Secondary dominant of a minor tonic?

Question

While trying to analyze Mike Oldfield's Nuclear, I got stuck.

The main chord progression is Fm-Cm-Bbm-C.

Up until C, it looks like in Fm (natural) key, i-v-iv-.... C would look like a V (which Fm natural does not have).

What are the ways to interpret this? Is this a modulation from Fm natural to Fm harmonic? Given that this is a single chord, I do not think this is a useful way.

Is it more useful to think of C as a secondary dominant, V/i, which resolves to i?

I tried to research the topic of modulation between minor natural and harmonic as well as secondary dominants over tonic, but could not find anything relevant.

Answer 1

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, but v is still found in pieces in minor keys. Theory seems to be somewhat lacking in publicity in this area. There's a few questions leading to answers explaining it all on this site - some to the right of your question.

It won't be a secondary dominant - that's a chord which leads (in theory) straight to another diatonic chord from the key (as in its V - V/ii, V/vi etc), but will be simply a dominant.

Answer 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 are natural, harmonic, and melodic. We have a lot more questions that go over minor key harmony that I recommend you take a look at:

• Understanding minor key harmony
• Chord progressions in Harmonic Minor

Answer 3

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 that it does in fact contain a very classical secondary dominant in the verse/bridge: an inverted D♭ augmented sixth chord.

b♭m - fm - D♭+6/B♮ - C
ⅳ   - ⅰ  - Ⅵ+6/+6 - Ⅴ

(I initially heard it as a diminished seventh chord; was thrown off by the prominent B♮ note in the electric piano)

Both augmented sixth chords and diminished seventh chords are strong dominants, working particularly well as secondaries towards the actual (tonic's) dominant. The b°⁷ chord shares three notes (b, d, f) with G⁷, which would be the plain Ⅴ-of-Ⅴ secondary dominant. Additionally, it adds the A♭ note for some extra bite and leading quality. The augmented sixth chord shares only b and f, which may not at first sight point to a G-ish chord, however these shared notes are the tritone, the heart of the dominant's leading character.

Note that D♭⁺⁶ is enharmonically equivalent to D♭⁷, i.e. the standard dominant G⁷ shifted down by a tritone (thus the description “tritone substitution”, which is what this would be called in jazz).

Answer 4

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 chord, but not into the subdominant.