The third is arguably the most defining note within a chord. It gives you the essential information you need to know about a specific chord: whether it’s major or minor. So, for example, as long as you play an E note over a C bass note, that will always mean C Major. On the other hand, if you switch to an Eb note over the same bass tone, you will get a C minor sound. That’s the power of the third. If you manage to find a way to highlight the thirds in your solos, you will always sound like you’re “glued” to the chords. Good improvisers can make you understand what harmony they’re playing over even when nobody plays chords behind them. While playing, the problem with thinking about scales is that not every note inside them is equal. For example, an A note over a C bass will give more of an A minor sound. An F note will provide you with an F power chord sound. These notes are in the C Major Scale, so they’re not “wrong”. Still, neither will make a C Major sound. Bear that in mind.