In the previous articles... Yes, I know I often begin my articles this way but it's simply because I like things to make sense chronologically.
So, as I was saying, in the previous articles I have introduced you to different chord substitution possibilities to make your compositions and improvisations more varied. And as you probably noticed, this is usually achieved by introducing notes and chords that do not belong to the song's key.
More often than not, the introduction of these non-chord tones implies nothing more than the adding of a new harmonic color to the song, as we saw in article 8. But in many other cases the song does change its actual key! That's called modulation. And it's not enough to just write down some alterations on the score to achieve that. As discussed in article 8, these could be simple passing notes or even just grace notes.
We also saw in another article that you can substitute one chord for another one without that implying that you are modulating towards another key. These substitutions could be simple embellishments of a chord with non-chord tones (see article 14). Or you might have to deal with secondary dominants (see article 15) which, rather than making the key of a song vary, they actually reinforce the status of the key degrees to which they lead. Or it might just be a "mere" tonal exchange (see article 16) which basically means replacing a chord of a given key with its equivalent from a parallel key (Emaj with Emin, for instance). And, again, this doesn't mean that the key is changing.
But then, what do you have to do in order for a modulation to take place? Well, the variations need to extend long enough so that your ears "understand" that you have moved to another key. And your ears won't know that unless the new key imposes itself. As we saw in the first articles of this series, the key of a song depends on very specific criteria related to the key signature, the intervals and the relationships between the degrees of the key. So, to be able to consider that the key has changed ─ that a modulation has taken place ─ these same criteria need to apply to the new key. This can be confirmed by the presence of new alterations that correspond to the new key, new chords and chord progressions that establish the perfect cadence of this same key, etc.
Still too abstract and obscure? Don't worry, I'll explain everything in more detail next time!