As far as intervals are concerned, it's all strictly mathematical.
Interval / # of notes seperating
2nd / next adjacent note(eg. C-D, F-G, Ab - Bb, etc.)
3rd / one note seperating(eg. C - E, Bb - D, F - A, etc.)
4th / three notes seperating(eg. C - F, Bb - Eb, F - Bb, etc.)
...and so on....
The terms "major" and "minor", as they apply to intervals, refer to all intervals except 4ths and 5ths. Simply put, for 2nds and 3rds, a minor interval is composed of an odd number of half steps, and a major interval is composed of an even number(eg. a minor 3rd has 3 half steps, a major 3rd has 4). The opposite is true for 6ths and 7ths(a minor 6th has 8 half steps and a major 6th has 9). Once again, this does not apply to 4ths and 5ths. These intervals(2nds, 3rds, 6ths & 7ths) can be further "augmented" or "diminished" by a half step, and the terms are self-explanatory as to which direction the change goes. These terms are rarely used beyond a compositional context, because they can be better described by a simpler term(eg. a diminished 3rd is actually a major 2nd, an augmented 6th is actually a minor 7th).
As for 4ths and 5ths, they can be "perfect", "diminished" or "augmented". "Perfect" refers to the root interval; in the case of a 4th, it is 5 half steps above the bottom note, and a "perfect" 5th(aside from being full -
- and another thread goes alky) is 7 half steps above the bottom note. As in the case with all other intervals, "augment" and "diminish" move the distance one half step accordingly. Interval of note(pun intended
): An augmented 4th and diminished 5th are the same interval(enharmonic is the term), and is known as a "tritone". It is the most strident interval in western music, and you hear one every time you hear a two-pitch car horn honk. It is also the interval used in emergency vehicle sirens, but alternating in pitch instead of simultaneous.
An additional note(pun once again intended): The signs "b"(flat) and "#"(sharp) move the note they are written with one half step down or up, respectively.
As for the second question, it is because the keys on a piano keyboard are not evenly distributed; there are alternating groupings of 4 white keys divided by 3 black keys, and 3 white keys divided by 2 black keys. If you look at a piano keyboard as simply successive notes instead of thinking in terms of white vs. black keys, it is simply a succession of half steps. The keys are organized the way they are mainly to assist the pianist in knowing where he/she is on the keyboard by feel, so they don't have to look down while reading music.
I fully expect *ig to correct me if I got anything wrong. My Theory 101 class was 27 years ago, and I'm just going on memory(and experience).
Clear as mud?
<small>[ 01-31-2006, 05:35 PM: Message edited by: OperaTenor ]</small>