How important it is to intonate correctly

This was realised while playing bass code on piano:


(Key E major)


E to E7 to E7b


ie


E bass and G# B E
E bass and G# B D#
E bass and G# B D


But the added 3rd ie G# was sung rather than played.


The above is the chord sequence of the song Kiss Me - Sixpence None the Richer
at the harmonica solo: G# F# B G# F B G# F# G# E which obviously concentrates on the 3rd since the other instruments concentrate on the 7th above bass [Bach].


But a human voice or a harmonica can play an infinite palette of frequencies around G#. And the brain of the player can choose the exact frequency that agrees with bass, its harmonics, the other instrument notes etc. That agrees with the particular bass instrument played as well.


This can not be done on the piano playing just the note G# as its is fixed as an equal temperament compromise for all scales.


So when singing or playing with harmonica this solo for example, the piano better not play G# as it will most likely conflict in frequency creating a beat etc.


But there is another reason. Leaving frequency space for the solo.


Like for example while playing on the piano Space Oddity - Bowie while singing....


Begining of verse the bass code or figured bass or numbered bass is F7 to E


Ie chord F A C E  while singing Ground control to major
chord     E G B E  Tom


But while discussing it with Vicky
F A E was played and then
E G E


Vicky felt that something is missing. But when it was sung along nothing was missing since the vocal is C C C D C B, ie it has the missing note(s) of the harmony.


See also Bach Bass Rules PDF


Musical Acoustics - Donald Hall