reason for 12-tone serialism (was: Digest Number 1794)

Hi Joe (and Bob),

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, January 02, 2002 8:59 PM
> Subject: [tuning] Re: Digest Number 1794
>
>
> --- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
>
> /tuning/topicId_32216.html#32216
>
> > >
> >
> > My take (and I stress, my take) on the serial technique is
> > that it is a recipe that can acheive a few different things
> > that seemed desireable when tonal materials blew up in
> > everyones faces through the musics of Wagner, Liszt and
> > Mahler.
> >
> > 1) it will statistically attempt to nullify the
> > creation of a tonal center by presenting each pitch
> > approximately the same number of times.
> > 2) if the row is chosen carefully such that no inadvertant
> > tonal references are made, then applying the usual serial
> > techniques should also result in no inadvertant tonal
> > references being made
> > (2a inadvertant tonal references are bad only in that
> > the point is to control the tension/release of
> > the composition and unplanned tonality, like
> > unplanned or maltreated dissonances in cookbooks
> > from prior centurys, is wresting control of the
> > tension/release from the composers hands).
> > 3) ...and it will do all this with a common thematic
> > material that should provide 'wholeness' and 'coherence'
> > to the work, much like theme and variations in prior
> > centuries, with the row (or portions of it) supplying
> > micro-motifs.
> >
>
> Hello Bob!
>
> Not to be a contrarian (or "crank" from "cancrizans") but I believe
> your notion of serialism is quite different from the original
> historical intentions of the practicioners...
>
> I'll let Monz, our "historical expert" elaborate on that if he gets a
> chance...

Joe, I didn't comment on Bob's post, but it's interesting that you
are being "contrary" here, because the first time I read it, I thought
it was an excellent summary of Schoenberg's (and his students's) goals
with the "12-tone method".

The only point about which I'd quibble is number 2, the bit about
"inadvertent tonal references". While Webern studiously avoided
these, Schoenberg knew they could happen and didn't try overly
hard to prevent it, and Berg positively made use of the idea.

Berg's _Violin Concerto_, in particular, has a row which is structured
so as to stack "3rds", so that he is able to create consonant
triads and "7th"-chords and thus emulate tonal harmony in a
fleeting manner.

But other than that, I'd say that Bob is right on the money.

Schoenberg made it clear in his paper _Problems of Harmony_
(as well as in other essays that have been published in
_Style and Idea_) that the original goal of the "atonal" style
was to explore using the higher harmonics (meaning above 5) as
consonant chord-members. The idea was to avoid all reference
to 3- and 5-limit harmony, and concentrate on tonal relationships
which imply prime-factors 7, 11, and 13. He states even there
that "a future time" may permit use of 3 and 5 along with the
higher primes, but that during those early days he and his
students wanted to concentrate on using the higher primes.

(This is *my* version of what I think Schoenberg meant...
he did not speak clearly in terms of prime-limits or ratios,
other than the endorsment of the "possibly incorrect overtone
theory", the strict application of which does indeed make it
possible to understand his theory in the terms I use.)

-monz

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

/tuning/topicId_32256.html#32256

>
>
> Joe, I didn't comment on Bob's post, but it's interesting that you
> are being "contrary" here, because the first time I read it, I
thought
> it was an excellent summary of Schoenberg's (and his students's)
goals
> with the "12-tone method".
>

Hi Monz...

My *own* understanding was that Schoenberg was not trying to *avoid*
*anything* at all. That's why he didn't like the term "atonal" and
preferred "pantonal..."

I'm surprised you didn't comment on this...

JP

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, January 03, 2002 6:30 AM
> Subject: [tuning] Re: reason for 12-tone serialism
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_32256.html#32256
>
> >
> >
> > Joe, I didn't comment on Bob's post, but it's interesting
> > that you are being "contrary" here, because the first time
> > I read it, I thought it was an excellent summary of
> > Schoenberg's (and his students's) goals with the
> > "12-tone method".
> >
>
> Hi Monz...
>
> My *own* understanding was that Schoenberg was not trying to
> *avoid* *anything* at all. That's why he didn't like the
> term "atonal" and preferred "pantonal..."
>
> I'm surprised you didn't comment on this...

Hi Joe,

You're right that I should have mentioned that, and you're
correct -- Schoenberg *detested* the term "atonal". He really
did think of the 12-EDO scale as representing a whole slew
of complex harmonic relationships, representable in today's
tuning-theory as complicated 11- or 13-limit periodicity-blocks.

But at the same time, Schoenberg was very clear that in the
serial music he and his students were composing, they *intended*
to avoid references to traditional harmonic structures such
as major/minor triads and tetrads, etc. Specifically, which
IIRC was the origin of this thread, he substituted "major 7ths"
"minor 9ths" for "8ves" in his melodies. Webern especially
picked up on this idea.

-monz

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

/tuning/topicId_32256.html#32268

>
> Hi Joe,
>
>
> You're right that I should have mentioned that, and you're
> correct -- Schoenberg *detested* the term "atonal". He really
> did think of the 12-EDO scale as representing a whole slew
> of complex harmonic relationships, representable in today's
> tuning-theory as complicated 11- or 13-limit periodicity-blocks.
>
> But at the same time, Schoenberg was very clear that in the
> serial music he and his students were composing, they *intended*
> to avoid references to traditional harmonic structures such
> as major/minor triads and tetrads, etc. Specifically, which
> IIRC was the origin of this thread, he substituted "major 7ths"
> "minor 9ths" for "8ves" in his melodies. Webern especially
> picked up on this idea.
>

****Hi Monz!

Thanks so much for your clarification on this. Yes, of course, I was
aware of the "octave avoidance" practiced by Schoenberg.

I wonder what J. Gill thinks about this, since it points to the
gravitational power of "octave equivalence..." :)

In any case, I had lunch with my conductor friend Charles Bornstein
(the former conductor of Xenakis in the US) and he reminded me of
this Schoenberg site... the Arnold Schoenberg Center in Vienna.

I'm sure you've seen this Website. There is also an extensive
Newsletter on the site free for readers:

http://www.schoenberg.at/

best,

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> Thanks so much for your clarification on this. Yes, of course,
> I was
> aware of the "octave avoidance" practiced by Schoenberg.
>
> I wonder what J. Gill thinks about this, since it points to the
> gravitational power of "octave equivalence..." :)

J Gill responds:

Gentlepersons,

Let it be know that my "official position"
is an "agnostic" one where it comes to conclusions
surrounding "Octavian" dogma. Therefore, I would
consider myself not to be an either an "octavian",
or an "anti-octave-ist". :)

For computational simplicities, I would *love it*
if we are (even in certain cases only) to ignore
powers of 2. My queries have simply been an effort
to survey the viewpoints of others. My hope is that
one *can* proceed reliably with such approximations...

Before the "party" begins, perhaps we should humbly
NOTE:

<< ..." Much has recently been written concerning
the dangers of assuming that correspondences
necessarily exist between structures as defined
compositionally and as apprehended perceptually.
The issue of octave equivalence provides a clear
case in point. It also illustrates the related
point that certain compositionally defined
structures may or may not be perceptually
apprehended, depending on the knowledge and
expectations of the listener. ...Octave
equivalence in melodic structures may either
be perceptually very salient or be totally
lost, depending on the body of information
that the listener contributes to the percept."

[Deutsch, Diana, and Richard C. Boulanger,
"Octave Equivalence and the Immediate Recall
of Pitch Sequences," Music Perception, Fall
1984, Vol. 2, No. 1, pg. 49] >>

AND NOTE:

<< "In the first experiment, subjects on
each trial rated the similarity of presented
tones. The results failed to show evidence
of octave equivalence. In subsequent
experiments, the range of frequency values
presented and the musical context were
manipulated. Evidence of octave equivalence
was found only when the range of tone height
differences presented was small; the effect
of musical context was negligible. (..) In
Experiment 3, a linear decrease in the
similarity ratings occurred over the range
of pitch differences from 11-13 semitones,
but no evidence of octave equivalence was
found. In contrast, in Experiment 5, which
was identical in design to Experiment 3
except that the range of pitch differences
was much smaller, no linear trend was
evident in the data from 11-13 semitones,
but evidence of octave equivalence was
found. This tradeoff between pitch height
and octave equivalence effects suggests
that subjects tended to base their
similarity ratings on the single most
salient stimulus dimension in an experiment,
or, at least, they directed most of their
attention to it. (..) Musical experience
was not a good predictor of octave-
equivalence effects in the present
experiments. (..) Even when the octave-
equivalent tones were judged as more
similar to each other than were tones
that were not octave equivalents, the
similarity ratings indicated that
octave equivalents were judged as
much less similar to each other than
were unisons. (..) ...Our theories of
musical perception must recognize that
the equivalence of octave equivalents
is clearly limited."

[Kallman, Howard
J., "Octave Equivalence As Measured
by Similarity Ratings," Perception &
Psychophysics, Vol. 32, No. 1, pp.
37-49, 1982] >>

AND FURTHER NOTE:

<< "The data suggest clearly that
real differences do in fact exist
between the perception of similarity
of octaves to non-octaves in musical
and non-musical subjects."

[Allen,
David, "Octave dicriminability of
musical and non-musical subjects,"
Psychonomic Science, Vol. 7, No. 12,
1967, pg. 422] >>

Any thoughts?, J Gill

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

> J Gill responds:
>
> Gentlepersons,
>
> Let it be know that my "official position"
> is an "agnostic" one where it comes to conclusions
> surrounding "Octavian" dogma. Therefore, I would
> consider myself not to be an either an "octavian",
> or an "anti-octave-ist". :)
>
> For computational simplicities, I would *love it*
> if we are (even in certain cases only) to ignore
> powers of 2.

Even if you don't, all my suggestions to you about Farey series,
Tenney limits, and a new suggestion to get familiar with Gene's
tuning-math, apply in full force.

> My queries have simply been an effort
> to survey the viewpoints of others. My hope is that
> one *can* proceed reliably with such approximations...

It might make your music more unique if you didn't . . . though it's
still likely that everyone who hears your music will hear it in terms
of the pitch-chroma helix, so that if any octave-repetitions do
exist, they will evoke a certain (perhaps unintended) effect.
>
> AND NOTE:
>
> << "In the first experiment, subjects on
> each trial rated the similarity of presented
> tones. The results failed to show evidence
> of octave equivalence. In subsequent
> experiments, the range of frequency values
> presented and the musical context were
> manipulated. Evidence of octave equivalence
> was found only when the range of tone height
> differences presented was small; the effect
> of musical context was negligible. (..) In
> Experiment 3, a linear decrease in the
> similarity ratings occurred over the range
> of pitch differences from 11-13 semitones,
> but no evidence of octave equivalence was
> found. In contrast, in Experiment 5, which
> was identical in design to Experiment 3
> except that the range of pitch differences
> was much smaller, no linear trend was
> evident in the data from 11-13 semitones,
> but evidence of octave equivalence was
> found. This tradeoff between pitch height
> and octave equivalence effects suggests
> that subjects tended to base their
> similarity ratings on the single most
> salient stimulus dimension in an experiment,
> or, at least, they directed most of their
> attention to it. (..) Musical experience
> was not a good predictor of octave-
> equivalence effects in the present
> experiments. (..) Even when the octave-
> equivalent tones were judged as more
> similar to each other than were tones
> that were not octave equivalents, the
> similarity ratings indicated that
> octave equivalents were judged as
> much less similar to each other than
> were unisons. (..) ...Our theories of
> musical perception must recognize that
> the equivalence of octave equivalents
> is clearly limited."

It would be good to know what the experiments actually consisted of.
It's also good to understand exactly what the notion of octave-
equivalence is used for in musical theories you find around here,
such as Partch's and most of the periodicity block stuff. The only
assumption it really represents is the assumption that you, as a
scale designer, wish to have the same scale of possible tones in each
and every octave span. There are many reasons you might want to do
this, independently of whether some particular definition of octave-
equivalence is experimentally shown to be true or false, and there
are many reasons you might not want to do this, independently of
whether some particular definition of octave-equivalence is
experimentally shown to be true or false.

> >
> > Hi Monz...
> >
> > My *own* understanding was that Schoenberg was not trying to
> > *avoid* *anything* at all. That's why he didn't like the
> > term "atonal" and preferred "pantonal..."
> >
> > I'm surprised you didn't comment on this...
>
> Hi Joe,
>
> You're right that I should have mentioned that, and you're
> correct -- Schoenberg *detested* the term "atonal".

I consider the "no tonal center" or "all tones are equal tonal
centers" (atonality vs pantonality) to be a non-argument, (for
those who remember its like ' "Less filling!" Great Taste!" ').

Whether one thinks of rules as a prohibition of one thing, or
an advice to emphasise other things is similar is a matter of
perception, and a matter of how the explainer treats it. In
traditional counterpoint, some of us were taught that
parallel fifths and octaves were 'prohibited', at which point
many of us started composing with ONLY fifths and octaves.

The issue with that rule is that, if your goal is creating
a music comprised of seperate melodys, then that seperation
has a tendency to be lost if they start turning into block
chords (homophony?) and/or doublings. Of course, the music of
the greats will have independent melodies that break these rules
all over the place. The rules are supposed to help the non-greats
get going and wrap ther ears around writing independent melodies
and gain all the tricks they want (or don't) so that they can
control the amount of independence, much the way the twelve
tone method may help a composer keep the 'a' or 'pan' tonal
aspects going.

My second point in my summary was meant to be optional, saying
that if you chose non-tonal material, the serial method would
help keep you from having it accidentally turn tonal on you. As
Monz pointed out, much of Schoenbergs work and certainbly Bergs
was near-tonal despite using the method. Webern certainly went
in the direction of creating rows that were atonal.

And how did he do it? The same way Bach and Beethoven (and many
others) created their most ambiguous passages : Through mucking
around with the diminished chord!

Monz, Thanks for the affirmation that I had at least a fairly
acceptable interpretion of this stuff. For what its worth, though
I wrote some twelve-tonish sounding stuff (in high school) my
only real serial piece was tonal, gently ambiguous and
unfortunately forgotten excet for the first few notes.

Bob Valentine
>
> -monz
>

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

/tuning/topicId_32256.html#32300

>
> It would be good to know what the experiments actually consisted
of.
> It's also good to understand exactly what the notion of octave-
> equivalence is used for in musical theories you find around here,
> such as Partch's and most of the periodicity block stuff. The only
> assumption it really represents is the assumption that you, as a
> scale designer, wish to have the same scale of possible tones in
each
> and every octave span. There are many reasons you might want to do
> this, independently of whether some particular definition of octave-
> equivalence is experimentally shown to be true or false, and there
> are many reasons you might not want to do this, independently of
> whether some particular definition of octave-equivalence is
> experimentally shown to be true or false.

Of course, one reason is simply ease of *performance.* A player (say
in 72-tET or whatever) only needs to know the pitches in *one* octave
and then can play his entire range with "equivalents..."

Otherwise, I believe things might get "kind of messy...."

JP

--- In tuning@y..., "bval_bobvalentine" <BVAL@I...> wrote:
/tuning/topicId_32256.html#32305
>
> My second point in my summary was meant to be optional, saying
> that if you chose non-tonal material, the serial method would
> help keep you from having it accidentally turn tonal on you. As
> Monz pointed out, much of Schoenbergs work and certainbly Bergs
> was near-tonal despite using the method. Webern certainly went
> in the direction of creating rows that were atonal.
>

Hi Bob...

I appreciate your contribution and understand your argument.
However, the paragraph above doesn't do much to help substantiate
it. If many works turned out sounding tonal *anyway* that doesn't
say all that much for the use of the serial method as an *avoidance*
technique.

It just seems to me that it was less a deliberate case of *avoidance*
in a sense of an "avoidance recipe" which is, seemingly, the way you
presented it, as a way to keep exploring *different* tonalities.

At least, that's the way *I* was taught this stuff...

best,

J. Pehrson

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> It just seems to me that it was less a deliberate case of *avoidance*
> in a sense of an "avoidance recipe" which is, seemingly, the way you
> presented it, as a way to keep exploring *different* tonalities.

If someone wants an avoidance recipe I suggest a random walk.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_32256.html#32318

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > It just seems to me that it was less a deliberate case of
*avoidance*
> > in a sense of an "avoidance recipe" which is, seemingly, the way
you
> > presented it, as a way to keep exploring *different* tonalities.
>
> If someone wants an avoidance recipe I suggest a random walk.

Hmmm... that's interesting, Gene! Essentially I believe that's what
Cage was getting at...

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> > If someone wants an avoidance recipe I suggest a random walk.

> Hmmm... that's interesting, Gene! Essentially I believe that's what
> Cage was getting at...

I don't think Cage ever did something like what I had in mind when I said that; I don't recall it, anyway. One could do a random walk on the tilings of 5 or 7-limit chords (dual to the corresponing lattices) and then work out the parts and timings in such a way as to attempt to give it some kind of shape. The result would be atonal but consonant. My experience suggests they also tend to be boring, but I never worked very hard on the shape part.

Joe,

Gene:
> If someone wants an avoidance recipe I suggest a random walk.

Joe:
> Hmmm... that's interesting, Gene! Essentially I believe that's
> what Cage was getting at...

I believe what Gene is talking about is a mathematical process, not a
haphazard or meandering approach. Try this:

http://mathworld.wolfram.com/RandomWalk.html

Gene can correct me if I'm wrong on this...

Cheers,
Jon

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> /tuning/topicId_32256.html#32300
>
> >
> > It would be good to know what the experiments actually consisted
> of.
> > It's also good to understand exactly what the notion of octave-
> > equivalence is used for in musical theories you find around here,
> > such as Partch's and most of the periodicity block stuff. The only
> > assumption it really represents is the assumption that you, as a
> > scale designer, wish to have the same scale of possible tones in
> each
> > and every octave span. There are many reasons you might want to do
> > this, independently of whether some particular definition of octave-
> > equivalence is experimentally shown to be true or false, and there
> > are many reasons you might not want to do this, independently of
> > whether some particular definition of octave-equivalence is
> > experimentally shown to be true or false.
>
>
> Of course, one reason is simply ease of *performance.* A player (say
> in 72-tET or whatever) only needs to know the pitches in *one* octave
> and then can play his entire range with "equivalents..."
>
> Otherwise, I believe things might get "kind of messy...."
>
> JP

J Gill: Messy, indeed. But it seems a bit "circular" to talk
about having the "same scale of possible tones in each
and every octave span" in a situation where (even some)
"particular definition of octave-equivalence is
experimentally shown to be true or false". How many
different ways could one imagine "octave equivalence"
to be interpreted? Perhaps - "equivalence of octaves"?

J Gill :)

> From: genewardsmith <genewardsmith@juno.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, January 04, 2002 7:43 PM
> Subject: [tuning] Re: overtone serialism
>
>
> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > > If someone wants an avoidance recipe I suggest a random walk.
>
> > Hmmm... that's interesting, Gene! Essentially I believe that's what
> > Cage was getting at...
>
> I don't think Cage ever did something like what I had in
> mind when I said that; I don't recall it, anyway. One could
> do a random walk on the tilings of 5 or 7-limit chords (dual
> to the corresponing lattices) and then work out the parts
> and timings in such a way as to attempt to give it some kind
> of shape. The result would be atonal but consonant. My
> experience suggests they also tend to be boring, but I
> never worked very hard on the shape part.

Hmmm ... this is very similar to the way I understand Erv Wilson's
theories of harmonic structures of Combination Product Sets.
They are centerless, and thus in a sense could be called atonal,
but made entirely of the most consonant ratios within whatever
given prime-limits, thus simultaneously implying ever-shifting
tonalities all the time.

(or are they odd-limits? What is Wilson's view on prime-vs-odd?).

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, January 04, 2002 7:09 PM
> Subject: [tuning] overtone serialism
>
>
> --- In tuning@y..., "bval_bobvalentine" <BVAL@I...> wrote:
> /tuning/topicId_32256.html#32305
> >
> > My second point in my summary was meant to be optional, saying
> > that if you chose non-tonal material, the serial method would
> > help keep you from having it accidentally turn tonal on you. As
> > Monz pointed out, much of Schoenbergs work and certainbly Bergs
> > was near-tonal despite using the method. Webern certainly went
> > in the direction of creating rows that were atonal.
> >
>
> Hi Bob...
>
> I appreciate your contribution and understand your argument.
> However, the paragraph above doesn't do much to help substantiate
> it. If many works turned out sounding tonal *anyway* that doesn't
> say all that much for the use of the serial method as an *avoidance*
> technique.
>
> It just seems to me that it was less a deliberate case of *avoidance*
> in a sense of an "avoidance recipe" which is, seemingly, the way you
> presented it, as a way to keep exploring *different* tonalities.
>
> At least, that's the way *I* was taught this stuff...

Joe, *please* read my post on this again!
/tuning/topicId_32256.html#32256

I'll quote the bit that's most relevant to this:

>> Schoenberg made it clear in his paper _Problems of Harmony_
>> (as well as in other essays that have been published in
>> _Style and Idea_) that the original goal of the "atonal" style
>> was to explore using the higher harmonics (meaning above 5) as
>> consonant chord-members. The idea was to avoid all reference
>> to 3- and 5-limit harmony, and concentrate on tonal relationships
>> which imply prime-factors 7, 11, and 13. He states even there
>> that "a future time" may permit use of 3 and 5 along with the
>> higher primes, but that during those early days he and his
>> students wanted to concentrate on using the higher primes.

So the goal was *simultaneously* to AVOID 3- and 5-limit harmonic
structures and to EMPHASIZE 7-, 11-, and (later) 13-limit ones.

In other words, in Schoenberg's expanded view of tonality (i.e.,
11- or 13-limit, as opposed to the 5-limit view of traditional
harmony textbooks), the already-familiar aspects of tonality
were to be avoided, but the new and as-yet-unexplored ones were
to be employed with abandon.

I think the misunderstanding of this idea is precisely at the root
of all the misguided attempts to "debunk" Schoenberg's harmonic
theory, as with William Thomson, Brian McLaren, etc. Schoenberg
sometimes spoke in terms of a higher-limit tonality in which
the 5 non-diatonic notes of the 12-EDO scale were to be taken
as high-prime tonality identites, and sometimes in terms of
traditional tonality in which the 5 non-diatonic notes were
considered "non-harmonic tones" or "atonal notes". Thus, in
the first case these notes were "more remote consonances" and
in the second case they were "dissonances", but Schoenberg uses
the concepts and the terms interchangeably, whereas in the
standard view of harmony consonances and dissonances are total
opposites.

From my point of view, Schoenberg's conception is entirely
comprehensible, because he saw his theory as growing out of
the practice of the German musical masters before him, and
that's also exactly how he taught it. So to learn the older
conception -- that is, 5-limit-JI/meantone-based -- it was
necessary to begin by treating the 5 non-diatonic pitches
as "dissonances", then to evolve toward Schoenberg's newer
conception of the 12-EDO pitch-universe, a shift had to be
made, and those pitches now viewed as "more remote consonances",
which in today's tuning theory we'd call higher-limit identities.

So the business about "reminiscences of tonality" in Schoenberg,
Berg, and Webern boils down to this: Berg enthusiastically
embraced the possibilities of weaving 5-limit-based harmony
into his serial (i.e., implied-13-limit) work, Schoenberg enjoyed
having the freedom to "regress" back to 5-limit when he wanted to,
and Webern studiously avoided 5-limit forever after adopting
pantonality (or atonality, if it must be referred to as that),
even before he copped Schoenberg's serial method in the 1920s.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "unidala" <JGill99@i...> wrote:
> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> How many
> different ways could one imagine "octave equivalence"
> to be interpreted?

About a hundred.

> Perhaps - "equivalence of octaves"?

That suggests a few.

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

> Hmmm ... this is very similar to the way I understand Erv Wilson's
> theories of harmonic structures of Combination Product Sets.
> They are centerless, and thus in a sense could be called atonal,
> but made entirely of the most consonant ratios within whatever
> given prime-limits, thus simultaneously implying ever-shifting
> tonalities all the time.
>
> (or are they odd-limits? What is Wilson's view on prime-vs-odd?).

The CPS has the factors specified in advance. In most cases, some of
the factors are _not_ primes, e.g.,

3)6 [1.3.5.7.9.11] Eikosany
3)6 [1.3.7.9.11.15] Eikosany

Problems arise with ascribing a "consonance-limit" construction to
CPSs with odd factors once you get beyond 7 -- for example, the
geometric structure of the CPS would not consider 1*9 to be consonant
with 3*7, though acoustically, the interval is the same interval as
that between 1*3 and 1*7. So to me the apparent beauty of the CPS is
broken.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "unidala" <JGill99@i...> wrote:
> > --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > How many
> > different ways could one imagine "octave equivalence"
> > to be interpreted?
>
> About a hundred.
>
> > Perhaps - "equivalence of octaves"?
>
> That suggests a few.

[1] "equivalence of octaves";
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[.....

Only 99 categories left to enumerate,

J Gill

--- In tuning@y..., "unidala" <JGill99@i...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > --- In tuning@y..., "unidala" <JGill99@i...> wrote:
> > > --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> >
> > > How many
> > > different ways could one imagine "octave equivalence"
> > > to be interpreted?
> >
> > About a hundred.
> >
> > > Perhaps - "equivalence of octaves"?
> >
> > That suggests a few.
>
>
> [1] "equivalence of octaves";
> [2]
> [3]
> [4]
> [5]
> [6]
> [7]
> [8]
> [9]
> [10]
> [11]
> [12]
> [13]
> [14]
> [15]
> [.....
>
>
> Only 99 categories left to enumerate,
>
> J Gill

"Equivalence of octaves" itself suggests a few possible formulations.

"Any dyad, with one note twice the frequency of the other, sounds the
same as any other dyad, also with one note twice the frequency of the
other".

See what I mean?

BTW, "octave equivalence" was a term invented by musicians. If
discussing this logically/mathematically, we should allow one
possible definition "octave equivalence" to be "pitch helicity". I'm
sure you can find something positive on the internet about the latter.

--- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:

/tuning/topicId_32256.html#32322

> Joe,
>
> Gene:
> > If someone wants an avoidance recipe I suggest a random walk.
>
> Joe:
> > Hmmm... that's interesting, Gene! Essentially I believe that's
> > what Cage was getting at...
>
> I believe what Gene is talking about is a mathematical process, not
a
> haphazard or meandering approach. Try this:
>
> http://mathworld.wolfram.com/RandomWalk.html
>
> Gene can correct me if I'm wrong on this...
>
> Cheers,
> Jon

Got it! I'll have to read that Wolfram website more, now that it's
back up...

Thanks

JP

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "unidala" <JGill99@i...> wrote:
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > > --- In tuning@y..., "unidala" <JGill99@i...> wrote:
> > > > --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > >
> > > > How many
> > > > different ways could one imagine "octave equivalence"
> > > > to be interpreted?
> > >
> > > About a hundred.
> > >
> > > > Perhaps - "equivalence of octaves"?
> > >
> > > That suggests a few.
> >
> >
> > [1] "equivalence of octaves";
> > [2]
> > [3]
> > [4]
> > [5]
> > [6]
> > [7]
> > [8]
> > [9]
> > [10]
> > [11]
> > [12]
> > [13]
> > [14]
> > [15]
> > [.....
> >
> >
> > Only 99 categories left to enumerate,
> >
> > J Gill
>
> "Equivalence of octaves" itself suggests a few possible formulations.
>
> "Any dyad, with one note twice the frequency of the other, sounds the
> same as any other dyad, also with one note twice the frequency of the
> other".
>
> See what I mean?

JG: Indeed this as well as other questions linger ...
But does the complexity of proposing sub-types
(or, perhaps, known limitations) of "octave
equivalence" preclude us from differentiating them,
or could the "intertia" of previous "assumptions"
now implicit within existing propositions, bind us?
>
> BTW, "octave equivalence" was a term invented by musicians. If
> discussing this logically/mathematically, we should allow one
> possible definition "octave equivalence" to be "pitch helicity".

"Spirality" of the "leaning tower"?

J Gill

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

> JG: Indeed this as well as other questions linger ...
> But does the complexity of proposing sub-types
> (or, perhaps, known limitations) of "octave
> equivalence" preclude us from differentiating them,
> or could the "intertia" of previous "assumptions"
> now implicit within existing propositions, bind us?

Why don't we talk about a specific example, "pitch helicity", first,
and see how far we can go with that.

> > BTW, "octave equivalence" was a term invented by musicians. If
> > discussing this logically/mathematically, we should allow one
> > possible definition "octave equivalence" to be "pitch helicity".
>
> "Spirality" of the "leaning tower"?

Why does it lean? Just imagine a spiral staircase -- each step is a
pitch, and you're always directly above and directly below other
pitches -- its "octave equivalents" if you will.

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

/tuning/topicId_32256.html#32331

>
> Joe, *please* read my post on this again!
> /tuning/topicId_32256.html#32256
>
> I'll quote the bit that's most relevant to this:
>
> >> Schoenberg made it clear in his paper _Problems of Harmony_
> >> (as well as in other essays that have been published in
> >> _Style and Idea_) that the original goal of the "atonal" style
> >> was to explore using the higher harmonics (meaning above 5) as
> >> consonant chord-members. The idea was to avoid all reference
> >> to 3- and 5-limit harmony, and concentrate on tonal relationships
> >> which imply prime-factors 7, 11, and 13. He states even there
> >> that "a future time" may permit use of 3 and 5 along with the
> >> higher primes, but that during those early days he and his
> >> students wanted to concentrate on using the higher primes.
>
>

Hi Monz!

Well, I *did* read your post, but I *haven't* ever read _Problems of
Harmony_ so it doesn't make much sense for me to continue the
discussion until I have...

Thank!

JP

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "unidala" <JGill99@i...> wrote:
>
> > JG: Indeed this as well as other questions linger ...
> > But does the complexity of proposing sub-types
> > (or, perhaps, known limitations) of "octave
> > equivalence" preclude us from differentiating them,
> > or could the "intertia" of previous "assumptions"
> > now implicit within existing propositions, bind us?
>
> Why don't we talk about a specific example, "pitch helicity", first,
> and see how far we can go with that.
>
> > > BTW, "octave equivalence" was a term invented by musicians. If
> > > discussing this logically/mathematically, we should allow one
> > > possible definition "octave equivalence" to be "pitch helicity".
> >
> > "Spirality" of the "leaning tower"?
>
> Why does it lean? Just imagine a spiral staircase -- each step is a
> pitch, and you're always directly above and directly below other
> pitches -- its "octave equivalents" if you will.

JG: If it did *not* demonstrate indications of "leaning"
(such that all is not necessarily so equivalent), this
thread would not (by my hand) exist.

I don't expect folks to be able to *explain* "why it leans",
am simply interested in verifying a reliable basis for the
utilization of such equivalences which arises out of more
than the (obvious) "intertia" and simplicity of repeating
"prior practice". Alas, this may be the true (conceptual)
"helicity" involved ...

J Gill

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

> > > "Spirality" of the "leaning tower"?
> >
> > Why does it lean? Just imagine a spiral staircase -- each step is
a
> > pitch, and you're always directly above and directly below other
> > pitches -- its "octave equivalents" if you will.
>
> JG: If it did *not* demonstrate indications of "leaning"
> (such that all is not necessarily so equivalent), this
> thread would not (by my hand) exist.

You're missing the point of the helix model. Remember, it is not
merely a _circle_, it is a _helix_. Each pitch can be placed
according to two independent dimensions: pitch height (the "vertical"
dimension") and chroma (say the "angle" your current position makes
with a vertical line on the wall, the central axis being considered
the origin).

Hi Joe,

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, January 05, 2002 9:06 PM
> Subject: [tuning] Re: overtone serialism
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_32256.html#32331
>
>
> >
> > Joe, *please* read my post on this again!
> > /tuning/topicId_32256.html#32256
> >
> > I'll quote the bit that's most relevant to this:
> >
> > >> Schoenberg made it clear in his paper _Problems of Harmony_
> > >> (as well as in other essays that have been published in
> > >> _Style and Idea_) that the original goal of the "atonal" style
> > >> was to explore using the higher harmonics (meaning above 5) as
> > >> consonant chord-members. The idea was to avoid all reference
> > >> to 3- and 5-limit harmony, and concentrate on tonal relationships
> > >> which imply prime-factors 7, 11, and 13. He states even there
> > >> that "a future time" may permit use of 3 and 5 along with the
> > >> higher primes, but that during those early days he and his
> > >> students wanted to concentrate on using the higher primes.
> >
> >
>
> Hi Monz!
>
> Well, I *did* read your post, but I *haven't* ever read _Problems of
> Harmony_ so it doesn't make much sense for me to continue the
> discussion until I have...
>
> Thank!
>
> JP

_Style and Idea_ is readily available at any bookstore or library.

But I covered this in my own book anyway, and you have a copy of that!
Take a look in the "13-limit" section, just after Partch and the 11-limit.
Almost that entire section is taken up with a disussion of Schoenberg.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "unidala" <JGill99@i...> wrote:
>
> > > > "Spirality" of the "leaning tower"?
> > >
> > > Why does it lean? Just imagine a spiral staircase -- each step is
> a
> > > pitch, and you're always directly above and directly below other
> > > pitches -- its "octave equivalents" if you will.
> >
> > JG: If it did *not* demonstrate indications of "leaning"
> > (such that all is not necessarily so equivalent), this
> > thread would not (by my hand) exist.
>
> You're missing the point of the helix model. Remember, it is not
> merely a _circle_, it is a _helix_. Each pitch can be placed
> according to two independent dimensions: pitch height (the "vertical"
> dimension") and chroma (say the "angle" your current position makes
> with a vertical line on the wall, the central axis being considered
> the origin).

JG: I think I understand your helical model quoted above
in the sense of a mathematical representation of the subject
at hand.

In message #32351, you stated:

<< BTW, "octave equivalence" was a term invented by musicians. If
discussing this logically/mathematically, we should allow one
possible definition "octave equivalence" to be "pitch helicity". I'm
sure you can find something positive on the internet about the latter. >>

And "octave equivalence" is specifically applied to systems
which (presumably) endeavor to imply something meaningful
about the experience of playing music. I do not see how
making a mathematical model of this changes anything ...

I feel like the subject itself, like an "elusive butterfly",
keeps "spiralling" upwards into rhetoric, all the while
farther from having "one's feet on the ground" ...

I guess that "octave invariance" is just a practice of which
everyone would be happy if it worked, but once dependant upon
it in conceptual models, cannot question without calling into
question all that it has been constructed upon its basis ...

Sort of a "gentlepersons' agreement" to "not throw stones
in glass houses". I think that I get the picture.

J Gill

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

> In message #32351, you stated:
>
> << BTW, "octave equivalence" was a term invented by musicians. If
> discussing this logically/mathematically, we should allow one
> possible definition "octave equivalence" to be "pitch helicity".
I'm
> sure you can find something positive on the internet about the
latter. >>
>
> And "octave equivalence" is specifically applied to systems
> which (presumably) endeavor to imply something meaningful
> about the experience of playing music. I do not see how
> making a mathematical model of this changes anything ...

Well, it should help you understand what exactly is _meant_
by "octave equivalence".

> I feel like the subject itself, like an "elusive butterfly",
> keeps "spiralling" upwards into rhetoric, all the while
> farther from having "one's feet on the ground" ...

It shouldn't feel that way. Let's keep plugging away!

> I guess that "octave invariance" is just a practice of which
> everyone would be happy if it worked, but once dependant upon
> it in conceptual models, cannot question without calling into
> question all that it has been constructed upon its basis ...
>
> Sort of a "gentlepersons' agreement" to "not throw stones
> in glass houses". I think that I get the picture.

No way dude! Keep throwing those stones . . . but you'll find that
less of the conceptual models are dependent on "octave equivalence"
than you keep asserting.

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

/tuning/topicId_32256.html#32371

>
> _Style and Idea_ is readily available at any bookstore or library.
>

****It is true, Monz, that is one work of Schoenberg's that I have
never read. I always spent my money on what I considered his
more "technical" theory books, but I realize now that I probably
missed quite a bit by not reading this.

> But I covered this in my own book anyway, and you have a copy of
that!
> Take a look in the "13-limit" section, just after Partch and the 11-
limit.
> Almost that entire section is taken up with a disussion of
Schoenberg.
>
>

******I reviewed your comments in this section. However, you say
yourself here on page 123:

".... he [Schoenberg] has reverted to the old-fashioned way of
thinking of dissonances as being *not* related to the "key," but as
being foreign, in the sense that these "dissonant" tones actually
belong to other fundamentals, because composing in this "atonal" style

'...renounces a tonal centre... avoiding the establishment of a
key...'

"If Schoenberg had been willing to LISTEN to his theoretical ideas on
just-tuned instruments, he may not have made that paradoxical
statement."

******So, essentially, Monz, you are saying that the notion
of "dissonance" or "avoidance" of tonality is an "old fashioned" way
of looking a things, rather than using your new concept "sonance."

This seems more to reinforce my *own* argument that "nothing is
avoided" that I have commented on previously...

best,

Joe

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_32256.html#32321

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > > If someone wants an avoidance recipe I suggest a random walk.
>
> > Hmmm... that's interesting, Gene! Essentially I believe that's
what
> > Cage was getting at...
>
> I don't think Cage ever did something like what I had in mind when
I said that; I don't recall it, anyway. One could do a random walk on
the tilings of 5 or 7-limit chords (dual to the corresponing
lattices) and then work out the parts and timings in such a way as to
attempt to give it some kind of shape. The result would be atonal but
consonant. My experience suggests they also tend to be boring, but I
never worked very hard on the shape part.

I believe, Gene, now that I understand what you are talking about,
that this relates to Dave Keenan's "tumbling decany" uses a
random process. Have you seen this construction of his??

http://www.uq.net.au/~zzdkeena/Music/StereoDekany.htm

I had trouble, though, getting this to play right from Dave's
webpage...

Does anybody know any other links for this... I'll ask Dave.

best,

JP

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

/tuning/topicId_32256.html#32329

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> >
> > /tuning/topicId_32256.html#32300
> >
> > >
> > > It would be good to know what the experiments actually
consisted
> > of.
> > > It's also good to understand exactly what the notion of octave-
> > > equivalence is used for in musical theories you find around
here,
> > > such as Partch's and most of the periodicity block stuff. The
only
> > > assumption it really represents is the assumption that you, as
a
> > > scale designer, wish to have the same scale of possible tones
in
> > each
> > > and every octave span. There are many reasons you might want to
do
> > > this, independently of whether some particular definition of
octave-
> > > equivalence is experimentally shown to be true or false, and
there
> > > are many reasons you might not want to do this, independently
of
> > > whether some particular definition of octave-equivalence is
> > > experimentally shown to be true or false.
> >
> >
> > Of course, one reason is simply ease of *performance.* A player
(say
> > in 72-tET or whatever) only needs to know the pitches in *one*
octave
> > and then can play his entire range with "equivalents..."
> >
> > Otherwise, I believe things might get "kind of messy...."
> >
> > JP
>
>
> J Gill: Messy, indeed. But it seems a bit "circular" to talk
> about having the "same scale of possible tones in each
> and every octave span" in a situation where (even some)
> "particular definition of octave-equivalence is
> experimentally shown to be true or false". How many
> different ways could one imagine "octave equivalence"
> to be interpreted? Perhaps - "equivalence of octaves"?
>
>
> J Gill :)

Hi J!

Well, theoretically there may be some confusion here, but, in
practical terms, most musicians (I *think*) can spot octave
equivalence when they hear it....

best,

Joe

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "unidala" <JGill99@i...> wrote:
>
> /tuning/topicId_32256.html#32329
>
> > --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > >
> > > /tuning/topicId_32256.html#32300
> > >
> > > >
> > > > It would be good to know what the experiments actually
> consisted
> > > of.
> > > > It's also good to understand exactly what the notion of octave-
> > > > equivalence is used for in musical theories you find around
> here,
> > > > such as Partch's and most of the periodicity block stuff. The
> only
> > > > assumption it really represents is the assumption that you, as
> a
> > > > scale designer, wish to have the same scale of possible tones
> in
> > > each
> > > > and every octave span. There are many reasons you might want to
> do
> > > > this, independently of whether some particular definition of
> octave-
> > > > equivalence is experimentally shown to be true or false, and
> there
> > > > are many reasons you might not want to do this, independently
> of
> > > > whether some particular definition of octave-equivalence is
> > > > experimentally shown to be true or false.
> > >
> > >
> > > Of course, one reason is simply ease of *performance.* A player
> (say
> > > in 72-tET or whatever) only needs to know the pitches in *one*
> octave
> > > and then can play his entire range with "equivalents..."
> > >
> > > Otherwise, I believe things might get "kind of messy...."
> > >
> > > JP
> >
> >
> > J Gill: Messy, indeed. But it seems a bit "circular" to talk
> > about having the "same scale of possible tones in each
> > and every octave span" in a situation where (even some)
> > "particular definition of octave-equivalence is
> > experimentally shown to be true or false". How many
> > different ways could one imagine "octave equivalence"
> > to be interpreted? Perhaps - "equivalence of octaves"?
> >
> >
> > J Gill :)
>
>
> Hi J!
>
> Well, theoretically there may be some confusion here, but, in
> practical terms, most musicians (I *think*) can spot octave
> equivalence when they hear it....
>
> best,
>
> Joe

Joe,

When Ella Fitzgerald was asked how she would verbally
explain the concept of "swing" in music, she smiled
and said something to effect of, "if you don't already
know what it is, I can't really explain it to you ... "!!!

I sympathize with this paradox, and give the musician
and listener wide latitude in their attempts to verbalize
what occurs "inside".

Mathematics is not well suited to such vagaries,
as is the human spirit. This is why the onus rests
upon the mathemetician to relate his/her numerical
relationships to the entire gestalt of the musician,
and not the other way around!

Best Regards, J Gill :)

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

> Mathematics is not well suited to such vagaries,
> as is the human spirit. This is why the onus rests
> upon the mathemetician to relate his/her numerical
> relationships to the entire gestalt of the musician,
> and not the other way around!
>
>
> Best Regards, J Gill :)

I agree. In my opinion, any attempt to understand music through
mathematics alone is destined for extremely limited success. The
missing link here, in any attempt at a "scientific" understanding of
music, is _psychoacoustics_. A tremendous amount has become known in
the field of psychoacoustics in the last half-century, far more than
in all of prior human history, though we have still barely scratched
the surface of the iceberg :) Personally, though, I approach this
subject as a _musician_, and like to base my premises on what my ear
enjoys, finding it interesting, wherever possible, to relate that to
some or another mathematical pattern, and to try to understand the
meaning of that relationship in _psychoacoustics_. Still, music is
more magic than anything else to me, and as I age, I seek to bring
my music closer to a pure (albeit inevitable culturally influenced)
expression of my heart and spirit.

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, January 06, 2002 7:04 AM
> Subject: [tuning] Re: overtone serialism
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_32256.html#32371
>
> >
> > _Style and Idea_ is readily available at any bookstore or library.
> >
>
> ****It is true, Monz, that is one work of Schoenberg's that I have
> never read. I always spent my money on what I considered his
> more "technical" theory books, but I realize now that I probably
> missed quite a bit by not reading this.

It depends on where Schoenberg stands in your own life.

Roy Carter (translator of _Harmonielehre_ into English)
writes a good deal in his Preface about the speculative
content of Schoenberg's book.

I agree with Carter that many of the best parts of
_Harmonielehre_ are those that deal with Schoenberg's
searching questions into aspects of harmony and timbre
that went beyond what previous writers had considered,
and that therefore only a complete translation gives a
good picture of Schoenberg's thought.

Since _Style and Idea_ is much more of a hodge-podge
(a collection of various essays and other writings),
you get considerably more of that kind of non-technical
stuff, and still some of the technical too.

>
> > But I covered this in my own book anyway, and you have a copy
> > of that! Take a look in the "13-limit" section, just after
> > Partch and the 11-limit. Almost that entire section is taken
> > up with a disussion of Schoenberg.
> >
> >
>
> ******I reviewed your comments in this section. However, you say
> yourself here on page 123:
>
> ".... he [Schoenberg] has reverted to the old-fashioned way of
> thinking of dissonances as being *not* related to the "key," but as
> being foreign, in the sense that these "dissonant" tones actually
> belong to other fundamentals, because composing in this "atonal" style
>
> '...renounces a tonal centre... avoiding the establishment of a
> key...'
>
> "If Schoenberg had been willing to LISTEN to his theoretical ideas on
> just-tuned instruments, he may not have made that paradoxical
> statement."
>
> ******So, essentially, Monz, you are saying that the notion
> of "dissonance" or "avoidance" of tonality is an "old fashioned" way
> of looking a things, rather than using your new concept "sonance."
>
> This seems more to reinforce my *own* argument that "nothing is
> avoided" that I have commented on previously...

Well, what I wrote there doesn't come across as well as I could
probably say it now.

I was trying to show that "my new" concept of "sonance" was
really the same as Schoenberg's, which was also the same as
Partch's, but that neither of them ever took the step of simply
chucking the two prefixes which designate the relativity
aspect (the poles of "con-" and "dis-") and keeping only the
essential root of the term (= "sonance") to express the totality
of the continuum itself.

Keeping the polarity in their terminology made it
more difficult for both of them to express the wholistic
sense of a continuum of sonance, and thus of feeling,
divided into infinitely many shades between the poles.
When presented with terminology which emphazises polar
opposites, it's only natural that a reader would tend to
see it as a dualistic rather than a wholistic issue.

Partch established specificity by exclusive use of
ratio numbers. He defined specific shades of consonance
(see "The One-Footed Bride" in _Genesis_) as a function
of the odd-limit of the ratios in an interval.

But Schoenberg was *much* more vague, and as a result,
his explanation of sonance is much more difficult to follow;
thus the ambiguity and richness of variety with which
posterity has interpreted his theories.

>> [Schoenberg, _Harmonielehre_ p 20, Carter trans. p 21]
>>
>> Now if I continue to use the expressions "consonance"
>> and "dissonance", even though they are unwarranted,
>> I do so because there are signs that the evolution
>> of harmony will, in a short time, prove the inadquacy
>> of this classification. The introduction of another
>> terminology at this stage would have no purpose and could
>> hope for little success. Since I still have to operate
>> with these notions, I will define consonances as... <etc.>

I would have strongly argued with Schoenberg about that,
pointing out as I did above that rather than introduce *new*
terminology, all that was necessary was to *simplify* the
existing terminology, but with such a powerful simplification
that it could change the metaphysical basis of the reader's
entire harmonic conception, so that it would come closer to
matching that of Schoenberg himself. If there was ever an
example of a missed opportunity in music-history, that was
one of them! (IMO)

As I've been pointing out here, Schoenberg understood
enough about tuning theory to know that previous theorists
(and primarily Schenker, who was his contemporary) had
pretty much assessed 5 as the odd- or prime-limit on
*consonant* harmonic ratios. And he also knew that in the
expression of harmonic ideas in his own music he was reaching
out to encompass intervals that he considered consonant
which contained prime-factors of 7 and 11 (and by 1934,
also 13).

In "Twelve Tone Composition", a previously unpublished paper
from 1923 [_Style and Idea_, p 207], Schoenberg begins:

>> In twelve-tone composition consonances (major and minor
>> triads) and also the simpler dissonances (diminished
>> triads and seventh chords) -- in fact almost everything
>> that used to make up the ebb and flow of harmony -- are,
>> as far as possible, avoided.

There's that magic word, Joe!

The next sentence is one of those great examples of how
Schoenberg sabotoges the clarity of his own thought by
presenting so many parenthetical commentaries:

>> But this is not because of any natural law of the new
>> art. It is, presumably, just one manifestation of a
>> reaction, one that does not have its own special causes
>> but derives from another manifestation -- which it tries
>> to contradict, and whose laws are therefore the same,
>> basically, as its own.

This does, however, set up his next point:

>> At the root of all this is the unconscious urge to try
>> out the new resources independently, to wrest from them
>> possibilities of constructing forms, to produce with them
>> *alone* [emphasis Monzo's] all the effects of a clear style,
>> of a compact, lucid and comprehensive presentation of the
>> musical idea. To use here the old resources in the old
>> sense saves trouble -- the trouble of cultivating the new
>> -- but also means passing up the chance of enjoying whatever
>> can *only* [emphasis Schoenberg's] be attained by new
>> resources when the old ones are excluded!
>>
>> A later time will perhaps be allowed to use both kinds of
>> resources in the same way, one alongside the other, ...

So here Schoenberg clearly states that the "old-fashioned"
compositional practices are to be avoided, so that the
new ones could be explored *exclusively*.

My interpretation of this is that Schoenberg sought a type
of 7-/11-/13-limit harmony which excluded the familiar 3-
and 5-limit relationships.

Schoenberg used the overtone-theory as a way to link between
his own practical experience of hearing overtones in
instrumental sounds, and the little that he understood of the
mathematics of tuning theory. It is what enabled Gene and
I to construct the periodicity-blocks describing the JI-based
aspect of Schoenberg's theory.

Schoenberg's statements can be followed logically to suggest
that he is saying that in the "atonal" music composed by he
and his students during the 1910s-20s, their intention was
to avoid the implication of 3- and 5-limit harmonies and
make full use of the implication of 7-, 11-, and 13-limit
harmonies, which are available within the periodicity-blocks
which may be constructed from Schoenberg's explanation of
the 12-EDO scale. The major exception after 1920 is the case
of Berg, who intentionally designed his serial rows to emulate
5-limit harmonic structures.

I started making a webpage version of Schoenberg's article
"Problems of Harmony" [_Style and Idea_ p 268-287], which
was never finished:
http://www.ixpres.com/interval/monzo/schoenberg/problems.htm

You should find some interesting reading there.

love / peace / harmony ...

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

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

> From: monz <joemonz@yahoo.com>
> : <tuning@yahoogroups.com>
> Sent: Sunday, January 06, 2002 7:48 PM
> Subject: Re: [tuning] Re: overtone serialism
>
>
> As I've been pointing out here, Schoenberg understood
> enough about tuning theory to know that previous theorists
> (and primarily Schenker, who was his contemporary) had
> pretty much assessed 5 as the odd- or prime-limit on
> *consonant* harmonic ratios. And he also knew that in the
> expression of harmonic ideas in his own music he was reaching
> out to encompass intervals that he considered consonant
> which contained prime-factors of 7 and 11 (and by 1934,
> also 13).
>
> In "Twelve Tone Composition", a previously unpublished paper
> from 1923 [_Style and Idea_, p 207], Schoenberg begins:
>
> >> In twelve-tone composition consonances (major and minor
> >> triads) and also the simpler dissonances (diminished
> >> triads and seventh chords) -- in fact almost everything
> >> that used to make up the ebb and flow of harmony -- are,
> >> as far as possible, avoided.

I was re-reading this and realized that here, with the exclusion
of "diminished triads and seventh chords", it's quite likely
that Schoenberg even intended to avoid the implication of
not only 3-ness and 5-ness, but also 7-ness, in his harmony.

While "diminished triads" and "7th chords" were developed
in the context of 5-limit-based meantone and 12-EDO tunings,
in 12-EDO -- the tuning finally embraced by Schoenberg --
these *very chords* are the ones that most strongly imply
7-ness: the proportions 5:6:7 for the former and 4:5:6:7
for the latter.

So thus, when I wrote:

> My interpretation of this is that Schoenberg sought a type
> of 7-/11-/13-limit harmony which excluded the familiar 3-
> and 5-limit relationships.

I'd say now that it's actually much more likely "that Schoenberg
sought a type of 11-/13-limit harmony which excluded the familiar
3-, 5-, and 7-limit relationships.

Now *this* I found most interesting!

By excluding even the rather-far-off 7-limit implications
of 12-EDO, Schoenberg is saying that his school is focusing
on 11- and 13-limit implications -- the *very prime-factors
which are LEAST well-implied by 12-EDO*!!!

In fact, both of them are nearly quarter-tones, the 11-limit
ratios almost exactly so and the 13-limit ones only about
10 cents away from that.

So Schoenberg's emphasis seems to be that the 12-EDO scale,
in his new style of composing, *is* indeed being made to
represent "quarter-tones", a tuning system with which he
and Webern experimented briefly in 1908 and then abandoned.

In fact, since the inclusion of prime-factor 13 in his theory
was a later development (no evidence earlier than the original
version of "Problems of Harmony", 1927), the early (_Harmonielehre_,
1911) inclusion of 11 is significant in this respect, since
*that is* the simplest-integer "quarter-tone" ratio.

IMO, this lends further weight to my argument that Schoenberg's
brief experience with microtonality played a very significant
role in the development of his harmonic theory.

love / peace / harmony ...

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

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

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

> In fact, both of them are nearly quarter-tones, the 11-limit
> ratios almost exactly so and the 13-limit ones only about
> 10 cents away from that.

Be careful, Monz -- 11-limit ratios _are_ 13-limit ratios, and the 13-
limit ratio 13:7, for example, is 22 cents away from a quartertone,
and the 13-limit ratio 13:11 is only 11 cents from a 12-tET minor
third.

BTW, it seems to me that Gene, on tuning-math, proved that very few
of the periodicity blocks implied by Schoenberg (according to your
list of Schoenbergian unison vectors) actually resulted in 12-tET.
>
> So Schoenberg's emphasis seems to be that the 12-EDO scale,
> in his new style of composing, *is* indeed being made to
> represent "quarter-tones", a tuning system with which he
> and Webern experimented briefly in 1908 and then abandoned.

Well, 24-tET would be a great tuning if your interest were chords
like 8:11:13. In 12-tET, you can't evoke that chord at all, to my
ears. The three possible interpretations of this chord in 12-tET, C-
F#-G#, C-F#-A, and C-F-G#, sound like inversions of an incomplete
dominant seventh chord, a diminished triad, and a minor triad,
respectively.

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

/tuning/topicId_32256.html#32407

>
> > From: jpehrson2 <jpehrson@r...>
> > To: <tuning@y...>
> > Sent: Sunday, January 06, 2002 7:04 AM
> > Subject: [tuning] Re: overtone serialism
> >
> >
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > /tuning/topicId_32256.html#32371
> >
>
> In "Twelve Tone Composition", a previously unpublished paper
> from 1923 [_Style and Idea_, p 207], Schoenberg begins:
>
> >> In twelve-tone composition consonances (major and minor
> >> triads) and also the simpler dissonances (diminished
> >> triads and seventh chords) -- in fact almost everything
> >> that used to make up the ebb and flow of harmony -- are,
> >> as far as possible, avoided.
>
> There's that magic word, Joe!
>
> The next sentence is one of those great examples of how
> Schoenberg sabotoges the clarity of his own thought by
> presenting so many parenthetical commentaries:
>
> >> But this is not because of any natural law of the new
> >> art. It is, presumably, just one manifestation of a
> >> reaction, one that does not have its own special causes
> >> but derives from another manifestation -- which it tries
> >> to contradict, and whose laws are therefore the same,
> >> basically, as its own.
>
> This does, however, set up his next point:
>
> >> At the root of all this is the unconscious urge to try
> >> out the new resources independently, to wrest from them
> >> possibilities of constructing forms, to produce with them
> >> *alone* [emphasis Monzo's] all the effects of a clear style,
> >> of a compact, lucid and comprehensive presentation of the
> >> musical idea. To use here the old resources in the old
> >> sense saves trouble -- the trouble of cultivating the new
> >> -- but also means passing up the chance of enjoying whatever
> >> can *only* [emphasis Schoenberg's] be attained by new
> >> resources when the old ones are excluded!
> >>
> >> A later time will perhaps be allowed to use both kinds of
> >> resources in the same way, one alongside the other, ...
>
>
> So here Schoenberg clearly states that the "old-fashioned"
> compositional practices are to be avoided, so that the
> new ones could be explored *exclusively*.
>

Thanks, Monz. Well, that's pretty clear, but I had never read
anything like that in any of his writings other than _Style & Idea_
which I don't know...

I should, obviously, get a copy of that...

best,

Joe

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

/tuning/topicId_32256.html#32407

> I started making a webpage version of Schoenberg's article
> "Problems of Harmony" [_Style and Idea_ p 268-287], which
> was never finished:
> http://www.ixpres.com/interval/monzo/schoenberg/problems.htm
>
> You should find some interesting reading there.
>

Actually, I believe this Webpage pertains to the Bob Wendell
discussion and the Terhardt as well, since the emphasis is so on the
first three partials of sounding pitches.... ??

J. Pehrson

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

/tuning/topicId_32256.html#32409

> I'd say now that it's actually much more likely "that Schoenberg
> sought a type of 11-/13-limit harmony which excluded the familiar
> 3-, 5-, and 7-limit relationships.
>
> Now *this* I found most interesting!
>
>
> By excluding even the rather-far-off 7-limit implications
> of 12-EDO, Schoenberg is saying that his school is focusing
> on 11- and 13-limit implications -- the *very prime-factors
> which are LEAST well-implied by 12-EDO*!!!
>

Is it possible that the emphasis on these remote overtones in 12-tET
and the fact that they are so badly mistuned possibly one of the
reasons that the serial method has not caught the "ear" of the
general populace...??

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_32256.html#32409
>
>
> > I'd say now that it's actually much more likely "that Schoenberg
> > sought a type of 11-/13-limit harmony which excluded the familiar
> > 3-, 5-, and 7-limit relationships.
> >
> > Now *this* I found most interesting!
> >
> >
> > By excluding even the rather-far-off 7-limit implications
> > of 12-EDO, Schoenberg is saying that his school is focusing
> > on 11- and 13-limit implications -- the *very prime-factors
> > which are LEAST well-implied by 12-EDO*!!!
> >
>
> Is it possible that the emphasis on these remote overtones in 12-
tET
> and the fact that they are so badly mistuned possibly one of the
> reasons that the serial method has not caught the "ear" of the
> general populace...??
>
> JP

Bob W.:
I would cojecture that the reason is much simpler. As I understand
it, the fundamental idea behind serialism for Schoenberg was the
ultimate extension of his perception of evolution in music from a
static or pitch-center-based tonality to a dynamic tonality based on
pitch movement rather than a perceived pitch center or "home pitch".

His reasoning seems good when one looks at the romantics (people like
Wagner et al and their successors) and the increasing way in which
chromaticism was making harmonic modulation so perpetual that any
sense of tonal center was becoming increasingly obscured. He just
abstracted the process with serialism to what he saw as its ultimate
conclusion.

I posit, however, that the human factors of musical perception (we
could call it the ergonomics of the human ear) do not favor this
extreme. The older harmonic chromaticism was indeed stretching the
limits of tonal perception in the sense of moving to new keys almost
before the previous one was established. However, although this
perhaps somewhat dizzying rate of harmonic modulation blurred the
sense of a specific pitch center, it did so by rapidly moving it and
not by obliterating totally any sense of it.

It is one thing to challenge with a carnival ride ones sense of
gravity and orientation in the immediate universe surrounding one,
and another to totally disorient the rider. The thrill of the former
is in the challenging and stretching of the sense of orientation, and
that is gone and so is the fun when all sense of orientation is
eliminated. Like the music, I don't think such a ride would be very
popular either.

> So Schoenberg's emphasis seems to be that the 12-EDO scale,
> in his new style of composing, *is* indeed being made to
> represent "quarter-tones", a tuning system with which he
> and Webern experimented briefly in 1908 and then abandoned.

Very interesting.

Webern tells about this a little in his "Path" lectures. He confirms the
'necessity' of the use of quarter-tones but he notes his recitation about
the 'readiness' of the time.

He also writes to Willi Reich that he was planning a "very different" vocal
composition after the completion of Cantat II. I'm uncertain if we can find
any coherence between these two incidences.

I'd be thankful if you can supply further information or point to resources
about the mentioned 1908 experiments.

Best,
Ertugrul

---
Decode address to reply:
ertugrulinanc-at-yahoo-dot-com

----- Original Message -----
From: monz <joemonz@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: Monday, January 07, 2002 6:09 AM
Subject: Re: [tuning] Re: overtone serialism

Hello Ertugrul,

> From: Ertugrul iNANC <ertugrulinanc@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, January 07, 2002 9:36 AM
> Subject: [tuning] Re: overtone serialism
>
>
> > So Schoenberg's emphasis seems to be that the 12-EDO scale,
> > in his new style of composing, *is* indeed being made to
> > represent "quarter-tones", a tuning system with which he
> > and Webern experimented briefly in 1908 and then abandoned.
>
> Very interesting.
>
> Webern tells about this a little in his "Path" lectures. He confirms the
> 'necessity' of the use of quarter-tones but he notes his recitation about
> the 'readiness' of the time.
>
> He also writes to Willi Reich that he was planning a "very different"
vocal
> composition after the completion of Cantat II. I'm uncertain if we can
find
> any coherence between these two incidences.
>
> I'd be thankful if you can supply further information or point to
resources
> about the mentioned 1908 experiments.

I gave a lecture on this last April at Microfest 2001, in Claremont, CA.
Brian McLaren videotaped my presentation (eventually I'll get a copy
of it from him) and is in the process of transcribing it for publication.

Meantime, the key which opened this door for me was the article by
Dominik Schweiger, "Weberns rejected microtones", from the _Mitteilungen
der Paul Sacher Stiftung_, no. 11 (April 1998), which I've translated
and made into a webpage (translation improved by Aaron Hunt, not finished):
http://www.ixpres.com/interval/monzo/webern/micro/Webernmicro.htm

love / peace / harmony ...

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

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

> From: robert_wendell <BobWendell@technet-inc.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, January 07, 2002 9:37 AM
> Subject: [tuning] Re: badly tuned remote overtones
>
>
> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > /tuning/topicId_32256.html#32409
> >
> >
> > > I'd say now that it's actually much more likely "that Schoenberg
> > > sought a type of 11-/13-limit harmony which excluded the familiar
> > > 3-, 5-, and 7-limit relationships.
> > >
> > > Now *this* I found most interesting!
> > >
> > >
> > > By excluding even the rather-far-off 7-limit implications
> > > of 12-EDO, Schoenberg is saying that his school is focusing
> > > on 11- and 13-limit implications -- the *very prime-factors
> > > which are LEAST well-implied by 12-EDO*!!!
> > >
> >
> > Is it possible that the emphasis on these remote overtones
> > in 12-tET and the fact that they are so badly mistuned possibly
> > one of the reasons that the serial method has not caught the
> > "ear" of the general populace...??
> >
> > JP
>
> Bob W.:
> I would cojecture that the reason is much simpler. As I understand
> it, the fundamental idea behind serialism for Schoenberg was the
> ultimate extension of his perception of evolution in music from a
> static or pitch-center-based tonality to a dynamic tonality based on
> pitch movement rather than a perceived pitch center or "home pitch".
>
> His reasoning seems good when one looks at the romantics (people like
> Wagner et al and their successors) and the increasing way in which
> chromaticism was making harmonic modulation so perpetual that any
> sense of tonal center was becoming increasingly obscured. He just
> abstracted the process with serialism to what he saw as its ultimate
> conclusion.

Again, Bob, I'd say that your assessment of Schoenberg is right on
the money.

> I posit, however, that the human factors of musical perception (we
> could call it the ergonomics of the human ear) do not favor this
> extreme. The older harmonic chromaticism was indeed stretching the
> limits of tonal perception in the sense of moving to new keys almost
> before the previous one was established. However, although this
> perhaps somewhat dizzying rate of harmonic modulation blurred the
> sense of a specific pitch center, it did so by rapidly moving it and
> not by obliterating totally any sense of it.
>
> It is one thing to challenge with a carnival ride ones sense of
> gravity and orientation in the immediate universe surrounding one,
> and another to totally disorient the rider. The thrill of the former
> is in the challenging and stretching of the sense of orientation, and
> that is gone and so is the fun when all sense of orientation is
> eliminated. Like the music, I don't think such a ride would be very
> popular either.

Can't really argue with my own feelings regarding what you say here,
but thought it would be good to point out again where and why
Schoenberg chose this route. It was primarily to *liberate* his
own compositional practice from the strictures imposed by more
traditional musical teaching. That's the key word. Around
1909, Schoenberg was seeking to express "pure feeling" in his
music.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

Many thanks, Joe.

I hope you'll let the list know when the conference is ready for publishing.

Ertugrul

---
Decode address to reply:
ertugrulinanc-at-yahoo-dot-com

----- Original Message -----
From: monz <joemonz@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: Monday, January 07, 2002 8:07 PM
Subject: Re: [tuning] Re: overtone serialism

> Hello Ertugrul,
>
> > From: Ertugrul iNANC <ertugrulinanc@yahoo.com>
> > To: <tuning@yahoogroups.com>
> > Sent: Monday, January 07, 2002 9:36 AM
> > Subject: [tuning] Re: overtone serialism
> >
> >
> > > So Schoenberg's emphasis seems to be that the 12-EDO scale,
> > > in his new style of composing, *is* indeed being made to
> > > represent "quarter-tones", a tuning system with which he
> > > and Webern experimented briefly in 1908 and then abandoned.
> >
> > Very interesting.
> >
> > Webern tells about this a little in his "Path" lectures. He confirms the
> > 'necessity' of the use of quarter-tones but he notes his recitation
about
> > the 'readiness' of the time.
> >
> > He also writes to Willi Reich that he was planning a "very different"
> vocal
> > composition after the completion of Cantat II. I'm uncertain if we can
> find
> > any coherence between these two incidences.
> >
> > I'd be thankful if you can supply further information or point to
> resources
> > about the mentioned 1908 experiments.
>
> I gave a lecture on this last April at Microfest 2001, in Claremont, CA.
> Brian McLaren videotaped my presentation (eventually I'll get a copy
> of it from him) and is in the process of transcribing it for publication.
>
> Meantime, the key which opened this door for me was the article by
> Dominik Schweiger, "Weberns rejected microtones", from the _Mitteilungen
> der Paul Sacher Stiftung_, no. 11 (April 1998), which I've translated
> and made into a webpage (translation improved by Aaron Hunt, not
finished):
> http://www.ixpres.com/interval/monzo/webern/micro/Webernmicro.htm
>
>
>
>
> love / peace / harmony ...
>
> -monz
> http://www.monz.org
> "All roads lead to n^0"
>
>
>
>
>
> _________________________________________________________
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--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > From: robert_wendell <BobWendell@t...>
> > To: <tuning@y...>
> > Sent: Monday, January 07, 2002 9:37 AM
> > Subject: [tuning] Re: badly tuned remote overtones
> >
> >
> > --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> > >
> > > /tuning/topicId_32256.html#32409
> > >
> > >
> > > > I'd say now that it's actually much more likely "that
Schoenberg
> > > > sought a type of 11-/13-limit harmony which excluded the
familiar
> > > > 3-, 5-, and 7-limit relationships.
> > > >
> > > > Now *this* I found most interesting!
> > > >
> > > >
> > > > By excluding even the rather-far-off 7-limit implications
> > > > of 12-EDO, Schoenberg is saying that his school is focusing
> > > > on 11- and 13-limit implications -- the *very prime-factors
> > > > which are LEAST well-implied by 12-EDO*!!!
> > > >
> > >
> > > Is it possible that the emphasis on these remote overtones
> > > in 12-tET and the fact that they are so badly mistuned possibly
> > > one of the reasons that the serial method has not caught the
> > > "ear" of the general populace...??
> > >
> > > JP
> >
> > Bob W.:
> > I would cojecture that the reason is much simpler. As I
understand
> > it, the fundamental idea behind serialism for Schoenberg was the
> > ultimate extension of his perception of evolution in music from a
> > static or pitch-center-based tonality to a dynamic tonality based
on
> > pitch movement rather than a perceived pitch center or "home
pitch".
> >
> > His reasoning seems good when one looks at the romantics (people
like
> > Wagner et al and their successors) and the increasing way in
which
> > chromaticism was making harmonic modulation so perpetual that any
> > sense of tonal center was becoming increasingly obscured. He just
> > abstracted the process with serialism to what he saw as its
ultimate
> > conclusion.
>
>
> Again, Bob, I'd say that your assessment of Schoenberg is right on
> the money.
>
>
> > I posit, however, that the human factors of musical perception
(we
> > could call it the ergonomics of the human ear) do not favor this
> > extreme. The older harmonic chromaticism was indeed stretching
the
> > limits of tonal perception in the sense of moving to new keys
almost
> > before the previous one was established. However, although this
> > perhaps somewhat dizzying rate of harmonic modulation blurred the
> > sense of a specific pitch center, it did so by rapidly moving it
and
> > not by obliterating totally any sense of it.
> >
> > It is one thing to challenge with a carnival ride ones sense of
> > gravity and orientation in the immediate universe surrounding
one,
> > and another to totally disorient the rider. The thrill of the
former
> > is in the challenging and stretching of the sense of orientation,
and
> > that is gone and so is the fun when all sense of orientation is
> > eliminated. Like the music, I don't think such a ride would be
very
> > popular either.
>
>
> Can't really argue with my own feelings regarding what you say here,
> but thought it would be good to point out again where and why
> Schoenberg chose this route. It was primarily to *liberate* his
> own compositional practice from the strictures imposed by more
> traditional musical teaching. That's the key word. Around
> 1909, Schoenberg was seeking to express "pure feeling" in his
> music.
>
> -monz
>
Bob:
Yes, it has always been clear to me that he was seeking some way out
of the rut that 12-EDO had created for musical expression, all the
more conventional modes of composition having pretty much exhausted
its possiblities in principle if not in practice. It seems ironic,
however, that his search for means of expressing "pure feeling" would
find a route that seems so sterile to so many in terms of precisely
that: FEELING!

> From: robert_wendell <BobWendell@technet-inc.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, January 07, 2002 10:43 AM
> Subject: [tuning] Re: badly tuned remote overtones
>
>
> Bob:
> Yes, it has always been clear to me that he [Schoenberg]
> was seeking some way out of the rut that 12-EDO had created
> for musical expression, all the more conventional modes of
> composition having pretty much exhausted its possiblities
> in principle if not in practice.

That's a great way to put that point ... glad you provided
the distinction.

> It seems ironic, however, that his search for means of
> expressing "pure feeling" would find a route that seems
> so sterile to so many in terms of precisely that: FEELING!

Yes, well ... the extremely negative reaction by most of
the public and just about all of the press to Schoenberg's
"break with tonality" in 1908 certainly pushed him and his
little band of followers into a very isolated world of
experience after that year. It's not surprising to me
that this was reflected in his subsequent music, and even
less surprising that many listeners have trouble sympathizing.

But now this is getting off-topic ...
continue on metatuning if desired.

-monz

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--- In tuning@y..., "robert_wendell" <BobWendell@t...> wrote:

/tuning/topicId_32256.html#32424

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > /tuning/topicId_32256.html#32409
> >
> >
> > > I'd say now that it's actually much more likely "that Schoenberg
> > > sought a type of 11-/13-limit harmony which excluded the
familiar
> > > 3-, 5-, and 7-limit relationships.
> > >
> > > Now *this* I found most interesting!
> > >
> > >
> > > By excluding even the rather-far-off 7-limit implications
> > > of 12-EDO, Schoenberg is saying that his school is focusing
> > > on 11- and 13-limit implications -- the *very prime-factors
> > > which are LEAST well-implied by 12-EDO*!!!
> > >
> >
> > Is it possible that the emphasis on these remote overtones in 12-
> tET
> > and the fact that they are so badly mistuned possibly one of the
> > reasons that the serial method has not caught the "ear" of the
> > general populace...??
> >
> > JP
>
> Bob W.:
> I would cojecture that the reason is much simpler. As I understand
> it, the fundamental idea behind serialism for Schoenberg was the
> ultimate extension of his perception of evolution in music from a
> static or pitch-center-based tonality to a dynamic tonality based
on
> pitch movement rather than a perceived pitch center or "home
pitch".
>
> His reasoning seems good when one looks at the romantics (people
like
> Wagner et al and their successors) and the increasing way in which
> chromaticism was making harmonic modulation so perpetual that any
> sense of tonal center was becoming increasingly obscured. He just
> abstracted the process with serialism to what he saw as its
ultimate
> conclusion.
>
> I posit, however, that the human factors of musical perception (we
> could call it the ergonomics of the human ear) do not favor this
> extreme. The older harmonic chromaticism was indeed stretching the
> limits of tonal perception in the sense of moving to new keys
almost
> before the previous one was established. However, although this
> perhaps somewhat dizzying rate of harmonic modulation blurred the
> sense of a specific pitch center, it did so by rapidly moving it
and
> not by obliterating totally any sense of it.
>
> It is one thing to challenge with a carnival ride ones sense of
> gravity and orientation in the immediate universe surrounding one,
> and another to totally disorient the rider. The thrill of the
former
> is in the challenging and stretching of the sense of orientation,
and
> that is gone and so is the fun when all sense of orientation is
> eliminated. Like the music, I don't think such a ride would be very
> popular either.

Hello Bob!

Well, your description above is *exactly* the way *I* was taught the
historical evolution proceeded.

That's why it seems more an "expansion" leading to a disorientation
rather than any kind of intentional "avoidance."

This is also why I was rather surprised at the Schoenberg quote that
Monz pointed out from _Style and Idea_ (which I haven't read)...

It seems some of Schoenberg's *other* writings feature more the
*evolutionary* aspects than the "avoidance" one.... and I believe
that was the approach taken in _Harmonielehre_ as well, if I recall.

But apparently, Schoenberg had the "avoidance" of tonality and lower-
limit consonance in mind, at least to a degree. That's why, I
believe, there was such a strict prohibition of octaves. I guess
triads are pretty much avoided, too... or when they come about,
they're almost like passing *dissonances!* The tables have been
turned *back*... almost to the Medieval days where the 5-limit triad
was a dissonance....

I don't want to argue with Monz, but I'm wondering the significance
of constructing "periodicity blocks" of higher-limit partials in
Schoenberg when the music *ultimately* ended up utilizing the 12-tET
system, where they are so "out of tune" and where the pitches are
*rotated* in a series, regardless of their upper-limit significances.

Well, Monz may come up with something here... but I think we would
have to see specific instances in the *music* where 11-limit and 13-
limit intervals lead to a certain consideration of row, etc, etc...

Maybe fodder for another great Monz webpage!

JP

Hi Joe,

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, January 07, 2002 4:35 PM
> Subject: [tuning] Re: badly tuned remote overtones
>
>
> I don't want to argue with Monz, but I'm wondering the significance
> of constructing "periodicity blocks" of higher-limit partials in
> Schoenberg when the music *ultimately* ended up utilizing the 12-tET
> system, where they are so "out of tune" and where the pitches are
> *rotated* in a series, regardless of their upper-limit significances.
>
> Well, Monz may come up with something here... but I think we would
> have to see specific instances in the *music* where 11-limit and 13-
> limit intervals lead to a certain consideration of row, etc, etc...

Well, back when I wrote that unpublished paper in 1988, when I
realized how much similarity there was in the music-theoretical
ideas of Partch and Schoenberg, this is exactly what I hoped
I'd be able to do someday. Sure, those 11- and 13-limit pitches
are *way* out of tune in 12-EDO ... but if Schoenberg really did
intend for them to be implied (as I think he did), then it might
make possible some really interesting JI-based analyses of his
pantonal ("atonal") music, and that's something I'd like to see!

The periodicity-blocks that Gene made from my numerical analysis
of Schoenberg's 1911 and 1927 theories are a good start.

> Maybe fodder for another great Monz webpage!

Almost certainly. My whole second book is intended to be about
"rational implications of Schoenberg's theories" ... if I can
focus on that and get away from my webpages, which is looking
less and less likely these days...

-monz

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

/tuning/topicId_32256.html#32494

>
> Well, back when I wrote that unpublished paper in 1988, when I
> realized how much similarity there was in the music-theoretical
> ideas of Partch and Schoenberg, this is exactly what I hoped
> I'd be able to do someday. Sure, those 11- and 13-limit pitches
> are *way* out of tune in 12-EDO ... but if Schoenberg really did
> intend for them to be implied (as I think he did), then it might
> make possible some really interesting JI-based analyses of his
> pantonal ("atonal") music, and that's something I'd like to see!

*****Hi Monz!

Well, I guess it would make more sense to analyze the "freely atonal"
methods by your system than it would for the, specifically, "serial"
works...

> The periodicity-blocks that Gene made from my numerical analysis
> of Schoenberg's 1911 and 1927 theories are a good start.
>

****Yes, indeed. It's nice to have the resources of the great
mathematicians and semi-mathematicians in our midst. (As well as the
few "math morons" who add local color...)

>
> > Maybe fodder for another great Monz webpage!
>
>
> Almost certainly. My whole second book is intended to be about
> "rational implications of Schoenberg's theories" ... if I can
> focus on that and get away from my webpages, which is looking
> less and less likely these days...
>

****Just a thought Monz... could it be possible to create a "modern"
book that integrates the *print* AND *web* media??

Possibly the "book" could actually be *on line* as your other pages
are, and you could simply print pages out on demand and bind them, in
case somebody wants to look at them that way?

Of course, that would mean a limited "print run" but it might make
for more *updated* materials and there's a somewhat limited demand
for these kinds of materials, anyway. (When Xenharmonicon started,
it had a "xerox run" of only 20 copies!)

best,

Joe

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

> Well, back when I wrote that unpublished paper in 1988, when I
> realized how much similarity there was in the music-theoretical
> ideas of Partch and Schoenberg, this is exactly what I hoped
> I'd be able to do someday. Sure, those 11- and 13-limit pitches
> are *way* out of tune in 12-EDO ... but if Schoenberg really did
> intend for them to be implied (as I think he did), then it might
> make possible some really interesting JI-based analyses of his
> pantonal ("atonal") music, and that's something I'd like to see!
>
> The periodicity-blocks that Gene made from my numerical analysis
> of Schoenberg's 1911 and 1927 theories are a good start.

Well, given that most of the periodicity blocks imply not 12-tone,
but rather 7-, 5-, and 2-tone scales, it strikes me that Schoenberg's
attempted justification for 12-tET, at least as intepreted by you,
generally fails. No?

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, January 10, 2002 10:10 AM
> Subject: [tuning] Re: badly tuned remote overtones
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > The periodicity-blocks that Gene made from my numerical analysis
> > of Schoenberg's 1911 and 1927 theories are a good start.
>
> Well, given that most of the periodicity blocks imply not 12-tone,
> but rather 7-, 5-, and 2-tone scales, it strikes me that Schoenberg's
> attempted justification for 12-tET, at least as intepreted by you,
> generally fails. No?

Ahh ... actually Paul ... no.

Now I realize my mistake: I had failed to take into
consideration the 5-limit enharmonicity required by Schoenberg.
To construct a periodicity-block according to his descriptions,
one would have to temper out one of the "enharmonic equivalents".

We may choose 2048:2025 =

[2]
[3] * [11 -4 -2]
[5]

Plugging that into the unison-vector matrix I had already
derived before:

2 3 5 7 11 unison vectors ~cents

[ 11 -4 -2 0 0] = 2048:2025 19.55256881
[ -5 1 0 0 1] = 33:32 53.27294323
[ 6 -2 0 -1 0] = 64:63 27.2640918
[ -4 4 -1 0 0] = 81:80 21.5062896

inverse (without powers of 2) =

[-1 0 0 2]
[-4 0 0 -4] 1
[ 2 0 -12 -4] * --
[ 1 12 0 -2] 12

So it looks to me like Schoenberg's explanation in
_Harmonielehre_ definitely implies a 12-tone periodicity-block.

I'd venture to say that Schoenberg had a good intuitive
grasp of all this, without actually knowing anything about
periodicity-block theory.

-monz

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--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > From: paulerlich <paul@s...>
> > To: <tuning@y...>
> > Sent: Thursday, January 10, 2002 10:10 AM
> > Subject: [tuning] Re: badly tuned remote overtones
> >
> >
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > > The periodicity-blocks that Gene made from my numerical analysis
> > > of Schoenberg's 1911 and 1927 theories are a good start.
> >
> > Well, given that most of the periodicity blocks imply not 12-
tone,
> > but rather 7-, 5-, and 2-tone scales, it strikes me that
Schoenberg's
> > attempted justification for 12-tET, at least as intepreted by
you,
> > generally fails. No?
>
>
> Ahh ... actually Paul ... no.
>
> Now I realize my mistake:

Etc. . . You seem to be brushing some of the unison vectors you had
previously reported, and from which Gene derived 7-, 5-, and 2-tone
periodicity blocks, under the rug. Face it, Monz -- without some
careful "fudging", Schoenberg's derviation of 12-tET as a scale for
13-limit harmony is not the rigorous, unimpeachable bastion of good
reasoning that you'd like to present it as. The contradictions in
Schoenberg's arguments were known at least as early as Partch's
Genesis, and he isn't going to weasel his way out of them now :) If
12-tET can do what you and Schoenberg are trying to say it can, it
can do _anything_, and there would be no reason ever to adopt any
other tuning system.

First, I'd like to start this post off with a link to my
"rough draft" of a lattice of the periodicity-block Gene
calculated for Schoenberg's theory:

http://www.ixpres.com/interval/monzo/schoenberg/harm/Genes-pblock.gif

This shows the 12-tone periodicity-block (primarily 3- and 5-limit,
with one 11-limit pitch), and its equivalent p-block cousins at
+/- each of the four unison-vectors.

Now to respond to Paul...

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, January 11, 2002 12:47 PM
> Subject: [tuning] Re: badly tuned remote overtones
>
>
> You seem to be brushing some of the unison vectors you had
> previously reported, and from which Gene derived 7-, 5-, and 2-tone
> periodicity blocks, under the rug.

Ah ... so then this, from Gene:

> From: genewardsmith <genewardsmith@juno.com>
> To: <tuning-math@yahoogroups.com>
> Sent: Wednesday, December 26, 2001 3:25 PM
> Subject: [tuning-math] Re: Gene's notation & Schoenberg lattices
>
> ... This matrix is unimodular, meaning it has determinant +-1.
> If I invert it, I get
>
> [ 7 12 7 -2 5]
> [11 19 11 -3 8]
> [16 28 16 -5 12]
> [20 34 19 -6 14]
> [24 42 24 -7 17]
>

actually *does* specify "7-, 5-, and 2-tone periodicity blocks".
Yes?

> Face it, Monz -- without some careful "fudging", Schoenberg's
> derviation of 12-tET as a scale for 13-limit harmony is not
> the rigorous, unimpeachable bastion of good reasoning that
> you'd like to present it as.

Your point is taken, but please try to understand my objectives
more clearly. I agree with you that "Schoenberg's derviation ...
is not the rigorous, unimpeachable bastion of good reasoning" etc.
I'm simply trying to get a foothold on what was in his mind when
he came up with his radical new ideas for using 12-tET to represent
higher-limit chord identities.

I've seen it written (can't remember where right now) that without
the close personal attachment to Schoenberg that his students had,
it's nearly impossible to understand all the subtleties of his
teaching. I'm just trying to dig into that scenario a bit, and
in a sense to "get closer" to Schoenberg and his mind.

> The contradictions in Schoenberg's arguments were known at least
> as early as Partch's Genesis, and he isn't going to weasel his way
> out of them now :) If 12-tET can do what you and Schoenberg are
> trying to say it can, it can do _anything_, and there would be
> no reason ever to adopt any other tuning system.

Ahh ... well, I think you've put on finger on the crux of the matter.

Schoenberg consciously rejected microtonality and also made a
conscious decision to use the 12-tET tuning as tho it *could* do
"_anything_".

As I've documented again and again, he *did* have a favorable attitude
towards adopting other tuning systems, but was of the opinion that
only in the future would the time be right for that. With us now
living *in* that future, it seems to me that perhaps he was right
after all. Perhaps it's even possible that Schoenberg's actions
in adopting the "new version" of 12-tET ("atonality") helped to
precipitate the current trend towards microtonality and alternative
tunings. ...?

Always curious about these things,

-monz

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