[Smt-talk] Different Labeling Systems

[David Bashwiner]

Dear all,


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.



*The first is the nature of the mapping*. 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?


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: “flutes on G6 and Bb5; oboes on Eb5;
clarinets on Eb5 and G4; bassoons on Eb4 and Eb3; horns on G4 and Eb4;
trumpets on Eb5 and Eb4; kettledrum on Eb3; first violins on G5, Bb4, Eb4,
and G3; second violins on G5, Bb4, Eb4, and G3; violas on Eb5, Eb4, and G3;
cellibass on Eb3 and Eb2.” 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 *Eroica*. 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?



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.



*The scope of the category determines what must be made explicit and hence
attended to by the student.* 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 *all* 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.



*Now we get to the difference between uppercase and lowercase roman numerals
*. 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,
*some*students may do
*some* extra work *some* of the time, but explicitly requiring the
important work from *all* the students seems to be a crucial strategy for a
teacher who wants all students to develop fully. Determining the scope or
zoom at which the category is set determines the level of detail the
student is required to enter into. Hence my argument that “category zoom”
is of sufficient pedagogical concern.



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 *somewhere* 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.



For advanced students—those who have *definitely* 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 *any* 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 *somewhere* in the analysis.



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 *fa* and *fi*, *te* and
*ti*for the above two distinctions) requires specificity at the level
of
specific interval. *If the student has any difficulty** distinguishing
specific intervals either on paper or with the voice,** **then** a
chromatically inflected system seems to be the level at which the student
should explicitly categorize*. 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 *this particular level*, 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"!)



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.



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 *one* 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.



*So to return to roman numerals*: 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.



-- 
*David Bashwiner*
Assistant Professor of Music Theory
University of New Mexico
Center for the Arts, Rm 2103
MSC04 2570
1 University of New Mexico
Albuquerque, NM  87131-0001
(505) 277-4449
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