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I've noticed that strumming from an F to an E chord, or even just the note itself, produces a characteristic flamenco sound, if the root is E. What are the other notes to this scale?

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That sound you're hearing known as the Flamenco Mode, or the Major Phrygian mode.

The traditional Phrygian mode is the third mode of the major scale - essentially starting the major scale on the third degree, so E Phrygian would be: E - F - G - A - B - C - D - E

The traditional Phrygian mode is used in Flamenco, too, but to turn this into Major Phrygian (aka the Flamenco mode), just raise the third degree, so: E - F - G♯ - A - B - C - D - E

There is another variation that also raises the seventh degree: E - F - G♯ - A - B - C - D♯ - E

I should note, though, that Flamenco is a whole genre of music that is not just based off one scale. Using this mode, you can make music that sounds kind of Flamenco-like, but it is just one small ingredient in creating real Flamenco music.

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    What's awesome is that by simply using the notes without any sharps or flats and choosing your lowest note as the root automatically makes you do phrygian on guitar. One might say flamenco is the most natural thing for guitar.
    – Džuris
    Dec 15 '20 at 11:59
  • When you raise the 3rd of the Phrygian mode that is equivalent to raising the 7th of the relative minor mode in the same key. Example, E phyg #3 is just A harmonic minor. The real question is what progression are you playing this over? E phyg (#3) over E min? Or over Am?
    – user50691
    Dec 15 '20 at 13:55
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The Simple Answer

The F to E transition marks the last two chords in an Andalusian Cadence (i - VII - VI - V, in your case Amin - G - F - E), which is a very prominent characteristic in Flamenco music. To think about Flamencos in a simple way, you can think about playing in a harmonic minor, which follows the pattern WS - HS - WS - WS - WS - HS - Aug 2nd - HS. You're in the key of A minor, so your harmonic minor would look like:

enter image description here

The G natural comes from the fact that the Andalusian scale is calculated from the natural minor. Because you are going for a major chord (indicated with V instead of v), the G# would arise as an accidental from your fifth step

The More Complicated Answer

To that point, there is such a thing called Flamenco Mode, which is the Major Phrygian mode.

In the (non-major) Phrygian mode,

Normal Phrygian scale

you follow the pattern of HS - WS - WS - WS - HS - WH - WH. To contrast, a Major Phrygian mode would have you raise the third (and seventh, as necessary). You would be playing in E Major Phrygian:

Major Phrygian scale

EDIT: As a little side note, you'll notice that if you don't sharp the seventh in your Major Phrygian scale, you'll end up with something that resembles a harmonic minor scale that starts from an E instead of an A. Something is afoot! :)

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    I think the “Andalusian Cadence” as ⅰ-Ⅶ-Ⅵ-Ⅴ is actually more common in Rock/Pop than it is in Flamenco! What really is characteristic about flamenco is how the Ⅵ-Ⅴ transition is played with. Dec 15 '20 at 10:59
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    To me E.... F G F E sounds like the most flamenco sequence
    – Džuris
    Dec 15 '20 at 11:56
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    This is a much better answer. It points out the relation (correct relation) to the progression. +1
    – user50691
    Dec 15 '20 at 13:57
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    Indeed, the Amin - G - F - E progression gives such a strong flamenco feels to it, particularly when it resolves from the II to the I, ie, F to E when strummed. The half-step gives it so much flavour. Dec 16 '20 at 1:42
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You’re certainly looking for the Andalusian Cadence:

https://en.wikipedia.org/wiki/Andalusian_cadence

If you’re strumming or picking triad-patterns with the chords of the Phrygian cadence Am-G-F-E and improvise on the notes mi-fa-si-la, you will have the typical Flamenco sound.

https://www.guitar-chord.org/articles/flamenco.html

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