Here's a cool little "secret" I found! If you play two notes a minor third apart and move that over each of the strings, you get the Dorian mode of the note you started on in alternating thirds.
Here's a TAB illustrating what I mean, for CGDA starting on the bottom open string. You get C dorian:
View attachment 4958419
(MuseScore still thinks the red notes are outside of the bass guitar's range even after I edited the string data

)
If you tried this with
major thirds instead, you get Lydian up until you reach the last note, which would be a sharp 15th instead! Reminds me of stacked fifths of George Russell's Lydian chromatic concept.
This begs the question. What are all the possible permutations of major and minor thirds in this fashion, and what "scales" do they produce? That would be 2^4 = 16 different permutations!
Since nobody asked, I'll list them out below. Having a major third at the very end will give us a sharp 15, so we can cut out half of the permutations and stick to the ones that will actually return us to the root. I'll list out the first three intervals, written as M or m for major third or minor third, respectively.
- M-M-M = Lydian
- M-M-m = Major
- M-m-M = Lydian dominant (4th mode of melodic minor, also called the acoustic scale)
- M-m-m = Mixolydian
- m-M-M = Melodic minor sharp 4
- m-M-m = Melodic minor
- m-m-M = Dorian sharp 4
- m-m-m = Dorian
Since we are keeping the same fret above the root, we will always get a perfect fifth, a major second, and a major sixth.