: What speed should I achieve for 8th note exersizes on the guitar I'm going through Linear Articulations by Pat Martino. He says "upon completions of this section, one should move to the next phase" after showing a bunch

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There are two things to consider here. First, very fast jazz compositions (such as Coltrane's Giant Steps ) are indeed often played close to 300 bpm. This is of course a consequence of the way the theme is notated. The standard notation for Giant Steps found in most real / fake books (see here) is to use half notes in the first two bars. Of course, if you used quarter notes instead you would end up at around 150 bpm, but that's just not the way it is done.

The other important thing is how to work with such a book. Even though you might come across eighth notes at 300 bpm, I would not recommend to wait until you master the first few exercises at that tempo. First of all, it's not only about speed. You want to cleanly execute all examples, and you want to learn how to choose the notes and how to play idiomatic solo lines. Try to play them cleanly and with good timing, and choose whatever tempo is appropriate for you, then move on. You move on to learn more phrases and to improve your solo vocabulary. At the same time you should try to improve your technique and increase the speed, but that's something you do while working through the book. If you try to play the first few examples at very high speeds, you will have almost no solo lines in your repertoire until you've learned enough technique, and that's frustrating and not useful. Because in practice, most pieces you'll come across are NOT played at 300 bpm.

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300bpm ? thats insanely fast, I wouldnt expect jazz (and its a broach church from slow jazz blues to fast ragtime) to ever go faster than about 140. If it were me, I would raise it by 10bpm each time.