RE: [tuning] Re: definition of COFT

Monz wrote,

>Hmmm... unless I'm misunderstanding something, you might want
>to rethink some of the absolutes you're seeing here. It's
>apparent to me that you're only considering 12-note fixed tunings.
>A fixed tuning with many more notes can certainly lead to drift.
>I'm thinking here of, say, 53-tET (maybe even 31-tET?).

>The 53-tET step-size is a 'mean comma' that gives a good
>approximation of both the Pythagorean and syntonic commas, and
>I could forsee lots of drift. Feedback appreciated.

Monz, in this context, fixed means "only one pitch per pitch-class" or
better yet, "only one pitch per notated note-name". So if you're playing a
diatonic piece in 53-tET, 53-tET would not be considered a fixed tuning, if
you use both degree 8 and degree 9 for the note "D".

Monz wrote,

>Hmmm... unless I'm misunderstanding something, you might want
>to rethink some of the absolutes you're seeing here. It's
>apparent to me that you're only considering 12-note fixed tunings.

Although it is true that John's program so far only handles 12-note fixed
tunings, there is nothing in his concept that prevents it from being adapted
to tunings with more notes, AS LONG AS ALL THE NOTES ARE NOTATED
DIFFERENTLY. The only reason it stops at 12 now is because all the MIDI
files he's been retuning have only 12 pitch classes, and contain no way of
distinguishing , say, G# from Ab, even if the composer originally made these
distinctions in the score. If MIDI files did contain these distinctions,
John would calculate COFTs with _different_ values for G# and Ab, and hence
fixed tunings with more than 12 notes. I'll let John expound on enhancements
to his program that he may forsee for the future . . .

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> http://www.egroups.com/message/tuning/12678
>
> Monz wrote,
>
> > Hmmm... unless I'm misunderstanding something, you might want
> > to rethink some of the absolutes you're seeing here. It's
> > apparent to me that you're only considering 12-note fixed tunings.
>
> Although it is true that John's program so far only handles
> 12-note fixed tunings, there is nothing in his concept that
> prevents it from being adapted to tunings with more notes,
> AS LONG AS ALL THE NOTES ARE NOTATED DIFFERENTLY. The only
> reason it stops at 12 now is because all the MIDI files he's been
> retuning have only 12 pitch classes, and contain no way of
> distinguishing , say, G# from Ab, even if the composer originally
> made these distinctions in the score. If MIDI files did contain
> these distinctions, John would calculate COFTs with _different_
> values for G# and Ab, and hence fixed tunings with more than
> 12 notes. I'll let John expound on enhancements to his program
> that he may forsee for the future . . .

Thanks for the clarification, Paul; makes perfect sense. I was
thinking 'theoretically' without considering the practical (MIDI)
limitations against which John was bumping.

This brings to mind another comment I had: we discussed the
Maneri/VanDuyne 72-tET book a little, with you and Daniel Wolf
(from an old post I dredged up) casting doubts against its
theoretical rigor. While I can't say I disagree with either
of you, I have worked thru the book (at least a bit) and see
it as an eminently useful *ear-training* guide. I think perhaps
the strongest criticism I can level against the book is that
it carries the title ('Peliminary Studies in the Virtual
Pitch-continuum), while aptly vague, could have been more
meaningful: it should be viewed as a *practical* ear-training
manual, and not as any kind of theoretical exegis.

The reason I go into this in such depth is that I was musing on
the old difference between 'theoretical' and 'practical', the
dialectic between which seems to have reached a head in the German
figured-bass treatises of the 1700s. Most of my tuning research
covers periods before this, and this particular area is one that
I haven't really studied in depth, but I am aware of this
distinction and thought I'd mention it here in hopes that someone
more knowledgeable, perhaps Margo?, could say something about it.
(Where's Daniel Wolf when you really need him?...)

-monz
http://www.ixpres.com/interval/monzo/homepage.html

seems to h

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

http://www.egroups.com/message/tuning/12679

>
> This brings to mind another comment I had: we discussed the
> Maneri/VanDuyne 72-tET book a little, with you and Daniel Wolf
> (from an old post I dredged up) casting doubts against its
> theoretical rigor. While I can't say I disagree with either
> of you, I have worked thru the book (at least a bit) and see
> it as an eminently useful *ear-training* guide. I think perhaps
> the strongest criticism I can level against the book is that
> it carries the title ('Peliminary Studies in the Virtual
> Pitch-continuum), while aptly vague, could have been more
> meaningful: it should be viewed as a *practical* ear-training
> manual, and not as any kind of theoretical exegis.
>

Thank you so very much, Monz, for sending this book to me. I only
have had time, of late, to glimpse an overview of it... but it surely
seems like a "practicul" compendium for a new kind of ear training.
This is significant, since SOME KIND of ear training is obviously
going to be necessary if we are to expect precision in these new
realms.

Thanks again!

joealso
_______ ____ __ __
Joseph Pehrson

Joseph -- the 31-tET model only makes sense if the composer _never_ used
enharmonic equivalent notation. For Handel, it certainly makes sense, since
G# and Ab were different notes for him. For Mozart, it still makes sense.
For Schubert, as we know, it does not -- his world was clearly a 12-tone
one. Do you really think it would make sense to distinguish enharmonically
equivalent notes for any Schoenberg piece? That certainly goes against
Schoenberg's later point of view, for which he is most famous.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/12730

> Joseph -- the 31-tET model only makes sense if the composer _never_
used enharmonic equivalent notation. For Handel, it certainly makes
sense, since G# and Ab were different notes for him. For Mozart, it
still makes sense.
> For Schubert, as we know, it does not -- his world was clearly a
12-tone one. Do you really think it would make sense to distinguish
enharmonically equivalent notes for any Schoenberg piece? That
certainly goes against
> Schoenberg's later point of view, for which he is most famous.

Hmmm. Well, no, we're pretty much stuck with 12 pitch classes... But
would it make any sense to try to tune Schoenberg sonorities in just
intonation by a "dynamic" system with 12 moving pitch classes.

Would that mean anything... or are the harmonies so based on extended
12-tET that such a transcription would be meaningless.

I was thinking more of very early works like Transfigured Night or
the String Quartet #2...

_________ ____ __ __ _
Joseph Pehrson

Joseph wrote,

>Hmmm. Well, no, we're pretty much stuck with 12 pitch classes... But
>would it make any sense to try to tune Schoenberg sonorities in just
>intonation by a "dynamic" system with 12 moving pitch classes.

>Would that mean anything... or are the harmonies so based on extended
>12-tET that such a transcription would be meaningless.

>I was thinking more of very early works like Transfigured Night or
>the String Quartet #2...

Certainly, it would make a lot of sense to throw these pieces at John
deLaubenfels's adaptive tuning programs, both 5-limit and 7-limit. Some
chords might try to come out in JI, while many others (like the CEGAD
example I love to remind people of) are inherently tempered in some way, and
a few chords, like augmented triads and diminished seventh chords, are in
certain respects ideal in 12-tET. John has already retuned pieces from the
Romantic period so the difference here would only be one of degree.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> http://www.egroups.com/message/tuning/12730
>
> Joseph -- the 31-tET model only makes sense if the composer
> _never_ used enharmonic equivalent notation. For Handel, it
> certainly makes sense, since G# and Ab were different notes for
> him. For Mozart, it still makes sense. For Schubert, as we know,
> it does not -- his world was clearly a 12-tone one. Do you really
> think it would make sense to distinguish enharmonically
> equivalent notes for any Schoenberg piece? That certainly goes
> against Schoenberg's later point of view, for which he is most
> famous.

Paul, you make good points here about Handel, Schubert, and
Schoenberg. But I have to express an opinon that's totally
contrary to yours on this one (of course, we've been here before,
so I'll keep it as brief as I can). This is a case where we agree
to disagree. :)

Just as jazz musicians see no harm in taking any tune and changing
it any degree up to and including beyond recognition, I see no
reason why no composer's music can't be used in a retuning
experiment.

I will qualify my opinion with the restriction that it should
be clearly labelled as a retuning experiment by the person doing
the retuning. Keep in mind that _a capella_ vocal ensembles
and unaccompanied string-quartets routinely perform music
nominally written in 12-tET in a quasi-JI without labelling.

In the particular case of Schoenberg, my opinion is certainly
harder to defend, because he spent hours coaching his string
quartet (the Kolisch Quartet) to match their intonation to a
strctly-12-tET piano, and his letters clearly state the need
for trained musicians playing his music to restrain their
tendency to tune intervals 'purely' (nature) but rather instead
make them 12-tET (art).

But the evidence for these beliefs and actions appears rather
late in Schoenberg's life (from his 50s on), and his entire
early practical musical experience was as a string player
playing chamber music, which, in tandem with his apparently
phenomenal sense of hearing and pitch (just like Partch),
argues (IMO) that he would have envisioned harmony in JI terms
in his early composing career, say 1890-1904 or so. It's
important to remember that except for lessons with Zemlinsky,
Schoenberg prided himself on being entirely self-taught.

I see 1905 as the crucial year when the Viennese and Parisian
composers, and Ives in New York, all began to envision a harmony
that worked on the same principles as the old tonal harmony,
but without a feeling of key-center. This would be the moment
when the 12-tET scale comes into its own as a distinctive
harmonic basis, as Schoenberg wrote about it in his _Harmonielehre_
in 1910-11.

Anyway, now I'm rambling on longer than I wanted. Anyone interested
in more of this can get it at _A Century of New Music in Vienna_:
http://www.ixpres.com/interval/monzo/schoenberg/Vienna1905.htm

-monz
http://www.ixpres.com/interval/monzo/homepage.html

Monz, you missed my point. I did not argue that Schoenberg wanted strict
12-tET, or that he wouldn't have wanted chords in JI, in his pre-serial
music. I just was arguing that treating the accidentals in this music as if
they came from 31-tET, with G# lower than Ab, etc., makes less sense then
treating them as enharmonic equivalents initially, and then trying to tune
chords adaptively toward JI from there (as is the case with Schubert as
well); while in the music of Handel or Mozart, there are distinct
advantages, when going for an adaptive JI rendition, of treating G# and Ab
as distinct starting points, with no "springs" tying them to a common pitch.
Read the exchange again.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> http://www.egroups.com/message/tuning/12754
>
> Monz, you missed my point. I did not argue that Schoenberg wanted
> strict 12-tET, or that he wouldn't have wanted chords in JI, in
> his pre-serial music. I just was arguing that treating the
> accidentals in this music as if they came from 31-tET, with G#
> lower than Ab, etc., makes less sense then treating them as
> enharmonic equivalents initially, and then trying to tune chords
> adaptively toward JI from there (as is the case with Schubert as
> well); while in the music of Handel or Mozart, there are distinct
> advantages, when going for an adaptive JI rendition, of treating
> G# and Ab as distinct starting points, with no "springs" tying
> them to a common pitch. Read the exchange again.

OK, gotcha. Thanks for the clarification.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

I wrote,

>>Certainly, it would make a lot of sense to throw these pieces at John
>>deLaubenfels's adaptive tuning programs, both 5-limit and 7-limit.

John wrote,

>Why, Paul! Can it be that you're "softening on seven"? My impression
>has been that you pretty much consider a 7-limit treatment of pieces
>originally written in 12-tET to be inappropriate, or am I mistaken?

You are mistaken -- read the exchanges again. It is for Baroque and
Classical-period music that I found a 7-limit treatment inappropriate. For
Schoenberg, like Wagner or Stravinsky, I'd say go for it!

>Right - as you know I aim for 12-tET for the examples you've given,
>including any chord with more than 3 fifths in a row (CEGAD has FIVE

um, I count four

>fifths in a row, so is doubly impossible to tune "correctly").

Why not aim for a mild meantone as in the optimal tunings I found for these
chain-of-fifth chords?