While playing around with some simple melodies on my piano i realized that tapping (like a single tone in a trill) the tone one half-tone below in a melody before playing the actual tone sometimes sounds a lot 'more right' than just playing the tone alone.
Why is that? What are the concepts behind it?
It's an approach note from below, and if it's a half-step below, it's a chromatic approach note. Why it sounds good:
Edit: there's been some interesting discussion in the comments. I'll just add that these phenomena I listed are why I use the technique described by the OP. I use it to make note attacks less monotonic and therefore more interesting, to create short bits of tension/release by flirting with a "wrong" note, and to add some ascending motion if I think there's too much soothing descending motion in the melody. YMMV, but I feel these things very strongly, just like Dm6 - B7 - E7 - Am6 feels very different from Cmaj7 - D7 - G7 - C in a concrete and real way. You can easily try it yourself - does adding approach notes to a few melody notes make a boring melody feel more varied and interesting or not? Does descending pitch motion feel more soothing than ascending pitch motion?
This is a technique common in jazz, blues, and pop styles. It is essentially mimicking the way vocal, string, and wind players scoop or slide into a note. Since a true portamento is not possible on piano, it is simulated by quickly hitting a note above or below the target note slightly before the target note. Though today it is more common popular music, it is similar to embellishments we see in Baroque and Classical music. They are usually notated as grace notes.
In the classical world, this is one form of acciaccatura, sometimes called the short appoggiatura.
More generally, these are kinds of ornaments. As noted in another answer, this kind of ornament is also common in other styles of music.
The precise meaning of acciaccatura has changed over time. One definition holds that it should be struck at the same time as the principal note, but released immediately while the principal note is held. The other definition is that it should be played immediately before the principal note, as in the short appoggiatura.
The precise nature of the distinction between the short appoggiatura and the acciaccatura seems to be a matter of controversy. It will in any case depend on the period of a piece of music or even its composer.
Not covered in any of the other correct answers (although alluded to in the comments), this can also be a compensation at a subconscious level for the artificiality of the tempering process.
The natural scale is formed by mathematical relationships between the frequencies of pitches. But all natural scales are formed in relationship to a single root note, and are therefore "attached" to a single key. To make instruments more flexible and able to handle multiple keys and key changes, a technique called "tempering" was invented. This tweaks the notes of the natural scale to slightly different notes that sound almost the same. Now, instead of having a piano in the key of A or the key of C, you have a piano that handles all keys in the chromatic scale.
This flexibility, however, comes at a price. There's some reason to believe that people are subconsciously aware the intervals are just slightly off. For that reason, some musical styles, such as blues and jazz, use pitch bending, grace notes and accidentals to suggest notes closer to the natural scale tones. (If this interests you, I have an essay on the topic here.)
