Major intervals are different from perfect intervals in that major intervals have four possible qualities: Major, Minor, Augmented, and Diminished, whereas perfect intervals only have three qualities: Perfect, Augmented, and Diminished.
To review Intervals go to Understanding Intervals.
For review on Major Intervals go to Major Intervals.
We have practiced the intervals of Unison through the 5th. Let's see what this looks like with the interval of a 6th.
Reminder: a key signature is just a short hand for all the accidentals in a key. The easiest way to know if a note is part of a scale is to have your key signatures memorized.
To review Major Key Signatures go to Major Key Signatures.
To review Major Scales go to Major Scales.
The bottom note is an A. Notice how the top note, F♯, is a note in the A major scale. In other words, there is an F♯ in the key signature for the key of A. Therefore, this is a Major 6th (M6). (A major 6th is also the distance of 9 half-steps.)
Notice how the top note, F double-sharp, is a half-step higher than the note in the A major scale, F♯. In other words, there are no double sharps in the key signature for the key of A (or any key) and the F double-sharp is one half-step higher than the F♯ in the key. Therefore, this is an Augmented 6th (A6). (An augmented 6th is the distance of 10 half-steps.)
Notice how the top note, F (natural), is a half-step lower than the note in the A major scale, F♯. In other words, F is sharp in the key signature for the key of A and F natural is one half-step lower than the F♯ in the key. Therefore, this is a minor 6th (m6). (A minor 6th is the distance of 8 half-steps.)
Notice how the top note, F♭, is a whole-step lower than the note in the A major scale, F♯. In other words, there are no flats in the key signature for the key of A and F♭ is one whole-step lower than the F♯ in the key. Therefore, this is a diminished 6th (d6). (A diminished 6th is the distance of 7 half-steps.)