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Can someone explain how the bass player reharmonises?

If you stay within the notes of the chord, i.e. R-3-5-7 but invert them 3-5-7-R you get another sound - same chord. Same harmony.

I've never been big on inversions. Piano guys do this a lot, as they can get all the chord tones in - with out moving the pattern - if they invert. I've always gone with what the old guys told me that my number one job, as a bassists is; to call attention to the root. Straight up R-3-5-7 does that so I let the other guys invert if they want to. I call attention to the root.

If you want to be more melodic inversions would help with that.
 
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how do the notes of the “original” chord become the notes of the new one?

saabfender nailed it in post #5: The way we hear chords has to do with the physical interaction of all the pitches...not just the chord tones themselves but each notes' overtones as well. When you add a pitch lower than all the other pitches in the chord our ear (often, but not always) gravitates towards hearing that lowest note as the root and recontextualizes all the other pitches accordingly.
 
I spent some time at a larger library than what we have in my home town. I was looking in the stacks for something on music harmony. One of the librarians came up and asked me what I was needing to know. I told her I needed to understand harmony. She gave me three books, I took them and spent several day going over what they had to say about harmony.

Sorry it has been so long I do not remember the titles, however, talk to your librarian. If they do not have what you need in their library, they can borrow from a larger library. There is no fee for this at my small library. Give it a try.

Good luck.
 
No one has mentioned the very basic approach of inversions. Like you have a C major chord C E G
you can put any one of those notes into the root without changing the function of the chord
first Inversion E G C, second inversion G C E

That said, the chord in root position is always going to have the strongest motion.
Throwing in inversions usually got me a "that sounded wrong" from the rest of the band.
My advice is to not change the harmony unless you consult the rest of the band.

The basics of harmony are outlined in the PDF in my signature
 
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So I know that the bass player can change the whole harmony of a chord by choosing another low note, but can someone explain how it works? Like how does the chord change, and what are good note choices in a scenario?
Grab yourself a "contemporary" jazz theory book. My favorite is by Arnie Berle, but there's hundreds of great books out there now.
I'd start with the classic substitution of chord qualities first; like swapping a ii chord for a IV, or a vii for a V chord.
Then maybe look into tri-tone substitutions, which involves building a chord (typically dominant) of the flatted fifth of an existing Minor or Dominant.
Those are just two examples you can try, there's countless other possibilities out there.

Make sure you study you chord tones and intervals first and foremost too. The key is in realizing what chords share what chord tones, and how you can manipulate this knowledge thereafter.
 
So I know that the bass player can change the whole harmony of a chord by choosing another low note, but can someone explain how it works? Like how does the chord change, and what are good note choices in a scenario?

It is called chord super imposing but in reverse.

Example: a piano player could decide to play a c maj7 chord. There are many ways of playing but this way means that we expand the harmony by super imposing an emin7 while playing the c in the bass or somewhere else. This way we actually get a cmaj9 sound. If you reverse the process and think of a piano player playing an emin7 chord, you can influence the chord as a bass player and play the note C in which case it will sound as a cmaj9 again.

So, there you go.
 
No sure if it counts as reharmonising, but Chris Squire's bass line on Perpetual Change where he holds the dominant for ages before finally moving to the tonic absolutely makes the end of that piece.
 
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Exactly that. But what note would the bassist be playing, and how do the notes of the “original” chord become the notes of the new one?
Simple, the chord is spelled differently if you are playing a different note that is not in the original key chord because it adds a note to the chord that was not already there, changing the chord from "what it was" to "what it is now".

Also, go look up "modes" in music theory. Basically if you start a scale on a different note other than the tonic and play through the scale it will give a different feel to the music even though the notes used are the same notes as in your normal scale. Each mode has a different name depending upon what note is used in the starting position. By the way, this can get real confusing real fast but it can definitely change the feel and the mood of the music when you use something out side of the tonic (the I, the root) in the bass or start a bass run from it.
 
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No one has mentioned the very basic approach of inversions. Like you have a C major chord C E G
you can put any one of those notes into the root without changing the function of the chord
first Inversion E G C, second inversion G C E

That said, the chord in root position is always going to have the strongest motion.
Throwing in inversions usually got me a "that sounded wrong" from the rest of the band.
My advice is to not change the harmony unless you consult the rest of the band.

The basics of harmony are outlined in the PDF in my signature
Inversions are not reharmonizing. Reharmonizing is playing a different chord than the original. In this case: playing a different basstone to create a new chord.
 

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