I understood how to get the secondary dominant of a major chord, but I don't understand how to get the secondary dominant of a minor chord, mainly because I don't know which minor mode (natural, harmonic or melodic) I should take to get it. So, what's your answer? :D So, what would we get if we tried to get the secondary dominant of Dm in C Major? Or of ii in any major key.
A secondary dominant is used to tonicize the chord you are moving to, ie, to make the chord of resolution feel like the I/i chord. This is accomplished through creating a dominant chord a fifth above the chord of resolution; the old V-I(i) resolution. In the vast majority of situations, this action requires altering a/some scale degree(s). This is essentially because each key will have only one naturally occurring dominant chord, so to create another, alterations need to be made. The only case where no alterations are needed (excluding modal music) would be in a minor key where you are tonicizing the III (the relative major), because that's where the naturally occurring dominant chord would appear.
So in the example that you give, we would just need the fifth of D to be the root of the dominant chord that will serve as the secondary dominant. This would be A7, which needs one alteration to create the chord: the C would become C#. As far as the scale is concerned, there are a lot of options and the best one would have to do with context and stylistic choices. If you were to alter only the C->C#, then you would end up with an A7 derived from the D Ascending Melodic Minor scale. If you make further alterations (still including the C->C#) you can have a different scale used for your dominant chord, such as B->Bb would make the scale derived from D Harmonic Minor, or D->D# and F->F# would make it an A Lydian Dominant (derived from the 4th degree of the E Ascending Melodic Minor scale). There are a lot of options for what sort of scale should be chosen to accompany such a chord. The least jarring would have the lest amount of alterations, which would just be the C->C# alteration (D Ascending Melodic Minor). The more alterations are needed, the less it has in common with what has been happening up to then, so it should feel more out of place. You can basically choose any scale that has a dominant chord, so the choice here is going to be based on taste more than anything. In Jazz, this sort of choice of scale happens a lot because there are a lot of secondary dominants used, so which scale the composer or improviser chooses for the secondary dominant either has to do with their personal tastes, or what style/era of Jazz they are going for.
Some others have provided answers that suggest that a minor chord could be used instead of a dominant chord. Strictly speaking, a secondary dominant would be a dominant chord, so I would suggest that that is inaccurate, however, I wouldn't say they are entirely wrong. You can create the feeling of tonicizing a chord without using a dominant chord but that's not specifically what a secondary dominant is referring to. In this particular example, the root of your secondary dominant is going to be A (without getting into tritone substitutions or other dominant substitutions), so if you were to use A minor, that would be a chord that is already within the scale and essentially just be circle of fifths motion, probably not adding any additional feeling of resolution that would lend itself to tonicization. So if you are taking a class on theory in an academic setting, you would want to consider a secondary dominant to have a dominant chord type. If you are just learning for yourself, ie, not being graded and held to a particular definition, then you can loosen that up a bit to include other chord types, though I would suggest that you consider whether or not there are alterations and to what extent it really feels like you are tonicizing another chord.
You would get an A7 chord, because you would build the secondary dominant chord based on the harmonic minor scale. The point of a secondary dominant chord is to make the chord you are basing it off feel like tonic, and this would be achieved by using the harmonic minor scale. This site would probably be helpful to better understanding http://www2.siba.fi/muste1/index.php?id=87&la=en
A secondary dominant won't have all its notes from the original key anyway. Take the secondary dominant from C major. Dominant is G, with all notes belonging to C, but the secondary dominant is D7, with an F#. So, your case - dominant of Dm is A7 ( or if you wanted, Am7), and its dominant will be E7 (or maybe Em7), making the secondary dominant.Generally, the 7 will sound better and more decisive than the m7.
Secondary dominants can resolve to any chord, regardless of the type of the next chord. The term "Secondary dominant" refers to a major-minor seventh chord set to resolve to a degree that is not the tonic.
In C-major, here are the dominant seventh and the secondary dominants that resolve to the diatonic triads:
- G7 - C (C: V7 - I)
- A7 - Dm (C: V7/ii - ii) (d: V7 - i)
- B7 - Em (C: V7/iii - iii) (e: V7 - i)
- C7 - F (C: V7/IV - IV) (F: V7 - I)
- D7 - G (C: V7/V - V) (G: V7 - I)
- E7 - Am (C: V7/vi - vi) (a: V7 - i)
- F#7 - Bm-5 (C: V7/vii° - vii°)
In minor keys, they appear as below, in the case of a-minor:
- E7 - Am (a: V7 - i)
- F#7 - Bm-5 (a: V7/ii° - ii°)
- G7 - C (a: V7/III - III) (C: V7 - I)
- A7 - Dm (a: V7/iv - iv) (d: V7 - i)
- B7 - E (a: V7/V - V) (E: V7 - I)
- C7 - F (a: V7/VI - VI) (F: V7 - I)
- D7 - G (a: V7/VII - VII) (G: V7 - I)