what your getting into is ......... well, scale teminology.
Each interval (arithmatical distance between pitches) consists of a specific number of half steps. The number of half steps in the interval determines the "quality" of the interval.
In your example of thirds, an interval of a third can have four different qualities.
Major, Minor, Augmented, or
Diminished.
A
Major third consist of
four half steps between pitches, a
Minor third has
three half steps between pitches. So you could effectively think of a Minor third as a flatted Major third, but for theoretical puprposes, that's not correct terminology. The terminology all has to do with distance between pitches.
The Diatonic Scale has, effectively, eight piches, or degrees. Each pitch has a specific name. 1= Tonic, 2= Supertonic, 3= Mediant, 4= Sub-Dominant, 5= Dominant, 6= Sub-mediant, 7= Leading tone, 8= Octave. The tonal separation between each pitch in the major scale, is whole tone, whole tone, half tone, whole tone, whole tone, whole tone, half tone.
Intevals 1, 4, 5, 8, can be either
Perfect,
Augmented, or
Diminished in quality, based half steps. Intervals 2, 3, 6, 7, can be
Major, Minor, Augmented or
Dminished in quality, again based on half steps.
In some cases, two intervals can
"sound" the same. For instance, an Augmeented third is
enharmonically the same as a Perfect fourth. But if the note is intended to be a third it must be written as a third, and so on...
I have NEVER seen an Augmented third, second, sixth, or seventh in real application, however, I have heard of their existence in some obscure classical pieces.
Sorry if this is a bit long winded, I hope you got something from it......... Jim