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I am learning "A Hard Day's Night" by the Beatles which is in G Mixolydian mode or C major. In the score I have of this song the writer notated the song in G major and used accidentals on the notes that are not part of the G major scale. Why couldn't they have just used C major as the home key as all the notes pertain to that key?

Is this because the song keeps going back to that G chord? If this is the reason, it seems silly, because you could have a C major song with these chords in a bridge, and then it would be notated in C major.

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    Closely related question here. I don't really believe, that G mixolydian and C major are similar, not to talk about exchangable, as suggested in the first sentence.
    – guidot
    Commented Jul 16, 2018 at 11:09
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    @guidot - they are more than similar in the notes each uses, they're identical ! But 'home' is a very different place.
    – Tim
    Commented Jul 16, 2018 at 11:21

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I think the song is more ambiguous than you state. If the G chord contains an F, then the song is in G mixolydian, but if the G chord contains an F♯, then the song is in G major. The problem is that the chords aren't voiced with a 7th at all. If we turn to the melody for guidance, we find that the melody never contains a 7th over the G chord. We do hear the F in the melody, but only over the FMaj chord. However, we also hear F♯ in the melody (numerous times in the bridge).

So for the person notating, it's ambiguous whether the song is based on G major or G mixolydian. On the one hand, if they write the key signature with an F♯, they'll have to specifically mark the F♮s in the chorus. On the other hand, if they write the key signature with an F♮, then they'll have to specifically mark the F♯s in the bridge. So neither choice is perfect. Given that fact, choosing G major for the key signature avoids any additional confusion: no one will mistake the song as being in the key of C major.

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    This is why I generally assign key signatures based on the tonic and whether the music sounds more major or minor, not the mode it sounds the most similar to. I find that music, just like this example song, doesn't tend to strictly adhere to modes.
    – Dekkadeci
    Commented Jul 16, 2018 at 14:08
  • I don't think this is a good way of deciding between mixolydian and ionian. Blues uses minor sevenths almost exclusively, yet it's not really mixolydian. And many tunes don't use any chords with a ⅶ note in them at all (most typically, only switching between Ⅰ and Ⅳ), yet can be clearly classified as either ionian or dorian. Because these are mostly a melodic affair, and if the melody keeps going between Ⅰ and ♭Ⅶ then it's clearly mixolydian.
    – leftaroundabout
    Commented Jul 16, 2018 at 14:41
  • ...I'd say the verse is clearly in mixolydian, whereas the bridge is ionian.
    – leftaroundabout
    Commented Jul 16, 2018 at 14:44
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    Additionally, the bridge is...the bridge. It's fairly common to modulate to a different key in the bridge, which could explain the difference.
    – John Doe
    Commented Jul 16, 2018 at 15:37
  • @leftaroundabout I think this sounds sensible to me, the writer chose ionian in this case. I hadn't realised that it was ionian further on. That explains it!
    – user35708
    Commented Jul 16, 2018 at 17:52
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I think that G Mixolydian uses the same notes as C major, therefore it should have the same key sig. - no # or b. It shouldn't really have a g major key sig., as it's not in G major.

However, it could be argued that because 'home' is a G note, when it's written in G (F# key sig.) and all the Fs are natural, it's a sign that it's not actually in G major, but G Mixolydian. But surely the main purpose of a key sig. is to obviate the need to keep using accidentals throughout the piece?

Your header hints of why Mixolydian is a major mode. Simply as it contains a major third above its root.

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    I disagree that the main purpose of a key signature is to avoid writing accidentals. Rather, the main purpose of a key signature is to signify the key. If you're notating something in minor, you don't worry about whether you're spending enough time in melodic minor that you could save some accidentals by writing it in major and lowering all the 3s; you always write it in minor, and the fact that there are lots of raised 6s and 7s is a strong signal that it is in a minor key and not the parallel major. I think it's not unreasonable to do the same for modes.
    – Micah
    Commented Jul 16, 2018 at 17:52
  • @Micah - we're probably agreeing here. The main purpose is to signify the key. Since modes have the key of their parent key, that's what happens. They never have a key of their own.
    – Tim
    Commented Jul 16, 2018 at 18:56
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    @Micah: Indeed, the "Dance of the Spooks" in the Thompson piano books is in D minor (one flat in the key signature), but there there are over a dozen B naturals and zero B-flats in the entire piece.
    – supercat
    Commented Jul 16, 2018 at 20:14
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Consider the song "Little Drummer Boy". If one writes the song with a key-note of G, the melody and some possible harmonizations would be devoid of F-sharps. On the other hand, the only F in the melody occurs in a rising passage where, in the absence of a printed accidental, a performer would likely be more likely to notice that the note is just below the key note of G (which, since the song seems to be in major, would imply that it should be just a half step below the key note, i.e. F#) than to remember that even though the piece seems to be in G, there's no F# in the key signature.

If putting a natural sign before the F would be necessary to ensure it gets performed correctly, having an F# in the key signature which gets canceled by the natural sign would be no less readable than omitting the F# in the key signature and using a cautionary accidental. Unless one is hand-transcribing a score, there's no need to try to minimize the total number of sharp signs on the page.

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