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I recently started experimenting with the Phrygian dominant scale. As I understand, it is the 5th mode of a harmonic minor scale.
For example an A Phrygian Dominant consists of the notes A-Bb-C#-D-E-F-G. Same as D harmonic minor, right?
I understand the "Phrygian" part of the name, being the 3rd mode of F Major. However, what makes it dominant? Doesn't dominant imply that it is a V chord/scale?
First off, the A Phrygian Dominant scale consists of the notes:
A - Bb - C# - D - E - F - G
You got the first part of the name right as the Phrygian part of the name does come from where Phrygian is typically derived. The dominant comes from the fact that you can build a dominant 7th chord off the tonic as A, C#, E, G spell A7. There are other scales named after this for example the Aeolian Dominant scale which is the typical Aeolian scale with a raised third.
When talking about music theory, many words, such as 'dominant' are recycled. However, what you're asking is why the scale is called dominant; when talking about scales, dominant refers to there being a major third and a minor seventh. In the case of A phrygian, there is normally a natural c and g, but in dominant phrygian, you sharp the c to get a major third, while leaving the g natural as a minor seventh, hence the 'dominant'.
That is also why when you see a chord with a '7' in it, like C7, (not to be confused with Cmaj7 or Cmin7,) you can call it a 'dominant' seventh chord, because it uses the mixolydian scale, which contains a major third and a minor seventh.
