Scales

A scale is a predetermined series of tones that define a musical context. A scale is defined as being major or minor according to whether the scale contains a major or a minor third, respectively. (If it contains both, as in the octatonic scale, it is considered to be neither major nor minor.) This holds true even if the scale in question is not "the" major or minor scale per se.

The most important kind of scale we are concerned with is the diatonic scale; that is, any scale containing the interval sequence W-W-H-W-W-W-H (where "W" represents a whole step and "H" is a half step). Note that any other cyclic permutation of this interval sequence is also considered a manifestation of the diatonic scale! What follows is a discussion of the different scales -- that is, of the various permutations of this interval sequence -- with some supplementary remarks on usage.

The Major Scale

Perhaps the most commonly encountered scale is the major scale. We arrive at this series of notes by beginning on any (fixed) tone -- the tonic -- and ascending verbatim through the interval sequence given above. Thus, the notes of the D major scale are D E F# G A B C# D. As an exercise, check for yourself that this series corresponds to our interval sequence. Note that the first and third scale degrees -- D and F# -- form a major third, the characteristic interval of the major scale.
C Major Scale on the Treble Clef Listen (help·info)

The Minor Scales

We obtain the "default" minor scale, called the natural minor scale, by choosing a note as our tonic and proceeding by the cyclic permutation W-H-W-W-H-W-W of our interval sequence. Note that a "shorthand" version of this process could consist in starting from the sixth note of the major scale and working our way up cyclically: using the example of the D major scale given above, we can see that the B minor scale is B C# D E F# G A B. There are also two other types of minor scales that deviate from the diatonic interval sequence: the harmonic and melodic minor scales. These two commonly-encountered variants and their usage will be discussed more in depth when your present author or another contributor has time for the discussion; for now, let it suffice to note that the harmonic minor scale differs from the natural minor one only in that its seventh degree is raised by a half step to form a leading tone, while the melodic minor scale is equivalent to a natural minor scale with its sixth and seventh degrees each raised a half step while the scale ascends; but on the way down, the melodic minor scale is identical to the natural minor.
C Harmonic Minor Scale on the Treble Clef
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C Melodic Minor on the Treble Clef
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Modes

While the major and minor scales are the most important ones occurring in tonal music, they are but two manifestations of the entire diatonic system, just two of seven possible cyclic permutations of our interval sequence. Each such permutation is spoken of by musicians as a mode. Their names are Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian: seven permutations, seven diatonic modes. There is a simple way to familiarize yourself with these modes: on a piano keyboard, start on the note C and ascend on only white keys, one at a time, until you reach the C an octave above your starting point. You have just played a C major scale, or equivalently, a C Ionian scale. Now start on D and play only white keys up to the next D. You have played a D Dorian scale. So on for Phrygian mode, Lydian mode . . . Notice the different and exotic characters imparted to the various modes by cyclically permuting the diatonic interval sequence. As long as the correct sequence of intervals is preserved, you may choose any note as the first degree of any scale you like. E.g. F# Dorian: F# G# A B C# D# E F#.