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A scale is an ordered pattern of pitch classes that fill in the space of an octave. This pattern may be composed of any number of pitch classes in any pattern. One of the most basic scales is the chromatic scale, which consists of all 12 pitch classes:


The chromatic scale consists of a pattern of all 12 pitch classes, each 1/2 step apart. If we form a scale using only include the white keys, and start on C, we get the following scale:


Now we have a scale consisting of seven pitch classes in the following pattern (where w= whole step or two 1/2 steps and h= 1/2 step):
If we start the scale on another pitch class, A for instance, but still include only the white keys, we get a different pattern of whole and half steps, which results in a different scale:

The music of the "common practice" period is based on scales primarily derived from the various white-key scales, which also form scales on the staff without using accidentals. Each has a different pattern of whole and half steps, resulting in a different sound or feel. These scales are refered to as modes. The ancient Greeks used various modes to stimulate different emotions and early theorists adopted these Greek names to their modes as well (even though we can't be sure what the exact patterns of the ancient greek modes were). Historically, some of these modes were prefered over others, with two modes, the Ionian and Aeolean being used most commonly. The Ionian mode is better known today as the major scale and the Aeolian as the minor scale.
Major Scale (Ionian)

Dorian

Phrygian

Lydian

Mixolydian

Minor Scale (Aeolian)

Locrian

When using the common practice modes and scales, we can refer to the various pitch classes of the scale by their scale degree. The first note of the scale is scale degree 1, and is also called the tonic. The second is scale degree 2, the third is scale degree 3, etc. - until we arrive at the tonic again. There are seven (7) scale degrees in each of the common modes.
The scale pattern may begin on any pitch class. As long as the pattern of whole and half steps remains the same, it is still heard and identified as the same type of scale. However, accidentals need to be added in order to form these patterns. For example, to form a Major Scale begining on D, we need to raise scale degrees 3 and 7 by a half step (we do this by adding a sharp to these pitches) to form the correct pattern of whole and half steps. The D Major scale has the same pattern of whole/half steps - identical to the C Major scale. When we move a scale or a pattern of notes to a new pitch level, we say that we have transposed it. Compare the sound of the D Major scale to the C Major scale as notated above (Major/Ionian).
D Major Scale:

D Major Scale:
C Major Scale: