There is in fact a name for such a composition: "etude" and it's a French word which means "an instrumental musical composition, usually short, of considerable difficulty, and designed to provide practice material for perfecting a particular musical skill." (quoted from Stepan Grytsay, one amazing violin player).
So instead of practicing some random tapping licks one after the other, you can string them together and thus create a composition you should play both to the click of a metronome and rubato (freely). This can make your practicing time more endurable, as you will be playing music and not just some exercises. It will also trigger your creativity.
There is a considerable amount of etudes for traditionally virtuoso instruments such as the piano and the violin. There are, however, enough etudes for classical guitar, and thanks to the rather non-academic character of electric guitar playing, technical proficiency is achieved mostly by endless and monotonous playing of exercises along the click of a metronome. Certain electric guitar methods acknowledge this and offer some etudes to make the learning process less tedious.
Besides writing your own etudes (musical exercises), you can also adapt those written for other instruments. It's fun and challenging, and you can also learn a good deal about composition. Today I want to offer you this cool piece by Heitor Villa-Lobos, perhaps the most famous Brazilian composer of classical music, who also penned a good amount of works for the guitar. I have adapted this etude to be played on the electric guitar, by means of sweep-picking and alternate-picking. The link to the download is included in the video description of the following YouTube video, where I play it myself.
Thanks for reading!
By Miguel Marquez