back in Cali.; meeting with Kees

Hello and Happy New Year to everyone!

I'm very happy to be back in warm, sunny San Diego... and yes,
the big snowstorm almost did prevent me from escaping!
But I made it.

It was wonderful to meet Kees van Prooijen during my stop-over
in San Francisco... I'm very sorry that my absurd flight delays
got me there too late to meet Heinz Bohlen, who was prepared for
my visit on Saturday; it would have been the three of us together.
But on Sunday, Kees took me on a very nice, albeit very short
(and very foggy) sight-seeing trip. (I missed the beautiful
weather in SF on Saturday...)

Kees also drove me to the airport and came in with me, where we
got to see a very interesting exhibit of percussion instruments
from all over the world, from the collection of Mickey Hart
(or is that Nicky?), who used to play drums for the Grateful Dead.
It was very strange that just that morning in my hotel room in
San Francisco, on the "CBS Sunday Morning" TV program, I had
seen a segment specifically about that percussion exhibit.
I recognized some of the instruments from TV when we actually
saw them at the airport.

It turns out that Kees and I have many interests in common...
such things as lattice diagrams, Schoenberg, maps, etc. There's
a rumor that we may be collaborating on a Schoenbergian project
some time in the future...
(hint: a film realization of _Die Glu:ckliche Hand_...)

... Wow! Look at that wave!! Gotta go!... ;-)

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
>
> It turns out that Kees and I have many interests in common...
> such things as lattice diagrams, Schoenberg, maps, etc. There's
> a rumor that we may be collaborating on a Schoenbergian project
> some time in the future...
> (hint: a film realization of _Die Glu:ckliche Hand_...)
>

Joe, Kees and all,

There is an important question I would like to ask you, with regard
to your ideas about retuning Schoenberg (or any other composers for
that matter).

Do you not see any ethical (or moral) problems with altering the
compositional intentions of the work of past composers (especially
those so recently deceased)? Do you not feel that this kind of
modification to other's compositions (whether public domain or not),
represents a kind of "distortion" of the original intent of the
composer?

One other thing too is this: If Schoenberg's intention was to attempt
to avoid "tonality" within the pitch set of 12tET, then is it your
intention to give Schoeny a tuning that would help him along the way,
such as 13tET? Or is it your intention to re-tune his (or other's)
music to an unintended "tonal" system, such as JI? It could be
perceived by many, that to impose something onto another's work,
which was not their intention could represent a kind of "trampling of
the sacred".

Let me pose by analogy: What if you composed a piece of music in "X-
Tuning", that you felt delivered the desired intention of the music,
and less than a hundred years from now, some future microtonalist(s)
came along and found your tuning theory to be ludicrous, and decided
to make "improvements" to your work, by imposing their own subjective
tuning views onto your compositions? How would you (or your ghost)
view this kind of "hi-jacking"? When you compose new music, are you
intending that others may be allowed to come along in the future and
make alterations to the original intent of your music?

Let me know if this is ok. When you guys have left for the big
microtone in the sky, I've got some great ideas I'd like to try out
on your midi files - of course - I'm unable to discuss these with
the "living" victims at this time (although I have been wondering how
Joe Monzo's work would sound with a "house beat", and tuned to a 8000
tone non-octave scale). }: )

Respectfully,

Jacky Ligon

(Sorry to have taken so long to respond to this request...
Upon resettling back home, I'm working a lot of hours and
also dealing with a rather severe personal crisis...)

Jacky Ligon
http://www.egroups.com/message/tuning/17093

raises the question of the ethics of retuning the music of
composers who had a definite intended tuning for their pieces,
specifically, the case of Schoenberg.

John deLaubenfels
http://www.egroups.com/message/tuning/17104

answers that he sees all music as fair game for retuning,
provided that the altered version is clearly labelled as
such and is not marketed as representing the composer's
intention, and that any living composer should be paid for
any work so used.

Bob Valentine
http://www.egroups.com/message/tuning/17121

says pretty much the same, arguing from the jazz musician's
perspective that a "tune" is little more than a melody and
chord changes, around which good jazz musicians will improvise
a piece that may sound nothing like the original tune.

Jacky answers Bob:
http://www.egroups.com/message/tuning/17126

> All your points are well taken and well put, but perhaps I
> neglected to make it clear that I was questioning the
> re-tuning of Schoenberg's music in particular. And as we
> know, his music (latter opus') dealt with the unique
> theoretical/philosophical approach of trying to avoid
> tonality with his serial techniques, using the 12tET pitch
> set. This concept was anchored in this tuning system. So
> with this in mind, I find it extremely difficult to be overly
> euphemistic with regard to imposing a tuning other than 12tET
> onto Big Daddy Schoenberg.
>
> Follow me in this line of reasoning for a moment, by
> considering 2 things:
>
> 1. If one attempts to impose a JI quality onto this music,
> where its intention is to avoid the feeling of tonality,
> then "distortion" IMHO spells more accurately what's being
> done to Schoenberg's music. The "Lense" analogy again!
>
> 2. If one wishes to "help him along the way" with a tuning
> system that would have surely been more beneficial to this
> already bizarre theory, then 13tET would be the perfect choice
> as far as avoidance of tonality (or perhaps an non-octave
> spiral tuning). But then, one is confronted with the fact
> that Schoenberg's music used highly specialized 12tET set
> theory, with the 12 tone row, and also to impose this onto
> his music (forgive me Bob!), would also amount to "distortion"
> of the geometries of his theory. This however would be the
> approach I would be most interested to hear - if Schoenberg
> wanted to avoid tonality, then supply his music with a tuning
> system with maximal tonal ambiguity, and PLEASE let me know
> when you've got the midi file ready!
>
> Just to clarify:
>
> I have absolutely no issues with 'interpretation' or
> 'realisation' or 'rendering. I also have been an active
> improvising musician for most of my music life, so all
> you said was in resonance with me, but when we speak of
> re-tuning music which is inseparable from its tuning theory/
> set theory, then we tread a thin line between "distortion"
> and the more euphemistic choices of 'interpretation' or
> 'realization' or 'rendering.
>
> ...
>
> P.S. This was really an attempt to get Monz to speak about
> how he intends to tune this music.

I agree very much with what both John and Bob said.

Please note emphatically that the compositions of Schoenberg's
in which I'm most interested, and those which I'd like to retune,
are *not* the later 12-tone serial pieces, but rather, the early
tonal and "free atonality" ones.

Schoenberg did indeed consider the question of using microtonal
tunings, experimented with quartertones a bit around the summer
of 1909, and rejected them by August 1909. (I'll be presenting
this info, along with much more concerning Webern and many German
and Austrian microtonalists of the early 1900s, in a lecture/
demonstration at Microfest 2001 in Claremont, CA, in April.)

So far, John has let his software do the work of retuning
Schoenberg's early masterpiece _Verkla:rte Nacht_, and I'm *very*
pleased with the results, agreeing with John that the 7-limit
version sounds best. In disagreement with John, I also very
much like the 11-/13-limit version and think that it sounds
not too much unlike what real string players might play.

It's difficult for me to give a real answer as to how I'd retune
this early Schoenberg work. I feel like there's still so much
research to be done. Schoenberg had a brilliant mind, which more
often than not was able to embrace two opposing poles of thought,
probably because he was able to see that they were merely the ends
of a continuum of possibility... very much like the way he described
the issue of consonance and dissonance (see my "sonance" Dictionary
entry). His rhapsodizing about the beauties of "untempered" music
while at the same time rigidly limiting himself to the 12-tET scale
are only one more example of this, and one which makes it extremely
difficult to divine exactly what he may have been "hearing in his
head" when he wrote these pieces. And ultimately, what I'm trying
to do is to give a presentation of the music which I think comes
as close as possible to what these composers heard in their heads.

One thing which would be good to bear in mind is that after 1904
Schoenberg idolized Mahler, and accepted wholeheartedly many of
Mahler's idiosyncratic performance practices. Mahler was roundly
criticized (by the newspapers) for his reorchestration of Beethoven's
9th, but Schoenberg entered all of Mahler's changes into his own
copy of that score. My point: Mahler had absolutely *no* qualms
about rewriting an older piece, and his intention was always to
"bring out the composer's intention". Usually, his changes were
based on things such as the increased size of the orchestra and
concert hall of his day compared with, say, Mozart or Beethoven's.
He realized that the different "room" in which the music was played
had a tremendous impact on the audience's reception, and tried
to adjust accordingly.

And again exemplifying the paradoxes inherent in Schoenberg's
thinking, he discussed in his _Harmonielehre_ [1911] how the
overtone series makes a good archtypical pattern which helps
guide the composer into using "new" harmonic structures, then
later (in a much-quoted letter to Joseph Yasser) insisted that
good musicians did not let their technique be dictated by
"natural" (= JI) tendencies, but rather learned how to alter
these tendencies to conform to "humanistic" (= 12-tET) art.

The only real arguments Schoenberg cited in abandoning
microtones were: 1) the inavailability of instruments so
tuned, and 2) his inability to comprehend the math. If it
weren't for those two limitations, he apparently would have
accepted microtonal tunings for use in his own work.

Joe Pehrson:
http://www.egroups.com/message/tuning/17133

> I'm sorry, Jacky, but I believe this reading is a totally
> inaccurate assessment of Schoenberg's intention. I will
> need Joe Monzo, an expert in these matters, to back me up,
> but in NO WAY was Schoenberg hoping to "destroy tonality."
> I think you need to read up a bit on your history (despite
> your great ability in sound manipulation, which I greatly
> admire!).
>
> Schoenberg considered himself a continuation of the great
> Germanic tradition from Mozart and Brahms onward, and his
> 12-tone system was rooted in the idea the EVERY SINGLE TONE
> was a tonality.
>
> In fact, Schoenberg didn't want his system to be called
> "atonality" or "serialism." He thought of it as a way of
> extending tonality post-Wagner.
>
> I believe the term he wanted was "pan-tonality," right Monz??

Right, Joe, Schoenberg preferred "pantonality" to describe what
he did between 1908 and roughly 1920 (when he began composing
serially), and which is today known as "free atonality". Schoenberg
very logically argued (as he always did) that since the very
substance of music was "tone", then "atonal" was an oxymoron
and could not describe anything having to do with music. His
point here was that the overtone series presented an extended
set of harmonic relationships which could be emulated and explored
in compositions, and that until his day composers had stopped
at 5-limit but he wanted to go beyond.

Schoenberg's big apparent error, as pointed out by Partch, was
the inconsistency (in the Erlichian sense) of his mapping of
13-limit ratios to the 12-tET scale. I say "apparent" because
Schoenberg had absolute pitch and certainly would have known,
had he heard them, that the 7th, 11th and 13th harmonics were
*far* off from their supposed 12-tET representatives. But most
likely, he never did hear them, and his argument would thus
be based entirely on theoretical considerations. He admitted to
being less than conversant in the mathematics of tuning, so
he probably never did realize how inaccurate his ideas were.

And note, in passing, that Jacky did not accuse Schoenberg of
wanting to "destroy tonality", but only of wanting to "avoid" it.
I'm not exactly supporting Jacky's interpretation, because at
least in his "pantonal" music, what Schoenberg clearly wanted to
do was to *expand* tonality. I suppose tho that "avoid" is a
good way to characterize what he was doing after the adoption
of the "12-tone method"; it's consistent with the language in
Schoenberg's later essays. There was clearly a major change
in his thoughts about harmony during the relatively barren
(in terms of compositions) period around World War 1. IMO,
his biggest concern was that he needed some type of systematic
limitation on his compositional possibilities after he chucked
old-fashioned tonality, and serialism was it.

What I'm interested in exploring is: how might Schoenberg have
actually used the overtone series as the paradigm for his set
of limitations if he had continued to experiment with microtones?

Jacky:
http://www.egroups.com/message/tuning/17137

> Your [John deLaubenfels's] work stands as a pinnacle of
> excellence to me in the area of midi files/tuning, but I
> do not see it as the same thing as re-tuning Schoenberg.
> This becomes a much deeper philosophical undertaking

What must be kept very clear is that Schoenberg had a very open
mind about intonation until around 1912 or so. This was when
he first contacted Hauer (the other, earlier, inventor of a
12-tone method) and began formulating his serial method.
Also note that Schoenberg never became proficient at the piano
or any other fixed-tuning instrument; he was and always remained
a fretless-string player (mainly violin and cello), which I
think certainly influenced the way he thought about tuning.
So while I agree with Jacky that Schoenberg's wishes for his
serial music should be respected, I think there are a multitude
of tuning possibilities for his earlier pieces without piano
(much of this was for string ensemble or orchestra).

Note that right around the time that Schoenberg rejected microtones
was also when he invented _sprechstimme_. This was a vocal technique
which he continued to incorporate in many of his compositions for
the rest of his life; the earliest example is "Klaus the Fool's
Narrative" from the _Gurrielieder_ [1910] and the last (that I
know of) is _A Survivor from Warsaw_ [1947]. It's very interesting
to me that while he abandoned the use of microtones on *instruments*,
he preserved them on voices.

The points made by Christopher Bailey
http://www.egroups.com/message/tuning/17150

about the way Schoenberg may have wished to mix various different
implied tunings are also relevant. By knowing that 12-tET distorted
the true harmonic intervals and accepting it anyway, he knew that
his 12-tET chords were not accurate reflections of the harmonic-series
structures he purported to be using as his basis. I think he very
much was thinking in terms of letting nature be his guide but
reshaping what he found there into "artistically acceptable"
(i.e., 12-tET) terms. He was also very much interested in exploiting
the ambiguities involved in the tempered approximations to the
JI ratios.

(Thanks for asking, Jacky... it's helped me put together a lot of
my upcoming lecture! One of these days I'll also get around to
publishing my early essay "Similarities between Partch and Schoenberg
as Originators of New Harmonic Concepts" on the web; there you
may find the reasons why I feel so strongly about Schoenberg's
"missed opportunity" to become the first truly great modern
microtonal composer.)

---

P.S.

In the original post, Jacky wrote:

> (although I have been wondering how Joe Monzo's work would
> sound with a "house beat", and tuned to a 8000 tone non-octave
> scale). }: )

Yes, PLEASE! Retune anything of mine that you'd like... some
of my stuff would sound *great* done like this!!! ;-)

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

http://www.egroups.com/message/tuning/17165
>

>
> (Thanks for asking, Jacky... it's helped me put together a lot of
> my upcoming lecture! One of these days I'll also get around to
> publishing my early essay "Similarities between Partch and
Schoenberg
> as Originators of New Harmonic Concepts" on the web; there you
> may find the reasons why I feel so strongly about Schoenberg's
> "missed opportunity" to become the first truly great modern
> microtonal composer.)
>

Thanks, Monz, for the historical backup and definitions! I knew it
was coming. By the way, if any listers have missed Monz' great page
on the Second Vienna School and earlier Viennese trends in music,
please see:

http://www.ixpres.com/interval/monzo/schoenberg/Vienna1905.htm

By the way, this page has LOTS of new MIDI files, so it is now quite
a "multimedia" experience.

My own personal contention is that, had Schoenberg been living today,
he would be doing the most far-out wacky microtonal music imaginable,
probably stuff that many people would reject as non-music even on
this list. That is the way he was in the framework of his own time
...
_________ ______ ____ ___
Joseph Pehrson

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
>
> (Sorry to have taken so long to respond to this request...
>
> Please note emphatically that the compositions of Schoenberg's
> in which I'm most interested, and those which I'd like to retune,
> are *not* the later 12-tone serial pieces, but rather, the early
> tonal and "free atonality" ones.

Monz,

Thanks for this great explanation - it's all clear now.

>
> And note, in passing, that Jacky did not accuse Schoenberg of
> wanting to "destroy tonality", but only of wanting to "avoid" it.
> I'm not exactly supporting Jacky's interpretation, because at
> least in his "pantonal" music, what Schoenberg clearly wanted to
> do was to *expand* tonality. I suppose tho that "avoid" is a
> good way to characterize what he was doing after the adoption
> of the "12-tone method"; it's consistent with the language in
> Schoenberg's later essays.

I'm glad you were perceptive about what I was alluding to here, as I
do recall reading about this years ago, and was intending to point
singularly to his latter 12 tone serial works.

Scales with maximal tonal ambiguity, represent and interesting "polar
opposite" to scales which are constructed for maximizing the
consonance of intervals. I think it's good to be able to understand
and make use of both ends of the spectrum of complexity and
simplicity, which I perceive Dan Stearns has built his musical house
upon (expect reply to 13tet posts).

>
> What I'm interested in exploring is: how might Schoenberg have
> actually used the overtone series as the paradigm for his set
> of limitations if he had continued to experiment with microtones?

Let us all know how this research develops - it's very interesting,
and JdL's name "springs" to mind as the perfect person for helping to
realize this vision.

>
> So while I agree with Jacky that Schoenberg's wishes for his
> serial music should be respected, I think there are a multitude
> of tuning possibilities for his earlier pieces without piano
> (much of this was for string ensemble or orchestra).

I'm glad to hear that you feel this way.

>
> (Thanks for asking, Jacky... it's helped me put together a lot of
> my upcoming lecture! One of these days I'll also get around to
> publishing my early essay "Similarities between Partch and
Schoenberg
> as Originators of New Harmonic Concepts" on the web; there you
> may find the reasons why I feel so strongly about Schoenberg's
> "missed opportunity" to become the first truly great modern
> microtonal composer.)
>

Thanks to you for the deeply informative response and rationale for
your work.

Jacky Ligon

--- In tuning@egroups.com, "Joseph Pehrson" <pehrson@p...> wrote:
>
> had Schoenberg been living today,
> he would be doing the most far-out wacky microtonal music
imaginable,
> probably stuff that many people would reject as non-music even on
> this list.

Not me, if it's microtonal, I want to hear it!!!

Jacky Ligon

--- In tuning@egroups.com, ligonj@n... wrote:

http://www.egroups.com/message/tuning/17170

> --- In tuning@egroups.com, "Joseph Pehrson" <pehrson@p...> wrote:
> >
> > had Schoenberg been living today,
> > he would be doing the most far-out wacky microtonal music
> imaginable,
> > probably stuff that many people would reject as non-music even on
> > this list.
>
> Not me, if it's microtonal, I want to hear it!!!
>
>
> Jacky Ligon

Hi Jacky!

Well, of course, there's no proving this... just a hunch based on,
well, "wacky then, wacky now." For better or worse, that's not a
deprecation in my book, but an accolade!
_________ _____ ____ _
Joseph Pehrson

--- In tuning@egroups.com, "Joseph Pehrson" <pehrson@p...> wrote:

> --- In tuning@egroups.com, ligonj@n... wrote:
>
> http://www.egroups.com/message/tuning/17170
>
> > --- In tuning@egroups.com, "Joseph Pehrson" <pehrson@p...> wrote:
> > >
> > > had Schoenberg been living today,
> > > he would be doing the most far-out wacky microtonal
> > > music imaginable, probably stuff that many people would
> > > reject as non-music even on this list.
> >
> > Not me, if it's microtonal, I want to hear it!!!
> >
> >
> > Jacky Ligon
>
> Hi Jacky!
>
> Well, of course, there's no proving this... just a hunch based on,
> well, "wacky then, wacky now." For better or worse, that's not a
> deprecation in my book, but an accolade!
> _________ _____ ____ _
> Joseph Pehrson

Just thought I should point out that Schoenberg himself did
not consider that he was doing "wacky" things with his music.
He always considered his progressive techniques to be a
further *evolution* of those propogated by composers who
came before him (specifically, Austrian and German composers
since Bach).

Reading Schoenberg's correspondence to Busoni sheds a lot
of light on what was in his mind around 1908, when he made
the break away from tonality. He expressed a desire to
*liberate* his music from all preconceived structural notions,
and to simply write down the fantastic new sounds he was
hearing in his mind. His intention was for his compositions
to be as pure an *expression of feeling* as possible.

It's also worth pointing out that Schoenberg and his pupils
claim to have tried to resist the move to "atonality" as much
as possible. Probably the main reason they eventually went
ahead with it was the support Schoenberg got from Mahler.

As I try to portray in my webpage
http://www.ixpres.com/interval/monzo/schoenberg/Vienna1905.htm
this was a time in Vienna when audiences were largely very
conservative but the artists themselves were interested in
breaking down the old boundaries of their particular arts.

The paradoxical situation led to Schoenberg becoming infamous
for the "scandals" at his premieres, which gave him great
notoriety while still not enabling him to make a living as
a composer. He became quite bitter over the experience, and
retained that bitterness for the rest of his life.

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

http://www.egroups.com/message/tuning/17179

>
> Just thought I should point out that Schoenberg himself did
> not consider that he was doing "wacky" things with his music.
> He always considered his progressive techniques to be a
> further *evolution* of those propogated by composers who
> came before him (specifically, Austrian and German composers
> since Bach).
>

Hi Monz!

I guess my point was simply that Schoenberg was always one of the
MOST progressive of composers, and, had he lived today, he would most
probably STILL be very progressive in relation to his peers. For me,
that seems to indicate (perhaps a bias) that he would be heavily into
microtonality, or something of the kind... or perhaps getting off
into some kind of theatre or conceptual art the way Stockhausan
has... although that seems to me to be somewhat less likely...

________ ____ ___ __
Joseph Pehrson

Joseph Pehrson wrote,

<< My own personal contention is that, had Schoenberg been living
today, he would be doing the most far-out wacky microtonal music
imaginable, probably stuff that many people would reject as non-music
even on this list. That is the way he was in the framework of his own
time ... >>

Yeah, hard to say what would jolt and confound contemporary listeners
in an analogous fashion to say the way Shoenberg did in his time.

Could something as relatively simple as say a set of piano pieces come
along today and get everybody in a similar fuss? I rather doubt it,
but who knows, maybe...

I do know however from my own experience that really unusual
sonorities and the like of instruments with which I'm unfamiliar
generally get me pretty wide-eyed!

I'd tend to think that radically new resources -- i.e., new
instruments, new tunings, etc. -- are probably going to be needed to
yank contemporary listeners far enough out of their familiar
frameworks so as to cause much of a riot today...

I dunno though, not something I've really thought too much about;
perhaps something very subtle would be able to do the same today by
way of carrying the paradigm over to a very different perspective...
Any ideas out there?

--Dan Stearns

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

http://www.egroups.com/message/tuning/17185

>I do know however from my own experience that really unusual
>sonorities and the like of instruments with which I'm unfamiliar
generally get me pretty wide-eyed!

>I'd tend to think that radically new resources -- i.e., new
>instruments, new tunings, etc. -- are probably going to be needed to
>yank contemporary listeners far enough out of their familiar
>frameworks so as to cause much of a riot today...
>
> I dunno though, not something I've really thought too much about;
> perhaps something very subtle would be able to do the same today by
> way of carrying the paradigm over to a very different perspective...
> Any ideas out there?
>
> --Dan Stearns

This is pretty funny. Dan, maybe it's right "under your nose..."
It seems to me your OWN work might be able to fit this "shocking"
paradigm... at least *I* can't always understand all of it, which
MUST mean it's good!!!

________ ____ ___ _
Joseph Pehrson

Several months ago,

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

/tuning/topicId_17073.html#17165

> Schoenberg's big apparent error, as pointed out by Partch, was
> the inconsistency (in the Erlichian sense) of his mapping of
> 13-limit ratios to the 12-tET scale. I say "apparent" because
> Schoenberg had absolute pitch and certainly would have known,
> had he heard them, that the 7th, 11th and 13th harmonics were
> *far* off from their supposed 12-tET representatives. But most
> likely, he never did hear them, and his argument would thus
> be based entirely on theoretical considerations. He admitted to
> being less than conversant in the mathematics of tuning, so
> he probably never did realize how inaccurate his ideas were.

I feel compelled to revise part of this.

I just tuned a Knabe Console piano, and was struck by how
clearly, on this particular piano, many of the 7th harmonics
could be heard when playing the notes in the second octave of
the keyboard, and in some cases even the 11th came out clearly.
Partials even higher than that could be distinctly perceived
on some of the lower notes.

(I have noticed this effect before, but it was much more subtle.
The harmonics never rang out as clearly as on this Knabe.)

So, depending on the make and model of piano he had at his
disposal, it is entirely possible that Schoenberg was able to
clearly hear at least 11th harmonics, and possibly also 13ths.
He certainly would have heard how far they diverged in pitch
from their 12-tET approximations.

And there is good reason to believe that he did indeed explore
exactly this phenomenon. Schoenberg was also the first composer,
AFAIK, to make use of piano "harmonics". In the first of his
_3 Pieces for Piano_ op. 11, he requires the performer to hold
down the notes of a triad in the middle register of the piano
without sounding the strings, and then to play with a strong
attack a single very low note that would be a "fundamental" of
those pitches, thereby inducing the strings of the triad (with
the keys still held down) to sound, vibrating in sympathy with
the 4th, 5th, and 6th harmonics of the low note.

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

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

/tuning/topicId_17073.html#21887

> And there is good reason to believe that he did indeed explore
> exactly this phenomenon. Schoenberg was also the first composer,
> AFAIK, to make use of piano "harmonics". In the first of his
> _3 Pieces for Piano_ op. 11, he requires the performer to hold
> down the notes of a triad in the middle register of the piano
> without sounding the strings, and then to play with a strong
> attack a single very low note that would be a "fundamental" of
> those pitches, thereby inducing the strings of the triad (with
> the keys still held down) to sound, vibrating in sympathy with
> the 4th, 5th, and 6th harmonics of the low note.
>

Yes, of course! That's a very important part of this piece!

________ _____ ____ ____
Joseph Pehrson

In a message dated 4/30/01 2:01:24 PM, jpehrson@rcn.com writes:

<< > _3 Pieces for Piano_ op. 11, he requires the performer to hold
> down the notes of a triad in the middle register of the piano
> without sounding the strings, and then to play with a strong
> attack a single very low note that would be a "fundamental" of
> those pitches, thereby inducing the strings of the triad (with
> the keys still held down) to sound, vibrating in sympathy with
> the 4th, 5th, and 6th harmonics of the low note. >>

But remember that a much better demonstration of the 4:5:6 and beyond is done
on a piano in _reverse: Hold down a low key like a D (do not hold down any
pedals) and have someone strike the keys which hit strings resonating closest
to harmonic members of this pitch, hard and fast. The keys don't have to be
in the actual harmoinic register placement to cause the effect. One person
can do it by holding the D with a pencil and really smacking a chord as hard
and fast as possible starting on the octave above D F# A C D E F# G# A B.
The held D string blossoms. A grand with the lid open works best, obviously,
but any old piano will do - even one that's way "out of tune." Hours of fun.

Aaron