All intervals are major and minor, except for 4th's and 5th's, which are perfect, diminished, or augmented. So yes, there is a major and minor interval of a sixth, the only problem is that the minor 6th is enharmonic to the augmented 5th. So, when documenting a sixth chord only the major 6th is used. If you wanted to label a chord tone as a minor 6th you would have to say b6. But like I said, adding the minor 6th interval into the minor chord creates a inverted major 7th chord. Ex:
Amaj.6 (A, C#, E, F#)
A minor6 (A, C, E, F#)
A minor b6 (A, C, E, F)
Fmaj7 in 1st inversion (A,C, E, F)
So yes, maj and min 6ths are talked about within intervals and melodies, but only maj 6ths are recognized within chords. Such is also true with the intervals of 9ths, 11ths, and 13ths.
[Edited by chris mood on 10-28-2003 at 11:40 PM]