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Double Bass joel quarrington ibook!!

Playing a half step, 1-3, in the lower positions is not something I was ever taught. It really comes in handy, though, and helps develop the strength of the 3rd finger. Basically, I never use it when playing 3 notes in a position. That's always 1-2-4. But if I am just playing a half step before shifting, I offers use 1-3. Especially if it is a trill or a goose egg. Playing 1-3 helps keep the hand compact, strong and reduces tension in the hand.
It's another tool in the toolbox.

p.s. one fingering that I like a lot is when playing a half step, followed by a shift up the same string to another two half step notes. for example: E-F-G-Ab or E-F-G#-A up the D string. Fingering it 1-3-2-4. It keeps the hand compact and powerful and eliminates the gliss if you finger it 1-2-2-4 and is a shorter distance than a fingering of 2-4-2-4 or 1-2-1-2.
 
Playing a half step, 1-3, in the lower positions is not something I was ever taught. It really comes in handy, though, and helps develop the strength of the 3rd finger. Basically, I never use it when playing 3 notes in a position. That's always 1-2-4. But if I am just playing a half step before shifting, I offers use 1-3. Especially if it is a trill or a goose egg. Playing 1-3 helps keep the hand compact, strong and reduces tension in the hand.
It's another tool in the toolbox.

p.s. one fingering that I like a lot is when playing a half step, followed by a shift up the same string to another two half step notes. for example: E-F-G-Ab or E-F-G#-A up the D string. Fingering it 1-3-2-4. It keeps the hand compact and powerful and eliminates the gliss if you finger it 1-2-2-4 and is a shorter distance than a fingering of 2-4-2-4 or 1-2-1-2.

Goose Egg = Whole Note
Yes, I like to play a whole step-half step with a 1-3-4 pivot on many occasions. Especially if those notes are all under a slur. But that's a pivot, not an extension. I don't like the idea of playing a whole step with 1-3.
I recently started studying JQ's e-book (2nd Ed, in PDF format). One thing (among many others) that was a real light-bulb moment to me is his use of the 3rd finger.

In some sense, he combines Simandl's 1-2-4 and Bille's 1-3-4 (Italian school) techniques.

Playing a half-step with 1-3 is so natural! (at least in the low range). The hand remains fully relaxed and this avoids the effort needed to spread 1 and 2. Same of course for playing a half-step with 2-4 (Simandl).

So when playing a minor 3rd with pivot, JQ plays 1-2-4 if it is divided in half+whole (like E-F-G on D string) and 1-3-4 if is divided in whole+half (like A-B-C) on G string.

Curiously, I find it more ergonomic to do the opposite, i.e., to play E-F-G with 1-3-4 (half-step 1-3 followed by pivot 3-4 for the whole step) and to play A-B-C with 1-2-4 (whole-step pivot with 1-2, followed with half-step 2-4).

Any thoughts on the latter point?
 
I recently started studying JQ's e-book (2nd Ed, in PDF format). One thing (among many others) that was a real light-bulb moment to me is his use of the 3rd finger.

In some sense, he combines Simandl's 1-2-4 and Bille's 1-3-4 (Italian school) techniques.

Playing a half-step with 1-3 is so natural! (at least in the low range). The hand remains fully relaxed and this avoids the effort needed to spread 1 and 2. Same of course for playing a half-step with 2-4 (Simandl).

So when playing a minor 3rd with pivot, JQ plays 1-2-4 if it is divided in half+whole (like E-F-G on D string) and 1-3-4 if is divided in whole+half (like A-B-C) on G string.

Curiously, I find it more ergonomic to do the opposite, i.e., to play E-F-G with 1-3-4 (half-step 1-3 followed by pivot 3-4 for the whole step) and to play A-B-C with 1-2-4 (whole-step pivot with 1-2, followed with half-step 2-4).

Any thoughts on the latter point?

Yeah seems like you could do it either way in that case. Your reasoning makes sense, and so does Joel's.

In a different scenario, if you want to shift higher with ~The Move~ it's better to be pivoted (supinated?) on 2nd finger than stationary on 3rd finger, if that makes sense.

I'm personally getting along fine without using the 3rd finger in lower positions so far. It seems like a cool challenge to add it in but 5ths tuning is hard enough to adapt to for now.