Don’t try to apply logic when dealing with music. That is why it’s called theory. Music is best understood that if it sounds good it is right. Thoery is needed only to communicate to someone else what you are playing.
The best way I can apply any logic to music would be mathematical. Think in a “base seven” system with no zero The major scale
is 1 2 3 4 5 6 7 C D E F G A B
not
(0) 1 2 3 4 5 6 7
AND THEN THE SCALE STARTS OVER. When you count up or down the intervals of notes; you count the one you start with as one. Example;
today we count 0 1 2 3 4 With music count 1 2 3 4
we count four but there are five digits this a forth interval it would be a fith if a zero was added.
Zero wasn’t used in math at the time of western music theory’s conception.