
> > != dominant seven).
>
> It was easier? A keyboard with split white keys in 19-et would have
> made sense, but would be harder to conceptualize. I don't think you
> can conlude anything about the 7-limit from this, because it would
> have made a lot more sense in the 5-limit.

Except that the most popular key, C, and the second most popular chord,
G7, was broken if they wanted 7-limit and used a single F. They clearly
invested a lot of disussion with the problems of the 81/80, however
this larger problem of 64/63 doesn't seem to have needed as much concern.
I suggest that maybe it didn't exist because F was F.

Again, we can tune anything any way we want NOW, and I suspect that
non-functional "dominant seventh" chords may well tend towards 4:5:6:7
in a non-fixed pitch though classical musician environment.

(Side note to Dimitri, evein if F=F and D=D, Gb != F#).

Bob Valentine

[Bob V wrote:]
>Everyone is free to tune things as they wish. However, if I decide to
>perform Monteverdi in 23-tet AND imply that it is historically
>accurate, then that merits a challenge.

I agree! It'd be nice if 12-tET renditions of Mozart and earlier
composers all came with a label ("Warning: the tuning used in this
piece is not historically accurate!"). And as you know, I've agreed
that the historical evidence strongly or overwhelmingly suggests that
4:5:6:7 was not used for dom 7ths in the past. I try very hard to
label my treatments accordingly, even as I "push" them as lovely!

JdL

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:

> > Why don't people sing Dunstaple and Dufay in a Pythagorean scale?

> Some do! Some of them claim historical accuracy in doing so.

So much the worse for this form of historical accuracy--the loving
way Dunstaple treats his thirds doesn't suggest such a thing to me.
However, it demonstrates my point.

> Okay, perhaps I misunderstood. There is no reason not to perform
> music in any tuning one wants. However, to make claims of
historical
> acccuracy, one should have performance notes from the time that
> support that viewpoint.

I was making no claim of historical accuracy for tuning the seventh
degree to a 7, which would be silly. What I *was* saying is that
considered purely vertically, we have what sounds like an out-of-tune
4-5-6-7, just as we had what sounded like an out-of-tune 4-5-6. The
fact that it is close to 4-5-6-7 is, in my opinion, central to the
nature of the sound, and ignoring that is not any kind of accuracy.
Moreover, saying people *chose* to make the seventh degree sharp is
not historically accurate, and is plain wrong. No choice was involved.

Singing a V7 with a 21/16 replacing the 4/3
> has melodic implications that would have been written about.

Singing a V7 with some degree of flattening would be another matter,
though here you run into the problem that you've already decided to
sharpen for the sake of the thirds.

> The evidence is that until you produce something that shows that F
> was supposed to move during the cadential passages, then there is no
> reason to think that it was supposed to.

I'm not proposing to move F, or suggesting it was supposed to move.
I'm asking where is the evidence people preferred the sound of
4:5:6:36/5 over 4:5:6:7 as a chord, and picked it because they liked
the sound of it. This I don't buy, and I think the historical
evidence needs to work harder if you are going to sell it.

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:

> > Why don't people sing Dunstaple and Dufay in a Pythagorean scale?
>
> Some do! Some of them claim historical accuracy in doing so.

Whoa! I missed this the first time around! Yes, Pythagorean tuning is
considered historically appropriate by all early-music ensembles (as
far as I know) playing or singing Western music from before the early
15th century. The way those dissonant thirds and sixths resolve is
unmistakable.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
>
> > > Why don't people sing Dunstaple and Dufay in a Pythagorean
scale?

> > Some do! Some of them claim historical accuracy in doing so.

> Whoa! I missed this the first time around! Yes, Pythagorean tuning
is
> considered historically appropriate by all early-music ensembles
(as
> far as I know) playing or singing Western music from before the
early
> 15th century. The way those dissonant thirds and sixths resolve is
> unmistakable.

I wouldn't bank on it. Here is what I think is the consensus view,
taken from <url: http://www.medieval.org/emfaq/harmony/pyth.html>.
Possibly it leaves open the question of what to do about Dunstaple or
Dufay, but the nature of the music they wrote pretty well answers
that; it would be "flawed" and "unsuitable" for the same reasons
that would apply to Ockeghem or Josquin. Assuming they should be
performed like Perotin or Machaut is absurd; that contemporary
theorists had not yet caught up with the avant garde is no surprise.

{{Remaining the standard theoretical approach in the High Gothic era
of the 13th century, Pythagorean tuning seems very congenial to the
complex polyphony and subtle harmonic continuum of composers such as
Perotin, Adam de la Halle, and Petrus de Cruce. It also nicely fits
the style of many 14th-century works, such as the famous Mass of
Guillaume de Machaut.

By around 1420 on the Continent, however, musical style had begun to
change in ways that invited new tunings. As composers such as Dufay
and Binchois emulated John Dunstable, and gave their music
an "English countenance" with a more and more pervasive emphasis on
thirds and sixths, fashion moved in the direction of intonations that
would make these intervals more smoothly blending. By the end of the
century, such tunings (e.g. meantone) were becoming the norm in
theory as well as practice.

The unsuitability of medieval Pythagorean intonation for Renaissance
music should not be seen as a "flaw," any more than Renaissance
meantone tuning is "flawed" because it is hardly suitable for the
works of Wagner or Max Reger. Rather, techniques of tuning and
notation interact creatively with musical style in each period, and
should all be taken into consideration in understanding and
recreating the music of a given age.}}

--- In tuning@y..., genewardsmith@j... wrote:

> I was making no claim of historical accuracy for tuning the seventh
> degree to a 7, which would be silly.

But that's what several people are doing (not that I object to them
doing it for their own and others' entertainment).

> What I *was* saying is that
> considered purely vertically, we have what sounds like an out-of-
tune
> 4-5-6-7, just as we had what sounded like an out-of-tune 4-5-6. The
> fact that it is close to 4-5-6-7 is, in my opinion, central to the
> nature of the sound,

Agreed 100%.

> and ignoring that is not any kind of accuracy.

Ignoring that where? For example, I've discussed how, according to
harmonic entropy theory, the root of this chord is extremely clear
and unambiguous -- so I'm not ignoring this fact by any means.

> Moreover, saying people *chose* to make the seventh degree sharp is
> not historically accurate, and is plain wrong. No choice was >
involved.

That's an awful lot you're claiming to be sure about, and I might
agree with you, but how do you know for sure?
>
> Singing a V7 with a 21/16 replacing the 4/3
> > has melodic implications that would have been written about.
>
> Singing a V7 with some degree of flattening would be another matter,

I thought it's what we were talking about!

> though here you run into the problem that you've already decided to
> sharpen for the sake of the thirds.

Don't forget -- lots of instruments are not limited to a finite
number of fixed pitches. All sorts of "adaptive" adjustments can take
place. Have you listened to John deLaubenfels' 5-limit vs. 7-limit
MIDI retunings (adaptune.com)? You might like the 7-limit ones, if
your philosophy holds true for your ears. For John's program can make
commas vanish you never thought possible!
>
> > The evidence is that until you produce something that shows that F
> > was supposed to move during the cadential passages, then there is
no
> > reason to think that it was supposed to.
>
> I'm not proposing to move F, or suggesting it was supposed to move.
> I'm asking where is the evidence people preferred the sound of
> 4:5:6:36/5 over 4:5:6:7 as a chord, and picked it because they
liked
> the sound of it.

It didn't happen that way.

> This I don't buy,

Good -- you invented it!

> and I think the historical
> evidence needs to work harder if you are going to sell it.

Musicians in Monteverdi's time didn't think of chords as entities
yet. They didn't "pick" harmonies in this way. They composed
individual melodic lines. Even later in the Baroque, the
understanding of "chords" was limited -- triads were chords of the
third and fifth or chords of the third and sixth. The chord with the
minor third and major sixth was special because of the tritone. No
one had yet decided that the chord of the minor third and minor
sixth, along with the chord of the major third and fifth, formed one
category (what we now call "major") while the chord of the major
third and major sixth, along with the chord of the minor third and
fifth, formed another ("minor"). No one even conceived of music as a
set of "chord progressions" like we do today. Listen to Victoria.
What's the "chord progression"?

Hello, there, and I'd like to offer a few comments on the question of
a "5-limit" interpretation of Dufay (c. 1397-1474), as well as a
"7-limit" interpretation of Monteverdi (1567-1643).

Here my views will generally follow yours, Paul, and those of Robert
Valentine, with a few qualifications. Specifically, I'd like to advocate
the usual historical tunings as a "mainstream" practice, while also
recognizing a place for "alternative" practices such as those proposed by
Euler in 1764 -- if my reading is correct -- and carried out by John
deLaubenfels today.

In the 18th century, as in the early 21st century, there was evidently
room for a range of views, and Euler's advocacy of a more "consonant"
tuning of the dominant seventh at 36:45:54:63 might serve as a precedent
for this kind of adaptive interpretation as a kind of minority alternative
to something like 36:45:54:64 (with 16:9 minor seventh), or a meantone
type of solution.

First of all, the question of intonation in Dufay might have a
somewhat different character in his earlier and later periods.

For the era of around 1420-1440, where the stable trine (2:3:4) serves
as the goal of directed progressions, and many 14th-century style
cadences occur, some form of Pythagorean tuning with some prominent
schisma thirds can be very attractive.

Indeed, I have found textures with sixth sonorities (fauxbourdon) very
attractive in either a traditional 14th-century Pythagorean tuning
such as Eb-G#, or in the likely early 15th-century scheme of Gb-B.

In a 17-note Pythagorean scheme for keyboard (Gb-A#), or with
flexible-pitch instruments and voices, one possibility is generally to
use regular Pythagorean thirds and sixths for traditional cadences
(Maj6-8, Maj3-5), and for melodic passages, while often favoring
schisma thirds for prolonged noncadential sonorities.

As we move into the later period of Dufay, sonorities involving thirds
and sixths seem to take on a more "nearly-stable" or "solid" quality,
where some approximation of 5-limit seems likely. This is also the
epoch of keyboard composers such as Conrad Paumann (c. 1450) where
meantone becomes a stylistically indicated choice according to
scholars such as Mark Lindley.

Even in the late 15th century, however, singers may have had some
tendency toward Pythagorean intonation in the performance of at least
some passages by composers such as Ockeghem, for example.

The theoretical mixture of Pythagorean, meantone-oriented, and
emerging "5-limit" concepts in this epoch may reflect a fluid
intonational situation.

One might guess that while meantone was standard practice for
keyboards in many parts of Europe by around 1480-1500, the 5-limit
paradigm for singers may have become more clearly evident by around
1520-1530, as _major_ thirds were increasingly preferred as the most
euphonious and conclusive, a trend reflected both in actual music and
in the writings and examples of a theorist such as Pietro Aron (1523,
1525, 1529).

Of course, the treatise on the syntonic diatonic by Fogliano (1529),
and Zarlino's great _Harmonic Institutions_ (1558), make the 5-limit
paradigm a definitive one -- a focus on just or near-just thirds also
being a vital element of Vicentino's treatise (1555).

Moving now to the 7-limit question, I consider the minor seventh at
several eras and periods.

First of all, the minor seventh is a bold interval and cadential
element in much music from Perotin (c. 1200) to Guillaume de Machaut
(c. 1300-1377) and some other 14th-century composers.

In a trinic context, it often, for example, contracts by directed
contrary motion to a fifth. Here the "closest approach" principle
nicely exemplified by a regular Pythagorean tuning -- rather narrow
cadential semitones at around 90 cents (256:243) -- might be yet
further amplified by tuning a cadential minor seventh at around 7:4,
or 969 cents. In Pythagorean tuning, it is 16:9, or about 996 cents.

This _might_ have happened in some Gothic practice, especially if we
assume that Marchettus of Padua is advocating an amplified "closest
approach" principle for cadential major thirds and sixths, taken
somewhat wider than Pythagorean. The same practice, by analogy, would
call for yet narrower cadential minor thirds and sevenths.

In the early 21st century, this is a routine _neo_-Gothic practice,
with sonorities like 12:14:18:21 (0-267-702-969 cents) contracting to
a stable fifth. Using the sign "v" to show a note a septimal comma or
64:63 lower than the usual Pythagorean step, we have

Dv4 C4 Fv4 E4
B3 C4 D4 E4
Gv3 F3 Bbv3 A3
E3 F3 or G3 A3

Personally, I would describe this as a 21st-century practice that just
_might_ have occurred sometime, somewhere in Europe, during the era of
1200-1400 -- in that amount of medieval time and geographic space,
lots of things could happen intonationally.

Moving to the use of prominent minor sevenths in the late modal era
around 1600, it's interesting that one of the first advocates of these
progressions, Vincenzo Galilei, gives the ratio for a minor seventh as
9:5, or around 1018 cents. He advocates bold minor seventh sonorities
including tritonic intervals as an expressive use of dissonance.

More generally, I might observe that an interval around 7:4 -- for
example the meantone interval often spelled as an augmented sixth --
does not _necessarily_ sound to all listeners as an outstanding
concord.

Writing in 1555, for example, and taking an interest in various
altered intervals -- "microtonal" inflections in 20th-century terms --
on his archicembalo with a 31-note meantone cycle, Vicentino finds the
augmented sixth (or interval a diesis smaller than a usual minor
seventh) rather dissonant, while finding a near-11:9 rather
concordant.

In this era, "seventh" generally means "dissonant," with either 9:5 or
a near-7:4 -- or the meantone minor seventh somewhere in between but
closer to 9:5 (around 1007 cents) -- having this general quality from
a 16th-century perspective. (The minor seventh in 1/4-comma meantone
with pure major thirds is more precisely midway between 9:5 and 16:9.)

Vicentino also finds a near-7:6 or "minimal third" leaning toward a
dissonant second. I happen to find this same interval rather
concordant, showing that adventurous "microtonalists" (again using a
20th-century characterization) can have a range of views.

Paul, I agree that the Manneristic and Baroque practices of the 17th
century -- whichever terms we prefer -- are based on the use of
sevenths and other "discordant" intervals as dissonances, often
provocatively mixed with concords such as thirds to produce sonorities
at once "bitter" and "sweet." It is not so much the seventh itself,
but the mixture of other intervals in the same sonority such as
thirds, which evidently makes them appear to have this "bittersweet"
quality, at least if we follow what some of the theoretical advocates
say.

However, one might investigate the use of the augmented sixth in a
meantone setting, for example, to look for evidence that this interval
might have been regarded as less dissonant or more concordant in some
of the repertory -- something on which you, Paul, or others familiar
with the 17th-18th century practices might comment.

By 1764, Euler does, as I read the translation made available by Monz,
advocate a dominant seventh tuned at 36:45:54:63 (4:5:6:7) as a
consonant development making this sonority yet more smooth or
attractive: <http://www.ixpres.com/interval/monzo/euler/euler-en.htm>.
If my reading is correct, we might well take him as an authority for
7-limit adaptive tunings as _an_ alternative interpretation with some
18th-century basis -- but not necessarily _the_ prevailing
interpretation.

One could argue that Euler's proposal for modified instruments able to
support this tuning of the dominant seventh suggests that the
prevailing practice was otherwise -- as does a consideration of the
meantone and well-temperament schemes for keyboards then in vogue.

People more involved with 18th-19th century styles might comment on
this more knowledgeably, or make more artfully educated guesses, and
that is a major theme of this thread.

However, my experience with the medieval or neo-Gothic minor seventh
question suggests that a range of tunings may be pleasing, depending
on one's taste or one's mood at a given moment. For E3-B3-D4, for
example, a sonority occurring prominently in Machaut, either a usual
Pythagorean 0-702-996 or a "7-flavor" 0-702-969 can be just fine for
me, with the contrast between these forms affording another element of
choice.

Similarly, I may love a cadential sixth sonority like G3-B3-E4
(resolving to F3-C4-F4) at a "7-flavor" 7:9:12, 0-435-933 cents, but
the regular Pythagorean 0-408-906 is just fine, also.

In a usual "historically oriented" performance, I'd stick with the
Pythagorean; in a neo-Gothic interpretation, or a guess as to what
singers following the kind of tradition described by Marchettus of
Padua _might_ have done with this sonority, I often go with 7:9:12.

My main point might be that low-integer JI, complex JI (Pythagorean
the most notable historical example), and approximations of various
tempered schemes are all possibilities.

Sometimes theorists do give us valuable clues. Both Zarlino and
Vincenzo Galilei, in an often intense debate on intonational and other
issues, agree that singers follow something close to the syntonic
diatonic, but avoiding comma problems or the dissonances (e.g. 40:27)
that would result from a fixed syntonic diatonic scale.

Zarlino argues that voices naturally seek the pure consonances of the
syntonic diatonic, but adjust to avoid discords; Galilei argues that,
if so, they are not singing precisely the syntonic diatonic, but
something very close. He also takes meantone as a rough model, again
noting that voices avoid the commas and dissonances of the syntonic
diatonic -- and suggesting a tendency toward whole-tones of the same
size.

Adaptive 5-limit JI would seem to meet all these criteria, providing a
way to reconcile the views of these two theorists.

With the 7-limit question, I would say that Euler in 1764 provides a
basis for tuning at least some dominant sevenths 4:5:6:7 as a likely
"minority" preference in the 18th century, especially with flexible
pitch instruments and ensembles.

However, I would be very hesitant to read any "7-based" viewpoint into
minor sevenths as used prominently either in medieval textures and
cadences of the era 1200-1400, or in later Manneristic or Baroque
practice starting in the era around 1600 (and advocated in Galilei's
counterpoint treatises of around 1588-1590).

It is certainly possible to perform, compose, or improvise music in
these medieval and early modern European styles using 7:4 minor
sevenths or close equivalents, and _some_ performances of the Gothic
or Manneristic and Baroque eras may have used them also, but I would
consider this as an "alternative" rather than main reading of
historical compositions.

Most respectfully,

Margo Schulter
mschulter@value.net

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

> Ignoring that where? For example, I've discussed how, according to
> harmonic entropy theory, the root of this chord is extremely clear
> and unambiguous -- so I'm not ignoring this fact by any means.

I thought this was precisely what you objected to--you certainly
didn't like my comment on Monteverdi and 7-thinking. I'm no longer
sure what your point is.

> > Moreover, saying people *chose* to make the seventh degree sharp
is
> > not historically accurate, and is plain wrong. No choice was >
> involved.

> That's an awful lot you're claiming to be sure about, and I might
> agree with you, but how do you know for sure?

Because they effectively lacked the means to make it flat, having
already decided to make it sharp.

> Have you listened to John deLaubenfels' 5-limit vs. 7-limit
> MIDI retunings (adaptune.com)? You might like the 7-limit ones, if
> your philosophy holds true for your ears. For John's program can
make
> commas vanish you never thought possible!

I've found that very interesting, hence my postings on a variation of
this idea I called adaptive tempering. I think that would be worth
testing.

> Musicians in Monteverdi's time didn't think of chords as entities
> yet. They didn't "pick" harmonies in this way. They composed
> individual melodic lines.

That's true of Palestrina or Byrd, but no longer so clear for
Monteverdi.

Even later in the Baroque, the
> understanding of "chords" was limited -- triads were chords of the
> third and fifth or chords of the third and sixth. The chord with
the
> minor third and major sixth was special because of the tritone. No
> one had yet decided that the chord of the minor third and minor
> sixth, along with the chord of the major third and fifth, formed
one
> category (what we now call "major") while the chord of the major
> third and major sixth, along with the chord of the minor third and
> fifth, formed another ("minor").

I somehow find it difficult to believe that the distinction between
major and minor had escaped the notice of Bach and Handel. What are
you really saying here?

No one even conceived of music as a
> set of "chord progressions" like we do today. Listen to Victoria.
> What's the "chord progression"?

I listen to Victoria, but I also listen to Bach, and they're not the
same.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
> >
> > > > Why don't people sing Dunstaple and Dufay in a Pythagorean
> scale?
>
> > > Some do! Some of them claim historical accuracy in doing so.
>
> > Whoa! I missed this the first time around! Yes, Pythagorean
tuning
> is
> > considered historically appropriate by all early-music ensembles
> (as
> > far as I know) playing or singing Western music from before the
> early
> > 15th century. The way those dissonant thirds and sixths resolve
is
> > unmistakable.
>
> I wouldn't bank on it. Here is what I think is the consensus view,
> taken from <url: http://www.medieval.org/emfaq/harmony/pyth.html>.
> Possibly it leaves open the question of what to do about Dunstaple
or
> Dufay, but the nature of the music they wrote pretty well answers
> that; it would be "flawed" and "unsuitable" for the same reasons
> that would apply to Ockeghem or Josquin. Assuming they should be
> performed like Perotin or Machaut is absurd; that contemporary
> theorists had not yet caught up with the avant garde is no surprise.
>
> {{Remaining the standard theoretical approach in the High Gothic
era
> of the 13th century, Pythagorean tuning seems very congenial to the
> complex polyphony and subtle harmonic continuum of composers such
as
> Perotin, Adam de la Halle, and Petrus de Cruce. It also nicely fits
> the style of many 14th-century works, such as the famous Mass of
> Guillaume de Machaut.
>
> By around 1420 on the Continent, however, musical style had begun
to
> change in ways that invited new tunings.

Note that I said "before the early 15th century" above!

> As composers such as Dufay
> and Binchois emulated John Dunstable, and gave their music
> an "English countenance" with a more and more pervasive emphasis on
> thirds and sixths, fashion moved in the direction of intonations
that
> would make these intervals more smoothly blending. By the end of
the
> century, such tunings (e.g. meantone) were becoming the norm in
> theory as well as practice.
>
> The unsuitability of medieval Pythagorean intonation for
Renaissance
> music should not be seen as a "flaw," any more than Renaissance
> meantone tuning is "flawed" because it is hardly suitable for the
> works of Wagner or Max Reger. Rather, techniques of tuning and
> notation interact creatively with musical style in each period, and
> should all be taken into consideration in understanding and
> recreating the music of a given age.}}

100% agreed.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > Ignoring that where? For example, I've discussed how, according
to
> > harmonic entropy theory, the root of this chord is extremely
clear
> > and unambiguous -- so I'm not ignoring this fact by any means.
>
> I thought this was precisely what you objected to--you certainly
> didn't like my comment on Monteverdi and 7-thinking. I'm no longer
> sure what your point is.

I thought we were debating the appropriateness of _targeting_ 4:5:6:7
proportions in an adaptively-tuned rendition of Monteverdi. I was
arguing that the upper minor third of the dominant seventh should be
targeted instead to 5:6, and that the generally meantone-like sizes
of the melodic intervals should be observed.

> > > Moreover, saying people *chose* to make the seventh degree
sharp
> is
> > > not historically accurate, and is plain wrong. No choice was >
> > involved.
>
> > That's an awful lot you're claiming to be sure about, and I might
> > agree with you, but how do you know for sure?
>
> Because they effectively lacked the means to make it flat, having
> already decided to make it sharp.

Most instruments were not fixed-pitch instruments. And what about the
fact that we never find Bb-D-F-G# resolving to Eb-G-Bb, even though
that would be a case where "they had the means to make it flat"?
>
> > Have you listened to John deLaubenfels' 5-limit vs. 7-limit
> > MIDI retunings (adaptune.com)? You might like the 7-limit ones,
if
> > your philosophy holds true for your ears. For John's program can
> make
> > commas vanish you never thought possible!
>
> I've found that very interesting, hence my postings on a variation
of
> this idea I called adaptive tempering. I think that would be worth
> testing.

John's program does better than adaptive tempering ever could, I
believe . . . the commas are distributed through small melodic
deviations as well as small harmonic deviations, all too small to
notice (in most cases). But the point here: have you _listened_ . . .
specifically to some 7-limit vs. 5-limit comparisons? What do your
ears say?
>
> > Musicians in Monteverdi's time didn't think of chords as entities
> > yet. They didn't "pick" harmonies in this way. They composed
> > individual melodic lines.
>
> That's true of Palestrina or Byrd, but no longer so clear for
> Monteverdi.
>
> Even later in the Baroque, the
> > understanding of "chords" was limited -- triads were chords of
the
> > third and fifth or chords of the third and sixth. The chord with
> the
> > minor third and major sixth was special because of the tritone.
No
> > one had yet decided that the chord of the minor third and minor
> > sixth, along with the chord of the major third and fifth, formed
> one
> > category (what we now call "major") while the chord of the major
> > third and major sixth, along with the chord of the minor third
and
> > fifth, formed another ("minor").
>
> I somehow find it difficult to believe that the distinction between
> major and minor had escaped the notice of Bach and Handel. What are
> you really saying here?

The concept of major and minor triads with their different inversions
was introduced by Rameau. Bach and Handel may have been familiar with
it, but I wouldn't be surprised if they weren't.

>
> No one even conceived of music as a
> > set of "chord progressions" like we do today. Listen to Victoria.
> > What's the "chord progression"?
>
> I listen to Victoria, but I also listen to Bach, and they're not
the
> same.

I think Bach understood chord progressions intuitively rather than
theoretically.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

> > By around 1420 on the Continent, however, musical style had begun
> to
> > change in ways that invited new tunings.

> Note that I said "before the early 15th century" above!

Notice that it said "on the Continent"; the article is not arguing
that Dunstaple is correctly performed in a Pythagorean tuning, it is
saying that when Continental composers started to follow Dunstaple,
the tuning changed. If anything, that suggests Dunstaple should *not*
be performed using Pythagorean thirds. I would suggest letting our
ears be our guide.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > > By around 1420 on the Continent, however, musical style had
begun
> > to
> > > change in ways that invited new tunings.
>
> > Note that I said "before the early 15th century" above!
>
> Notice that it said "on the Continent"; the article is not arguing
> that Dunstaple is correctly performed in a Pythagorean tuning, it
is
> saying that when Continental composers started to follow Dunstaple,
> the tuning changed. If anything, that suggests Dunstaple should
*not*
> be performed using Pythagorean thirds. I would suggest letting our
> ears be our guide.

I would agree with the article -- its author is none other than our
own Margo Schulter. But my point, with which Margo agrees, is that a
4:5:6:7 tuning for dominant seventh chords in the Baroque era is no
more appropriate than a 5-limit tuning for chords of thirds and/or
sixths in earlier Continental Medieval music . . . say Perotin.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

> John's program does better than adaptive tempering ever could, I
> believe

That's a wild leap off the cliff of speculation, it seems to me. The
first question to be answered would be what the difference amounted
to.

. . . the commas are distributed through small melodic
> deviations as well as small harmonic deviations, all too small to
> notice (in most cases).

If you make a change, the frequency doesn't know if it is amelodic or
a harmonic change; however if I understand what you are saying, both
systems do this.

But the point here: have you _listened_ . . .
> specifically to some 7-limit vs. 5-limit comparisons? What do your
> ears say?

My ears say that Verklarte Nacht sounds wrong in the 5-limit, wrong
but interesting in the 11-limit, and not very good in the version it
was written in when compared to the 7-limit, which is the best. My
ears like Rhapsody in Blue best in the version which says it is
"7-limit adaptive tuning, grounded to COFT, with fairly soft vertical
springs, targeting 7th degree at 7/4 of root. Melody springs are of
negligible strength", but now the 12-et sounds pretty good too,
though perhaps a little on the bland side. There aren't a lot of
7-vs-5 comparisons so far as I know.

> > I somehow find it difficult to believe that the distinction
between
> > major and minor had escaped the notice of Bach and Handel. What
are
> > you really saying here?

> The concept of major and minor triads with their different
inversions
> was introduced by Rameau. Bach and Handel may have been familiar
with
> it, but I wouldn't be surprised if they weren't.

Bach was not a learned man except when it came to music, but there he
knew a great deal, and I somehow doubt he needed to read a book
written by contemporary in order to understand the obvious. As for
Handel, he could always ask his cook, who knew more counterpoint than
Gluck, and maybe some harmony too. :)

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
>
> > John's program does better than adaptive tempering ever could, I
> > believe
>
> That's a wild leap off the cliff of speculation, it seems to me.
The
> first question to be answered would be what the difference amounted
> to.
>
> . . . the commas are distributed through small melodic
> > deviations as well as small harmonic deviations, all too small to
> > notice (in most cases).
>
> If you make a change, the frequency doesn't know if it is amelodic
or
> a harmonic change; however if I understand what you are saying,
both
> systems do this.
>
> But the point here: have you _listened_ . . .
> > specifically to some 7-limit vs. 5-limit comparisons? What do
your
> > ears say?
>
> My ears say that Verklarte Nacht sounds wrong in the 5-limit, wrong
> but interesting in the 11-limit, and not very good in the version
it
> was written in when compared to the 7-limit, which is the best. My
> ears like Rhapsody in Blue best in the version which says it is
> "7-limit adaptive tuning, grounded to COFT, with fairly soft
vertical
> springs, targeting 7th degree at 7/4 of root. Melody springs are
of
> negligible strength", but now the 12-et sounds pretty good too,
> though perhaps a little on the bland side. There aren't a lot of
> 7-vs-5 comparisons so far as I know.
>
> > > I somehow find it difficult to believe that the distinction
> between
> > > major and minor had escaped the notice of Bach and Handel. What
> are
> > > you really saying here?
>
> > The concept of major and minor triads with their different
> inversions
> > was introduced by Rameau. Bach and Handel may have been familiar
> with
> > it, but I wouldn't be surprised if they weren't.
>

Bob: What are we talking about here? It was common practice in Bach
and Handel's day to improvise over a figured bass. The notation for
that embraces a clearly implicit understanding of inversions, modes,
and chordal structure at a practical and extemporaneously (real-time)
executed level so deeply ingrained and visceral it was coming out of
your pores.

Unless I'm really missing something here, this seems to exemplify the
strange nit-picking intellectualism that is sometimes wildly off the
mark for any realistic appraisal of what was actually going on
historically. These people weren't exactly intellectual dwarfs no
matter what their specializations and level of broader academic
preparation.

> Bach was not a learned man except when it came to music, but there
he
> knew a great deal, and I somehow doubt he needed to read a book
> written by contemporary in order to understand the obvious. As for
> Handel, he could always ask his cook, who knew more counterpoint
than
> Gluck, and maybe some harmony too. :)

Ha-ha-ha! Yyyyyeeeeeeeessssssss!!!!!!!!

--- In tuning@y..., genewardsmith@j... wrote:

> > But the point here: have you _listened_ . . .
> > specifically to some 7-limit vs. 5-limit comparisons? What do
your
> > ears say?
>
> There aren't a lot of
> 7-vs-5 comparisons so far as I know.

Have you listened to the various Bach, Mozart, Chopin . . . retunings
John has done??

Paul said:
The concept of major and minor triads with their different inversions
was introduced by Rameau. Bach and Handel may have been familiar with
it, but I wouldn't be surprised if they weren't.

Bob comments:
I do not regard this kind of interpretation of historical evidence as
valid. Far from it. The current concept of intellectual property, its
thorough documentation, and the consequent economies of the academic
and commercial environments that reward it today tend to tie
discoveries to their dicoverers quite intimately and quickly. In a
musical environment in which what we would call plagiarism was taken
as doing honor to the original author, this is most assuredly not the
case.

On the contrary, in the baroque era there was a pervasive tradition
of directly passing down technology, technique (including
compositional and tuning technique) and a pedogical infrastructure
that was much more directly human- than paper-oriented.
Apprenticeships and direct transmission of the contemporary common
practice by both verbal means and practical demonstration were the
norm in that social structure.

Should we really assume that as interpreters of history we must
behave like good little librarians and catalog the first explicit
documentation of ANY historical technique or technology from this age
and tag it irrevocably to its author as synonymous with the
discoverer of that which it documents?! I can personally think of
little that could more effectively guarantee the most grievous
distortions of the historical realities.

Further, in my view, it defies all common sense to assume on such a
weak basis that a pervasive musical culture that customarily
improvised extemporaneously over a figured bass did not have the most
ready, intimate, and widespread understanding of these matters
imaginable, no matter how they were intellectualized or not
intellectualized.

We need to learn to see the forest in spite of such trees. A goodly
chunk of the broader historical context in which we can embed such
pieces of documentary evidence is, after all, also available.

--- In tuning@y..., BobWendell@t... wrote:

> > > > I somehow find it difficult to believe that the distinction
> > between
> > > > major and minor had escaped the notice of Bach and Handel.
What
> > are
> > > > you really saying here?
> >
> > > The concept of major and minor triads with their different
> > inversions
> > > was introduced by Rameau. Bach and Handel may have been
familiar
> > with
> > > it, but I wouldn't be surprised if they weren't.
> >
>
> Bob: What are we talking about here? It was common practice in Bach
> and Handel's day to improvise over a figured bass. The notation for
> that embraces a clearly implicit understanding of inversions,

That isn't clear. There was no identification of a chord with fifth
and major third with the chord with minor third and minor sixth, as
one category, as opposed to the chord with fifth and minor third with
the chord with major third and major sixth as another category, in
figured bass. The concept of "major triad" and "minor triad" with
there inversions gained prominence only later!

> modes,
> and chordal structure at a practical and extemporaneously (real-
time)
> executed level so deeply ingrained and visceral it was coming out
of
> your pores.

Yes, I agree -- I said that Bach understood modern harmony
intuitively (he pretty much invented it!). All I'm getting at with
this particular point is that musicians of Monteverdi's era
didn't "select chords" the way Gene was implying -- common-practice
harmony as we know it today developed, little by little throughout
the Baroque era, out of various proportions of intuition and
putative "rules" about how to combine melodic lines. Thinking
explicitly in terms of autonomous chord types, chord progressions,
and harmonic functions only came later.

--- In tuning@y..., BobWendell@t... wrote:

> Should we really assume that as interpreters of history we must
> behave like good little librarians and catalog the first explicit
> documentation of ANY historical technique or technology from this
age
> and tag it irrevocably to its author as synonymous with the
> discoverer of that which it documents?!

Of course not! Geez, Bob, hmmm . . . maybe Margo has something to say
about this issue. The point is that one can go back and read about
how people thought about music and music theory and chords and the
like, and learn _something_ -- not _everything_, but _something_,
from that, that one would not have known otherwise. Have you done
much of this kind of reading, Bob?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

> That isn't clear. There was no identification of a chord with fifth
> and major third with the chord with minor third and minor sixth, as
> one category, as opposed to the chord with fifth and minor third
with
> the chord with major third and major sixth as another category, in
> figured bass. The concept of "major triad" and "minor triad" with
> there inversions gained prominence only later!

Why are there so many minor chords in Bach's Mass in b minor? It's
hardly an accident.

> Yes, I agree -- I said that Bach understood modern harmony
> intuitively (he pretty much invented it!). All I'm getting at with
> this particular point is that musicians of Monteverdi's era
> didn't "select chords" the way Gene was implying -- common-practice
> harmony as we know it today developed, little by little throughout
> the Baroque era, out of various proportions of intuition and
> putative "rules" about how to combine melodic lines.

If it's fair to say I implied this, then it is equally fair to say
you have implied that Monteverdi simply let his harmonies be
determined as a kind of vertical byproduct of his horizontal
polyphony, and that isn't true, as listening to him should make
clear. In fact, even with Lassus and Gesualdo we find chromatic
harmonies used to produce a particular kind of striking effect; they
were *not* thinking purely in terms of polyphony when they did that
sort of thing.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > That isn't clear. There was no identification of a chord with
fifth
> > and major third with the chord with minor third and minor sixth,
as
> > one category, as opposed to the chord with fifth and minor third
> with
> > the chord with major third and major sixth as another category,
in
> > figured bass. The concept of "major triad" and "minor triad" with
> > there inversions gained prominence only later!
>
> Why are there so many minor chords in Bach's Mass in b minor? It's
> hardly an accident.

Bach was going for a certain sound/mood.
>
> > Yes, I agree -- I said that Bach understood modern harmony
> > intuitively (he pretty much invented it!). All I'm getting at
with
> > this particular point is that musicians of Monteverdi's era
> > didn't "select chords" the way Gene was implying -- common-
practice
> > harmony as we know it today developed, little by little
throughout
> > the Baroque era, out of various proportions of intuition and
> > putative "rules" about how to combine melodic lines.
>
> If it's fair to say I implied this,

You framed the debate by saying that I, and those on my side, had to
show that Monteverdi and his contemporaries selected the chord
4:5:6:7.2 over the chord 4:5:6:7. I replied that it wasn't a question
of "selecting chords" at all.

> then it is equally fair to say
> you have implied that Monteverdi simply let his harmonies be
> determined as a kind of vertical byproduct of his horizontal
> polyphony, and that isn't true, as listening to him should make
> clear.

Not a byproduct, no. But neither were the melodies determined as a
horizontal byproduct of his "chord progressions".

> In fact, even with Lassus and Gesualdo we find chromatic
> harmonies used to produce a particular kind of striking effect;
they
> were *not* thinking purely in terms of polyphony when they did that
> sort of thing.

Not purely in terms of polyphony, no. But melodic considerations were
always strongly present as well . . .

BobWendell@technet-inc.com schrieb:
>
> Paul said:
> The concept of major and minor triads with their different inversions
> was introduced by Rameau. Bach and Handel may have been familiar with
> it, but I wouldn't be surprised if they weren't.
>
> Bob comments:
> I do not regard this kind of interpretation of historical evidence as
> valid. Far from it. The current concept of intellectual property, its

But news of new concepts getting around doesn't mean that they
are immediately accepted/used with all the implications. I, too,
would argue that the training of composers -- and their idea of
artful music -- was based on counterpoint: looking at isolated
intervals. Consonances in thorough bass were a third (major or
minor depending on the mode), the fifth, and a sixth (again
depending on the mode). The mode took care of what in later
terms could be called chord quality.

klaus schmirler

--- In tuning@y..., klaus schmirler <KSchmir@z...> wrote:
>
>
> BobWendell@t... schrieb:
> >
> > Paul said:
> > The concept of major and minor triads with their different
inversions
> > was introduced by Rameau. Bach and Handel may have been familiar
with
> > it, but I wouldn't be surprised if they weren't.
> >
> > Bob comments:
> > I do not regard this kind of interpretation of historical
evidence as
> > valid. Far from it. The current concept of intellectual property,
its
>
> But news of new concepts getting around doesn't mean that they
> are immediately accepted/used with all the implications. I, too,
> would argue that the training of composers -- and their idea of
> artful music -- was based on counterpoint: looking at isolated
> intervals. Consonances in thorough bass were a third (major or
> minor depending on the mode), the fifth, and a sixth (again
> depending on the mode). The mode took care of what in later
> terms could be called chord quality.
>
> klaus schmirler

Thank you Klaus. It is sometimes difficult to respond when one's
thinking and scholarship are placed into tiny little boxes!

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> You framed the debate by saying that I, and those on my side, had
to
> show that Monteverdi and his contemporaries selected the chord
> 4:5:6:7.2 over the chord 4:5:6:7. I replied that it wasn't a
question
> of "selecting chords" at all.

So I said. It seems to me this started when you said 4:5:6:7 had
essentially nothing to do with the matter, a statement you have in
effect disclaimed in emphatic terms, so I'm not sure we have that
much left to argue about.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > You framed the debate by saying that I, and those on my side, had
> to
> > show that Monteverdi and his contemporaries selected the chord
> > 4:5:6:7.2 over the chord 4:5:6:7. I replied that it wasn't a
> question
> > of "selecting chords" at all.
>
> So I said. It seems to me this started when you said 4:5:6:7 had
> essentially nothing to do with the matter,

Relative to the context in which I thought it was being brought
up . . .

> a statement you have in
> effect disclaimed in emphatic terms,

In a different context . . .

> so I'm not sure we have that
> much left to argue about.

Then our argument is over. I'll still maintain (against Bob) that one
should not tune dominant seventh chords 4:5:6:7 in "authentic"
performances of Baroque music; and that, if some have cultivated an
aesthetic of doing so, it is not because it's the "one true way", and
it doesn't necessarily imply that many musicians in the Baroque era
did anything like it.

Yes, I find the same kind of occasionally radical adjustment and
moving target in our discussions. I sometimes get the feeling that
the positions taken are only temporary "devil's advocate" phenomena
that do not necessarily represent actual opinions. There is often a
lot of shifting going on between one statement and the next that
makes the issues harder to understand or address clearly.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > You framed the debate by saying that I, and those on my side, had
> to
> > show that Monteverdi and his contemporaries selected the chord
> > 4:5:6:7.2 over the chord 4:5:6:7. I replied that it wasn't a
> question
> > of "selecting chords" at all.
>
> So I said. It seems to me this started when you said 4:5:6:7 had
> essentially nothing to do with the matter, a statement you have in
> effect disclaimed in emphatic terms, so I'm not sure we have that
> much left to argue about.

Paul:
I'll still maintain (against Bob) that one
should not tune dominant seventh chords 4:5:6:7 in "authentic"
performances of Baroque music; and that, if some have cultivated an
aesthetic of doing so, it is not because it's the "one true way", and
it doesn't necessarily imply that many musicians in the Baroque era
did anything like it.

Bob:
Hi, Paul. Good. You have already commented favorably on my statement
that in a brief passing seventh over a dominant triad, I wouldn't
necessarily expect performers of any era to suddenly veer as far
south of the normal diatonic position of the seventh as a strict 7-
limit 4:5:6:7 would dictate. We agree here. and i have never proposed
that it is the "one true way".

However, many singers and flexible pitch instruments such as strings
make quick, smooth pitch adjustments of this order of magnitude all
the time, even when it is simply fixing an initial pitch error not
justifiable as 7-limit or any other coherently related tuning.
Consequently, I find it difficult to believe that in practice anyone
would perceive a sustained 7th in 4:5:6:7 occurring over a dominant
as objectional or being out of tune, or even melodically
inappropriate unless they had some academic axe to grind.

We should bear in mind always that the midi files with which we test
some of our ideas with our ears are generally quite inflexible pitch-
wise (excluding the adaptive JI software from JdL) and therefore do
not represemt well what happens in practice with voices, strings,
etc. For example, the comma problem that occurs when tuning first
finger E on the D string of a violin to the open G and then to the
open A in sequence does not generate anything like the same kind of
melodic earthquake in practice with adaptive JI-oriented string
playing as it does in a midi file. We've already agreed on that.

Further, I think you underestimate the attractive power of the 7th
harmonic in this context if this harmonic structure is sustained for
any significant time. I have already explained how I have trained
musically, and ESPECIALLY intonationally naive singers using
exercises very explicitly based on the difference product phenomenon.

(I have explained long ago that I think flexibly-pitched
instrumentalists use this intuitively and usually unconsciously to
tune harmony accurately. There is not time to do this with beats
between common harmonics, since the beats are usually too slow unless
we include huge pitch errors or very long notes. Also pitch training
using the beat approach is terribly and demonstrably ineffective with
amateurs when contrasted with the difference products approach except
for unisons and octaves, in which case the beat phenomenon is easily
detectable at the fundamental of both or one of the tones
respectively and there are no difference products at frequencies not
duplicating a fundamental.)

This training initially involved only perfect fifths and fourths and
major thirds. Yet once sensitivity to the presence of difference
products was developed, it was spontaneously transferable to more
complex harmonies, including a natural gravitation toward the 7th
harmonic version of the V7 chord. It should be clear, therefore, that
this is not based on a pre-conditioned preference specific to a
particular harmonic structure, but a more general underlying
psychoacoustic phenomenon to which the subjects in question had been
senstizied, easily extensible to new harmonic experience, and that
forms a highly significant and powerful component of the
psychoacoustic phenomena at the very basis of the appeal of harmony
in the first place.

As I've stated previously, I have no good reason to believe that this
phenomenon is peculiar to our time. Why would it be, and why would
anyone want to propose that it is? To do so would defy any sense of
theoretical economy, as would invoking other, less objectively
verifiable explanations.

So just as I believe the psychoacoustically attractive power of 5:4
effectively "conspired" with the dominant use of polyphonic vocal
ensembles in the church music of the late medieval and early
Renaisance eras to nudge the expansion of 3-limit JI to 5-limit, I
also believe that the attractive power for flexibly pitched voices or
instruments of the 7-limit V7 is no respecter of theoretical
preferences and intonational belief systems now or at any time in the
past.

If this is correct, it constitutes a clear example of a universal
human perceptual metastructure that lies at the basis of an
evolutionary process that cannot be explained on the basis of
historical and anecdotal evidence alone. Moreover, it is NOT
dependent on the inappropriate imposition of aesthetics from other
times or conditioned phenomena that may not have existed during the
era in question.

Once we understand the time- and culture-independent psychoacoustic
phenomena behind such an evolutionary process, our reading of the
historical evidence is not prejudiced, but simply informed in a way
that allows us to appreciate the broader context of that evidence in
order to give it an appropriately enlightened interpretation.

--- In tuning@y..., klaus schmirler <KSchmir@z...> wrote:
>
>
> BobWendell@t... schrieb:
> >
> > Paul said:
> > The concept of major and minor triads with their different
inversions
> > was introduced by Rameau. Bach and Handel may have been familiar
with
> > it, but I wouldn't be surprised if they weren't.
> >
> > Bob comments:
> > I do not regard this kind of interpretation of historical
evidence as
> > valid. Far from it. The current concept of intellectual property,
its
>
> But news of new concepts getting around doesn't mean that they
> are immediately accepted/used with all the implications. I, too,
> would argue that the training of composers -- and their idea of
> artful music -- was based on counterpoint: looking at isolated
> intervals. Consonances in thorough bass were a third (major or
> minor depending on the mode), the fifth, and a sixth (again
> depending on the mode). The mode took care of what in later
> terms could be called chord quality.
>
> klaus schmirler

Bob:
I am saying Rameau was just documenting current practice already in
place widely and for a period of time, and perhaps, PERHAPS, putting
new conceptual wrinkles on it, but not coming up with anything
fundametally new in terms of practice.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., genewardsmith@j... wrote:
> > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> >
> > > > By around 1420 on the Continent, however, musical style had
> begun
> > > to
> > > > change in ways that invited new tunings.
> >
> > > Note that I said "before the early 15th century" above!
> >
> > Notice that it said "on the Continent"; the article is not
arguing
> > that Dunstaple is correctly performed in a Pythagorean tuning, it
> is
> > saying that when Continental composers started to follow
Dunstaple,
> > the tuning changed. If anything, that suggests Dunstaple should
> *not*
> > be performed using Pythagorean thirds. I would suggest letting
our
> > ears be our guide.
>
> I would agree with the article -- its author is none other than our
> own Margo Schulter. But my point, with which Margo agrees, is that
a
> 4:5:6:7 tuning for dominant seventh chords in the Baroque era is no
> more appropriate than a 5-limit tuning for chords of thirds and/or
> sixths in earlier Continental Medieval music . . . say Perotin.

Bob comments:
Given certain natural proclivities of human hearing demonstrably not
dependent on cultural conditioning, I question whether we can package
the tunings appropriate to each period so neatly as these and similar
statements made elsewhere seem to imply, especially for non-fixed-
pitch musical media. Although much historical evidence may seem to
suggest we can, such evidence represents only current
conceptualizations and belief systems of the times, much of which,
although informative (never said worthless, Paul), may only apply to
fixed-pitch instruments.

I have also stated elsewhere my belief that we cannot lend an
adequately enlightened interpretation to this evidence without taking
into account the universals implicit in human auditory processing,
independent of time, space, and cultural conditioning. Also, to
pretend that we can always and reliably infer that pitch accuracy
based on melodic memory was always adequate in the common practice of
the era in question to imitate exactly the way these fixed-pitch
instruments were tuned seems a bit of a stretch.

Such thinking would assume that melodic memory (not in the sense of
"carrying a tune", but in the precise sense of exact imitation with
microtonal accuracy) is more compelling than the appeal to the human
ear of harmonic consonance. Maybe some rare human beings had
developed such a microtonally precise melodic memory (Johnny Reinhard
comes to mind), but that would be highly exceptional and certainly
not the norm.

It obviously doesn't work that way in common practice today. Why
should it have ever? Yet documentary evidence of the relatively
exquisite sense of harmonic pitch accuracy is extensive for times
extending from the middle ages to the dawn of pervasive 12-tET and
its virtually total relegation to tuning professionals when
this sensitivity began to erode. At the level of fine, microtonal
precision, harmonic attraction toward the JI "sweet spots" powerfully
dominates over melodic subtleties of the same order of magnitude.

Hmmmmm........I'm realizing that I've just hit on the fundamental
psychoacousitc premise upon which most of my arguments are based:

At the level of fine, microtonal precision, harmonic attraction
toward the JI "sweet spots" powerfully dominates over melodic
subtleties of the same order of magnitude.

I believe this to be a time-, space- and culture-independent
psychoacoustic characteristic of human auditory perception in light
of which all historical evidence must be weighed and interpreted. The
7-limit 4:5:6:7 chord issue is not totally resolved by this, however,
since the roughly 30-cent difference between it and other
alternatives, depending on the tuning, is among the largest of
microtonal shifts generated by harmonic means. It lives at a nebulous
border between microtonal and chromatic, just as the related 7:8
whole step lives at the border between stepwise motion and thirds.

--- In tuning@y..., BobWendell@t... wrote:
> Yes, I find the same kind of occasionally radical adjustment and
> moving target in our discussions. I sometimes get the feeling that
> the positions taken are only temporary "devil's advocate" phenomena
> that do not necessarily represent actual opinions. There is often a
> lot of shifting going on between one statement and the next that
> makes the issues harder to understand or address clearly.

Sorry -- I've often been guilty of this "devil's advocate" syndrome
during the past six years on this list! Hopefully, you guys
appreciate that I'm doing this in the spirit of friendly debate, and
to make you sharpen your own arguments and opinions, against the
kinds of retorts you are likely to receive from scholars. You and
Gene are two of the coolest people to ever join this list -- welcome!

Ha-ha-ha! (Genuine belly laugh!!!) Well, it is certainly serving this
purpose. Thank you, Paul! You don't seem to have gotten yet to 28428
"Re: 7-limit thinking" where your statements stimulated an explicit
recognition in me of the single most important and fundamental
premise behind all my arguments on the tuning issues we've been
discussing.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
> > Yes, I find the same kind of occasionally radical adjustment and
> > moving target in our discussions. I sometimes get the feeling
that
> > the positions taken are only temporary "devil's advocate"
phenomena
> > that do not necessarily represent actual opinions. There is often
a
> > lot of shifting going on between one statement and the next that
> > makes the issues harder to understand or address clearly.
>
> Sorry -- I've often been guilty of this "devil's advocate" syndrome
> during the past six years on this list! Hopefully, you guys
> appreciate that I'm doing this in the spirit of friendly debate,
and
> to make you sharpen your own arguments and opinions, against the
> kinds of retorts you are likely to receive from scholars. You and
> Gene are two of the coolest people to ever join this list --
welcome!

--- In tuning@y..., BobWendell@t... wrote:
> Paul:
> I'll still maintain (against Bob) that one
> should not tune dominant seventh chords 4:5:6:7 in "authentic"
> performances of Baroque music; and that, if some have cultivated an
> aesthetic of doing so, it is not because it's the "one true way",
and
> it doesn't necessarily imply that many musicians in the Baroque era
> did anything like it.
>
> Bob:
> Hi, Paul. Good. You have already commented favorably on my
statement
> that in a brief passing seventh over a dominant triad, I wouldn't
> necessarily expect performers of any era to suddenly veer as far
> south of the normal diatonic position of the seventh as a strict 7-
> limit 4:5:6:7 would dictate. We agree here. and i have never
proposed
> that it is the "one true way".
>
> However, many singers and flexible pitch instruments such as
strings
> make quick, smooth pitch adjustments of this order of magnitude all
> the time, even when it is simply fixing an initial pitch error not
> justifiable as 7-limit or any other coherently related tuning.
> Consequently, I find it difficult to believe that in practice
anyone
> would perceive a sustained 7th in 4:5:6:7 occurring over a dominant
> as objectional or being out of tune, or even melodically
> inappropriate unless they had some academic axe to grind.

Believe it. And I'm certainly not the only person who reacts this
way. You might want to look in the archives to a discussion of
various tunings of a I-IV-V7-I progression, which we all listened to
and reacted to.

Perhaps your vocal group isn't producing dominant seventh chords as
close to 4:5:6:7 as you think. This is what John deLaubenfels
suggested. Did you have a specific reply to this, in your post that
didn't get posted?

> We should bear in mind always that the midi files with which we
test
> some of our ideas with our ears are generally quite inflexible
pitch-
> wise (excluding the adaptive JI software from JdL) and therefore do
> not represemt well what happens in practice with voices, strings,
> etc. For example, the comma problem that occurs when tuning first
> finger E on the D string of a violin to the open G and then to the
> open A in sequence does not generate anything like the same kind of
> melodic earthquake in practice with adaptive JI-oriented string
> playing as it does in a midi file. We've already agreed on that.

Yes, and there was an adaptive version of I-IV-V7-I, with a 4:5:6:7
dominant seventh, in which the septimal comma was distributed into
three equal parts, among the three chord changes. This did not sound
so bad melodically, though I still felt the 4:5:6:7 was lacking
the "tug" toward the tonic that I like to hear in dominant seventh
chords.
>
> Further, I think you underestimate the attractive power of the 7th
> harmonic in this context if this harmonic structure is sustained
for
> any significant time. I have already explained how I have trained
> musically, and ESPECIALLY intonationally naive singers using
> exercises very explicitly based on the difference product
phenomenon.

I'm a big fan of 7-limit harmony. I just don't hear the dominant
seventh in common-practice tonal music as wanting this kind
of "consonance".

> (I have explained long ago that I think flexibly-pitched
> instrumentalists use this intuitively and usually unconsciously to
> tune harmony accurately. There is not time to do this with beats
> between common harmonics, since the beats are usually too slow
unless
> we include huge pitch errors or very long notes.

What do you mean? Beats between common harmonics, in 12-tET for
example, tend to be very fast, for thirds and sixths. How do
combinational tones allow for a faster reaction/adjustment time in
acheiving good tuning than the process of eliminating beats?

> Also pitch training
> using the beat approach is terribly and demonstrably ineffective
with
> amateurs when contrasted with the difference products approach
except
> for unisons and octaves, in which case the beat phenomenon is
easily
> detectable at the fundamental of both or one of the tones
> respectively and there are no difference products at frequencies
not
> duplicating a fundamental.)

Piano tuners are taught to listen for the beats of _all_ consonant
intervals. "Difference products" (why do you use that term -- do you
mean something different from combinational tones) are not used at
all by piano tuners, though that may be due to the inharmonicity of
piano strings.

> This training initially involved only perfect fifths and fourths
and
> major thirds. Yet once sensitivity to the presence of difference
> products was developed, it was spontaneously transferable to more
> complex harmonies, including a natural gravitation toward the 7th
> harmonic version of the V7 chord. It should be clear, therefore,
that
> this is not based on a pre-conditioned preference specific to a
> particular harmonic structure, but a more general underlying
> psychoacoustic phenomenon to which the subjects in question had
been
> senstizied, easily extensible to new harmonic experience, and that
> forms a highly significant and powerful component of the
> psychoacoustic phenomena at the very basis of the appeal of harmony
> in the first place.

Probably true, at least for singers singing in harmony, especially
amateurs who never developed a strong inner intonational sense from a
melodic basis.
>
> As I've stated previously, I have no good reason to believe that
this
> phenomenon is peculiar to our time. Why would it be, and why would
> anyone want to propose that it is? To do so would defy any sense of
> theoretical economy, as would invoking other, less objectively
> verifiable explanations.

What do you have to say to those (like Margo) who claim that, in the
days of Perotin, thirds, sixths, and triads tended to be sung in
Pythagorean intonation, despite the gross violation of "the very
basis of the appeal of harmony" as you see it?

--- In tuning@y..., BobWendell@t... wrote:
> Although much historical evidence may seem to
> suggest we can, such evidence represents only current
> conceptualizations and belief systems of the times, much of which,
> although informative (never said worthless, Paul), may only apply
to
> fixed-pitch instruments.

Except when the discussions get into the particulars of how vocal
practice departs from the intonation of fixed-pitch instruments (read
Margo's last 10 posts carefully).
>
> I have also stated elsewhere my belief that we cannot lend an
> adequately enlightened interpretation to this evidence without
taking
> into account the universals implicit in human auditory processing,
> independent of time, space, and cultural conditioning. Also, to
> pretend that we can always and reliably infer that pitch accuracy
> based on melodic memory was always adequate in the common practice
of
> the era in question to imitate exactly the way these fixed-pitch
> instruments were tuned seems a bit of a stretch.

I suspect, rather, that fixed-pitch instruments were tuned in such a
way (meantone) as to best imitate the way many singers and flexible-
pitch instrumentalists had, though their own trial and error and
intuition, come to perform music, in the 15th century. By the 16th
century, fixed-pitch instruments may have begun to impose
an "abstract interval standard" (see below) upon musical practice of
the time.
>
> Hmmmmm........I'm realizing that I've just hit on the fundamental
> psychoacousitc premise upon which most of my arguments are based:
>
> At the level of fine, microtonal precision, harmonic attraction
> toward the JI "sweet spots" powerfully dominates over melodic
> subtleties of the same order of magnitude.

For stable, consonant, final sonorities, I wholeheartedly agree.
However, in progressions in which melodic guidance toward a goal is
very powerful (such as where a tritone resolves by contrary semitones
to a major third), I hear the melodic integrity of the voices as the
stronger tuning consideration, and accept whatever vertical
dissonance may occur as simply strengthening the drive toward
resolution. THAT'S THE FUNDAMENTAL AESTHETIC PREMISE UPON WHICH MY
ARGUMENTS ARE BASED. My evidence is primarily based on my own
experimentation and my own musical ear (which I consider my best
feature). But the historical writings play some role, as do published
experiments such as:

"Rasch's study (1985) of large sequences of simultaneous tones found
that mistuning of the intervals of the melody was more disturbing
than mistuning of simultaneous intervals. This suggests that
listeners compare melodic intervals to an abstract interval standard.
Since Vos only used two-voice polyphonic settings, it is likely that
his attempts to isolate preferences of harmony were partially
undermined by melodic mistunings."
(http://music.dartmouth.edu/~kov/lerdahl/tuningPaper.html)

In a message dated 9/21/01 4:05:27 PM Eastern Daylight Time,
BobWendell@technet-inc.com writes:

> Such thinking would assume that melodic memory (not in the sense of
> "carrying a tune", but in the precise sense of exact imitation with
> microtonal accuracy) is more compelling than the appeal to the human
> ear of harmonic consonance. Maybe some rare human beings had
> developed such a microtonally precise melodic memory (Johnny Reinhard
> comes to mind), but that would be highly exceptional and certainly
> not the norm.
>
>

But the highest level professionals are not the norm. Neither was J.S. Bach
the norm. I remember Odetta (also not the norm) rehearsing for hours before
her performance on an AFMM concert on May 14, 1988. She had what might best
be called "etched" intervals for "God's Gonna Cut You Down" and "Black Woman"
that had an exact placement in her mind, and it was repeatable...if she
practiced. (I do have recordings of 2 different performances on the same day
and they could be contrasted.) Odetta would have been Harry Partch's ideal
vocalist, and he would have preferred her instead of many a male part (or so
he said in a letter).

Bach was a chromaticist each time he used all 12 notes in a piece (which was
pretty often). The etched sound of Werckmeister's scales are exact in
character based on key, as if one went back into time. This is one of the
very few cases where one can have certainty with a composer's tuning. At
least if one comes to believe that Werckmeister's tuning is Bach's, then
there is a one-cent exactness or better to each note. It is not much of a
leap to suggest that the melodic traditions that Bach inherited were well
served by an exact set of 12 major and minor keys which were "exactly"
different. Such wonders could be achieved, all quite mastered by the highly
exceptional. An exceptional, like Bach, could influence tremendously the
performance results of others, as does Bob. When only one person hears it,
others can achieve, too.

Consider, anyone who can believe in any of a number of "odd/West tunings"
would have to believe that one "could" believe most any set of tones or
sounds as legitimate, even reproducible. Why allow a modern comfort zone
with just intonation to set a standard for music of strangers?

Johnny Reinhard

Johnny Reinhard

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
> > Paul:
> > I'll still maintain (against Bob) that one
> > should not tune dominant seventh chords 4:5:6:7 in "authentic"
> > performances of Baroque music; and that, if some have cultivated
an
> > aesthetic of doing so, it is not because it's the "one true way",
> and
> > it doesn't necessarily imply that many musicians in the Baroque
era
> > did anything like it.
> >
> > Bob:
> > Hi, Paul. Good. You have already commented favorably on my
> statement
> > that in a brief passing seventh over a dominant triad, I wouldn't
> > necessarily expect performers of any era to suddenly veer as far
> > south of the normal diatonic position of the seventh as a strict
7-
> > limit 4:5:6:7 would dictate. We agree here. and i have never
> proposed
> > that it is the "one true way".
> >
> > However, many singers and flexible pitch instruments such as
> strings
> > make quick, smooth pitch adjustments of this order of magnitude
all
> > the time, even when it is simply fixing an initial pitch error
not
> > justifiable as 7-limit or any other coherently related tuning.
> > Consequently, I find it difficult to believe that in practice
> anyone
> > would perceive a sustained 7th in 4:5:6:7 occurring over a
dominant
> > as objectional or being out of tune, or even melodically
> > inappropriate unless they had some academic axe to grind.
>
> Believe it. And I'm certainly not the only person who reacts this
> way. You might want to look in the archives to a discussion of
> various tunings of a I-IV-V7-I progression, which we all listened
to
> and reacted to.

Bob answers:
It appears likely to me that the members of this group already have
an academic bias on this issue. What about the tons of musically
untrained listeners out there (the importance of whose ears you have
so defended in past discussions on pitch vs. frequency..."devil's
advocate" again?) who don't even grimace when a tenor sings a whole
song 30 cents flat!?

What about my choir, which initially slowly but without coaching made
the shift between a 7-limit 7th embedded in C-G-C and the 31 cent
higher Bb a perfect fourth above a 12-tET F, but had no idea that
they had done so? It has taken many months of training to teach them
to explicitly distinguish this shift and do it quickly instead of
having to wait for them to slowly migrate to it spontaneously on the
basis of previous training exclusively on fifths, fourths and thirds.
The ears on this list are microtonally prejudiced and far from
innocent test cases!

Paul:
> Perhaps your vocal group isn't producing dominant seventh chords as
> close to 4:5:6:7 as you think. This is what John deLaubenfels
> suggested. Did you have a specific reply to this, in your post that
> didn't get posted?
>
Bob:
I effectively answered you and John in a later post to which you
responded. I have repeated that response (included above) within the
last day and you also responded to that. I do not claim that my choir
or even I always sing 4:5:6:7, expecially not when singing brief
passing tone 7ths over V, but when it is sustanined, I already
explained above in this post what happens.

Bob had said earlier:
> > We should bear in mind always that the midi files with which we
> test
> > some of our ideas with our ears are generally quite inflexible
> pitch-
> > wise (excluding the adaptive JI software from JdL) and therefore
do
> > not represemt well what happens in practice with voices, strings,
> > etc. For example, the comma problem that occurs when tuning first
> > finger E on the D string of a violin to the open G and then to
the
> > open A in sequence does not generate anything like the same kind
of
> > melodic earthquake in practice with adaptive JI-oriented string
> > playing as it does in a midi file. We've already agreed on that.
>
Paul had answered:
> Yes, and there was an adaptive version of I-IV-V7-I, with a 4:5:6:7
> dominant seventh, in which the septimal comma was distributed into
> three equal parts, among the three chord changes. This did not
sound
> so bad melodically, though I still felt the 4:5:6:7 was lacking
> the "tug" toward the tonic that I like to hear in dominant seventh
> chords.
> >

Bob had previously said:
> > Further, I think you underestimate the attractive power of the
7th
> > harmonic in this context if this harmonic structure is sustained
> for
> > any significant time. I have already explained how I have trained
> > musically, and ESPECIALLY intonationally naive singers using
> > exercises very explicitly based on the difference product
> phenomenon.
>
Paul replied:
> I'm a big fan of 7-limit harmony. I just don't hear the dominant
> seventh in common-practice tonal music as wanting this kind
> of "consonance".

Bob:
I do not find the low 7th of 7-limit over the V any more "consonant"
in the sense of not wanting a resolution than I do a clean 15:16
against a "tonic" drone in Indian classical music, for example. I
think the 15:16 ratio is deliciously rich and beautiful in a harmonic
sense and love it when the singers linger on it, but it wants
resolution in a melodic sense. I feel the same about the low 7th.

Bob has previously said:
> > (I have explained long ago that I think flexibly-pitched
> > instrumentalists use this intuitively and usually unconsciously
to
> > tune harmony accurately. There is not time to do this with beats
> > between common harmonics, since the beats are usually too slow
> unless
> > we include huge pitch errors or very long notes.
>
Paul:
> What do you mean? Beats between common harmonics, in 12-tET for
> example, tend to be very fast, for thirds and sixths. How do
> combinational tones allow for a faster reaction/adjustment time in
> acheiving good tuning than the process of eliminating beats?

12-tET is quite far off on the thirds, as you know. If you are
wanting accurate JI and the note is short, there is no time for beats
to tell
you much. That's it. I'm speaking from direct experience as a string
player whose ear favors adaptive JI when free to do so. I don't
listen for beats! But I can hear the difference tones INSTANTLY at
any volume. It is this experience and my understanding of physical
theory that lead me to the choral training techniques I use.
>

Bob had previously said:
> > Also pitch training
> > using the beat approach is terribly and demonstrably ineffective
> with
> > amateurs when contrasted with the difference products approach
> except
> > for unisons and octaves, in which case the beat phenomenon is
> easily
> > detectable at the fundamental of both or one of the tones
> > respectively and there are no difference products at frequencies
> not
> > duplicating a fundamental.)
>
Paul replied:
> Piano tuners are taught to listen for the beats of _all_ consonant
> intervals. "Difference products" (why do you use that term -- do
you
> mean something different from combinational tones) are not used at
> all by piano tuners, though that may be due to the inharmonicity of
> piano strings.
>
Bob answers:
I have previously mentioned that my father was an expert piano tuner
as well as a prodigiously talented classical musician and jazz
improviser. He taught me to tune ET when I was in high school. I'm
intimately familiar with the beat phenomenon. Tuners don't use
differential tones because they're only good for just intervals. I
call them difference products because of my engineering bias and
electronics background. That is technically what they are, partially
generated by frequency mixing in the human ear, which has enough
built-in non-linearity to produce difference products. There is also
a significant neurological component, as you have reiterated, too.

Bob had previously said:
> > This training initially involved only perfect fifths and fourths
> and
> > major thirds. Yet once sensitivity to the presence of difference
> > products was developed, it was spontaneously transferable to more
> > complex harmonies, including a natural gravitation toward the 7th
> > harmonic version of the V7 chord. It should be clear, therefore,
> that
> > this is not based on a pre-conditioned preference specific to a
> > particular harmonic structure, but a more general underlying
> > psychoacoustic phenomenon to which the subjects in question had
> been
> > senstizied, easily extensible to new harmonic experience, and
that
> > forms a highly significant and powerful component of the
> > psychoacoustic phenomena at the very basis of the appeal of
harmony
> > in the first place.
>
> Probably true, at least for singers singing in harmony, especially
> amateurs who never developed a strong inner intonational sense from
a
> melodic basis.
>
Bob has previouly said:
> > As I've stated previously, I have no good reason to believe that
> this
> > phenomenon is peculiar to our time. Why would it be, and why
would
> > anyone want to propose that it is? To do so would defy any sense
of
> > theoretical economy, as would invoking other, less objectively
> > verifiable explanations.

Paul replied:
> What do you have to say to those (like Margo) who claim that, in
the
> days of Perotin, thirds, sixths, and triads tended to be sung in
> Pythagorean intonation, despite the gross violation of "the very
> basis of the appeal of harmony" as you see it?

Bob answers:
How can they know what they actually did in flexibly-pitched vocal
practice in a cappella performance? Sure, the melodic tendencies from
keyboard infuences would have had their effect, but why did 5-limit
emerge from 3-limit? You can find some academically arcane reasoning
to explain it, but I think the obvious explanation is the simple
aural attraction of the 4:5 sweet spot with no intellect-based
keyboard tuning to pull the ear away from it!!! I bet you could
repeat similar condidions over an over and the same evolution would
take place for the same reason! I have effectively done this in the
late 20th and 21st century.

--- In tuning@y..., BobWendell@t... wrote:

> > Believe it. And I'm certainly not the only person who reacts this
> > way. You might want to look in the archives to a discussion of
> > various tunings of a I-IV-V7-I progression, which we all listened
> to
> > and reacted to.
>
> Bob answers:
> It appears likely to me that the members of this group already have
> an academic bias on this issue.

Academic bias? Argghhh . . . that rubs me the wrong way on several
different levels. Does Joseph Pehrson have an academic bias, or a non-
academic bias . . . Come on, most of us are musicians first, and care
about how the music sounds more than anything else . . . And wasn't
it a blind test, anyway?

> What about the tons of musically
> untrained listeners out there (the importance of whose ears you
have
> so defended in past discussions on pitch vs. frequency..."devil's
> advocate" again?) who don't even grimace when a tenor sings a whole
> song 30 cents flat!?

I'd be happy to put these sequences to musically untrained listeners.

> What about my choir, which initially slowly but without coaching
made
> the shift between a 7-limit 7th embedded in C-G-C and the 31 cent
> higher Bb a perfect fourth above a 12-tET F, but had no idea that
> they had done so? It has taken many months of training to teach
them
> to explicitly distinguish this shift and do it quickly instead of
> having to wait for them to slowly migrate to it spontaneously on
the
> basis of previous training exclusively on fifths, fourths and
thirds.

May I suggest that doing it quickly was precisely what required
deliberate coaching, and that this supports my assertion that the
attraction of JI "magnets" really is of utmost importance only for
long, sustained chords?

> The ears on this list are microtonally prejudiced and far from
> innocent test cases!

"Microtonally prejudiced"? Wouldn't that mean "predisposed toward
liking unusual or microtonal melodic intervals" rather than
otherwise? But sure, I'd rather have some truly innocent test cases
too . . .
>
> Paul replied:
> > What do you have to say to those (like Margo) who claim that, in
> the
> > days of Perotin, thirds, sixths, and triads tended to be sung in
> > Pythagorean intonation, despite the gross violation of "the very
> > basis of the appeal of harmony" as you see it?
>
> Bob answers:
> How can they know what they actually did in flexibly-pitched vocal
> practice in a cappella performance?

I'll defer to Margo on this . . .

> Sure, the melodic tendencies from
> keyboard infuences would have had their effect, but why did 5-limit
> emerge from 3-limit? You can find some academically arcane
reasoning
> to explain it,

A new style from the Western Islands began to spread . . . what's
academically arcane about that? And saying "why did 5-limit emerge
from 3-limit" ignores the fact (or fiction, depending on your point
of view) that 3-limit practice, with its dissonant thirds and sixths,
persevered for many centuries . . .

--- In tuning@y..., genewardsmith@j... wrote:

/tuning/topicId_28224.html#28229

> --- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
>
> > Again I am not sure exactly what you are asserting here. We
cannot change historical fact, to be sure (though we are free to
doubt something which is _presented_ as historical fact), but we
certainly can impose any tuning at all on any music at all.
>
> It's done all the time, as I pointed out before. If Glenn Gould can
> sit down and hum along to Bach on his Steinway then it seems absurd
> to cavil at retuning V7, so long as it works. To say composers
> *wanted* it sharp makes no sense, since they didn't have a choice
and
> therefore did not choose to make it sharp. To say they wrote their
> music with it sharp is certainly true, and may very well effect the
> result of any retuning. The only way to decide is to try it and see
> if it sounds good.
>

That's a pretty funny Glenn Gould comment, Gene! Maybe Glenn Gould
was singing along a 7:4! He certainly *wasn't* singing in 12-tET, if
I remember correctly!

_______ ______ ________
Joseph Pehrson

BobWendell@technet-inc.com wrote:

> Bob:
> I am saying Rameau was just documenting current practice already in
> place widely and for a period of time, and perhaps, PERHAPS, putting
> new conceptual wrinkles on it, but not coming up with anything
> fundametally new in terms of practice.
>

I would put Rameau's ideas with a more folksy tradition of
homophonic settings, where e.g. the melody ended up in the
treble. There may have been 3 chord guitar players accompanying,
say, a frottola before "real composers" took up the genre
(amounting to, if you like, writing a melody and a harmonization
for it).

The use of sixth chords might then have been the late
renaissance way of chord substitution, making movement in the
accompanying voices possible while preserving the tonal content
(assuming that a guitar would just be strumming the same old
chord as long as possible). But if Rameau was thinking of folk
music and its imitation by composers, other composers would have
recognized this background. This concept would have been
despised in a world where most music (known to posterity) was
used to embellish high secular and liturgical acts.

Without the idea of chord inversions it is much easier to
explain that the third inversion should be considered dissonant,
or that the V "always" has to be a major chord.

Coming up:
On-topic question

--- In tuning@y..., genewardsmith@j... wrote:

/tuning/topicId_28224.html#28338

>
> My ears say that Verklarte Nacht sounds wrong in the 5-limit, wrong
> but interesting in the 11-limit, and not very good in the version
it was written in when compared to the 7-limit, which is the best. My
> ears like Rhapsody in Blue best in the version which says it is
> "7-limit adaptive tuning, grounded to COFT, with fairly soft
vertical springs, targeting 7th degree at 7/4 of root. Melody
springs are of negligible strength", but now the 12-et sounds pretty
good too, though perhaps a little on the bland side. There aren't a
lot of 7-vs-5 comparisons so far as I know.
>

This is really interesting, because the deLaubenfels' 7-limit version
of Verklarte Nacht was *my* particular favorite, too... And the 11-
limit version sounded strange but interesting. I was *also* enamored
of the 7-limit Gershwin, although I realize there are some list
members here who didn't like it...

> > The concept of major and minor triads with their different
> inversions was introduced by Rameau. Bach and Handel may have been
familiar with it, but I wouldn't be surprised if they weren't.
>

Isn't it legendary that Bach copied out lots of works by Telemann?
He would have had practice in triadic inversions that way, I would
presume...??

__________ _______ _______
Joseph Pehrson

In a message dated 9/23/01 5:00:09 PM Eastern Daylight Time, jpehrson@rcn.com
writes:

> Isn't it legendary that Bach copied out lots of works by Telemann?
>

It was Vivaldi, though Bach knew the older Telemann in Eisenach. Many years
later, after his parents' deaths, he asked Bach asked Telemann to be
godfather for his son. And Bach lead the "Telemann Society" in Leipzig for a
decade.

Johnny Reinhard

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_28224.html#28377

> > Bob: What are we talking about here? It was common practice in
Bach and Handel's day to improvise over a figured bass. The notation
for that embraces a clearly implicit understanding of inversions,
>
> That isn't clear. There was no identification of a chord with fifth
> and major third with the chord with minor third and minor sixth, as
> one category, as opposed to the chord with fifth and minor third
with the chord with major third and major sixth as another category,
in figured bass. The concept of "major triad" and "minor triad" with
> there inversions gained prominence only later!
>

Maybe I'm missing something, or not understanding something here, but
in figured bass the major and minor chords are certainly related,
aren't they? They are the same inversion, the same chord?!

There is just a chromatic alteration before the figures to indicate
whether it is a major or minor chord, if it's not the one in the key
signature...

That would mean a relationship, wouldn't it??

__________ ________ ________
Joseph Pehrson

--- In tuning@y..., BobWendell@t... wrote:

/tuning/topicId_28224.html#28428

> At the level of fine, microtonal precision, harmonic attraction
> toward the JI "sweet spots" powerfully dominates over melodic
> subtleties of the same order of magnitude.
>

Well, these are "fighting words" to our favorite "nutty professor"
Brian McLaren, and you might wish to examine his exhaustive (whew!)
and somewhat flawed but inciteful tome called, _Microtonality, Past,
Present and Future_.

McLaren spends *lots* of time debunking the idea that we have a just
intonation "hard wiring" in our hearing, and even if you don't agree
with him, the arguments are worth considering.

(Despite Paul's believe that it's 99.999% bunk -- Oh, .001% is OK,
according to Paul...)

He can be found, controversially, here:

/crazy_music/messages

________ _______ ________
Joseph Pehrson

So So sorry, Joseph :)

What's the "7-limit" thing ?
Why everytime i read that ?
Is it good or bad ? :))

Dimitrov

--- jpehrson@rcn.com a �crit�: > --- In tuning@y...,
BobWendell@t... wrote:
>
> /tuning/topicId_28224.html#28428
>
> > At the level of fine, microtonal precision,
> harmonic attraction
> > toward the JI "sweet spots" powerfully dominates
> over melodic
> > subtleties of the same order of magnitude.
> >
>
> Well, these are "fighting words" to our favorite
> "nutty professor"
> Brian McLaren, and you might wish to examine his
> exhaustive (whew!)
> and somewhat flawed but inciteful tome called,
> _Microtonality, Past,
> Present and Future_.
>
> McLaren spends *lots* of time debunking the idea
> that we have a just
> intonation "hard wiring" in our hearing, and even if
> you don't agree
> with him, the arguments are worth considering.
>
> (Despite Paul's believe that it's 99.999% bunk --
> Oh, .001% is OK,
> according to Paul...)
>
> He can be found, controversially, here:
>
> /crazy_music/messages
>
> ________ _______ ________
> Joseph Pehrson
>
>
>

___________________________________________________________
Do You Yahoo!? -- Un e-mail gratuit @yahoo.fr !
Yahoo! Courrier : http://fr.mail.yahoo.com

Hi, Joseph! Well, I've had considerable (many years) of empirical
experiences with totally untrained, musically naive ears who could
not sight sing with any reasonable precision and did not sing in tune
with standard practice 12-tET either melodically or harmonically.
Many had frequent errors and/or habitual pitch offsets in the 25-40
cent range.

The clearly, repeatably demonstrable power and IMMEDIACY of the JI
"sweet spot's" attraction for these same ears, as illustrated in my
recounting of my experiences in previous postings, gives the lie to
any theoretical arguments you might mention that dismiss this power
as non-existent.

He might as well argue that I was born without any involvement on the
part of my mother. I somehow find little motivation to entertain such
vain musings. No person with his understanding of intonation could
ever have trained my choir to sing at the standard of quality it now
does simply because his ideas could have found no value in any
approach that would have WORKED! Theoretical speculation that does
not yield or even potentially lead toward positive practical results
fails to interest me.

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., BobWendell@t... wrote:
>
> /tuning/topicId_28224.html#28428
>
> > At the level of fine, microtonal precision, harmonic attraction
> > toward the JI "sweet spots" powerfully dominates over melodic
> > subtleties of the same order of magnitude.
> >
>
> Well, these are "fighting words" to our favorite "nutty professor"
> Brian McLaren, and you might wish to examine his exhaustive (whew!)
> and somewhat flawed but inciteful tome called, _Microtonality,
Past,
> Present and Future_.
>
> McLaren spends *lots* of time debunking the idea that we have a
just
> intonation "hard wiring" in our hearing, and even if you don't
agree
> with him, the arguments are worth considering.
>
> (Despite Paul's believe that it's 99.999% bunk -- Oh, .001% is OK,
> according to Paul...)
>
> He can be found, controversially, here:
>
> /crazy_music/messages
>
> ________ _______ ________
> Joseph Pehrson

Paul:
> "Rasch's study (1985) of large sequences of simultaneous tones
found
> that mistuning of the intervals of the melody was more disturbing
> than mistuning of simultaneous intervals. This suggests that
> listeners compare melodic intervals to an abstract interval
standard.
> Since Vos only used two-voice polyphonic settings, it is likely
that
> his attempts to isolate preferences of harmony were partially
> undermined by melodic mistunings."
> (http://music.dartmouth.edu/~kov/lerdahl/tuningPaper.html)

Bob comments:
In those who do not specifically pay close attention to tuning
harmonies (which represents the vast majority of singers, for
example, in the common practice music of today), melodic habit is
essentially all there is. Since it is quite common that keyboardists
have no experience whatsoever with tuning, singers none with other
than single tones in real-time performance, and even wind players
only with the simple pulling in or out of a barrel for the sum total
of theirs, large numbers of today's common practice musicians have no
significant experience paying any really precise attention to tuning
vertical harmonic structures.

In my view, this is all the cited study shows. It should not pretend
to present a finding that qualifies as some kind of humanly intrinsic
psychoacoustic tendency that applies across the board to
considerations of harmonic vs. melodic integrity.

Paul also said:
However, in progressions in which melodic guidance toward a goal is
> very powerful (such as where a tritone resolves by contrary
semitones
> to a major third), I hear the melodic integrity of the voices as
the
> stronger tuning consideration, and accept whatever vertical
> dissonance may occur as simply strengthening the drive toward
> resolution. THAT'S THE FUNDAMENTAL AESTHETIC PREMISE UPON WHICH MY
> ARGUMENTS ARE BASED. My evidence is primarily based on my own
> experimentation and my own musical ear (which I consider my best
> feature).

That this observation reflects a valid component of historical
realities in the perception of harmony is unquestionable. However, I
take this in the context of fixed tunings as a cultural GIVEN
provided by the theoretical constructs of the time. I don't think
anyone here would disagree (?) that the thirds having been perceived
in medieval times as dissonances that want to resolve outward to
fifths or inward to unisons is a direct result of the complex
relationship between the tones constituting thirds in Pythagorean
tuning.

Neither do I disagree that the thin diatonic half-steps conditioned
by Pythagorean tuning in the minds of the musicians of that era were
melodically very compelling. It must have taken both time and
something else pretty powerful to dislodge that conditioning and move
harmonic evolution towared the pure and nearly pure thirds and the
relatively quite fat diatonic half-steps of the mean-tone
temperaments that predominated later.

However, I feel it important to distinguish between tuning dissonance
and harmonically intrinsic dissonance. Aren't tuning dissonances like
thirds in Pythagorean scales a historical circumstance that DO NOT
necessarily represent some intrinsic NEED for such dissonance in
order to drive harmonic progressions toward resolution? Thirds tuned
as 4:5 ratios certainly do not exhibit any such tendency, yet there
are just intervals that beg for resolution with no such tuning
dissonances involved.

In this light and that of my statement above, "It must have taken
both time and something else pretty powerful to dislodge that
conditioning...", what was that "something else pretty powerful"? I
propose it was the intrinsically attractive power of the 4:5 ratio in
flexible-pitch polyphonic ensembles that drove the performers' ears
intuitively in this evolutionary direction.

--- In tuning@y..., BobWendell@t... wrote:

/tuning/topicId_28224.html#28523

> Hi, Joseph! Well, I've had considerable (many years) of empirical
> experiences with totally untrained, musically naive ears who could
> not sight sing with any reasonable precision and did not sing in
tune
> with standard practice 12-tET either melodically or harmonically.
> Many had frequent errors and/or habitual pitch offsets in the 25-40
> cent range.
>
> The clearly, repeatably demonstrable power and IMMEDIACY of the JI
> "sweet spot's" attraction for these same ears, as illustrated in my
> recounting of my experiences in previous postings, gives the lie to
> any theoretical arguments you might mention that dismiss this power
> as non-existent.
>
> He might as well argue that I was born without any involvement on
the part of my mother. I somehow find little motivation to entertain
such vain musings. No person with his understanding of intonation
could ever have trained my choir to sing at the standard of quality
it now does simply because his ideas could have found no value in any
> approach that would have WORKED! Theoretical speculation that does
> not yield or even potentially lead toward positive practical
results fails to interest me.
>

Thanks for your message, Bob. Personally, I tend to agree with you,
or I wouldn't have the interest in the "Blackjack" scale that I do.
However, McLaren dregs up some substantial psychoacoustic literture
of studies at so on post-Helmholtz, so it's not just theoretical
conjecture... I tend not to believe much of it, but it is an
interesting "other side..."

________ _______ ______
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_28224.html#28377
>
> > > Bob: What are we talking about here? It was common practice in
> Bach and Handel's day to improvise over a figured bass. The
notation
> for that embraces a clearly implicit understanding of inversions,
> >
> > That isn't clear. There was no identification of a chord with
fifth
> > and major third with the chord with minor third and minor sixth,
as
> > one category, as opposed to the chord with fifth and minor third
> with the chord with major third and major sixth as another
category,
> in figured bass. The concept of "major triad" and "minor triad"
with
> > there inversions gained prominence only later!
> >
>
> Maybe I'm missing something, or not understanding something here,
but
> in figured bass the major and minor chords are certainly related,
> aren't they? They are the same inversion, the same chord?!

Exactly . . . but the different triads were not usually categorized
into "inversions of major" and "inversions of minor" they way they
are today (since Rameau).

> There is just a chromatic alteration before the figures to indicate
> whether it is a major or minor chord, if it's not the one in the
key
> signature...
>
> That would mean a relationship, wouldn't it??

Yes . . . that's not the relationship I was talking about, which was
between different inversions of a single "chord quality" as we think
of it since Rameau . . .

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_28224.html#28538

> > There is just a chromatic alteration before the figures to
indicate whether it is a major or minor chord, if it's not the one in
the key signature...
> >
> > That would mean a relationship, wouldn't it??
>
> Yes . . . that's not the relationship I was talking about, which
was between different inversions of a single "chord quality" as we
think of it since Rameau . . .

Hmmm... I guess you're right. The inversions were a little "looser"
in that respect... more "linear" thinking there...

_______ _______ _______
Joseph Pehrson

I think we're fundamentally in agreement on many points here, Johnny.
However, I think that among even the highest level of professional
musicians, for fine pitch differences the harmonic fit is more
powerful an influence than the melodic. I'm no virtuoso on
the violin and never have been even close, but that was always true
for me personally as a string player, even though initially I had no
intellectual basis for understanding the tendency.

I DO NOT mean to imply here that an 8:9 7th in the dominant is going
to give way to a 7:8 7th in top level professionals! These are both
just intervals! That the implied fundamental (and primary
combinatorial tone) of the 8:9 interval falls on the 7th instead of
the root is a fairly subtle difference, but I believe it explains why
otherwise intonationally naive singers who have learned to savor just
3rds, 4ths, and 5ths tend to gravitate toward 7:8 under sustained
conditions.

I have stated elsewhere in these threads that a 7th as a brief
passing tone over a dominant would not likely veer so low as 7:8,
since melodic habit bids heavily against this. I believe we're all in
agreement here! But I would bet that in a choral ensemble full of
harmonically sensitive ears the sopranos would spontaneously tend to
pick the low 7th on F in a sequence like this, where the bass G is a
fourth under middle C:

S: D E F - - - - - - E
A: G - - - - - - - - - G
T: B - - - - - - - - - C
B: G - - - - - - - - - C

Here the primary (most audible) combinatorial tone between the alto
and tenor B is the D a fourth below the bass, reinforcing two octaves
lower the initial soprano fifth. The one between the Bass G and tenor
B is the G two octaves below the bass, reinforcing the root.

The F at 8:9 would not fit harmonically poorly into this scheme,
since the primary combinatorial tone with the alto G would fall on F
three octaves below the sung one, but it's harmonically alien to the
root and below it. On the other hand, the 7:8 version generates the
primary combinatorial tone on G two octaves below the alto G, and
also reinforcing the octave higher bass root.

Similarly, none of the other combinatorial tones 7:8 generates with
the other tones of the chord are harmonically alien to the root. This
fits much more neatly to the ear harmonically and its proximity to
the E begs for resolution, since the MELODIC interval is
chromatically thin.

--- In tuning@y..., Afmmjr@a... wrote:
> In a message dated 9/21/01 4:05:27 PM Eastern Daylight Time,
> BobWendell@t... writes:
>
>
> > Such thinking would assume that melodic memory (not in the sense
of
> > "carrying a tune", but in the precise sense of exact imitation
with
> > microtonal accuracy) is more compelling than the appeal to the
human
> > ear of harmonic consonance. Maybe some rare human beings had
> > developed such a microtonally precise melodic memory (Johnny
Reinhard
> > comes to mind), but that would be highly exceptional and
certainly
> > not the norm.
> >
> >
>
> But the highest level professionals are not the norm. Neither was
J.S. Bach
> the norm. I remember Odetta (also not the norm) rehearsing for
hours before
> her performance on an AFMM concert on May 14, 1988. She had what
might best
> be called "etched" intervals for "God's Gonna Cut You Down" and
"Black Woman"
> that had an exact placement in her mind, and it was repeatable...if
she
> practiced. (I do have recordings of 2 different performances on
the same day
> and they could be contrasted.) Odetta would have been Harry
Partch's ideal
> vocalist, and he would have preferred her instead of many a male
part (or so
> he said in a letter).
>
> Bach was a chromaticist each time he used all 12 notes in a piece
(which was
> pretty often). The etched sound of Werckmeister's scales are exact
in
> character based on key, as if one went back into time. This is one
of the
> very few cases where one can have certainty with a composer's
tuning. At
> least if one comes to believe that Werckmeister's tuning is Bach's,
then
> there is a one-cent exactness or better to each note. It is not
much of a
> leap to suggest that the melodic traditions that Bach inherited
were well
> served by an exact set of 12 major and minor keys which were
"exactly"
> different. Such wonders could be achieved, all quite mastered by
the highly
> exceptional. An exceptional, like Bach, could influence
tremendously the
> performance results of others, as does Bob. When only one person
hears it,
> others can achieve, too.
>
> Consider, anyone who can believe in any of a number of "odd/West
tunings"
> would have to believe that one "could" believe most any set of
tones or
> sounds as legitimate, even reproducible. Why allow a modern
comfort zone
> with just intonation to set a standard for music of strangers?
>
> Johnny Reinhard
>
> Johnny Reinhard

--- In tuning@y..., BobWendell@t... wrote:

> However, I feel it important to distinguish between tuning
dissonance
> and harmonically intrinsic dissonance. Aren't tuning dissonances
like
> thirds in Pythagorean scales a historical circumstance that DO NOT
> necessarily represent some intrinsic NEED for such dissonance in
> order to drive harmonic progressions toward resolution?

I don't understand this question. Can you rephrase it?

> Thirds tuned
> as 4:5 ratios certainly do not exhibit any such tendency, yet there
> are just intervals that beg for resolution with no such tuning
> dissonances involved.

Can you give some examples?

--- In tuning@y..., jpehrson@r... wrote:

> Thanks for your message, Bob. Personally, I tend to agree with
you,
> or I wouldn't have the interest in the "Blackjack" scale that I
do.
> However, McLaren dregs up some substantial psychoacoustic literture
> of studies at so on post-Helmholtz, so it's not just theoretical
> conjecture... I tend not to believe much of it, but it is an
> interesting "other side..."

He takes select quotes from the psychoacoustic literature completely
out-of-context, and uses them to knit together a fabric of total
prevarication . . . he thinks nothing of completely misrepresenting
the opinions of others, not to mention nasty ad hominem attacks . . .
my suggestion is to forget about him, and start with a good book like
Juan Roederer's _Physics and Psychophysics of Music_ . . . if you'd
like to go deeper, follow up with the references found in the
footnotes and bibliography . . .

BobWendell stated :

> In this light and that of my statement above, "It must have taken
> both time and something else pretty powerful to dislodge that
> conditioning...", what was that "something else pretty powerful"? I
> propose it was the intrinsically attractive power of the 4:5 ratio in
> flexible-pitch polyphonic ensembles that drove the performers' ears
> intuitively in this evolutionary direction.
>

This is very interesting, and if I look at the "evolutionary" aspect,
would seem to support the development of meantone over pythagorean
tuning. To what would we attribute the return of neo-pythagorean AKA
12et?

Its very interesting that major thirds are still considered consonant,
despite the typical modern performance of them being closer to
pythagorean than to just.

A related question, in a V7 chord does your ensemble sharpen the
leading tone? (I know you have heard what you've heard, but I haven't
heard it so bear with me.) If I understand completely, then the
following voicings (low to high going up the page)

F F E
D D C
C B C
A G G

would be tuned to the following.

8/3 21/8 5/4
20/9 9/4 2/1
2/1 15/8 2/1
5/3 3/2 3/2

What I'm looking for by asking about a sharpened leading tone (or
any other tones that might move) is to see if some of this
tremendous melodic movement in the D and F and complete change
in the D-F interval is being absorbed somewhere else.

Just curious and not doubting anything...

Bob Valentine

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
>
> > However, I feel it important to distinguish between tuning
> dissonance
> > and harmonically intrinsic dissonance. Aren't tuning dissonances
> like
> > thirds in Pythagorean scales a historical circumstance that DO
NOT
> > necessarily represent some intrinsic NEED for such dissonance in
> > order to drive harmonic progressions toward resolution?
>
Paul:
> I don't understand this question. Can you rephrase it?
>
> > Thirds tuned
> > as 4:5 ratios certainly do not exhibit any such tendency, yet
there
> > are just intervals that beg for resolution with no such tuning
> > dissonances involved.
>
Paul:
> Can you give some examples?

Bob:
The 5:7 tritone and its inversion, 7:10.
This answer is a great way to illustrate the statement above that you
had trouble understanding. I DO NOT consider lack of harmonicity as a
requirement for tension toward resolution. I see these intervals in
their JI form as begging for resolution, "harmonically consonant" as
they may be. Otherwise do we not imply that anything in strict JI
could never have any harmonic drive toward resolution? I don't find
that to be a particularly palatable position.

On the other hand, the drive of Pythagorean thirds toward resolution
inward to a unison or outward to a fifth is owing to the complex,
relatively inharmonious nature of the way the interval is tuned, and
is not intrinsic to thirds (e.g., 5:4). This is all I'm saying with
the statements above.

I think we need to distinguish between these two kinds of drive
toward resolution. I used the terms tuning dissonance (e.g.,
Pythagorean thirds) vs. harmonically intrinsic dissonance (e.g., just
tritones). When a 5:7 tritone moves inward by contrary motion to a
major third, the difference tones produced by the third reinforce the
root two octaves below it. The tritone had no such harmonically
stable acoustic structure.

Hi, Bob! Thanks for your query. We do not sharpen the leading tone,
at least not consistently and with any intention to do so. (My choir
is not intonationally so perfect and consistent as your numbers might
imply.)

First, the syntonic shift in your D above and the septimal comma
shift downward in the F are not compensated in any rigorous way in
our practice. I simply train members to prefer just tunings, mainly
on fourths, fifths and major thirds, and leave the rest to intuition.
Since we also work on pitch stability, not in any locally rigorous
way, but simply, generally entertain the goal of ending up on the
same pitch base as we started, harmonic drift is eliminate by subtle,
unconscious adaptive JI "fudging" that is mostly melodic, since too
much fudging harmonically destroys the justness of JI harmony.

I find that most people, even highly trained common practice
musicians, do not perceive easily and are not bothered by microtonal
MELODIC shifts well-disguised by the fudging that occurs in adaptive
JI by flexibly pitched performers. There is a habit pattern of
perceiving anything substantially less than chromatic half-steps as
the "same" pitch when the ear is accustomed to perceiving
diatonically and even in terms of conventional harmonic chromaticism.
Typical common practice pitch errors among flexibly pitched
performers such as singers are of this order of magnitude or greater
anyway.

I find that most common practice musicians in this area are incapable
of pinpointing the source of the "professional" sound they attribute
to our ensemble. They most often have no clue that the major
distinguishing component of our clean choral blend is harmonic pitch
accuracy. Kind of pitiful, but true nonetheless.

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
>
> BobWendell stated :
>
> > In this light and that of my statement above, "It must have taken
> > both time and something else pretty powerful to dislodge that
> > conditioning...", what was that "something else pretty powerful"?
I
> > propose it was the intrinsically attractive power of the 4:5
ratio in
> > flexible-pitch polyphonic ensembles that drove the performers'
ears
> > intuitively in this evolutionary direction.
> >
>
> This is very interesting, and if I look at the "evolutionary"
aspect,
> would seem to support the development of meantone over pythagorean
> tuning. To what would we attribute the return of neo-pythagorean AKA
> 12et?
>
> Its very interesting that major thirds are still considered
consonant,
> despite the typical modern performance of them being closer to
> pythagorean than to just.
>
> A related question, in a V7 chord does your ensemble sharpen the
> leading tone? (I know you have heard what you've heard, but I
haven't
> heard it so bear with me.) If I understand completely, then the
> following voicings (low to high going up the page)
>
> F F E
> D D C
> C B C
> A G G
>
> would be tuned to the following.
>
> 8/3 21/8 5/4
> 20/9 9/4 2/1
> 2/1 15/8 2/1
> 5/3 3/2 3/2
>
> What I'm looking for by asking about a sharpened leading tone (or
> any other tones that might move) is to see if some of this
> tremendous melodic movement in the D and F and complete change
> in the D-F interval is being absorbed somewhere else.
>
> Just curious and not doubting anything...
>
> Bob Valentine

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
>
> This is very interesting, and if I look at the "evolutionary"
aspect,
> would seem to support the development of meantone over pythagorean
> tuning. To what would we attribute the return of neo-pythagorean AKA
> 12et?

This was clearly a result of composers wanting to modulate more and
more, and musicians being unwilling to accomodate the complexities of
having, say, 31 notes on their instruments.
>
> Its very interesting that major thirds are still considered
consonant,
> despite the typical modern performance of them being closer to
> pythagorean than to just.

The slope of the dissonance curve between 400 cents and 408 cents is
very steep. Therefore, even though it's only an 8-cent difference,
it's a big difference in consonance. Guitarists, in my observations,
tend to stop and retune their guitars if they land on major triad
where the tuning is approximately Pythagorean.

Still, a musician confronted with Pythaogorean tuning today is
unlikely to automatically revert to a 13th century style . . . the
style they grew up with will tend to prevail, however poorly it is
represented in the tuning.
>
> A related question, in a V7 chord does your ensemble sharpen the
> leading tone? (I know you have heard what you've heard, but I
haven't
> heard it so bear with me.) If I understand completely, then the
> following voicings (low to high going up the page)
>
> F F E
> D D C
> C B C
> A G G
>
> would be tuned to the following.
>
> 8/3 21/8 5/4
> 20/9 9/4 2/1
> 2/1 15/8 2/1
> 5/3 3/2 3/2

Bob has said his ensemble uses adaptive JI . . . so this would not be
a fair representation.

--- In tuning@y..., BobWendell@t... wrote:

> > > Thirds tuned
> > > as 4:5 ratios certainly do not exhibit any such tendency, yet
> there
> > > are just intervals that beg for resolution with no such tuning
> > > dissonances involved.
> >
> Paul:
> > Can you give some examples?
>
> Bob:
> The 5:7 tritone and its inversion, 7:10.

You appear to be in agreement with Blackwood, who says such intervals
are "concordant" but not "consonant". However, I think it's just a
question of musical style. If one invents (as I have tried to do) a
musical system where 7-limit harmony has the same logic as 5-limit
harmony does in common-practice music, and a culture immerses itself
in the task of composing, performing, and listening to such music,
then such intervals will become "consonant".

> This answer is a great way to illustrate the statement above that
you
> had trouble understanding. I DO NOT consider lack of harmonicity as
a
> requirement for tension toward resolution. I see these intervals in
> their JI form as begging for resolution, "harmonically consonant"
as
> they may be.

In a particular style, yes.

> Otherwise do we not imply that anything in strict JI
> could never have any harmonic drive toward resolution?

Of course not -- clearly there are "limits" (q.v. harmonic entropy).
>
> On the other hand, the drive of Pythagorean thirds toward
resolution
> inward to a unison or outward to a fifth is owing to the complex,
> relatively inharmonious nature of the way the interval is tuned,
and
> is not intrinsic to thirds (e.g., 5:4). This is all I'm saying with
> the statements above.

Again, it's just a question of musical style. Margo has mentioned
that, when immersing herself in Gothic style for a long time,
switching to a tuning with harmonious thirds does little to change
the thirds' drive to resolve outward to fifths or inward to unisons.
I'll let Margo elaborate . . .

> I think we need to distinguish between these two kinds of drive
> toward resolution. I used the terms tuning dissonance (e.g.,
> Pythagorean thirds) vs. harmonically intrinsic dissonance (e.g.,
just
> tritones).

Blackwood would use the terms "discordance" and "dissonance",
respectively.

> When a 5:7 tritone moves inward by contrary motion to a
> major third, the difference tones produced by the third reinforce
the
> root two octaves below it. The tritone had no such harmonically
> stable acoustic structure.

When part of a V7 chord (4:5:6:7), as we've been assuming, it
certainly is part of a "harmonically stable acoustic structure", no?
And what if the resolution is to a minor third?