On representing musical harmony with multidimensional vectors

If it is said that little Ionas for example can be good at mathematics and not good at music may not be true.


How can one be good at mathematics and not good at music?


For they are one and the same.





And now trying to find a way to write chords as vectors (ordered pairs etc).


Usually in music melody somewhat goes up.


So usually bass goes down as Bach recommends that hands move in a mirror like fashion [Bach].


For example:
Old and Wise - Alan Parsons Project
(Writen in A minor scale ie
La Si Do Re Mi Fa Sol La or
A   B  C   D  E    F   G    A


So naturally bass starts at A


Almost quite commonly bass goes down step by step:


A  then G then F then E then F then E then D then E then A
(Introduction, orchestra strings etc)


What makes it so beautiful is the bass code ie:

A ie A C E
G6 ie G B E
F7 ie F C C E
E7 ie E G B D
F7 ie F A C E
E7 ie E G B D
D7 ie D D A C
E7 ie E D B D
A#3 ie A #C E


Now since Ionas is quite good at negative numbers too...


Can't we call like we do at electronic engineering, ground level potential at 0.
Like sea level height 0


So tonic bass ie A is just 0.


So bass becomes:


0 then -1 then -2 then -3 etc


Then complete Harmony becomes


(0,3) ie A minor 3rd


(-1,6) ie G major 3rd major 6th


(-2,7) ie F major 3rd major 7th


(-3,7) ie E minor 3rd minor 7th


(-2,7) ie F major 3rd major 7th


(-3,7) ie E minor 3rd minor 7th


(-4.7) ie D minor 3rd minor 7th


(-3,7) ie E minor 3rd minor 7th


(0,#3) ie A major 3rd


Easy peasy.


Problem is that it is still hard to visualize that disonant intervals are prepared to the listener's brain as required by Bach. For example in above example the high note E is being played in a pedal constant sustained way by the right hand creating all those fantastically sounding intervals with respect to bass. Ie A E, G E, F E, E D, F E, E 6, D E etc
Whereas when we play it we can see it happening. Or when we look at the score we can see it happening.


But we can hear or feel it anyway.


Even those who do not "know" music can feel it anyway. Those millions of satisfied listeners.



Reference:


Bach Bass Rules
https://normanschmidt.net/scores/bachjs-general_bass_rules.pdf