Yahoo Tuning Groups Ultimate Backup tuning Re: counterpoint

Hi Joe,

My little "counterpoint schmounterpoint" quip was just my way of
saying that I think if you don't intuitively have a clue here to begin
to start with, well then your dead in the water... and no amount of
textbookin' is ever gonna help!

The Maneri's (Joe and Mat), and by extension drummer Randy Peterson,
lay down some of the most astonishingly fresh "traditional"
counterpoint I've personally ever had the pleasure of hearing. It's
subtle, it's complex, it breaths... it be the real deal to these ears.

Anyway, in my own music I try to take my counterpoint cue from the
wildness and the weirdness of the natural world as I see it. And when
I look into the early winter thicket and dearticulating blur of a
leafless forest, or when I see the hard wind rip through the tall
grass of a summer's field, well that's when I really sense the kind of
counterpoint that I'm most interested in!

But if you take this as too direct an analogy then this would seem to
be a rather static thing. Perhaps a "statistical" thing in the vein of
say Xenakis... this isn't what I mean. But hopelessly nebulous things
like what I do mean are NOT the sort of things I'd want to endorse as
teachable. And teachable, while better suited for some than others, is
obviously okay...

I just don't want a teacher (or his/her student) telling me what's not
okay if I happen to think what's not okay is pretty okay, 'cause I'm a
stubborn spoiled loon!

But back to jazz: baroque counterpoint in the fashion of say Tristano
and those West Coast guys, well that always just bored me to tears.
And to my mind it's not that it's "too white" or any such thing (as it
was often slagged). It's just that it's neither visceral nor dynamic
enough to engage me in the way I apparently am wired to be engaged.

It's all well and fine but I find that I need something else...
something not so, err, square (sorry, that's not quite right but it's
probably the best I can do right now).

I can sympathize with the Fux quote you posted earlier today. Honest,
I really truly can. But I can also sympathize with Anthony Braxton
when after a soundcheck spent running through some standards he
writes, "I wish we hadn't played *tunes*, I've played enough tunes to
last a lifetime. I mean, I'm interested in harmony, but there has to
be another way."

Indeed. BTW, that bit's from the book Forces In Motion. Here's another
bit where the author, Graham Lock, is discussing composition with
Braxton:

'How do you compose?' I ask. 'What's the process?"

He Shrugs. 'Oh, I just sit down and start writing.'

'You never get stuck for inspiration?'

'Composition's not the big deal they make it at collages. They
paralyze people with rules. I just sit down, write out an idea, and
work on it.'

--Dan Stearns

🔗D.Stearns <STEARNS@CAPECOD.NET>

🔗jpehrson@rcn.com

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

/tuning/topicId_20520.html#20524

> Hi Joe,
>
> My little "counterpoint schmounterpoint" quip was just my way of
> saying that I think if you don't intuitively have a clue here to
begin to start with, well then your dead in the water... and no
amount of textbookin' is ever gonna help!
>

Why sure, Dan! That makes a lot of sense. So does the rest of your
post. And, frankly, counterpoint is really not so much something I
would associate with Xenakis... Well, it's there, but it's more the
evolution of a natural state, as you intimate, and not as ACTIVE a
process as what you are doing. Obviously just a different "method.."

>
> I just don't want a teacher (or his/her student) telling me what's
not okay if I happen to think what's not okay is pretty okay, 'cause
I'm a stubborn spoiled loon!
>

Of course... this is what composers always object to. They thought
Debussy was a crazy loon at the Paris Conservatory at that time.
Fortunately, he didn't believe his harmony and counterpoint was
"wrong..."

> But back to jazz: baroque counterpoint in the fashion of say
Tristano and those West Coast guys, well that always just bored me to
tears.

I hate to confess that I really don't know what this is. Is it a
kind of "Swingle Singers" kind of square jazz or some such? There's
a
"black hole" in my experience on this, obviously...

>
> I can sympathize with the Fux quote you posted earlier today.

Well, I posted it as a "funny." I hope you didn't take it SERIOUSLY.
It was just funny that some of the same issues about "schooling" were
being written about in 1730, and we were discussing the same things a
couple of days ago!

Honest,
> I really truly can. But I can also sympathize with Anthony Braxton
> when after a soundcheck spent running through some standards he
> writes, "I wish we hadn't played *tunes*, I've played enough tunes
to last a lifetime. I mean, I'm interested in harmony, but there has
to be another way."
>

Why of course. For me, it's personally more "experimental" jazz like
Ornette Coleman that hits the mark...

> Indeed. BTW, that bit's from the book Forces In Motion. Here's
another bit where the author, Graham Lock, is discussing composition
with Braxton:
>
> 'How do you compose?' I ask. 'What's the process?"
>
> He Shrugs. 'Oh, I just sit down and start writing.'

Seems like a pretty good method to me!

________ _____ ____ _
Joseph Pehrson

🔗Neil Haverstick <STICK@USWEST.NET>

🔗jpehrson@rcn.com

🔗Seth Austen <klezmusic@earthlink.net>

🔗monz <MONZ@JUNO.COM>

🔗Graham Breed <graham@microtonal.co.uk>

Joe Monzo wrote:

> One of the main reasons Schoenberg rejected microtones (after
> having considered using them) was becuase he felt that his type
> of free contrapuntal use of 12-tET offered him more than enough
> new possiblities for expression.

It seems that counterpoint will lead towards a closed system of
pitches. So then you can transpose to every degree of the scale
without falling off the edge. This may or may not be microtonal.
Counterpoint, if it can be made independent of harmony, would be
instantly applicable to any equal temperament.

Harmony, at least vertical harmony, is more sensitive to tuning. Once
you decide how you want the chords tuned, they have to stay close to
that or the music suffers.

This is why I've become interested in the 16th and early 17th
centuries. Harmony and counterpoint were pulling together, with the
harmonic focus on well tuned 5-limit consonances. And the rules
(whatever they might have been) supported this.

So there were two pulls towards xenharmonicism: a desire for new
harmonies, investigated by Vicentino, and the seductive goal of
infinite transposition which became dominant. Today, 12-equal is no
longer xenharmonic, so counterpoint is happy staying where it is, but
harmony leads us on to new sonorities and new tunings.

Except that "harmony" as covered in universities is also rooted to
12-equal. That's because it's become a set of rules that are
independent of the sound of pure triads that started it all. Maybe
those rules became too powerful, so you could still write great music
following them while all the time the chords became dulled through the
excesses of temperament. And the engineering principle of "do the
simplest thing that can possibly work" took over.

In addition, the sonorities Gershwin and Schoenberg were finding
depend on 12-equal and don't sound right shoe-horned into another
tuning.

As I see it, harmony, when it's important, pulls strongly towards
those tunings it resonates with. Whereas counterpoint pulls weakly
towards some simple, closed system, but will happily adapt to any
environment you place it in. So harmony is actively, and counterpoint
passively xenharmonic.

At least, that's the crazy theory I came up with...

Graham

🔗jpehrson@rcn.com

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

/tuning/topicId_20520.html#20563

>
> It seems that counterpoint will lead towards a closed system of
> pitches. So then you can transpose to every degree of the scale
> without falling off the edge. This may or may not be microtonal.
> Counterpoint, if it can be made independent of harmony, would be
> instantly applicable to any equal temperament.
>

Hello Graham...

I can see why you might think that counterpoint would be immediately
applicable to a closed equal system. However, there is NO reason why
it must be confined to that. It can include the linear relationship
between ANY pitches, and does not ADVOCATE ANY style... at least, I'm
not seeing how you could say that...

> Harmony, at least vertical harmony, is more sensitive to tuning.

Yes, true. But harmony is also more susceptible to rules and
formulas... Therefore all your "traditional" harmony courses... I
must be followed by vi, must be followed by ii, etc., etc. I believe
that "rule making" would pertain to xenharmonic systems as well.
Counterpoint is "freer" in nature, since each note is not so bound by
"regulations" of whatever nature, to another note...

Once you decide how you want the chords tuned, they have to stay
close to that or the music suffers.

Yawohl! And more and more rules for harmony.

> Today, 12-equal is no
> longer xenharmonic, so counterpoint is happy staying where it is,
but harmony leads us on to new sonorities and new tunings.
>

It seems to me that BOTH counterpoint and harmony are constantly
changing in new music, depending on the composer and style...

> Except that "harmony" as covered in universities is also rooted to
> 12-equal. That's because it's become a set of rules that are
> independent of the sound of pure triads that started it all.

I think you would have just as many "rules" with that kind of
harmony.... In fact, you might have MORE rules. Look at all the
"rules" that John deLaubenfels has in his ADAPTIVE just intonation.
It takes a constantly number-crunching computer to figure out all the
rules!

Maybe
> those rules became too powerful, so you could still write great
music following them while all the time the chords became dulled
through the excesses of temperament. And the engineering principle
of "do the simplest thing that can possibly work" took over.
>

Ummm. I'm not following this. No great composers ever followed the
"rules," anyway. I'm just saying that, by its nature, there are more
"rules" in harmony than in counterpoint. Take a few courses in both
subjects, and you'll see what I mean!

>
> As I see it, harmony, when it's important, pulls strongly towards
> those tunings it resonates with. Whereas counterpoint pulls weakly
> towards some simple, closed system, but will happily adapt to any
> environment you place it in.

Naah... Counterpoint is whatever you want to make of it. It only
goes toward a "closed system" if that is the objective. There is
nothing INHERENT in it that makes it do that. Getting out of my area
of "expertise" for a moment, whatever that is, most probably Margo
would agree that in the Middle Ages and Renaissance there was lots of
counterpoint going on that was in "open" rather than "closed"
systems... Or, at least, musicians hadn't totally figured out how or
why to "close them all up" yet!

So harmony is actively, and counterpoint passively xenharmonic.
>

Oh, I would disagree entirely. Harmony is "restrictive" and
DISCOURAGES xenharmonics, since the old "rules" and "chords" are so
ingrained. Counterpoint is freer. People can "bend" pitches, and
things do not always coincide, so there is more "liberty." This can
lead to intentional or unintentional xenharmonicity...

>
> At least, that's the crazy theory I came up with...
>
>
I'm on the other side of this issue. Sit through some theory
classes, and take painful harmonic dictation and you'll see what I
mean!

_________ _______ _________
Joseph Pehrson

🔗monz <MONZ@JUNO.COM>

--- In responding to me, "Graham Breed" <graham@m...> wrote:

/tuning/topicId_20520.html#20563

> It seems that counterpoint will lead towards a closed system of
> pitches. So then you can transpose to every degree of the scale
> without falling off the edge. This may or may not be microtonal.
> Counterpoint, if it can be made independent of harmony, would be
> instantly applicable to any equal temperament.
>
> Harmony, at least vertical harmony, is more sensitive to tuning.
> Once you decide how you want the chords tuned, they have to
> stay close to that or the music suffers.
>
> This is why I've become interested in the 16th and early 17th
> centuries. Harmony and counterpoint were pulling together, with
> the harmonic focus on well tuned 5-limit consonances. And the
> rules (whatever they might have been) supported this.

This is very interesting to me, because years ago I began (but
unfortunately never finished) a xenharmonic analysis of Fux's
book, studying how his rules supported 5-limit JI.

> In addition, the sonorities Gershwin and Schoenberg were finding
> depend on 12-equal and don't sound right shoe-horned into another
> tuning.

That's exactly right - at least in the case of Schoenberg.
It's important to remember that the term "atonality" was applied
to his post-1908 music mainly by a negative press campaign.

The term he always preferred was "pantonality", because he
felt that thru strict adhesion to 12-tET he was able to represent
(with varying degrees of error) the complexities of 13-limit JI.
(See his essay _Problems of Harmony_ in _Style and Idea_.)

I don't know enough about Gershwin's ideas on tuning to comment,
with the exceptional note that he did study with Schoenberg
in Los Angeles for a while during the 1930s, around the time
he was working on _Porgy and Bess_.

(They were both also passionate tennis players, and often played
against each other, BTW.)

-monz
http://www.monz.org
"All roads lead to n^0"

🔗D.Stearns <STEARNS@CAPECOD.NET>

Joe Monzo wrote,

<<this reminds me very much of one of my favorite Mahler anecdotes.
One day during the summer he was walking with a friend. There were
able to hear sounds of two different bands playing popular tunes in
outdoor bandstands. The friend complained about the cacophony, but
Mahler felt just the opposite, saying, "Do you hear that? Now
*that's* polyphony! Each voice blending into the whole but yet
retaining its own individual distinctness!">>

Neat, this sounds like another one of those curious little Mahler Ives
tidbits too.

I spent a lot of time experimenting with the effects of strict
quodlibet when and I was first starting out and I still find them
intoxicating and full of potential.

I think the inherent malleability of what one can perceive as normal
given the juxtaposition and "climate" of the presentation offers a
whole avenue of fascinating possibility. I remember once reading that
the Russian film director Vsevolod Pudovkin conducted some experiments
were he would film say an expressionless close-up of an actor and then
splice that same shot so that it would follow footage of things like a
plate of soup, a young girl lying dead in her coffin, a child at play.
He would then show the finished results to an audience who had to tell
what they had seen. They all noticed how the actor gazed hungrily at
the soup, sadly at the death scene, happily at the child, and yet they
had all seen the same impassive face each time.

I think it's possible to do many like things with less clinical and
more subtle results given the proper set of circumstances. The
Turntable Quartet pieces I had up at the tuning punks site for quite a
while were super bare boned studies in strict quodlibet and manual
adaptive retuning on the fly. And I think the use of familiar
structural source material only heightened what I could get away
with... what sorts of rhythms pitches and harmonies the ear could
accept as "normal".

I would think that the foremost practitioner of this type of
"polyphony" today is still Henry Brant: As far back as 1950 Brant had
come to feel that single-style music could no longer evoke the new
stresses, layered insanities, and multidirectional assaults of
contemporary life.

Interestingly the effect of certain Brant simultaneities ("Western
Springs" for example) is not altogether different from some of the
phasing and massed effects that I would associate with say Xenakis.
And the other day I mentioned Xenakis because he used a sort of
statistical density (like that of rain on a roof where the overall
sound is quite unambiguous but the individual rain drops are) but
thought that the increasing density of linear polyphony contained the
seeds of its own destruction. So clearly he did not see statistical
density as a type of polyphony. And by extension I would say not a
type of counterpoint either.

The moral of the story...? I guess that it's very difficult to
precisely pinpoint any exact line between polyphonic density and
statistical density. But I think if you allow for as liberal a
definition of counterpoint as Joseph Pehrson has been hinting at, then
counterpoint can also easily include music whose very design is a
direct opposition to "counterpoint". So, some manageable definition or
clear-cut meaning is probably not such a bad idea here either!

Anyway, the effect I generally go for there is one of unity as opposed
to clash. This is why I mentioned the density of the Natural world.
But unlike Xenakis, I'm not so much interested in too literal an
analogy (though I think his is fascinating).

To me the analogy or model is much more like some sort of
protean-psychoid phenomena that is very much linked to the observer.
So for me these things are more like autobiographical talismans that
hope to take advantage of music's ability to express and "say" what
words can't.

The Natural world that I'm interested in is very much akin to "the
land beyond the rim" of Sigurd Olson. And expressing something of that
impact *emotionally*, however imperfectly as a direct analogy, is what
it's really all about in the end for me. And over the years I've found
that polychromatic densities have often been some of the most
user-friendly structural devices when it comes to getting some of this
business up and off the ground. (Ives' Housatonic and the Fourth
Symphony Finale were landmarks for me in this regard.)

--Dan Stearns

🔗monz <MONZ@JUNO.COM>

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

/tuning/topicId_20520.html#20572

> Joe Monzo wrote,
>
> <<this reminds me very much of one of my favorite Mahler
> anecdotes. One day during the summer he was walking with a
> friend. They were able to hear sounds of two different bands
> playing popular tunes in outdoor bandstands. The friend
> complained about the cacophony, but Mahler felt just the
> opposite, saying, "Do you hear that? Now *that's* polyphony!
> Each voice blending into the whole but yet retaining its own
> individual distinctness!">>
>
> Neat, this sounds like another one of those curious little
> Mahler Ives tidbits too.

Yup. The more I learn about Ives, the more similarities I see
between he and Mahler (about whom I already know more than I
should).

> I would think that the foremost practitioner of this type of
> "polyphony" today is still Henry Brant: As far back as 1950
> Brant had come to feel that single-style music could no longer
> evoke the new stresses, layered insanities, and multidirectional
> assaults of contemporary life.

It's very interesting that you put this bit about Brant right
here, Dan, because many modern commentators say exactly the same
thing about Mahler: that the main reason he wasn't accepted in
his own time while he is so popular now is because *his* music
reflects the "new stresses, layered insanities, and multidirectional
assaults of contemporary life". Hmmm...

Lest this veer too far off-topic, I thought I'd mention that
I see Johnny Reinhard's kind of "polytonality" in this light too.

-monz
http://www.monz.org
"All roads lead to n^0"

🔗jpehrson@rcn.com

--- In tuning@y..., "monz" <MONZ@J...> wrote:

/tuning/topicId_20520.html#20559

>
> --- In tuning@y..., jpehrson@r... wrote:
>
> /tuning/topicId_20520.html#20522
>
> > --- In tuning@y..., Afmmjr@a... wrote:
> >
> > /tuning/topicId_20520.html#20520
> >
> > > and counterpoint is precisely why Bach used Werckmeister's
> > chromatic, to distinguish the voices. Johnny
> >
> > See, everybody? Counterpoint is xenharmonic from the get-go!
>
>
> Well, don't tell that to Schoenberg's ghost.
>
> One of the main reasons Schoenberg rejected microtones (after
> having considered using them) was becuase he felt that his type
> of free contrapuntal use of 12-tET offered him more than enough
> new possiblities for expression.
>

Of course, at that time this technique was "new." NOW contrapuntal
use of serial 12-tET is "old hat" at best... in fact, depressingly so.

> He insists over and over again in his writings of 1908-1912
> (the beginning of "atonality" and also when he wrote his
> _Harmonielehre_) that his inspirations came to him in contrapuntal
> and *not* harmonic form, and that the strange chords that found
> their way into his music at this time were simply the result
> of the clashing of the different voices.
>

Well, perhaps my former Schoenberg studies are partially where I get
the idea of counterpoint as "linear." Indeed, it does seem that
Schoenberg is one of those artist who, in some middle period pieces,
was much more interested in the horizontal than the vertical. His
vertical achivements are, thereby in this form, "happy accidents" as
I have discussed in a previous post...

_______ _____ ______ _
Joseph Pehrson

🔗graham@microtonal.co.uk

Joseph Pehrson wrote:

> I can see why you might think that counterpoint would be immediately
> applicable to a closed equal system. However, there is NO reason why
> it must be confined to that. It can include the linear relationship
> between ANY pitches, and does not ADVOCATE ANY style... at least, I'm
> not seeing how you could say that...

Because I didn't say that :)

Well, what I said is that counterpoint will pull weakly towards a closed
system. If you're using 18 pitches, but everything could be understood if
you moved to 12 pitch classes, there has to be some reason for keeping the
extra complexity. In Gesualdo's time that reason was provided by harmony.

Closed systems needn't be equal. It's harmony that makes that last step.
But you can do more with counterpoint in a closed system. You can take
a line, transpose it, and find the two lines have notes in common that
they wouldn't otherwise. That's useful, and it requires a closed system.
If you'd prefer they weren't the same, you can ignore the coincidence, it
doesn't really matter.

> > Harmony, at least vertical harmony, is more sensitive to tuning.
>
> Yes, true. But harmony is also more susceptible to rules and
> formulas... Therefore all your "traditional" harmony courses... I
> must be followed by vi, must be followed by ii, etc., etc. I believe
> that "rule making" would pertain to xenharmonic systems as well.
> Counterpoint is "freer" in nature, since each note is not so bound by
> "regulations" of whatever nature, to another note...

I, vi, ii, etc, etc are for horizontal rather than vertical harmony. I
meant to exclude that part of the theory, which may well be most of what
you get taught in "harmony" courses.

And there's a lot more to harmony than the "traditional" (presumably
Common Practice) kind. Palestrina doesn't seem to be following those
rules, Margo showed us a different set of rules for earlier music, and the
past century has thrown up a wide range of new ideas. I include all
these, and those yet to come, as "harmony".

Harmony may be partly to blame here, but mostly it's conservatories that
make rules. Those rules are used to describe conventions that composers
can be shown to follow. Beyond that, it's undergraduate assignments that
turn those rules into formulas that have to be strict because it's harder
to grade imagination.

I'm not sure music can really be xenharmonic without rules making it so.
Otherwise, you'd convert it to 12-equal to make it easier to play.

> > Once you decide how you want the chords tuned, they have to stay
> > close to that or the music suffers.
>
> Yawohl! And more and more rules for harmony.

Rules for harmony will tend to fix it into a particular tuning. But then
new harmonies will suggest new tunings. It seems harmony is continuously
evolving. Now that economics and technology allow for it, so can tuning.

> > Today, 12-equal is no
> > longer xenharmonic, so counterpoint is happy staying where it is,
> but harmony leads us on to new sonorities and new tunings.
> >
>
> It seems to me that BOTH counterpoint and harmony are constantly
> changing in new music, depending on the composer and style...

Counterpoint can change a lot within a closed pitch set without needing to
escape. But harmony, given its freedom, will always want new notes to
play with. We've seen that there's a lot of variety possible within the
same few notes. When instruments are expensive, and all built around the
same tuning, that's the only kind of variety you'd expect to see.

> > Except that "harmony" as covered in universities is also rooted to
> > 12-equal. That's because it's become a set of rules that are
> > independent of the sound of pure triads that started it all.
>
> I think you would have just as many "rules" with that kind of
> harmony.... In fact, you might have MORE rules. Look at all the
> "rules" that John deLaubenfels has in his ADAPTIVE just intonation.
> It takes a constantly number-crunching computer to figure out all the
> rules!

Adaptive tuning is a way of getting the two sets of rules to work
together. Rules about pure triads would naturally tend towards 5-limit
JI, and leave the commas to be discovered.

> Maybe
> > those rules became too powerful, so you could still write great
> music following them while all the time the chords became dulled
> through the excesses of temperament. And the engineering principle
> of "do the simplest thing that can possibly work" took over.
> >
>
> Ummm. I'm not following this. No great composers ever followed the
> "rules," anyway. I'm just saying that, by its nature, there are more
> "rules" in harmony than in counterpoint. Take a few courses in both
> subjects, and you'll see what I mean!

It would be out of all proportion to go to such lengths in order to win an
argument.

I have two Mozart pieces here (K573 and K300h) both of which end on a V-I
progression. That's the rule I would have expected him to follow. He
obviously did something right, because once you get the hang of it it's
easy to tell when a Mozart piece finishes. So the rule works. The old
rule used to be to end on a consonance and have the music finish with a
semitone. But if you can establish the key, bringing in V and I does the
trick without them needing to be so consonant.

If you hear enough of them, you come to associate major chords with stable
consonances, even if they've been tempered so far as to lose the
brilliance of a pure consonance. So the rules invented for consonances
can transfer over to their approximations in Equal Temperament.

> > As I see it, harmony, when it's important, pulls strongly towards
> > those tunings it resonates with. Whereas counterpoint pulls weakly
> > towards some simple, closed system, but will happily adapt to any
> > environment you place it in.
>
> Naah... Counterpoint is whatever you want to make of it. It only
> goes toward a "closed system" if that is the objective. There is
> nothing INHERENT in it that makes it do that.

Counterpoint has an inherent tendency to enlarge the gamut of an open
system. It also has no inherent problem with the system closing.

> Getting out of my area
> of "expertise" for a moment, whatever that is, most probably Margo
> would agree that in the Middle Ages and Renaissance there was lots of
> counterpoint going on that was in "open" rather than "closed"
> systems... Or, at least, musicians hadn't totally figured out how or
> why to "close them all up" yet!

According to Watkins (p.182) "Gesualdo's introduction of chromatic
semitones in each instance is only a mildly unconventional licence
reflecting the contrapuntal theory of the time, which considered B and Bb
and F and F# as contrapuntally identical". That suggests, to me, a closed
system of 7 pitch classes. Which isn't what Gesualdo was really working
with, as most examples are "correct" for both 7 and 12 pitch classes, and
the music as a whole requires more then 7. But it seems likely to me that
the theory is a throwback to a time when counterpoint (but not harmony)
did work with a closed system of 7 classes to the octave.
>
>
> > So harmony is actively, and counterpoint passively xenharmonic.
>
> Oh, I would disagree entirely. Harmony is "restrictive" and
> DISCOURAGES xenharmonics, since the old "rules" and "chords" are so
> ingrained.

This may be true of the variety of harmony you were taught.

> Counterpoint is freer. People can "bend" pitches, and
> things do not always coincide, so there is more "liberty." This can
> lead to intentional or unintentional xenharmonicity...

This doesn't contradict anything I said.

Graham

🔗graham@microtonal.co.uk

Monz wrote:

> > This is why I've become interested in the 16th and early 17th
> > centuries. Harmony and counterpoint were pulling together, with
> > the harmonic focus on well tuned 5-limit consonances. And the
> > rules (whatever they might have been) supported this.
>
> This is very interesting to me, because years ago I began (but
> unfortunately never finished) a xenharmonic analysis of Fux's
> book, studying how his rules supported 5-limit JI.

When I get my Fux I can think about that.

> I don't know enough about Gershwin's ideas on tuning to comment,
> with the exceptional note that he did study with Schoenberg
> in Los Angeles for a while during the 1930s, around the time
> he was working on _Porgy and Bess_.

I don't know about Gershwin's ideas, but his music seems to work with
12-equal. John deLaubenfels did a 7-limit retuning of Rhapsody in Blue.
I don't remember if he made it public. It sounds good after a while, with
all the clean chords, but not what I thing Gershwin would have expected.
Although for all we know the same could be true of those pure renditions
of Palestrina.

Follow the chords to I Got Rhythm, and you get to a G mi 7 with C. This
is a slight misnomer, as the third isn't sounded, but whatever. Why would
you play a G7 chord against C? The melody is one note in C. Play the
chord in meantone and it's really strained (at least the way he voiced
it, spread it out and it's all fifths). But in 12-equal, well, it's a
Jazz chord, so what? I think that Gershwin chose the chords to sound good
on a piano. Moderate temperaments like Valotti/Young suit him best.

Or that's the impression I get, which is why I gave the example. I'm not
a Gershwin scholar on the quiet ;)

Graham

🔗jpehrson@rcn.com

--- In tuning@y..., graham@m... wrote:

/tuning/topicId_20520.html#20601

Hi Graham...

Thanks for your continuing discussion on counterpoint and harmony
and how they pertain to "alternate" tunings...

(I'm putting a couple of names in, since this was getting confusing
to read...)

Breed:
> Closed systems needn't be equal. It's harmony that makes that last
step. But you can do more with counterpoint in a closed system. You
can take a line, transpose it, and find the two lines have notes in
common that they wouldn't otherwise. That's useful, and it requires
a closed system. If you'd prefer they weren't the same, you can
ignore the coincidence, it doesn't really matter.
>

Pehrson:

Well, I would see a closed system, then, as possibly providing more
OPPORTUNITIES for literal counterpoint. But counterpoint needn't be
literal in order to be defined by that term...

Breed:
> > > Harmony, at least vertical harmony, is more sensitive to
tuning.

Pehrson:
> > Yes, true. But harmony is also more susceptible to rules and
> > formulas... Therefore all your "traditional" harmony courses... I
> > must be followed by vi, must be followed by ii, etc., etc. I
believe that "rule making" would pertain to xenharmonic systems as
well. Counterpoint is "freer" in nature, since each note is not so
bound by "regulations" of whatever nature, to another note...
>

Breed:

> I, vi, ii, etc, etc are for horizontal rather than vertical
harmony. I meant to exclude that part of the theory, which may well
be
most of what you get taught in "harmony" courses.
>

Pehrson:

How can Roman Numeral analysis be used for anything other than
VERTICAL harmony?? Generally that's the usage one sees... (with
broader implications, of course)

Breed:

> And there's a lot more to harmony than the "traditional"
(presumably Common Practice) kind. Palestrina doesn't seem to be
following those rules, Margo showed us a different set of rules for
earlier music, and the past century has thrown up a wide range of new
ideas. I include all these, and those yet to come, as "harmony".
>

Pehrson:

Well yes, of course you can do that if you wish. However, it isn't
the "generally accepted" usage of the term... But, who cares...I
would also prefer an "expanded" definition...

Breed:

> Harmony may be partly to blame here, but mostly it's conservatories
that make rules. Those rules are used to describe conventions that
composers can be shown to follow. Beyond that, it's undergraduate
assignments that turn those rules into formulas that have to be
strict because it's harder to grade imagination.
>

Pehrson:

Ummm, it goes through most of the courses unless you happen to have a
particularly "enlightened" instructor. Traditional
harmony courses are taught as a set of rules, just like poor music
history courses are taught as a set of dates. And yes, they ARE
easier to grade, of course (all thinking optional...)

Breed:

> I'm not sure music can really be xenharmonic without rules making
it so. Otherwise, you'd convert it to 12-equal to make it easier to
play.
>

Pehrson:

I can't see why xenharmonic music would have any more or fewer rules
than 12-tET or anything else... It all depends on how you want to
use it... Perhaps I don't see the "conversion to 12-tET" as such a
strong pull presently...

Breed:

> > > Today, 12-equal is no
> > > longer xenharmonic, so counterpoint is happy staying where it
is, but harmony leads us on to new sonorities and new tunings.

Pehrson:

I'm not getting this, since as soon as you change your basic sound
material, your scalar materials, the counterpoint changes equally as
well...

Breed:
>
> Counterpoint can change a lot within a closed pitch set without
needing to escape. But harmony, given its freedom, will always want
new notes to play with.

Pehrson:

Not necessarily. What are Phillip Glass and Arvo Part all about??

Breed:

> > > Except that "harmony" as covered in universities is also rooted
to 12-equal. That's because it's become a set of rules that are
> > > independent of the sound of pure triads that started it all.
> >

Pehrson:

Well, gee, Grahm... why not go back even FURTHER than that to
Pythagorean?? I think the rules change over time for each period and
EQUALLY for BOTH harmony and counterpoint. In MY view (probably
stemming from Schoenberg studies) counterpoint leads to NEW harmonies
and new possibilities and harmony seems more "codified" for a given
period.... It's obviously just a viewpoint.

Breed:

> > > As I see it, harmony, when it's important, pulls strongly
towards those tunings it resonates with. Whereas counterpoint pulls
weakly towards some simple, closed system, but will happily adapt to
any environment you place it in.
> >

Pehrson:
> > Naah... Counterpoint is whatever you want to make of it. It
only goes toward a "closed system" if that is the objective. There
is
> > nothing INHERENT in it that makes it do that.
>

Breed:

> Counterpoint has an inherent tendency to enlarge the gamut of an
open system. It also has no inherent problem with the system closing.
>

Pehrson:

There you go! So it has an incredible flexibility. It can increase
an open system and can be extremely flexible in a closed system. So
it really doesn't have any given TENDENCY to move toward a CLOSED
system, unless one wants it to!

Breed:

> > > So harmony is actively, and counterpoint passively xenharmonic.
> >

Pehrson:

> > Oh, I would disagree entirely. Harmony is "restrictive" and
> > DISCOURAGES xenharmonics, since the old "rules" and "chords" are
so ingrained.
>

Breed:

> This may be true of the variety of harmony you were taught.
>

Pehrson:

Well, it's just "standard Western practice." Maybe your Mathieu book
is more "all-encompassing." Drat... more money to Amazon.com.

So basically, Graham, when we go to a Deli, I will order counterpoint
in my sandwich and you can have all the harmony in yours that you
want. My sandwich will be leaner and tastier and I will emerge a
healthier individual for having ingested it!

_______ ______ _____ __
Joseph Pehrson

🔗Graham Breed <graham@microtonal.co.uk>

--- Joseph Pehrson wrote:

/tuning/topicId_20520.html#20604

> Pehrson:
>
> Well, I would see a closed system, then, as possibly providing more
> OPPORTUNITIES for literal counterpoint. But counterpoint needn't be
> literal in order to be defined by that term...

If it isn't literal, it cares even less how it's being tuned. You
have to take consonances literally, or they stop being consonant.

> Pehrson:
>
> How can Roman Numeral analysis be used for anything other than
> VERTICAL harmony?? Generally that's the usage one sees... (with
> broader implications, of course)

The vi of C major is the same as the ii of G major. If you take a
minor triad in isolation, it matters very much how it's tuned. I
think harmony should concern itself more with the sounds of chords,
and by implication how they are tuned. This has to be left out of
traditional accounts because they assume a particular tuning.

If you're using the sonorities of the harmonic series, there's a
maximum amount of temperament you can use without the chords sounding
wrong. This leads you into xenharmonic considerations before you even
start to think about how one chord relates to the other. Some
consider any form of temperament to be unacceptable, and this has been
a driving force behind xenharmonic innovation over the past century.

Horizontal harmony can have xenharmonic implications. I think the
tendency to narrow leading tones counts as harmony. But it can also
require temperament, like the way diatonic scales imply a tempering
away of the syntonic comma. Beyond that, two major chords a semitone
apart could look like this:

E---B---F#
/ \ /
C---G
\ /
Eb

You can't get all the 5-limit intervals, both horizontal and vertical,
to be in tune at the same time. So you could smudge it into Equal
Temperament, or give one of the chords a car-horn third in meantone.

When you start to consider this kind of thing, I'm not at all sure
what would be "harmony" and what "counterpoint".

In functional harmony, to understand the progression you only need
consider the roots. By blurring the distinctions between different
chords, this also removes tuning from the picture. Perhaps that was
the intention.

> Breed:
>
> > And there's a lot more to harmony than the "traditional"
> (presumably Common Practice) kind. Palestrina doesn't seem to be
> following those rules, Margo showed us a different set of rules for
> earlier music, and the past century has thrown up a wide range of
new
> ideas. I include all these, and those yet to come, as "harmony".
> >
>
> Pehrson:
>
> Well yes, of course you can do that if you wish. However, it isn't
> the "generally accepted" usage of the term... But, who cares...I
> would also prefer an "expanded" definition...

I don't think a subject should be constrained by the rules it is
conventionally explained by. Any sounding together of notes implies
"harmony". That seems obvious to me, if it goes against the accepted
usage perhaps we need a new word.

> Breed:
>
> > > > Today, 12-equal is no
> > > > longer xenharmonic, so counterpoint is happy staying where it
> is, but harmony leads us on to new sonorities and new tunings.
>
> Pehrson:
>
> I'm not getting this, since as soon as you change your basic sound
> material, your scalar materials, the counterpoint changes equally as
> well...

Yes, but the counterpoint takes a passive, rather than active, role.

> Breed:
> >
> > Counterpoint can change a lot within a closed pitch set without
> needing to escape. But harmony, given its freedom, will always want
> new notes to play with.
>
> Pehrson:
>
> Not necessarily. What are Phillip Glass and Arvo Part all about??

Not all composers will use the freedom to expand. But the return to
simple consonances should also lead to a return to the purity of those
consonances.

> Pehrson:
>
> Well, gee, Grahm... why not go back even FURTHER than that to
> Pythagorean?? I think the rules change over time for each period
and
> EQUALLY for BOTH harmony and counterpoint. In MY view (probably
> stemming from Schoenberg studies) counterpoint leads to NEW
harmonies
> and new possibilities and harmony seems more "codified" for a given
> period.... It's obviously just a viewpoint.

The codification of harmony often happens in retrospect. Trabaci,
within his limited gamut, was happy to mis-spell a diminished triad,
but not major or minor. I don't think any rules of his time, or
standard harmony texts, would explain that. But *we* can say it was
okay for him to use a 7-limit third as the tritone already implies
7-limit harmony.

The consonances of the Common Practice era can't be expressed in
Pythagorean intonation. Although some modern rules can be traced back
that far, like the use of contrast between consonance and dissonance,
and the preference for semitone motion in cadences. Making thirds
consonant meant the tuning had to change.

> Pehrson:
> > > Naah... Counterpoint is whatever you want to make of it. It
> only goes toward a "closed system" if that is the objective. There
> is
> > > nothing INHERENT in it that makes it do that.
> >
>
> Breed:
>
> > Counterpoint has an inherent tendency to enlarge the gamut of an
> open system. It also has no inherent problem with the system
closing.
> >
>
> Pehrson:
>
> There you go! So it has an incredible flexibility. It can increase
> an open system and can be extremely flexible in a closed system. So
> it really doesn't have any given TENDENCY to move toward a CLOSED
> system, unless one wants it to!

Nothing happens in music unless you want it to. But composers will
tend towards the simplest system that allows them to do what they
want.

> > > Oh, I would disagree entirely. Harmony is "restrictive" and
> > > DISCOURAGES xenharmonics, since the old "rules" and "chords" are
> so ingrained.
> >
>
> Breed:
>
> > This may be true of the variety of harmony you were taught.
> >
>
> Pehrson:
>
> Well, it's just "standard Western practice." Maybe your Mathieu
book
> is more "all-encompassing." Drat... more money to Amazon.com.

It's a book on traditional harmony, which goes as far as Jazz. But I
don't know if you'd find it that helpful if you've already gone
through the usual system. The chapters on JI vocal technique might be
different.

> So basically, Graham, when we go to a Deli, I will order
counterpoint
> in my sandwich and you can have all the harmony in yours that you
> want. My sandwich will be leaner and tastier and I will emerge a
> healthier individual for having ingested it!

I don't know how you could have one without the other. And they both
seem to involve bread, so I wouldn't touch them.

Graham

Re: counterpoint

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