Just a harmonic doubt

[billybraga]

Hi, im an intermediate student of piano, and im trying to figure out how the functional harmony works in some pieces. Im here because i want to learn what this type of notation in green means, like Iv 3 2/ V (sorry for the quality of the photos):

[ranjit]

A V/V is a secondary dominant. Basically, it refers to the V chord of the key which has the fifth scale degree.
So if you are in C, it would refer to the V chord in the key of G, i.e., D major.

The numbers are figured bass notation to refer to the inversion of the chord. Look up c Roman numerals for chord inversions.

[billybraga]

So, if V/V are secondary dominants, whats a V/iv, or iv/ii?

[j_tour]

So, if V/V are secondary dominants, whats a V/iv, or iv/ii?

I hope I'm not overstepping my bounds by butting in, but I'll do it anyway.  Same thing.  Absolutely you can prepare a IVm chord with its own dominant7 chord.  Any chord, really. The authentic cadence (i.e., V7-->I in major or minor) is so...definitive, or authoritative, IMHO the only way to avoid it is by (i) trying for an ambiguous tonality or (ii) disguising a bit of the underlying harmony by way of specific voicings, like the various augmented sixths.  And "deceptive cadences," which really exist only in opposition to the authentic cadence, although the term has a little more technical meaning, which I can't remember enough to write a little sentence about that's no more than partially right.

It really boils down to the same thing, though.

Except that the "IIm7" or the half-diminished II chord (in a minor key) is, according to a certain school of thought, really just a disguise for a IV chord:  the notation is supposed to help understand the bass motion.  At least that's how I interpret it when, particularly in jazz music, but by no means exclusively, you see all kinds of preparations for the V7 chord (including in temporary modulations) taking the form of a iim7-->V7-->I. 

If I had to guess, it's that the V7-->I cadence is so strong that all kinds of schemes of preparing for the dominant 7 chord have been devised, so that one has more room to play around, harmonically.

That's just what I've seen, and I'd love to be shown wrong, but IMHO that's the basic idea.

[ranjit]

A V/IV would also be a secondary dominant, leading to the 4th scale degree. I'm not sure if you come across iv/ii often, so I can't say for sure. However, it would appear to be a plagal cadence leading to the minor tonality of the second scale degree.

According to basic functional harmony, there are perfect cadences (V-I), plagal cadences (IV-I), and deceptive cadences (V-vi), and you can replace any of the chords by their functional equivalents. There might be a bunch of other things, but an expert would need to step in for that.