Analyzing Polarity(William Renwick)

1. Teresa is absolutely right that Levy and Levarie base their viewpoint on Plato and on the Judeo-Christian view of creation (see Teresa's essay). It's amazing though, and correct, that this view also encompasses a Darwinian model, as Teresa says!

2. I hope that Teresa cites where Levarie and Levy denigrate "other" forms of music, because, by and large, I think, polarity cannot be used as a way of distinguishing here. (Nevertheless, I am not surprised if they denigrate other forms of music. They are certainly entirely within the western philosophical tradition. Of course, Schenker was so, too!)

3. Teresa, do you think that if you buy polarity you have to limit it's application as Levarie and Levy do? Especially, how is the "the palindrome structure that defines Bartok's 5th String Quartet exluded from this kind of thought."? I think that the key that you are driving at is that the palindrome structure subverts the natural order of time itself in a symbolic way. And the logic of unidirectional time is confounded. But at the same time the supposition of a palindromic structure implies--from its mid-point--in the most forceful way the ultimate termination of the work, as Jennifer ponts out. (And how would a "melodic" as opposed to harmonic or cadential based approach to pre-enlightenment music be less supportive of a growth and limitation type of model?)

3a. Teresa, you raise a marvellous point that "Growth-Limitation" suggests that there is a critical turning point where "growth is either confounded or no longer sustainable". I think that you are right from a theoretical point of view, and perhaps we could look for such a point in certain pieces. Doctors (I think) say that we begin dying from the moment we are born. Regular people think of such landmarks as "age 40", "age 65" etc. Philosophers would say that death (limitation) is the most undeniable implication of birth (growth). But I thought that Levie and Levarie were making a good case that the principles of growth and limitation act and react--play with each other, precisely in the manner dscribed by Jennifer as The Grey. From the beginning of a piece, which starts with unlimited potential for growth and development, factors such as motivic repetitions and developments, and certain tonal and formal patterns, begin to determine the future course of the work and ultimately to determine its closure at some point that becomes increasingly determinate as the piece progresses. Indeed, this is the manner in which a sense of "Organic Unity" is made sensible.

4. On the cadence idea, I have just been introducing cadence (modal and renaissance) in my counterpoint class, by reference to the writings of Tintoris (ca. 1450). Tinctoris seemed to think that resolution on perfect unity (i.e. closure, limitation) was important.

5. On meter, I should clarify that the authors have a musico-philosophical basis heavily indebted to the ideas of Hugo Riemann, whether in terms of harmony or of metre. This application of dualism (polarity) has a long history of about 150 years now, and ultimately ties in with the Hegelian dialectic.

6. On Synthesis or Union or "The Grey": I expect that we all agree with Jennifer, that the significance of understanding opposites is that then we can go about understanding union or interplay (or play--Agawu's term) or synthesis of opposites. And that this is the locus where significant development of understanding and "wisdom" takes place.

7. On the topic of opera, I should point out that coming out of Riemann's philosophies of music were Lorenz's theories of musical form, applied to the operas of Wagner. But even much earlier, I am sure that the authors would assert that sonata principles are very much connected with the development of the da capo aria. Indeed, Charles Rosen argues as much in his very interesting book, Sonata Forms. Incidentally, Rosen was the original candidate to write the New Grove article on sonata form, but was replaced when the editors concluded that his take on sonata form was too radical.

8. Theory and Analysis are opposites in that Theory is, ideally, deductive, whereas analysis is inductive. While they have the same subject matter (musical structure), they stem from ideological opposites. Much of what is loosely termed "music theory" is more along the lines of "music analysis." This may be the reason that Sandra feels that theory and analysis are not opposites.