Are "direct 5ths" only a problem if they occur between the same voices?

Question

I am studying part writing and there is an example of what is considered good and bad part writing. One that confuses me a little is this one:

The reason cited for this being bad is: "Leading-tone in soprano not resolved. Also causes direct fifth between outer voices." I understand the leading tone error but I am confused by the second reason. I can only see that the bass moves down by a 5th and the Soprano moves down by 3rd. Can anyone please explain this?

Answer 1

This is a very convoluted rule, and it's tough to explain succinctly. But the notion of "direct" (or "hidden") fifths/octaves is this:

If two voices move in similar motion into a perfect fifth or perfect octave, the upper voice must move by step; only the lower voice may leap.

In the overwhelming majority of cases, this guideline only applies to the soprano/bass pairing; thus the soprano must move by step, but the bass can leap. I have, however, seen one instance of someone claiming this rule applies to all voice pairings. (Which, for what it's worth, I think is absolutely silly: it's exceedingly common anytime an inner voice moves its leading tone down to scale-degree five.)

Your example is an instance of direct fifths because the soprano moves by more than a step. If it just stepped down to that D, there would be no part-writing error.

Three other considerations:

1. Yes, this is only a problem between the same two voices. If your soprano resolved up to G and your alto was on D, these would not be direct fifths, because the D/G would suddenly be alto/bass instead of soprano/bass. This reasoning is explained more fully in Do parallel octaves “count” across multiple voices?
2. Direct fifths are pretty low on the list of part-writing errors; it's a simple misdemeanor when compared to the outright first-degree murder of parallel octaves or a doubled leading tone. In a situation where you have to choose the less disagreeable error, opt for these direct fifths instead of something more problematic.
3. Lastly, these direct fifths are such a relative non-issue that plenty of people don't even worry about teaching it. It's not that big of a deal, and the rule is pretty convoluted, so bringing it up is often more trouble than it's worth.

Answer 2

The underlying problem that leads to "hidden fifths" (or "hidden octaves") comes from the historical performance practice of diminution — "filling in" the spaces between two notes some interval apart.

The idea is explained by Fux:

Josephus [the student]. — What kind of mistake have I made?...
Aloysius [the teacher]. — ... You moved from the third to the fifth in direct motion against the rule: from an imperfect consonance to a perfect consonance¹ one must go in contrary motion....
Josephus. — Do you mind explaining to me the reason [for that rule]?...
Aloysius. — ...One may not do it because two fifths follow each other immediately, of which one is apparent or open, the other, however, concealed or hidden, and would stand out by the diminution of the interval [emphasis mine], as I shall show you now in the example:

Below is Fux's example, adapted to use the notes given in the OP above.

X: 1
T: Hidden Fifths
T: by diminution
M: none
K: none
L: 1/1
V:V1
V:V2 clef=bass middle=d
[V:V1] F D || F x1/2 E/4 D |]
[V:V2] d G ||  d c/4 B/4 A/4 G |]

(Johann Joseph Fux, The Study of Counterpoint, revised edition, translated and edited by Alfred Mann [W. W. Norton & Co., 1971], page 32.)

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¹ _{Fux defines "perfect consonances" as perfect unisons, fourths, fifths, and octaves. "Imperfect consonances" are major and minor thirds and sixths.}

Answer 3

You have parallel thirds in the example, which is not verboten. When we say parallel 5th or octaves we mean this. I'm specifically referring to the octaves between the bass and the tenor voices.

When you have chord repetition then the repeating of the same octaves or fifths is also not considered parallel. So in other words the first picture is bad, this one is acceptable.

And yes the concept of parallel intervals is specific to a pair of voices. In your example you have parallel thirds between the soprano and the alto voices, which is fine. In my example I have parallel octave bass and tenor voices, which is poor.

As for the quality of the voice leading you could probably improve it by just taking out the parallel movement of the chords and just introducing contrary movement. Contrary movement is just a good way to prevent problems with octaves or fifths.

It is hard to say without knowing what goes in front or after those two chords, there may very well be a situation where you are forced into a movement like that, but you very easily could have done the following with those two chords.

That looks like it could be G: V-I which would mean your leading tone does not resolve, which is a bad thing, you can easily remedy that by having the F# resolve to a G, like this.