Question regarding intervals

Hi, I would like to clarify my doubts regarding intervals. The following is what I have gathered from online resources and please correct me if there is any mistake.

In order to work out intervals between 2 notes, we always use major scales by taking the lower note and treat it as the tonic of its major scale. For eg., if the lower note is A and the upper note is E, we use A major scale and since E is the 5th degree hence, this is a perfect 5th interval.

a) If note falls in Major scale: perfect unison, major 2nd, major 3rd, perfect 4th, perfect 5th, major 6th, major 7th, perfect 8ve.

b) If note does not fall in Major scale:
i) 1 semitone smaller than major --> minor
ii) 1 semitone larger than perfect/major --> augmented
iii) 1 semitone smaller than minor/ perfect --> diminished

my question is if the note is 1 tone smaller than major, it is a diminished?? as seen in the picture, part B where the tonic is F#.

Your understanding seems to be correct.

And yes, one tone (two semitones) smaller than a major interval would be a diminished interval.

So, F# up to E# would be a major seventh
F# to E-natural would be a minor seventh
F# to Eb would be a diminished seventh

Check out this textbook on Four Part Harmony.

thanks for the clarification.