Several topics on Music Theory - Various sources

MUSIC THEORY
Intervals
An interval is the distance between two notes. Intervals are always counted from the lower note to the higher one, with the lower note being counted as one. Intervals come in different qualities and size. If the notes are sounded successively, it is a melodic interval. If sounded simultaneously, then it is a harmonic interval. The smallest interval used in Western music is the half step. A visual representation of a half step would be the distance between a consecutive white and black note on the piano. There are two exceptions to this rule, as two natural half steps occur between the notes E and F, and B and C. A whole step is the distance between two consecutive white or black keys. It is made up of two half steps
Qualities and Size

Intervals can be described as:
Major (M)
Minor (m)
Perfect (P)
Augmented (A)
Diminished (d)

Intervals come in various sizes:
Unisons
Seconds
Thirds
Fourths
Fifths
Sixths
Seventh
2nds, 3rds, 6ths, and 7ths can be found as Major and Minor.
Unisons, 4ths, 5ths, and Octaves are Perfect.

When a major interval is raised by a half step, it becomes augmented.
When a major interval is lowered by a half step, it becomes minor.
When a major interval is lowered by two half steps, it becomes diminished.
When a minor interval is raised by a half step, it becomes major.
When a minor interval is raised by two half steps, it becomes augmented.
When a minor interval is lowered by a half step, it becomes diminished.
When a perfect interval is raised by a half step, it becomes augmented.
When a perfect interval is lowered by a half step, it becomes diminished.
INVERSIONS OF INTERVALS Intervals can be inverted, which basically means you turn them upside down. The lower note is raised up an octave so that the top note/bottom note relationship is reversed. The chart below shows the inversions of intervals.
Qualities
Major becomes Minor
Minor becomes Major
Perfect