Major and Minor Interval

Interval is the distance between two notes. In a scale, interval is measured from the root note. The root note is counted as 1.

For example, in C Major:
C-C
C-D = Major Second
C-E = Major Third
C-F = Perfect Forth
C-G = Perfect Fifth
C-A = Major Sixth
C-B = Major Seventh
C-C = Perfect Octave

For C Minor:
C-D = Major Second
C-Eb = Minor Third
C-F = Perfect Forth
C-G = Perfect Fifth
C-Ab = Minor Sixth
C-Bb = Minor Seventh
C-C = Perfect Octave

Major interval can only be used for the 2/3/6/7 notes in Major scale

Minor interval can only be used for the 3/6/7 notes in Minor scale. Minor interval is always half step shorter than the major interval of the same name.

Pythagoras, born circa 580 BC, initiated the idea that if a vibrating string is divided in half, it produces the octave above the open vibrating string.  In other words, the ratio of the fundamental string to to the divided string is 1:2 will create a octave interval.

Perfect intervals (unison, forth, fifth and octave) is perfect because they are produced from perfect or pure frequency ratio.  For fifth, the ration is 2:3 and for forth is 3:4