4
ii -> V -> I -> vi (or V/ii) -> (starts over on ii)
I think it is unlikely that enough people have referred to that progression by a specific non-systematic description to justify claiming that it has a name. Why I think so:
Chord progressions are usually referred to by their systematic descriptions that consist of numeric scale degree names, ...
4
F minor is a key. F harmonic, melodic and natural minors are scales.
Modulation occurs between keys, not scales. The scales are simply sets of notes ordered. It happens that in minor keys, there are more notes in general use than the 7 expected, as we find in major keys. Hence the different minor scales (and that's before modes).
The major V is commonplace, ...
3
We can go considerable modulatory distances by using secondary dominants of closely related what would be minor keys as secondary dominants of major keys instead.
One such example that gets you from A flat major to D major with 2 intermediate keys would be this:
A♭: I -> V7/iii = C: V7 -> I -> V7/vi = A: V7 -> I -> V7/IV = D: V7 -> I
As you ...
2
Functional harmony typically prefers V over v since V makes use of the leading tone and has a stronger pull to the tonic. So the analysis would just be V-i. No modulation, just how minor harmony works.
There's in general a lot more going in minor key harmony since scale degrees 6 and 7 are typically modified leading to the three distinct minor scales which ...
2
We can re-write the question as how one makes x+y+z=6 mod 12 then reinterpret the numbers as scale steps. A quick answer is -2-2-2 or 2+2+2 moving the harmony by whole steps. Another is 1+2+3 (in some order) making moves of a minor second, a major second, and a minor third; this can be done as -1-2-3.
Other possibilities are +4+5-3 or 4-3+5, etc.
2
Consider that a commonly used key change, or probably modulation here, is up a semitone. That's easily achieved, and used often, as the pivot V of the new 'key' contains one of the old tonic notes - the tonic itself.
That would take us to key A major. That happens to be the V of the target key - D, so it's quite simple to move into that. Thus, two simple, ...
2
As the other answers already said, Ⅴ is in fact the standard dominant in the key of f-minor. Speaking in terms of common-practice harmony, it's rather the cm that's the odd one out – a minor Ⅴ chord doesn't really act as a dominant at all, lacking the (classically) all-important leading tone ♯7.
But while we're discussing this song, it's worth mentioning ...
1
There are many ways!
Quite stereotypical is using any tone as dim7/V to I46-V-I. With this we can go directly from Ab to G#dim7 (=vii°7 of A) instead of A you take A46 - A7 - D. (Note that the V46 chord is the same as the 2nd inversion of the tonic.)
But with this trick you can try any other way like e.g.
Tonization of Ab: Ab-Fm-Ddim7-Eb46-Eb7-Ab
...
1
As Tim said, natural/harmonic/melodic minor are scales, not keys.
In this case you have correctly determined the cadence to be
i - v - iv - V - (i)
The major dominant before the tonic of course a standard cadenza. The minor dominant before the subdominant is nescessary as a major dominant would have a leading tone which implies a resoltion into a tonic like ...
1
TL;DR
Beethoven is using a combination of common-tone and enharmonic modulation. Common-tone diminished chords are discussed in various posts here; a list can be found here. Enharmonic modulation, as used in mm. 5–8, is where a diminished chord is reinterpreted according to an enharmonically equivalent diminished chord.
Analysis
measure 5
Begins in III (E♭),...
1
You could do this. If it breaks any rules, I don't think they're ones that matter!
1
In addition to your 2–4–3 in the soprano, I would include the next scale-degree 2, as well. This way, a 2–4–3–2 soprano line could be harmonized with voice exchanges in contrary motion in the bass to prolong ii.
The 2–4 in the soprano could be harmonized with 4–2 in the bass, moving from a ii6 to a ii. Then, the 4–3–2 in the soprano could be harmonized with ...
Only top voted, non community-wiki answers of a minimum length are eligible