[Smt-talk] Fwd: First Species Question

[Dmitri Tymoczko]

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