Re: Pythagorean tuning and Ives

Hello, there, and in response to certain recent remarks, I might say that
Pythagorean (3-limit just) intonation may be motivated by either melodic
or vertical factors, depending on the style. This raises the question:
what is the vertical style of the Ives pieces being discussed?

In tertian music, where major and minor thirds are stable and primary
concords (or "5-limit" music), Pythagorean intonation may, as suggested,
be seen as emphasizing melodic factors (narrow semitones at cadences, for
example) rather than vertical factors (ideally favoring pure thirds).
These two goals are "out of equilibrium" in a 5-limit system, so to speak.

In quintal/quartal harmony, however, Pythagorean tuning can serve both
melodic ideals (generously wide whole-tones at 9:8, narrow semitones at
256;243) and vertical directedness (thirds and sixths, serving in such a
musical language as "relatively concordant but unstable, have greater
acoustical complexity or tension).

Of course, either tertian or quintal/quartal music can have sonorities
reflecting the "overtone series": 2:3:4 and 4:6:9 are in this category
just as much as 4:5:6 or 10:12:15.

The argument might be made that 5-limit includes _more_ low-numbered
partials than 3-limit, and we might similarly argue that 7-limit is more
"based on the overtone series" than 5-limit, given its recognition of
something like 4:6:7 or 6:7:9 (the last 7-prime-limit, at least, although
9-odd-limit).

With Ives's music, I'd wonder about the harmony. If it's quintal/quartal,
with fifths and fourths as the main concords and maybe thirds and sixths
used as cadential intervals leading to such sonorities (as in medieval
practice), then Pythagorean could be serving vertical as well as melodic
interests. If it's tertian harmony, then the idea of a melodic rather than
vertical motivation could fit.

Most respectfully,

Margo Schulter
mschulter@value.net

[Margo Schulter:]
>This raises the question: what is the vertical style of the Ives
pieces being discussed?

The _Unanswered Question_ operates on three very distinct planes, and
unlike a lot of Ives, the distinct planes are very easy for most
anyone to discern and follow, as they are first and foremost
programmatic planes... but to a certain extent, the _Unanswered
Question_ could also be said to (vertically) stack and (horizontally)
layer three distinct planes, and as such I think that one would be
hard pressed to collapse the whole into some neatly refined analytical
(intonational) equilibrium.

Ives worked with an extremely broad and inclusive harmonic palette
(see _114 SONGS_), but most of Ives mature output (a phrase I truly
loathe, but one that is commonly used here, and as such would seem
orthographically charitable) seems (to me anyway) to consist of a
vertical style that is more (lacking a better term) 'narrative driven'
than anything else... and yet Ives (like most composers) certainly had
his particular harmonic sound, and often times the characteristic
stresses and equilibriums of certain stylistic bold stokes (the rag,
the march, the hymn, etc.) seem to operate as non-harmonically
inclined biographical (auto- and otherwise) projections into that
sound... in other words, while Ives grew up with the rag, and the
march, and understood how they should sound, he tended to use them
symbolically, and this could assume guises as diverse as a more or
less (rote) pictorial interjection (the _Country Band March_ in the
_Hawthorne_ movement of the _Concord_ for example), or as an extremely
integrated gesture (the rags in the _First Piano Sonata_ come to mind,
though the end movement of the second violin sonata is probably my
very favorite Ivesian hymn and rag collision).

So, while there *is* quantifiable harmonic data aplenty to analyze and
address here, I really think that you would be hard pressed to
effectively (i.e., meaningfully) measure Ives' "vertical style" in an
overly traditional, or historically (intonationally) contextual
manner... for though he was neither traditionally inclined, nor a
(self-conscious) redresser of the traditional in novel new harmonic
cloths; if firmly held to some such analytical measure, he would
probably appear to sit right in some uneasy place between the two...
And while I'm shuddering to think of what a perfectly lousy excuse all
of this must be for answering your question ("what is the vertical
style of the Ives pieces being discussed?"), perhaps it can at least
offer some inkling of the dilemmas that arise when one tries to
categorically square Ives with the question... personally I would
guess (and that's really all it is, a guess) that most any
straightforward analytical account of Ives "vertical style" is going
to have to end up sectioning off certain aggregates of stylistic
equilibriums, and as such will eventually windup addressing the whole
as some combining of these...

FWIW, my initial attraction to Ives was purely emotional (he struck a
nerve deep within me as a sort of Sigurd Olson of music), and had
nothing whatsoever to do with any technical particulars... so I have
no doubt that there are others on this list that are much better
suited (in orientation and demeanor) to address this (technical
particulars) than I, and perhaps (hopefully) they will be able to
offer a more advantageous, practical, and orderly answer to your
question.

Dan

[Dan Wolf:]
> I disagree with Dan Stearns here a bit. The chorale texture of the
strings in _The Unanswered Question_ is can be easily heard as a
single coherent unit, with a tonal, triadic character. A tuning in
either pythagorean (Johnny Reinhard's choice -- where the triadic
resolutions will never really resolve) or 5-limit JI (which I'd like
to hear someday) is completely plausible.

Actually, I still think that we more agree than disagree here, and
that I just haven't made myself clear enough, so I'll give it another
try... What I said was: "to a certain extent, the _Unanswered
Question_ could also be said to (vertically) stack and (horizontally)
layer three distinct planes, and as such I think that one would be
hard pressed to collapse the whole into some neatly refined analytical
(intonational) equilibrium," and that most any straightforward
analytical account of Ives "vertical style" is probably going to end
up sectioning off certain stylistic equilibriums, and eventually
windup addressing the whole as some combining of these... So yes while
it's easy enough to see the strings of the _Unanswered Question_ in a
couple of a "tonal, triadic" lights, I don't think that the winds and
trumpet can be so easily collapsed into the same.

I guess the problem with using the _Unanswered Question_ as a model of
an Ivesian poly-mosteveryting, is that the plains are all so distinct
and (programmatically) obvious (and the entire composite is also not
nearly as dense as most poly-mosteveryting Ives), so while it is much
harder for me to really see the distinct planes of the _Unanswered
Question_ as a singe horizontally layered entity, I do think that this
is more the exception than the norm with Ives, and that the multiple
layers (even if quite clear and distinct) in Ives generally tend to
coalesce into a single Ivesian sound (and here I'm specifically
meaning a vertical sound).

So as I said before, there certainly *is* quantifiable harmonic data
aplenty here to analyze and address, but I don't think that you will
be able to effectively (i.e., meaningfully) measure Ives' "vertical
style" by collapsing the whole of it into any one quantifiable
harmonic (or vertical) paradigms.

Dan