If you are willing to dare to challenge the dictionary definition you will find great value in accepting that diatonic is the same as 'di-tonic'– two tonics.
The two tonics are the first and fifth notes (I and V) as the V is harmonically closest to the I.
This is exactly why modern music theory is built on fifths – the fifth is where the scales increment – first C, then G is the next key, then D ... a fifth up, etc.
Now look at the composition of each fifth interval, such as CDEFG.
CDEFG's intervals are WWHW.
WWHW is also the interval pattern for GABCD.
Point being that major scales are build on overlapping patters of WWHW ... each V becomes the I for the major scale of the next incremental key (incrementing by the number of accidentals).
Would you like minor you say?
Ok, why not go backwards ... WHWW ... going down by fourths.
Each of these two patters is 'diatonic' because the beginning and end are the same ... a "W" ... like a puzzle piece so they fit end to end in each direction... like a puzzle piece where the left side is the inverse of the right side so they perfectly fit.
A pattern like HWWW isn't diatonic. It's the pattern of a mode.
A pattern like HHWW can't work because the two H's are together. In diatonic patterns:
1) Matching ends so they can fit like puzzle pieces.
2) Two or three W's between the H's ... as they overlap at the V note ... the I note of the next key is the V note of the previous key.
