Scales and Modes

Theoretical Information

A scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale.Due to the principle of octave equivalence, scales are generally considered to span a single octave, with higher or lower octaves simply repeating the pattern. The chromatic scale is a musical scale with twelve pitches, each a semitone above or below its adjacent pitches.  

semitone, also called a half step or a half tone, is the smallest musical interval commonly. One tone + 2 semitone.

The major scale, the Ionian mode , is a diatonic scale. A measure of the width of each scale step provides a method to classify scales. For instance, in a chromatic scale each scale step represents a semitone interval, while a major scale is defined by the interval pattern T–T–S–T–T–T–S, where T stands for whole tone (an interval spanning two semitones), and S stands for semitone. Based on their interval patterns, scales are put into categories including diatonic, chromatic, major, minor, etc.
Harmonic Major Scale. Harmonic type of the major scale is a kind of major scale, in which the sixth step is lowered.
The minor scale, the Aeolian mode, is also a diatonic scale: T-S-T-T-S-T-T. The term minor scale is more complicated than the term major scale because it generally refers to three scale formations – the natural minor scale (or Aeolian mode),
The harmonic minor scale (The harmonic minor scale has the same notes as the natural minor scale except that the 7th degree is raised by one semitone, creating an augmented second between the 6th and 7th degrees. The harmonic minor scale comes from the augmented second between its 6th and 7th scale degrees. The raised 6th appears in the ascending form of the scale, while the lowered 7th appears in the descending form of the scale.)
The melodic minor scale — the raised 6th appears in the ascending form of the scale, while the lowered 7th appears in the descending form of the scale. 

A mode is a type of musical scale coupled with a set of characteristic melodic behaviors. There are seven Diatonic Modes in a scale and they are Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Locrian (scarce).

Ionian mode
The modern Lydian mode is a seven-tone musical scale formed from a rising pattern of pitches comprising three whole tones, a semitone, two more whole tones, and a final semitone.
The Mixolydian is the fifth mode of the major scale (Ionian mode). That is, it can be constructed by starting on the fifth scale degree (the dominant) of the major scale. Because of this, the Mixolydian mode is sometimes called the dominant scale.
Aeolian mode
The Dorian mode (also called «Russian minor» by Balakirev), is a strictly diatonic scale corresponding to the white keys of the piano from D to D.
The Phrygian mode is related to the modern natural minor scale, also known as the Aeolian mode, but with the second scale degree lowered by a semitone, making it a minor second above the tonic, rather than a major second.
An easy way to memorize the modes of diatonic scales is to build them in succession from all the C major notes.

More info Wikipedia