I was watching an instructional video and the guy's talking about Mixolydian #11 being one of the modes of the melodic minor.

The regular G mixolydian looks like: G A B C D E F G

And the G Mixolydian #11 looks like: G A B C# D E F G

So why is it called #11 and not #4 since we sharped the 4th degree? Also, at what point do you call a mode a dominant. I recall when the 3rd scale degree of Phrygian is sharped, they call it the Phrygian Dominant.

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    I've heard it called both. The #11 emphasizes the chord-aspect, but I suspect that most people don't give too much thought to which way they name the scale. Note that Mixolydian #11 (I usually call it Lydian Dominant) is a mode of the Melodic Minor scale, not Harmonic Minor, though. – ex nihilo Apr 9 '19 at 15:17
  • He also calls it 'b5', which is possibly worse - as you've now lost the C note (in key G Mix.) and have two Ds! I see no good reason for using 11 at all. The 4th note is affected as well. – Tim Apr 9 '19 at 15:17
  • @DavidBowling - good catch with melodic rather than harmonic. That 6th note is key. – Tim Apr 9 '19 at 15:18
  • You can derive the same mode by lowering the seventh degree of the Lydian scale, so you might also call it Lydian flat 7 (or flat 14?). But it might make more sense just to pick another Greek place and name it after that. – phoog Apr 9 '19 at 15:39
  • I think I remember seeing once, perhaps in Levine's The Jazz Theory Book, that the difference comes in either chord quality or function, as in major chords it's #11, minor chords it's #4 OR dominant chords it's #11 and tonic chords it's #4 (these are meant as illustrative examples and not meant to indicate the actual rules/conventions for chord nomenclature). – John Doe Apr 12 '19 at 22:58

In my experience, I've always heard scales referred to with their scale degrees altered, not chord extensions. Therefore, it's Mixolydian ♯4 in my book (or at least in my answer).

"Dominant" as part of a scale name (or any name) always means that the third is major and the seventh is minor. Usually, when it's something like "(mode name) Dominant", it means that it's just that mode but with the necessary alterations to make it a dominant scale. So, Phrygian Dominant is like Phrygian but with a major third, since it already has the minor seventh. Mixolydian Dominant doesn't exist, for obvious reasons. A lot of the modes don't really have a "dominant" version; Dorian Dominant would just be Mixolydian.

Phrygian Dominant and Lydian Dominant are the only two scales I've heard named using this convention, although I suppose one could have a Locrian Dominant scale.

TL;DR: Scales take scale-degree alterations, and Dominant in the name means M3 and m7.

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I have heard it called "Mixolydian #4" or "Lydian Dominant."

Maybe I have seen "Mixolydian #11" but I probably ignored that as an obvious mistake and understood it to mean #4 in the scale.

#4 makes sense in a scale description. #11 makes sense in a chord description.

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Both names are used and both make sense. You're right that it's the fourth scale degree that is sharpened, but as a tension, that scale degree is usually added to harmonies in the higher octaves, hence #11.

As for your question on the name "dominant" in phrygian dominant, it's about the major third. Phrygian has a minor third, and its basic seventh chord (made of the 1st, 3rd, 5th, and 7th scale degrees) is a minor seventh chord. If you change the third to a major third you get phrygian dominant, which has a dominant seventh chord as its basic seventh chord. That's also how this scale is used very often: over a dominant chord in minor. E.g., over A7(b9) resolving to Dm (6,7) you can play A phrygian dominant (which is just the fifth mode of D harmonic minor). Unlike the phrygian mode, phrygian dominant has the leading tone resolving to the tonic. E.g., in the key of the D minor, A phrygian dominant has a C# which resolves to the tonic D.

Any scale with scale degrees 1, 3, 5, and 7 that form a dominant seventh chord can be considered a "dominant" scale, e.g., mixolydian, mixolydian #11, phrygian dominant. Of course, there are also other scales that can be used over dominant chords, such as the half-whole (8-tone) scale, or the altered scale (seventh mode of melodic minor).

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