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I have read that hidden direct octaves between two voices are not always forbidden, but that there are some circumstances in which they are acceptable. As I have understood it, the following general rules are observed:

  • If one of the voices moves by jump and the other by contiguous movement, then they are allowed.

Exception: in the case of bass and the soprano, they are not allowed if the soprano jumps and the bass moves contiguously.

  • If both voices move by jumping, then they are forbidden.

However, two cases have occurred to me about which the text I have read says nothing:

  • What if both voices move by contiguous movement?
  • What if one of the voices does not move?

Would hidden direct octaves produced in this two ways be valid?

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You question is kind of confusing, because you're mixing terms.

Hidden and direct and synonymous. Both are used in describing movement to a perfect interval by similar motion when the first interval is different that the second. Like a sixth to an octave with both voices ascending.

Parallel is more specific within the class of similar motion. Both intervals will be of the same type. Ex. a perfect octave to a perfect octave. "Hidden parallel octaves" is mixing terms. It's either hidden octaves or parallel octaves.

What if both voices move by contiguous movement?

If you move to an octave, and both voices move in contiguous (step-wise) similar motion, then by definition the previous interval must be an octave and the motion is parallel octaves.

What if one of the voices does not move?

By definition this is oblique motion. It's not similar motion therefore there can't be direct or parallel anything.

A few important concepts that you probably want to consider - if you haven't heard them already - are...

  • Independence of lines. Parallel perfect intervals are avoided at least in part because the consecutive intervals are exactly the same. Such lines are merely a transposition. Lines in similar - or parallel imperfect intervals - are not literal transpositions. There a slight changes in the exact linear contour of the part and that provides some basic level of independence.
  • Emphasize interval variety. In Fux the rule of thumb limit was 3 times for any consecutive interval. So even parallel thirds and sixth have a "limit." This is sort of a specific statement about linear independence. In effect it means you need to put in some contrary and oblique motion for variety's sake.
  • Third and sixth help define the modal aspects of a key. Perfect fifths and octaves help define the important tonal degrees. In practical terms third and sixth are better in the interior of phrases and perfect fifth and octave for cadences.
  • Relative motion "rules" are of special concern with the outer voices, the bass and soprano. When one of the voices is an inner voice, tenor or alto, there is less sensitivity about relative motion.

Some times it's good to keep positive ideas like those in mind. Those are the things you strive to do instead of worrying about prohibitions.

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  • How are lines in parallel imperfect intervals - e.g. minor 6ths - not literal transpositions of each other? Parallel 6ths in a diatonic scale I get. But minor 6ths?
    – Dekkadeci
    Nov 7 '20 at 14:18
  • @Dekkadeci, well sure imperfect intervals of only one type would be transpositions ...and that would be very out of step with tonal harmony. Nov 11 '20 at 17:17
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As I read various counterpoint summaries, the only problematic case is the soprano jumping (and turning state's evidence?). This emphasizes the octave and sounds like a voice dropped out. The best check is to listen for a noticeable "thinning" of the sound.

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