Music in Trains

I just finished reading Matthew Brown’s Explaining Tonality: Schenkerian Theory and Beyond and wanted to take note of some observations.

“In Terms of the Inner Voices”

Some of the most important ideas I learned while studying with Gregory Proctor involved the power of voice leading. I also became intrigued with the careful explanation for every single pitch in a piece as graphically analyzed by my colleague David Tomasacci. These ideas have been a central pursuit in my own compositions over the past two or three years. One further impetus for a careful interest in voice leading was described by Brown:

… [A]lthough certain aspects of tonal motion are controlled by the outer voice counterpoint, others can be understood only in terms of the inner voices. When graphing a particular piece, the analyst should not simply trace the motion of the soprano and bass voices; he or she should also monitor the behavior of the tenor and alto voices. … In parcitular, we found that bass motion by fifth inevitably arises when the upper voices move by step in a single direction by parallel thirds or sixths. (136)

I was somewhat surprised to realize that if you take “voices mov[ing] by step in a single direction by parallel thirds or sixths” you must generate a sequence in order to maintain good counterpoint with a third voice and that all of the typical tonal sequences can come about as such.

Furthermore, given that “voices mov[ing] by step in a single direction by parallel thirds or sixths” can simply be understood as a harmonized Zug (“a direct, unimpeded motion from one place to another,” Snarrenberg), they can be readily related to activity over a pedal tone—a relationship that Brown makes quite obvious. I find this interesting given that I tend to find sequences as the most direct way of experiencing prolongation despite the constant activity. While I could explain that sensation through the incessant repetition and the lessened impact of a clear end-goal through endless cycling, I find this tonal explanation much more salient.

I recently found myself encouraging a composition student to generate this sensation of what I described at the time as “floating.” I felt that the piece could use some breathing space from its harmonic motion. The solution was to lift the bass voice up into a more tenor-like range. I can’t help but wonder now if the result (which worked well) could have been playing off of inner-voice motions with an implied pedal. I find this idea of the bass part leaving the bass voice to join with inner-voice motions as a means of suspending harmonic motion in time worth further consideration.

“The Myth of Scales”

Also in part due to Tomasacci and Proctor, I have remained interested in the viability of scale-like pitch collections that can be used in a prolongational manner. Tomasacci has uncovered an interesting phenomenon in the harmonic bass motion of Skryabin’s music that works rather well. However, the upper voice is consistently best explained in terms of an octatonic scale that lacks the specificity of a asymmetric scale. Proctor dealt with this scale in terms of a ‘transposition operation’ rather than a harmonic-contrapuntal process.

Brown notes that in general, “scales have only limited explanatory power.” (169) He quotes Mary Louise Serafine as saying that:

[S]cales… have figured disproportionately in music research, chiefly through their influence on the design and conception of studies.

and David Huron as noting that:

In comparison to most of the world’s music, Western music tends to be highly harmonically oriented. Where scales provide the basis for predominantly melodic music, explaining the harmonic properties of these scales may be inappropriate.

But he begins his demonstration of the limited explanatory power of scales with a quote by Taruskin:

Just as we get our sense of Mozart’s C major not only from his use of the “C scale on C” but also from the way the “black keys” are related hierarchically to the tones of the scale, so, if we are able to conceive of the octatonic collection as a tonality, we must be able to account for the use of the “other” four tones in relation to it.

This quote captures two important concepts on opposite ends of musical complexity. On the basic level, it is simply unhelpful to use scale-membership as a means to determine key. Brown explains further:

Even on an intuitive level, we know that scale membership is neither necessary nor sufficient for determining the tonality of a passage or piece. … It is easy, for example, to imagine how a key might be defined by progressions that do not contain every note of the relevant scale. … Similarly, the mere presence of a given scale need not guarantee that a passage is “in” the corresponding key. … To complicate matters further, we can also establish a tonality using progressions built from pitches outside the diatonic collection. … [T]onality does not simply depend on the presence of the “right” notes, but rather on the fact that particular notes appear in the “right” order according to some general laws of tonal voice leading and harmony. (144)

And yet, basic theory courses most often associate scale and key as interrelated concepts. It’s no wonder why students can sometimes get so confused when they are first asked to determine the key of a passage that does not reflect the key signature. For that matter, I suppose it should not be a surprise that students often forget to raise leading tones as those notes are not in the key signature. It might be worth discussing keys divorced from key signatures just to keep separate the idea of scale or mode and key.

On the more complex level, I find the Taruskin quote interesting due to what it says about the “other” four pitches not in the octatonic scale. It brought to my attention the fact that when I come across a passage that can be described as octatonic (or possibley whole-tone or pentatonic and the like) it is almost inevitably limited to the pitches of that particular scale. That is very different from what we experience in tonal idioms. As Brown put it:

The beauty of Schenkerian theory is that it is powerful enough to explain surfaces that are almost continuously dissonant and chromatic. (186)

I find the lack of some way of interpreting those “other” four tones outside of an octatonic scale—or some other complementary set to another scale form—an intriguing difference from tonality. This is also not merely a result of modern constructs given that modal music likewise used a limited set. Rather, it would appear that tonality is rather unique in having a set of behavioral expectations (depending on context) for each pitch of the 12-tone aggregate.

This last point may be one of the more interesting facets of tonality that permeated Brown’s book: the uniqueness of tonality may be more a result of particular behavioral expectations than anything related to pitch content. Not only does each pitch have particular behavioral expectations, but also, tonal music exhibits recursive applications of such behaviors. This is not inherently necessary, nor is it necessarily impossible with other pitch collections. Rather, these recursive strings of simple relationships simply make for a unique idiom that allow for some fascinatingly organic constructions.

Proctor and Huron

Finally, I just want to note how incredible it is to have studied/worked with two musicians who would show up in important ways throughout a book that is trying to “explain tonality.” I have truly been blessed!