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I don't know much about chords and scales, so sorry if this question sounds misinformed. This just seems like witchcraft to me. Here's playable sheet music for this 1848 composition by Charles-Valentin Alkan: https://musescore.com/user/1795986/scores/731721

As you can see, the composition is mostly scale runs in octaves. Very Alkan!

sample

He never modulates anywhere, that I can tell. And yet there is not a single B flat in the entire piece. And doesn't just dodge them; all of his B's get naturals. This entire etude could have had a C major or A minor signature. Yet, the melody naturally lands on the F major chord, and I never get the feeling that something funky is going on harmonically. It is especially apparent in the final bar, where the right hand just plays every white key in a row - yet it ends on the F, and it sounds right! second sample

Is there a name for this "fake F major" key? Or a technique that is consistently being used to avoid having to use a black key? I would love to know how this works.

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This piece is in F Lydian. The Lydian is the fourth mode of the Major Scale: you can think of this as being the notes of any particular Major Scale but using the 4th degree as the tonic (root note). A simple example of a Lydian Mode would be the notes of C Major, but using the 4th degree (F) as the tonic. Coincidentally, this is exactly the mode used here. (It is also useful to think of F Lydian as being C Major notes from F-F, or as the Major Scale with a sharpened 4th degree. Either way of thinking is fine; they are different ways of looking at the same relationship to a Major Scale.)

Because a large amount of “traditionally” composed sheet music is not modal, but is instead based around one or more keys, it makes sense to use the key signature of the Major Scale of the tonic (F in this case), even though this piece is in F Lydian, not F Major. You’re right, this could be written with the key signature of C Major, but convention (usually) dictates that you allow the key signature to suggest the tonic note to the reader, even if this is “subverted” by the actual pitch material used.

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    Bit like with a key sig. of say one flat - Bb, one doesn't know if a piece is in F major or D minor. A look at the end is a good clue, as woud be some C# along the way (or lack of them!). I still think a better key sig. for this ought to be that of C major. Technically more accurate, at least? +1. – Tim Mar 27 '20 at 15:57
  • @Tim I don't think the C major key sig. would be more accurate. As Bob clarified at the end of the answer, convention (usually) dictates that you allow the key signature to suggest the tonic note to the reader. The tonic here is F. Not C. The C maj. key sig. would suggest the key is in C maj., but that would not be correct. – 89f3a1c Mar 27 '20 at 16:29
  • @89f3a1c So if the piece was in D minor, which key signature would be the most accurate? – JiK Mar 27 '20 at 23:49
  • The amusing part is that Alkan's Allegro Barbaro is the F major etude in a cycle of etudes in all major keys (he has a related cycle of etudes in all minor keys, too). – Dekkadeci Mar 28 '20 at 12:52
  • @Dekkadeci yes, that almost feels like a composer having a laugh, or possibly just being contrary for the sake of it! – Bob Broadley Mar 28 '20 at 14:59
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I know this has already been answered and accepted but just for another perspective I think this actually is in F Major and not F Lydian. The composer is simply focusing on the dominant, C major, which has the B natural. It's extremely common for pieces to modulate to the dominant (V, C major) and this one just does it immediately.

This was a common Romantic and modern technique to give the piece an unstable or floating quality. The home key is barely present and when it finally resolves it is not as strong as normal tonic resolution. Many of his contemporaries did this. Chopin does this, as well as Liszt and basically all of Wagner's music.

Once in C, there're lots of V > I there, G7 > C. One of the contrasting sections is in a minor, which is the natural minor of C major, which is a normal progression for any classical piece, in terms of high level sections, I (F) > V (C) > vi/V (Six of Five, a minor).

Also, the real test is does it sound like a mode or does it sound like a major minor piece. I will admit it does have an unusual tonality and sound, maybe even modal at times, but it still mostly feels major minor to me. I would compare this this Mussorgsky's Pictures at an Exhibition, which are mostly modal and also sound very modal and this sounds nothing like that. It also doesn't sound or feel at all like Jazz.

I do agree that the composer was having some fun, and gave himself the constraint of not using Bb, but my opinion is that it is still in F major.

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