The terms Major, minor, Augmented and diminished also apply to SIXTHS. A Major SIXTH can also be defined by looking at basic SIXTHS (unaltered by accidentals). The following example shows all the basic SIXTHS within an octave.
FOUR BASIC SIXTHS ARE MAJOR AND THREE BASIC SIXTHS ARE MINOR. DRAG YOUR MOUSE over the next example to discover which basic SIXTHS are Major and which are minor.

Major SIXTHS contain nine (9) half steps and minor SIXTHS contain eight (8) half steps.
The next example illustrates a Major SIXTH on the keyboard. POINT YOUR MOUSE at the two pitches on the keyboard that will change the Major SIXTH to a minor SIXTH.

You should have noticed a relationship between THIRDS and SIXTHS. Those intervals are the inversion of each other. In other words when a THIRD is inverted, it becomes a SIXTH. If you understand THIRDS, then you can relate to SIXTHS as well.
ALSO...regarding quality. On page nine, we spoke about how quality changes when intervals are inverted. If three basic THIRDS are major, then those three THIRDS become minor SIXTHS when inverted.
This has been a lengthy chapter with lots of information, so the next page contains a summary of some of this information.