<p class="MsoNormal">Dear all,<br></p><p class="MsoNormal"><br></p><p class="MsoNormal">Thanks to Dr. Ninov for the opportunity to reflect on roman
numeral systems. In thinking about this it seems useful to abstract outside of
the purely musical realm to consider how categories and labels are used in
teaching/learning. I feel that two general principles are useful here. </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><b>The first is the
nature of the mapping</b>. All acts of categorization, it seems to me, involve
a mapping from a larger number of phenomena to a smaller (or, in the trivial
case, equal) number of groups of them. How small should this number of groups
be? If there were one group, the categorization would be devoid of value.
(E.g., all notes fit into the category of “music.” This doesn’t get us very
far!) If there were as many groups as there were phenomena, similarly there
would be no gain to categorizing. Obviously there must be a middleground. What
is the ideal setting—the “zoom” or “scope”—for this middleground?</p><p class="MsoNormal"><br></p><p class="MsoNormal"><font>Lewin, in his phenomenology article of 1986, describes a
chord played “fortissimo and staccato,” lasting “about third of a second,” and
containing the following notes<span>: “flutes on G6 and B</span><span style="font-family:Maestro"></span><span><span>b</span>5; oboes on E</span><span>b</span><span>5; clarinets on E</span><span>b</span><span>5 and G4; bassoons on E</span><span>b</span><span>4 and E</span><span>b</span><span>3; horns on G4 and E</span><span>b</span><span>4; trumpets on E</span><span>b</span><span>5 and E</span><span>b</span><span>4; kettledrum on E</span><span>b</span><span>3; first violins on G5, B</span><span>b</span><span>4, E</span><span>b</span><span>4, and G3; second violins on
G5, B</span><span>b</span><span>4, E</span><span>b</span><span>4, and G3; violas on E</span><span>b</span><span>5, E</span><span>b</span><span>4, and G3; celli</span>bass
on E<span>b</span>3 and E<span>b</span>2.” He goes on to say that, if forced to
guess, a responsible musician or conductor might suppose this to be the opening
chord of Beethoven’s <i>Eroica</i>. And yet this
guess would be wrong: the chord is taken from m. 690 of the same movement and
is subtly different. Such differences, he proposes, while “in theory”
perceptible, may not be “practically” so. To the extent we call these chords
effectively identical, we place them into a single category. To the extent that
we call them different, we place them into separate categories. Which is right?
Should all E-flat major chords with E-flats in the bass be lumped into the same
category? </font></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">The answer depends on the context. In a lower-division
theory class, arguably yes. In a class on Beethoven’s orchestration, or on
advanced aural skills for conductors, arguably no. At issue is what the
practical purpose of the category is. How does the scope or zoom of the
category aid the student? What role in learning does categorization play? This
takes me to my second principle. </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><b>The scope of the
category determines what must be made explicit and hence attended to by the
student.</b> Sometimes, some students pay attention to some things that they
don’t have to. But this can’t be counted on. By explicitly asking students to
pay attention to certain things, we help <i>all</i>
of them pay attention to specifically those things that (we think) are
important. The sorts of categories we establish as important clearly
channel student
attention in this way (I don't have data on this but I'm admitting it as
an assumption). When we ask them to determine what the root of a given
chord is, they must look at all notes and then hierarchize them (but
they don’t
have to know anything about key, for instance, save for being aware of
accidentals). When we
ask them to provide figures, they must either calculate the generic
interval of
each note above the bass and then reduce it mod 12, or they must
determine the
root and inversion of the chord and provide a label accordingly (note
the
difference there). When we ask them to provide a roman numeral (capital
for
now), they have to additionally determine the key (for the
first time!) and what degree of the scale the root of the chord is on.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><i>Now we get to the difference between uppercase and lowercase
roman numerals</i>. Is there an extra level of specificity that the
student is
required to enter into, an extra level of attention that they are asked
to pay
to the structure of the music, when they must distinguish explicitly
between capital and lowercase, corresponding to major and minor (also
diminished, etc.)? Yes, it seems quite straightforward that to have
to determine whether a chord on the fifth degree, say, is major or minor
requires the student to do extra work, to be more explicit. As I stated
earlier, <i>some</i> students may do <i>some</i> extra work <i>some</i> of the time, but explicitly requiring the important work from <i>all</i> the students seems to be a crucial
strategy for a teacher who wants <span>all</span>
students to develop fully.
Determining the scope or zoom at which the category is set determines the level
of detail the student is <span>required</span> to
enter into. Hence my argument that “category zoom” is of sufficient
pedagogical concern.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Do students need to explicitly know the quality of a harmony
they are charged with understanding, hierarchizing, and situating within an
analytical context? It seems obvious that the answer is yes. Does being forced
to label the quality of a harmony <i>somewhere</i>
increase the likelihood that the student will consider the quality the chord? I
would again anticipate no arguments to this. Is the roman numeral a reasonable
place to label chord quality? Sure, why not. Are there other ways to label
chord quality? Probably an infinite number. I would argue that, for
lower-division students, requiring at least one of these is a good idea.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">For advanced students—those who have <i>definitely</i> internalized the assessment of chord quality, and for
whom overly nitpicky labeling will therefore not be of benefit—there can be no
reason that I can see for requiring overt specifications in the labeling system
regarding chord quality. But for <i>any</i>
student who has not yet mastered this basic task (and at my university there
are many, even at upper levels), it seems a mistake to not require the labeling
of quality <i>somewhere</i> in the analysis.
</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">I will give a final, brief illustration of what I mean by
category specificity and how I think it relates to teaching. When students are
asked to sight-sing a melody, they are sometimes told to “sing on ooh,” or
“sing on scale degrees,” or “sing on note names,” or “sing using (chromatically inflected) moveable do.”
Some among us will argue that each of these is as valuable as the other. I
would counter that the amount of category specificity each requires does amount
to a pedagogical difference. To sing on “ooh” is to not require any
identification of interval beyond recognition of general contour. To sing on
any sort of uninflected diatonic system (in which raised-7 and natural-7, say, are
treated as identical, or in which sharp-4 and natural-4 get the same
syllable), requires specificity about genus of interval but not species of interval.
To sing using a chromatically inflected system (such as using <i>fa</i> and <i>fi</i>, <i>te</i> and <i>ti</i> for the above two distinctions) requires specificity at the
level of specific interval. <i>If the
student has any difficulty</i><i>
distinguishing specific intervals either on paper or with the voice,</i><i> </i><i>then</i><i> a chromatically inflected system seems to be the level at
which the student should explicitly categorize</i>.
If the student is not having trouble with this, or alternatively if the student
is not ready for this level (in the case of younger children), then an
uninflected system is satisfactory. But for students seeking to achieve
mastery at <i>this particular level</i>,
forcing them to explicitly label not only the genus but also the species
of
interval seems ideal. College students, in my experience, tend to be at
about
this level, which is why I tend to use chromatically inflected systems.
But
again it’s 100% dependent on ConteXT. (I couldn't resist invoking Lewin
again here. Note his own characteristic use of a verbal "mixed system"!)
</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">None of this is intended to argue for one system over
another in an absolute sense. There are numerous ways in which categorization
systems are formally isomorphic with one another, and differences amount simply
to differences in naming. There are quite obviously historical and regional
issues as well, with teachers trained in one method wanting to continue that
method because of comfort level; or, alternately, teachers trained in a different
method from the majority of their students teaching the method their students
know best despite personal discomfort.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">However, without in any way implying that one
method is
better than another for all contexts, it seems important to dissociate
the
formally isomorphic differences between systems from the formally
non-isomorphic differences. There are ways in which using both an
inflected
fixed do system and an uninflected scale degree system in combination
(as is done at Eastman, for instance, or so I'm told) is equivalent to
using inflected moveable do, in the purely formal
sense of categorical specificity outlined above. But using only <i>one</i> of the two former systems without
the other would ultimately be less categorically explicit than the latter. If
more categorical specificity in solfège singing can be determined to be more
beneficial to a given student or student population (that’s an if, but it’s no
doubt a reasonable one), then the moveable do method could be logically concluded
to be preferable. Again, this is highly dependent on context and
empirical validation, but the if/then statement holds water in at least the logical
sense.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><b>So to return to roman numerals</b>: The “mixed” system requires
the student to be more explicit than the “just-capital” system. To the extent
that it is useful to require the student to be aware of the quality of each
individual chord, and to the extent that being forced to write down a chord's
quality increases the student’s awareness of it, it
follows that the mixed system is preferable, all other things being equal.
(Such other things include the comfort level of the teacher and the familiarity
of the majority of the students with the systems at issue.) I believe that Dr.
Ninov’s claim to use different systems for different contexts (including jazz
formats, etc.) indicates that he would agree with this logical framework,
though I am looking forward to hearing his reply. Thanks for asking an
interesting question.</p><div><div><img src="https://mail.google.com/mail/images/cleardot.gif"></div></div><br><br clear="all"><br>-- <br><b style="color:rgb(102,0,0)">David Bashwiner</b><br>
Assistant Professor of Music Theory<br>University of New Mexico<br><font size="1">Center for the Arts, Rm 2103</font><div><font size="1">MSC04 2570</font><div><div><font size="1">1 University of New Mexico</font></div><div>
<font size="1">Albuquerque, NM 87131-0001<br><a href="tel:%28505%29%20277-4449" value="+15052774449" target="_blank">(505) 277-4449</a></font><br></div></div></div><br>