The rules concerning merging the noteheads of different notes are more complex than this. It's covered in Elaine Gould's book on page 52. Generally, black noteheads can be merged, since the presence/absence of flags makes the length obvious. Noteheads where the notes have the same value can be merged. Open notes (minims, etc.) should be kept separate from other open notes of different duration and from black headed notes.
It is acceptable for the dotted note to share a notehead with a note without a dot as long as the rhythm of both parts is absolutely clear.Should the rhythms appear ambiguous , use separate noteheads as this will always be the clearest arrangement.
Does this mean that the single note head is actually a chord of "G" and "G sharp" ?
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