I'm reading a book on music theory, which says that a diatonic scale is any seven-note scale that uses the notes ABCDEFG in an arrangement of 5 tones and 2 semitones.
I wanted to clarify one point: Consider the scale G major. It has one sharp, F#. Is it still a diatonic scale? Can a diatonic scale have sharps and flats?
If G major is a diatonic scale, then I assume that all major scales, and all minor scales, are diatonic.
You are correct. The pattern of tones and semitones that make up a diatonic scale can be transposed to any starting pitch without altering the "diatonic-ness" of the scale. All major and natural minor scales are diatonic.
If you look at the T/S pattern for the scale you list (starting on A) it's: TSTTSTT. A diatonic scale is any rotation of this pattern (the different rotations are called "modes"), which can then be transposed to any starting pitch.
If you're wondering what's so special about this pattern, wikipeida explains it well:
This pattern ensures that, in a diatonic scale spanning more than one octave, all the half steps are maximally separated from each other (i.e. separated by at least two whole steps).
Yes the G major scale is diatonic. The basic idea of something being diatonic is that you would be able to "pass though" all letter named notes in the scale. By doing this each scale degree would get an individual letter name. 'Dia' itself means though and any scale that goes through all 7 letter named notes and repeats is diatonic.
So in the key of G major you have G, A, B, C, D, E, and F#. You have one of each letter name in the scale so the scale is diatonic including any major or minor scale.
There is confusion with the term diatonic. Most sources I've checked refer to the notes in major and minor scales. This is reflected within the key signatures. Thus any note from G major, including F# but not F, will be diatonic. So a tune which uses only those notes, in that key, at that point in the piece, will be diatonic. The minors have a bit of vagueness about them. The natural minor is fine, in that it contains the same notes as its relative major, reflected in the key sig. But both the harmonic and melodic contain notes not indicated in the key sig. However, most sources seem to be happy that they are also diatonic. As in a piece written in,say, A minor, can contain F, F#, G, G#, which may not be found in the key sig.
This means, according to some sources, that modes, as in Dorian, etc., can also be construed as diatonic.
The 'opposite' of diatonic is chromatic, where notes other than those specifically found within the key are used.
