Although I sometimes use a 1-2-3-4 fingering technique below the half point of the string (12th fret, if we had frets), I often find a thumb position fingering to be more efficient, easier on the hand and, most importantly, more accurate.
Of course, many bass players first learn thumb position starting at the half point of the string (G harmonic on the G-string). It’s an easy place to learn it, and thumb position is the most common fingering system used from this point of the string and higher. Because of this, it’s nice to have some introductory exercises for using thumb in the lower positions.
For those who are just starting to use thumb position below G-string the exercises below are a good introduction. They are simple and tonal, which helps ensure proper finger spacing. They work the region between the half point of the string (12th fret, if we had them) and traditional 4th position (7th fret, if we had frets).
Here they are:
* Most hands will require the use of a small “pivot” to the second and third fingers.
Once you are comfortable with these, feel free to expand on them and incorporate these ideas into your scale practice. Use of thumb in the lower position will open up a myriad of possibilities on the bass.