if you are not confused by the above post then continue here for the more tricker stuff
so now that you know the basic intervals lets move on to some harder ones
perfect intervals can only be turned into diminished, or augmented. while Major intervals can be changed into augmented, diminished or minor intervals.
lets use the C scale again(C,D,E,F,G,A,B)
if you have a perfect 5 interval (from C to G) and you raised that G note up a half step to G# then this would make it an Augmented 5 interval (usually written as +5) now if you took that same G note and lowerd it a half step to Gb then it becomes a diminished 5 interval (written as dim5 or with a degree sign before the # like *5).
if you DONT have a perfect interval and you have a Major interval
then the augemented works the same. so if you had a major 2 (C-D) and you raised it a half step to D# then you would have an Augmented 2 (+2).
BUT if you took the same note and lowered it a half step you DO NOT get a diminished like you do with the perfects. if you took that major2 and lowerd it a half step you end up with a minor 2 (written as min2 or mi2 with a line over the "mi")
now unlike perfects you can lower it another half step so lets take our major2 (C-D) and lowerd it two half steps(one full step) and you end up with Dbb(its the same note as a C but diff name) this would then be a diminished 2 (dim2)
a perfect lowerd a half step=diminished
a perfect raised a half step=augmented
a major lowerd 2 half steps=diminished
a major lowerd a half step=minor
a major raised a half step=augmented
you encounterd a double flat above (bb) there is also a double sharp(notated with a "x")
so say you were in the scale of F#(F#,G#,A#,B,C#,D#,E#)
and you had a perfect 5 (F#-C#) and you made it a +5 then you would end up with F#-Cx or C double sharp
to play a double sharp or flat, you would
take the sharp and raise it up another half step
take the flat and lower it another half step