The one-finger-per-fret rule applies to all fretted instruments. It specifically refers to fretted instruments like guitar or bass, but the rule also works on other fretboard instruments that don't actually have frets, like a violin or cello.
The one finger per fret rule implies that each finger is assigned a fret to play and only plays the notes occurring on that fret. The bass example given in this lesson is a warm up exercise. You can easily transpose it onto guitar or any other fretted (not-fretted) instrument if you wish.
Notice in the bass tab the the exercise is played at the 5th fret. To play this exercise play each note on the fifth fret with your first finger, each note on the sixth with your second finger, each note on the seventh with your third and each note on the eighth with your fourth finger. The numbers on the hand image help you know which fingers apply to which fret.
An exercise like this is a great warm up exercise. Play it regularly to build up hand strength and dexterity. And, while you're at it make sure your other hand is accurately hitting strings also. That's a crucial element that is so often ignored by many players. Get both your hands working in sync.
Play this exercise all over your fretboard. You'll find that up near the nut you need wide stretches, and way up high things can get a little claustrophobic.
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