A regular dominant chord on the violin is a triad (which is a fancy name for a three-note chord) formed on the dominant note (V) of any scale. A dominant 7th makes an even richer sound, using the same triad plus one more note: the seventh note above the dominant on which the chord begins.
You form a dominant 7th chord by adding a seventh interval on top of the third and fifth you already have on a dominant chord. For example, you make the dominant 7th of C major by playing G, B, D, and F.
The dominant is the fifth note of the scale, and it gets its name because the dominant is the most important note of the scale after the tonic. In both melody and harmony, this note tends to demand our attention.
This is what dominant 7ths look like when they’re built on G, D, and A, the same notes as your open strings. When you look at these dominant 7ths, you see all four notes together, to understand the full chord.
Because of the characteristics of the instrument, violinists would have considerable difficulty playing all four notes at once on most dominant 7th chords. So they usually play dominant 7ths in adapted forms, either arpeggiating the notes, or leaving out one or two of the four notes, but still giving the listener the impression of the full dominant 7th chord. You see two possible ways below.
To play the broken-chord dominant 7th in the first part, use a separate bow on each note. For the second part, violinists play just the two outer notes from the chord to give the effect of a dominant 7th. Place finger 2 on F on the D string before you begin to bow, and then balance the bow lightly on the G and D strings together, just like when you’re tuning the open strings. Draw a very smooth stroke. The second and third examples work exactly the same way, but on the other pairs of strings.
Here’s the last bit of Brahms’s famous “Lullaby,” for you to try with your dominant 7th harmony. Just place finger 2 on the note C (on the A string), and then bow gently on the D and A strings together, so as not to wake anyone! Prepare the fingers and the up-bow on the strings before they have to play, listen calmly to the first couple of bars on audio track, and then come in (as musicians call starting to play) at the third full measure with your dominant 7th.
Start that up-bow near the tip.