[Smt-talk] Fwd: First Species Question

Thu Jul 8 23:41:16 PDT 2010

Dear Dmitri and All,

I apologize: the confusion is not Dmitri's but that of history of music theory. If one teacher allows for contrary fifth, and another does not, it is pretty confusing. Since earler teachers allowed for it and later ones did not, I see the tendency to consider an interval more and more as a pitch class, separate from actual voice leading context. On the circular pitch space, the parallel 5th and contrary 5th look the same (although in Dmitri's software, the objects move differently). I wonder, what Rachel Hall thinks about this in terms of economy of voice leading?

Best,

Ildar Khannanov
Peabody Conservatory
solfeggio7 at yahoo.com

--- On Thu, 7/8/10, Dmitri Tymoczko <dmitri at Princeton.EDU> wrote:

From: Dmitri Tymoczko <dmitri at Princeton.EDU>
Subject: Re: [Smt-talk] Fwd: First Species Question
To: "smt-talk smt" <smt-talk at societymusictheory.org>
Date: Thursday, July 8, 2010, 7:03 PM

I wanted to thank everyone for their help with my first-species question.  In particular, Yosef Goldenxberg (off list) directed me to a discussion in Cherubini about "antiparallel fifths," which he permits in general, but forbids in first-species.  (Like others, Yosef also pointed to Schenker's discussion in "Counterpoint.")  I was also very pleased to get Prof. Peter Schubert's illuminating examples of antiparallels in Palestrina and Bach.

What interests me about the issue is the distinction between (1) conceiving of the "parallel fifths rule" as forbidding a specific kind of *motion*, and (2) conceiving of the rule as forbidding a more general musical state.  As David Feurzeig points out, there are various ways to avoid the motion while still creating an impression of "parallel fifthiness."  (For instance, there's a Palestrina motet in which a root position triad {C3, G3, C4, E4} moves up by step to {D3, A3, D4, F4}, creating the unmistakable impression of parallels; but because of an alto/tenor crossing there are no actual parallels.)  My sense is that earlier composers and theorists tend to focus on the motion in particular, whereas later musicians tend to emphasize the more general state.  For example, I would be somewhat surprised to find lots of examples of Bach writing (C3, G3, C4, E4)->(D3, D4, A3, F4).  For this reason, we might suspect that the prohibition on parallel fifths
 got broader over time.

I'm still interested in the relation between musical practice and the actual literature.  My sense is that, even in Renaissance music, there are relatively few "antiparallel fifths," suggesting that they were somewhat frowned-upon if not forbidden outright.  (I have no statistical evidence for this, just intuition.)  And another correspondent suggested (privately) that the near total absence of "antiparallels" in first species (or more generally, two-voice Renaissance counterpoint) may be, in part, an artifact of registral issues: to get antiparallels, you need voices separated by an octave and a fifth, which is fairly wide for first species/two-voice counterpoint.

So, if anyone has any two-voice Renaissance antiparallels, I'd love to get them.  (I can write a computer program to search MIDI files for them, which I'll try in the next couple days.)  Similarly for other pre-twentieth-century discussions of the prohibition, or -- more generally -- for any evidence in favor of the idea that the parallel fifths prohibition *broadened* over time.  (That is: changed from being a prohibition on specific motion to being a prohibition on a more general class of musical states.)

One final issue.  Ildar Khannanov wrote:

> As for the source of Dmitri's confusion, it is, again, the concept of so-called pitch class. The reduction of the notes in many octaves into one is undesirable, unnecessary and confusing.

I think Ildar is onto something here, though I'm not sure that I'm actually confused.  The issue is how abstract, or how general, the prohibition on parallel fifths is, and whether it changed over time.  It's a pretty complicated question, and it can't be reduced to a simple distinction between "pitch and PC."  Part of the issue involves what constitutes a voice: like many contemporary musicians, I take it for granted that a passage like (C3, G3)->(A3, D3) defines the *registral* voices C3->D3 and G3->A3.  This is precisely why I take this progression to be "parallel fifthy." But this concept of registral voice may be less obvious to a Renaissance composer.

Ildar is right that, in PC space, we can't distinguish the upper voice from the lower, so there's no distinction between parallel fifths (which are forbidden) and parallel fourths (which can be OK in upper voices).  However, it's worth pointing out that the concept of a "path in pitch class space" allows us to talk about parallel motion even when we're in PC space.  For instance, consider the two voice leadings in PC space

A: (C, G)--(+2, +2)-->(D, A)
B: (C, G)--(-10, +2)-->(D, A)

Here the numbers indicate how each voice moves: in the first, the note C moves up by two, while in the second it moves down by 10.  (In my published stuff, I write these numbers above the arrows, but that's hard to do with plain text.)  The first of these involves parallel motion, the second does not.  Of course, we can instantiate the first so as to create parallel fourths rather than fifths, so Ildar is right that PC space is not optimal for dealing with this issue.

For more on paths in PC space, see my MTO "key signatures" article, my Music Analysis voice leading article, or my Science article by Callender, Quinn, and Tymoczko.

DT

Dmitri Tymoczko
Associate Professor of Music
310 Woolworth Center
Princeton, NJ 08544-1007
(609) 258-4255 (ph), (609) 258-6793 (fax)
http://music.princeton.edu/~dmitri

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