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Double Bass Fingering for "Afternoon in Paris"

On July 24 of 2019, @Garagiste, posted:
"'I'm trying to get more in the habit of being able to both sing and play the heads to the tunes, preferably arco and pizzicato. Right now I'm working on "Afternoon in Paris" . . .

I'm about where @Garagiste was two years ago: trying to learn heads and working on "Afternoon in Paris." I've memorized the tune, but I ran into trouble. I found that my fingering is not working well for me as I get up to speed (around 133).

Not to make anyone work that hard, but I'm looking for either some general tips on best practices for efficient left hand fingering, or a fingering for that works for you.

Right now, I'm finding that linear-fingerboard thinking seems to work better for my left hand than cross-fingerboard thinking. I'm starting at E on the first string (G). Part of the problem is that I'm only just learning thumb position, so it's hard for me to evaluate the comparative ease of more vs. less of it when it comes to getting this tune up to speed.
 
I do not define my fingering strategy in terms of longitudinal-fingerboard or cross-fingerboard, but rather in terms of kind of shifting I favor or avoid.

I play mostly with Simandl technique (1-2-4), plus pivots when I am at the neck heel.

I usually avoid shifting twice in a row as this is detrimental to my intonation. So I strive to always play at least 2 consecutive notes (or 1 long note) in position before shifting again. Exceptions to this are for notes accessible by a 1/2 step pivot when I am in the neck heel region.

An other thing I try to avoid is simultaneously shifting and string crossing with same finger as it is difficult to play legato when doing this. If I have to do this (only across adjacent strings) I use a combination of finger rolling across the strings and gliding along the target string.

Using appropriately open strings is very useful, in particular to manage long shifts (a 4th or more).

NB. what I discussed here is for pizzicato playing in the low and medium register. Arco and high register (thumb position) may require different fingering strategies.
 
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If you haven't already, take a look at George Vance's book "Vade Mecum". He presents two octave scales with a variety of fingerings. Slowly working through these scales will expose you to fingering options as well as forcing you to use more of the fingerboard. If you are not comfortable in thumb position, you could start with F or G major. The book also has some exercises to help with thumb position. Then, you can move to more straightforward scales that incorporate thumb position (e.g., Bb, C). Anyway, it's a book that will keep you busy for a few months.
 
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I like to perform musical sequences as physical fingering sequences when possible. In the case of AIP, each measure exists within a 3 half step block that can be played mostly across the top 2 strings, with the descending 6th leap in mm 2 and 4 being the only 1st to 3rd string crossing needed.
 
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I'm good at this point. I think I have something figured out. The trick is going to be that it will hold up as I get it up to speed. I'm not really a jazz player. I'm more of an "enhanced melody" player. The goal is to make the enhancements not sound like clams.