What theory do I need to know to figure in-between notes for a blues riff?

Hello people. My question is as follows.

Let’s say I don’t have ears to help me decide what sounds good.
And let’s say I have a standard blues line that goes → root, 3rd, 5th, 6th, root

What kind of music theory do I need to know, to figure out which notes will sound good in-between my bass line, to fill in the gaps.

Thank you.

[mod edit - title edited to more fully reflect the question]

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Well, as the old blues masters used to say…
“If it sounds good, it is good!”. Trust your ears and experiment. (Because they didn’t know theory too).

I’m sure there will be some mathematical equation or something like that, telling you that this or that note works perfect “in between”, but in the end, it all comes down to “a feeling”.

How you interpret the song you’re playing, what you’re feeling at that moment in time, what you’re trying to communicate to your listeners, etc…

You can ask a thousand people this question and get a different answer every time.

Music theory is, in my view, needed if you want to dive deeper into how music’s made.
It will help you with chord building, extensions, reading sheet music, finding notes, building chords on the fretboard on the go, etc…
There isn’t, afaik, no “kind of music theory”. There’s theory, and that’s it.
If you want to know where it all started, there’s this:
“a raw musical form derived from African musical traditions, religious spirituals, work songs, and the field hollers of Mississippi slaves. The blues emerged in the Delta region of Mississippi during the late nineteenth century”

Source: What Came First, Blues or Jazz? | TheCollector
You could go down that path to get an deep dive into blues.

Or you could listen to a bunch of stuff, old and new and listen how it evolved.

So experiment. Try different things, learn your ears to listen to what you’re doing. You’ll find that some notes sound better than others. Those same notes will even have a chance of sounding different in your ears on a different day. (Here’s that feeling again).

Good luck!

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Thank you for answering. I’m asking specifically about that “mathematical equation” if it exists, regardless of what my ears are perceiving as good.

I’m gonna read the article too. Thanks for that.

If you add the 2nd you have the major pentatonic scale.
Are these played as single notes or as chords? If they are chords you could arpeggiate the notes of each chord to create a melody.

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My instructor would scoff at that idea, even if it existed (there’s probably math behind it, but I wouldn’t know it).

His process is learning and getting comfortable with scales and then experimenting within them. Learn them multiple ways, too. Not just the “patterns” but also the full length of the neck. Staying within the patterns works, but he says it can sound formulaic if that’s all you ever use. According to him, if you do those things, nothing is “wrong” per se.

He comes from a jazz and blues background with a ton of improvisation. He can noodle around and just sound good.

Everything else is about how you want to sound and what you’re trying to convey.

That’s what he set me up with and wants me to use to improvise on backing tracks and within “solo breaks” within songs. I’m still learning and getting comfortable with the scales.

Only notes, not chords. The bass line goes like in this one - starting with the A note - but Justin plays each bass note twice.

I play each bass note once and add the two open thinner strings in-between the bass notes. I think the combination is better with some of the bass notes.

And I was wondering how would I use music theory to say “these notes might work better than others as in-between notes because of a certain relation with the bass notes”.

I should have given a clearer example from the start.

Yes, I’m all about that in the sense that, if I play something that sounds good but the theory says “it should’t sound good” I will not care.
If it sounds good, it is good.
I just want to use music theory as extra guidance. Thank you for replying