[Smt-talk] P5–d5 combinations (was: Bach Quiz)

[Olli Väisälä]

Dr. Dimitar Ninov wrote:

>
> Bach is not so strict with the parallel fifths of unequal size,  
> though. Some theorists consistently call them “unequal fifths” as  
> if they are not parallel and may be used indiscriminately for this  
> sole reason. I am afraid that none of these possible assumptions is  
> true, however. When you move in thirds, you usually say that is a  
> motion in parallel thirds, no matter whether one third is major or  
> another is minor. The same is the case with the fifths. When two  
> parallel fifths (one perfect and one diminished) are perfectly  
> acceptable, they are usually covered by the bass or another voice  
> which moves in parallel thirds and sixths with the voices that form  
> the fifths, such as in the connection I-V4/3-I6 or I-VIIdim.6-I6  
> with Mi-Fa-Sol as melodic contour. Bach explores these  
> possibilities amply in his compositions. Of course, we also have  
> expansions of this principle.
>
> Because of this misunderstanding that if two fifths are of unequal  
> size, they may be used just like that,  sol-fa-mi soprano profile  
> is often harmonized by some musicians with cad.6-4 V7-I, while this  
> harmonization is the least characteristic for that contour and the  
> parallel fifths are not covered in the manner described above. They  
> do not sound very appealing there at all, but “we read somewhere  
> that they are allowed.” In this particular case, it is much better  
> to place this contour and the fifths between inner voices.  
> Otherwise, more typical harmonizations for this soprano are V6-6/5  
> or V-V6/5 or I6-V4/3-I.

This raises several interesting questions.

First, I have always taught (and thought) that there is a fundamental  
difference between P5–d5 and d5–P5 successions: The former contains  
no approach to a perfect interval and is therefore unproblematic,  
whereas the latter contains "hidden parallels" and only occurs in  
certain idioms, such as the ones Dr. Ninov mentions. In particular, I  
don't think Bach uses the d5–P5 succession between the bass and  
another voice. Moreover, the idioms involved always (?) seem to have  
^7–^4 moving to ^1–^5, whereas a motion from ^2–^6 to ^1–^5 in minor  
seems to be avoided.

HOWEVER, Dr. Ninov's post raises the interesting question whether the  
P5–d5 succession might also be avoided for some reason (such as "not  
sounding appealing"). Dr. Ninov, if I understand your post correctly,  
you suggest that such fifths are generally avoided, but occur in the  
I6–V4/3–I progression with parallel tenths between ^3^2^1 in the bass  
and ^5^4^3 in an upper voice. This is an interesting proposition and  
one that we might ask Prof. Tymoczko to illuminate empirically  
through his data of Bach chorales.

On the other hand, if, for example, it turns out (as I believe it  
does) that you won't find many cases of cad.6/4–V7–I with ^5^4^3 top  
voice in that repertoire, that does not yet prove that the reason for  
this is the avoidance of P5–d5 succession, because there might be  
alternative explanations. One might suggest, for example, that when  
resolving the cad. 6/4, ^3–^2 and ^1–^7 motions are more effective in  
the soprano.

In any case, P5–d5 and d5–P5 successions is surely an issue towards  
which different composers had different attitudes. Incidentally,  
while Dr. Ninov mentions I–V4/3–I6 as a possibility "amply explored"  
by Bach, I doubt whether this is actually common at all in Bach's  
music. I think Bach strongly favors I–VII6–I6, whereas I–V4/3–I6  
becomes more common in music by other (later) composers. This, again,  
is an issue that should be illuminated empirically. Does anyone know  
occurrences of I–V4/3–I6 in Bach with ^3^4^5 upper voice?

Some other examples:

Bach: WTC I, A-minor Prelude, mm. 1–2. The voice leading goes from A– 
E to B–F (P5–d5). Would Bach perhaps have avoided this voice leading  
in block-chord texture?

Bach, WTC II, E-minor Prelude, mm. 60–61. Here we have a rare example  
of ^4^5 with implied d5–P5 succession, WITHOUT the bass providing the  
^3 (VII4/3–I instead of VII4/3–I6). The effect of the fifth is  
enhanced by its openness (no third at the downbeat). This is clearly  
an example in which Bach deliberately deviates from norms for  
creating a special memorable effect.

Brahms, Symphony No. 1, Second movement, m. 56. A d5–P5–d5 succession  
in upper voices.

Olli Väisälä
Sibelius Academy
ovaisala at siba.fi


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