You have a few options here. Your preferred way is completely fine. Most musicians would pick up on the mode by seeing the F sharp in the key signature and then seeing the F's being natural in the music. Alternatively, you could simply let your musicians know what mode it is in by writing "G mixolydian" near the key signature. That would make it very clear. Another practice, common in jazz, is to have the key signature be "key-less". This would simply look like C major or A minor as you stated, with any accidentals being notated in the music.
Key signature for writing in modes other than major and minor?
I have trouble deciding what accidentals to put in the key signature for pieces in Dorian, Phrygian, Lydian or Mixolydian modes. There seem to be trade-offs associated with each choice.For example, when writing in G Mixolydian, setting an empty key signature makes it look like C major or A minor. Having the F# in the key signature forces me to put accidentals all over the piece to mark F naturals.I prefer to use (in this example) the key signature of G major and natural signs on every F, especially when writing for choir. Singers with varying reading skills will often unconsciously assume that if the piece has G as the tonic, then it is in G major. The natural sign on every F will help them remember there is something special about it.Is there any kind of convention to follow?
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