Werntz at PNM

I have not read Julia Werntz' dissertation, but I have read her article in
PNM. I am going to give a critique, but it is only my view, as th earticle
is hers. It is lengthy, but I hope that the length is justified by the
material under discussion.

First of all, her article is polemical. I am surprised that it managed to be
peer-reviewed into PNM, but there we go. Controversy is something that has
to be courted. I am no stranger to that. Still, if controversial statements
are allowed to be made, equally controversial statements may be made in
reply. (No offence to those who chose not to post, but I feel that even the
article in PNM deserves rougher treatment than some think necessary - let us
not toss something in the bin lightly when it should be hurled with great
force.)

Let us take the 'simple, essential truths' and see what we make of them:

'whereas the pure intervals are the correct ones, are truly consonant, and
must be better to listen to.'

Werntz states this as a preamble to the much-trumpeted view that in some way
just intervals (in the sense of ratios of small integers), are better than
others and that all music written in an equal temperament is all 'unjust'
music and the misjustice has been done to music through the usage of it. Of
course, she decides that pursuit of just intervals is a misnomer as they can
be just as dissonant. I like the fact that she chooses the high prime 13/8
as a 'just minor sixth' rather than the more usual 8/5, which is a proper
just minor sixth. Music is about consonance and dissonance, about the
interest and qualities of one against the interest and qualities of the
other. This does not mean that just intonation is about the abolition of
dissonance, but rather that just intervals achieve a greater purity of
dissonance: we behold the massifs of dissonance free from the fog of
temperament, and can appreciate their qualities better.

Worse still, that paragon of temperament, the piano is used to listen to
intervals that in their context, with the instrument that sounds them, has
little to do with her argument. In addition, the very inharmonicity of this
instrument is bypassed, without regard for the 'more faint tenth, twentieth,
etc. partials.' And just how far from 10/8 or 20/16 they may be (and often
are).

Werntz assumes that the 'flaws' of temperament as named by JI musicians,
lies in the temperament - which is incorrect - and berates these same
people for engendering in composers a /dread of complex ratios/ due to their
'feared incorrectness' that would lead to 'restricting oneself to pure
triads or sevenths'. The flaw in temperament is not in any one direction,
not in the ratios, but in the /inexpressible relationships/ that inform
temperament. We cannot obtain a proper interval, and must make do with a
substitute; in 5-limit harmony we can and /must/ hear the augmented 6th as
such, but temperament tempers this and other intervals out, and levels the
augmented and the diminished, until they are the same. Their color is
sacrificed, so to speak.

Werntz argues that 'musical context has enormous significance concerning our
perception of intervals as consonant or dissonant'. While this may be true
for the example she provides, it does not resolve the fact that the interval
is still the same size. The ear skips or 'leaps' as Partch puts it, between
the real and the imagined. The context of her example is not of the G sharp
to B, but of the intervals C to G sharp and C to B which are fundamental to
understanding the 'dissonance' in the C minor harmonic scale. We /hear/ the
keynote, and it is this that informs the relationships. As for the 'jarring'
octaves and fifths, then this is based on comparative dissonance: how many
of us are struck by the dissonant qualities of an octave if placed in the
context of say, Webern? This has nothing to do with intervals in the raw,
but rather that the ear expects one thing: a minor ninth or a major seventh,
and is 'jarred' by what is unexpected: the octave, and so the tension flow
collapses. This does not make the interval dissonant, but rather it is
'unwanted', and undesirables are always ugly and are thus musically
'dissonant'

Then we have the passage, which I will need to quote at length:

'it almost goes without saying that just intonation, if truly adhered to in
order to maintain the indisputably simple consonant harmonic language that
is the credo, also limits the composer /stylistically/ to a sparse, simple
triadic idiom'

I wonder where 11/8 and 7/4 fit into triads? or where the most beautiful and
fantastic sonorities that can be made from other ratios, or where a vast
proportion of non-harmonic but nevertheless *justly tuned* monodic music
fits into this 'akkordweltanschauung'?

And then we find, straight away: 'accustomed to playing diatonic music in
equal temperament'. I doubt this, and the 'colouristic inflections', which
are if nothing else /an attempt to render the intervals more faithfully/. A
purer intonation, and more obviously a just one. Perhaps everyone only plays
keyboards these days, or the Werntz assumes this.

And then there is '[just intonation's] origin lies in extramusical
ideologies' The extra-musical ideologies of the monochord? The ideologies of
the human voice? I find it incredible that someone would find ideology in
these simple relationships, the medievalists aside, who transplanted an
ideology onto music and not the other way round.

To follow: 'incorrect triad tunings'. This defies commentary, but I will
try. Werntz assumes that the denunciation of 20th century music by Just
intonationalists is a a consequence of the rejection of the just triad. In
other words, because the triad is out of tune, JI people state that all 20th
C music is a failure. That's a bit like saying that the Mona Lisa is not
great because Leonardo used the wrong shade of green. Great art uses the
materials it has, and greater art fashions new materials for itself. How
else do we interpret the rise of the richness of harmony in Bach but due to
the fashioning of the new materials of chromatic harmony, forgotten since
the days of d'India and Marenzio.

Next comes 'they have emphasised those higher partials which sound the most
unusual to our twelve-note, equal-tempered ears'
!!!!!!!! <please forgive this exclamation>

Just those intervals which we are /denied/ by the use of equal-temperament!

If we are to go about 'adding pitches', then surely, what better place to
start, but with those sounds that are simplest in one sense, yet
/unfamiliar/. These new sounds are 'interesting', without resorting to
artificial divisions of the musical space that Werntz suggests.

As for 'making pieces interesting', I can say for certain that some
microtonal ET scales make for very interesting music, but that, ultimately,
is not what we seek: we are not all 'dissonance chasers', nor do we find the
constant playing of 'new' sounds interesting, but rather we prefer the
contrast, the mixing of the startling with the commonplace, of the stark
with the florid or with plainness. These are the components of music, and
too often temperaments of some kinds are eternally 'interesting' but offer
no contrast. This is my personal definition of 'Tonality': to contrast and
to blend, to oppose and to combine. Whether it is tones to make chords or
thematic or melodic material (tunes if you wish), or chords to make phrases,
or phrases to make forms.

Now we come to the Added Pitches section:

'The choice to add pitches appears to be in general motivated by the
stimulating sound of the new intervallic relationships'

Back to the formula of 'excitement at every tone' again, and yet, what scale
is proposed: 72ET. The one that quite a number of composers and theorists
and performers like because it approximates well to JI. /That it comes
closer to the truth/, perhaps?

Then Werntz quotes Perle in Serial Composition and Atonality, in one of his
notes (in Werntz, p206, n40): 'The "rightness" of a note depends not upon
its possible containment within a preestablished harmonic unit, as it does
in tonality, but upon larger compositional factors whose meaning must be
discovered within the work itself'

Yet, Perle continues, in the conclusion to Twelve-Tone Tonality, p162:

'As in modern poetry, "reflexive reference" is entirely relevant and
sufficient only and explanation of an ideal, rather than an actual, musical
condition. ... in atonal music ... there may be normative and
precompositional, as well as reflexive, referential elements.'

Therefore, as the remainder of Ch 30 from Twelve-Tone Tonality goes on to
show, music always asserts an order, a 'Tonality', independent of the
context of the tones. And so it is with equal temperaments, wherever their
relationships have mathematical or acoustical resonances, through cycles of
intervals or through correspondences with other structures existing
independently of music itself. Schoenberg hoped that his serial 'Method'
would 'replace those structural differentiations provided formerly by tonal
harmonies', yet it cannot do this, nor can it be reflexive, as Babbitt and
many others, including Perle, have proved.

Even so, these preestablished relationships are not often acoustic in
origin: c.f. Chopin Prelude in Eb, which proves that 12ET has gained
functional use through this non-diatonic, yet structural use of its scale.

But I digress (!)

Werntz asserts that '/the smaller microintervals must constitute most of the
linear material/' [her italics], yet, with this approach, the very
independence of the tones is sacrificed. Instead, we hear a tone, and a
kaleidoscopic variation of it. No system based on arbitrary combinations of
tones from a serially treated microtonal set, that restricts itself to such
tiny melodic movement, can surely be said to be free. If something is
controlling the usage of the tones, the approach, then that something is the
tonality, not the set of tones. You might as well give up on the set, and
instead concentrate on the small intervals themselves. Another failing of
this schizophrenic approach to microtonality is that it makes no attempt to
understand its materials, the intervals themselves. They are merely 'quanta'
without colour or function, applicable in any direction or any combination
(so would a serial approach demand), and yet the examples all show a
completely thematic, linear, small intervalled approach, which, again from
the examples, I see more and more a need for registral space-filling. Which
is not 'composition' but merely a fascination for a certain kind of sound
without regard to the larger possibilities, or its integrated use.

Maneri's Microtonalism

Is tonal. Is definitely tonal, as it has 'stepwise progressions and a
balanced and artful contour'. I also like the clean, distilled sound of
Webern, and even Sibelius likes major sevenths, as does Janacek, as does
Mahler. As do a great many other composers, whose music, in spite of the
failure to use "stepwise" progressions, is still 'artful'.

The small intervals are, in Manieri's work, again used in a space-filling
way, and seem to be stylistic rather than 'theoretic', of which the latter
must be the focus of any study of new materials in music. All style must be
stripped from them, else we confuse style with correctness.

Werntz Microtonalism

Is serial. And therefore avails itself of serial techniques. Her 'String
Trio with Homage to Chopin" is clearly composed with regard to her view that
pitches are 'innocent', and are /not/ 'related to each other', and yet it is
these relationships which are the essence of music, the inherent
relationships of the tone that form tonality. You cannot have innocent tones
and still join them together in 'realtionships' and 'relate them only to
each other.' If we must do without innocence, then we must do with a
'marriage' instead, and enjoy the relationships of the tones as they exist,
not as we would wish them to be. Incidentally, do you not find that 'with
Homage to Chopin', extraneous, like 'Hawaiian with side salad' or 'Steak
with onion rings'? Is the music a dish, to which we can add side orders? If
the Chopin is integral, then the title must be integral, lest it be tacked
on and can therefore be easily 'untacked', with no loss to art nor
enjoyment. If we are to make allusion, then best we allow the listener to
recognize it for themselves, than be directed, in neon, to something, whose
whole ethos is, by its very nature, outside that of the music which seeks
'Homage'?

As for the remainder of Werntz article, Schoenberg again states it best:
'But aesthetics alleges that it has discovered eternal laws' (Harmonielehre,
Trans Roy Carter, n, p34)

In conclusion

I find nothing in Werntz to suggest that her 'rudimentary' 'issues' are
pertinent to microtonalism. All we have is one composer's response to an
aesthetic, a response which itself is also an aesthetic. The whole point of
microtonalism is not the 'new notes' nor the 'purer relationships'; for in
time we will seek to make the former 'old' and the latter 'impure,' and both
with the instrument of temperament. The need for these extra notes is in the
more sophisticated relationships that can be formed, and the deeper
understanding of the 'nature of the tone' that results. We must seek to
bring forth 'only that which is in the notes', as Mahler says. All we need
to do now, is discover /which notes/.

MG

Mark,

I found that I will have to go to one of the university libraries, as today I went to the central City library and they ended PNM subscription 20 years ago. So... I have not yet read the article.

But!

Thank you for a reasoned and measured response. You have covered a lot of ground, and I look forward to reading the article, with the caveat that you have already confirmed many of my suspicions.

And I'm not suspicious by nature!

Thanks for your review,
Cheers,
Jon

--- In tuning@y..., Mark Gould <mark.gould@a...> wrote:

> This does not mean that just intonation is about the abolition of
> dissonance, but rather that just intervals achieve a greater purity
of
> dissonance: we behold the massifs of dissonance free from the fog of
> temperament, and can appreciate their qualities better.

i'd like to understand better your view on this (perhaps to debate
you on it). can you elaborate with some examples?

> Werntz assumes that the 'flaws' of temperament as named by JI
musicians,
> lies in the temperament - which is incorrect - and berates these
same
> people for engendering in composers a /dread of complex ratios/ due
to their
> 'feared incorrectness' that would lead to 'restricting oneself to
pure
> triads or sevenths'. The flaw in temperament is not in any one
direction,
> not in the ratios, but in the /inexpressible relationships/ that
inform
> temperament. We cannot obtain a proper interval, and must make do
with a
> substitute; in 5-limit harmony we can and /must/ hear the augmented
6th as
> such, but temperament tempers this and other intervals out, and
levels the
> augmented and the diminished, until they are the same. Their color
is
> sacrificed, so to speak.

they are not the same in meantone temperament, for example. so this
may be a flaw of 12-equal, but i wouldn't call it a flaw in
temperament . . .

> Werntz argues that 'musical context has enormous significance
concerning our
> perception of intervals as consonant or dissonant'. While this may
be true
> for the example she provides, it does not resolve the fact that the
interval
> is still the same size. The ear skips or 'leaps' as Partch puts it,
between
> the real and the imagined. The context of her example is not of the
G sharp
> to B, but of the intervals C to G sharp and C to B which are
fundamental to
> understanding the 'dissonance' in the C minor harmonic scale.

i read the 24-page summary on the web url that was provided. i didn't
see the intervals formed with C figuring in this argument in any way.
but since you say 'example', i must assume that the perspectives
article contains one with said intervals. can you reproduce it for us?

> Then we have the passage, which I will need to quote at length:
>
> 'it almost goes without saying that just intonation, if truly
adhered to in
> order to maintain the indisputably simple consonant harmonic
language that
> is the credo, also limits the composer /stylistically/ to a sparse,
simple
> triadic idiom'

what bothered me in the 24-page synopsis was this kind of 'straw man'
portrayal of 'just intonation' as a philosophy with the tenets Werntz
says it has: 'just intonation says' this, 'just intonation says'
that . . . these tenets are almost set up to contradict one another
from the start . . . in fairness to julia, i have seen similar
presentations of 'just intonation' as a philosophy with untenable
tenets in many places, by its proponents . . . but is there no room
for a more reasoned, sensible approach to these issues? or must one
throw out the baby with the bathwater? i tend to think not -- hence,
my posts here for the last six years, which mostly reflect an attempt
to think more carefully out of a kind of 'weak just intonation'
philosophy . . .

> And then we find, straight away: 'accustomed to playing diatonic
music in
> equal temperament'.

what was the context?

> I doubt this, and the 'colouristic inflections', which
> are if nothing else /an attempt to render the intervals more
faithfully/. A
> purer intonation, and more obviously a just one.

there seems to be too much evidence against this interpretation in
the scientific studies of performers' intonation -- and think of
pablo casals' instructions, for example -- though one can of course
assert with bob wendell that those (the majority?) who inflect
contrary to the demands of purer intonation are merely poorer
musicians . . . i'd prefer to simply draw stylistic distinctions
where appropriate without declaring one approach superior to
another . . .

> And then there is '[just intonation's] origin lies in extramusical
> ideologies' The extra-musical ideologies of the monochord?

hmm . . . what exactly is your argument here?

> The ideologies of
> the human voice? I find it incredible that someone would find
ideology in
> these simple relationships,

a lot of people find a lot of things incredible. one could read the
opinions of many an intelligent music theorist and find the exact
opposite opinion (opposite from you, mark, it seems) about simple
ratios and the like (how about balzano, for example) . . . though if
you flesh out both the original comment in Werntz' article and your
response to it, i'd be happy to indulge this more directly . . .

> the medievalists aside, who transplanted an
> ideology onto music and not the other way round.

clarification please?

> To follow: 'incorrect triad tunings'. This defies commentary, but I
will
> try. Werntz assumes that the denunciation of 20th century music by
Just
> intonationalists is a a consequence of the rejection of the just
triad.

just intonationalists rejected the just triad? hmm . . .

> In
> other words, because the triad is out of tune, JI people state that
all 20th
> C music is a failure.

still lost . . .

> How
> else do we interpret the rise of the richness of harmony in Bach
but due to
> the fashioning of the new materials of chromatic harmony, forgotten
since
> the days of d'India and Marenzio.

this could be a paper onto itself . . . care to indulge in a 'gentle
introduction' to the issues you're referring to here? as it is, i'm
in the dark . . .

> Next comes 'they have emphasised those higher partials which sound
the most
> unusual to our twelve-note, equal-tempered ears'
> !!!!!!!! <please forgive this exclamation>
>
> Just those intervals which we are /denied/ by the use of equal-
temperament!
>
> If we are to go about 'adding pitches', then surely, what better
place to
> start, but with those sounds that are simplest in one sense, yet
> /unfamiliar/. These new sounds are 'interesting',

well, mark, now you're speaking my language. if intervals like 7:6
are unfamiliar, novel, yet retain some of the qualities we expect
from the basic constructing intervals of the harmonies of the music
we know and love, then what better place to start? let's try to find
some melodically cogent structures that are conducive to these novel
harmonic intervals!! there is no restriction of artistic choice
implied in this act -- only a *directing* of one's *own* self-(re)-
training toward, and ultimately, an *informing* of one's capacities
for free artistic choice *of*, the sonorities that appeal most to
one's own ears. is that the pro-academic view to counter to
Werntz' "anti-academic" one? maybe, but i know of no academy that
currently proceeds in such a direction!

> As for 'making pieces interesting', I can say for certain that some
> microtonal ET scales make for very interesting music, but that,
ultimately,
> is not what we seek:

you can say for certain what 'we' seek? who is 'we'?

> we are not all 'dissonance chasers', nor do we find the
> constant playing of 'new' sounds interesting, but rather we prefer
the
> contrast, the mixing of the startling with the commonplace, of the
stark
> with the florid or with plainness.

well, i'd include myself in this 'we' then . . . but microtonal ET
scales such as 72-equal don't allow for these??

> These are the components of music, and
> too often temperaments of some kinds are eternally 'interesting'
but offer
> no contrast.

can you give some examples of temperaments that offer no contrast?

> Now we come to the Added Pitches section:
>
> 'The choice to add pitches appears to be in general motivated by the
> stimulating sound of the new intervallic relationships'
>
> Back to the formula of 'excitement at every tone' again, and yet,
what scale
> is proposed: 72ET. The one that quite a number of composers and
theorists
> and performers like because it approximates well to JI. /That it
comes
> closer to the truth/, perhaps?

at the risk of having a faulty memory (again), i'd like to report
that when i spoke with julia, she said there was no a priori reason
that any other arbitrary equal division of the tone wouldn't work as
well for her as twelfthtones . . . (didn't pursue the question of
whether the 'whole-tone' itself is sacred) . . . again, i haven't
read the _perspectives_ article, and i'm not quite sure what your
point is, but going by the best of my understanding, might you not be
being a little unfair here?

> Even so, these preestablished relationships are not often acoustic
in
> origin: c.f. Chopin Prelude in Eb, which proves that 12ET has gained
> functional use through this non-diatonic, yet structural use of its
scale.
>
> But I digress (!)

please do . . . i'd like to hear more about your views on this piece,
perhaps on metatuning . . .

> I find nothing in Werntz to suggest that her 'rudimentary' 'issues'
are
> pertinent to microtonalism. All we have is one composer's response
to an
> aesthetic, a response which itself is also an aesthetic.

well that's the whole crux of the matter. julia hears music in a
certain way, which leads her to make music in a certain way, while
thinking less of certain other approaches. is this not inescapably
true of all musicians? hopefully, her articles will be helpful for
those beginning along a similar aesthetic path as that she has tread.
personally, the idea of making melodies out of really small
intervals, without tonal harmonic support, is about as far from my
own musical desiderata as i can imagine. but live and let live!

> The whole point of
> microtonalism is not the 'new notes' nor the 'purer relationships';
for in
> time we will seek to make the former 'old' and the latter 'impure,'
and both
> with the instrument of temperament.

again, who is 'we'? i'm mystified -- earlier, temperament was flawed;
now, it's inevitable?

finally, there are lots of picky technical troubles (for example, on
details of partch's theory) i had with the 24-page summary, but i see
no reason to post these here rather than taking them up with julia in
e-mail . . .

Paul,

Just to comment on one small section of your response:

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> well that's the whole crux of the matter. julia hears music in a
> certain way, which leads her to make music in a certain way, while
> thinking less of certain other approaches. is this not inescapably
> true of all musicians?

No, it is not inescapably true. In fact, you yourself say at the end of your comment "but live and let live!", indicating that you are happy to see others do thing their way. The opening paragraph of her paper stated quite clearly that she did not believe either just intonation or exotic tunings provided convincing rationales for microtonal composition; she obviously would like to see music made in fewer ways than people like to make it.

> hopefully, her articles will be helpful for
> those beginning along a similar aesthetic path as that she has
> tread.

Promoting her own aesthetic while denigrating others through wrong information and differences in personal preference? I'd rather people be shown a myriad of possibilities without the pejoratives.

Cheers,
Jon