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To work out dominant sevenths for exams etc. you will need to know what key you are in (see key signatures). Once this is established, find the fifth degree (dominant) and build an arpeggio. To complete the dominant seventh, include the seventh note from the start of the arpeggio making note of the original key. To understand this a little better, follow the example.
What is the dominant seventh of G Major?
1. Find out the key signature of G Major (this has an F# in it)
2. Find the dominant (the dominant or fifth degree of G is D)
3. Build an arpeggio on D (D, F#, A & D)
4. Add the seventh note of the arpeggio keeping in the original key (Because we are in G Major, this is C not C#)
Put them all together to make the dominant seventh- D, F#, A, C & D.
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