wondering about scales in thirds

[Bob]

In terms of jumping with the hand. 

And being able to play legato.

For fingerings, should you use ones that repeate 24 13 a lot?

Or use ones that don't keep repeating 24/13 so much and use 35?  But if you get to 35, then you have to have your hand leap which makes legato much more difficult, if not impossible -- It's more difficult to keep one finger down while leaping with the hand. 

[stevebob]

It depends on context (e.g., chromatic or diatonic, major or minor, or some combination thereof).  Within repertoire, a further consideration is whether a fingering choice facilitates the desired execution—phrasing, articulation, dynamics, rhythm and tempo—or hinders it.

For what it's worth, Carl Tausig's extract of 29 exercises from Clementi's Gradus ad Parnassum concludes with scales in double thirds (along with the fingering he prescribes).  Major and melodic minor scales are present in all keys, followed by scales in chromatic minor and chromatic major thirds.  They start at p. 110 of this file:

https://imslp.info/files/imglnks/usimg/1/18/IMSLP03742-Clementi-Tausig_Gradus_1.pdf

Hanon, too, offers the chromatic minor thirds scale plus the major and harmonic minor scales with fingering "in the "keys most used" (exercises 50 and 52, respectively, of The Virtuoso Pianist):

https://imslp.info/files/imglnks/usimg/7/73/IMSLP00876-Hanpart3.pdf

At any rate, there are many possible fingering sequences.  In his prefatory remarks to Chopin's "Thirds" Etude (Op. 25 No. 6), for example, Alfred Cortot lists no less than 10 possible options for the ascending chromatic scale at mm. 5 and 6—and he recommends cultivating fluency in all of them!  

[Bob]

I was thinking major scales.  Straight up and down.  I've glanced at the Tausig and that's what got me thinking about repeating 42 31 a lot.  I came up with my own fingerings but I think I have 53 in them more.   And some 12 to 13.  I was thinking doing a lot of 42 to 31 was being as efficient.  But having to jump after a 53 chops up the smoothness.  So now I'm wondering if lots of 42 to 31 is ok because it makes them smoother.