Thinking of music chords like vectors

A 2 dimentional vector is any vector of the form (a,b)


A nth dimentional vector is any vector of the form (a,b, c,...,n)


Can chords be represented by vectors?


For example:


F A D
ie F major 3th, major 6th
ie (F,3,6)


C E G B
C major 3rd major 7th
(C,3,7)


A chord progression
eg
say key or scale is G minor ie all keys white except Bb, Eb
Let's take in Bach's numbered bass code an example chord progression:
G
F6
E7

Ie
G Bb D
F A D
E G Bb D


Can it also be written


(G,3,5)
(F,3,6)
(E,3,7)


Problem is that the above is all D but they are not shown. But it is very useful as the colors or language letters in music are the intervals. A sixth has a certain very important atmosphere. A 7th too, a 9th too etc.
G B D
F A D
E G D
(Remember also that all B, E are flat on this example)


It sounds great because D is pedal ie the interval of 6th, 7th is prepared for the listener's brain
But
,,5
,,6
,,7
Comes from the fact that intervals are referenced with respect to bass


We see the notes on the score. And we understand the code by numbered or figured bass [Bach, Niedt]. This is like looking at the schematic of an electronic circuit, or a computer program. Anyway...


It looks like music can be represented by a say 3 dimensional vectors. Ie points in space moving sensations in our brain



Later addition:
Other ways. (G,B,D)
(F,A,D)
(E,G,D)
or G(1,3,5) F(1,3,6) E(1,3,7)or G
F6
E7
Back to Bach's notation
We see Bach and his contemporaries were light years ahead of their time.
reference: Bach Bass Rules pdf