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In the field of mathematics, scale is very important because it is used in measurement. It has four types; (1) the nominal or the scale that differentiates the two items, (2) ordinal scale that allows for rank orders, (3) interval scale that is in the degree of difference of items, and (4) the ratio type used in the estimation of the ratio of the continuous quantity.
There are two types of scales you may learn, both are contrary motion scales - the first is the diatonic scale, for example, the D chromatic scale would contain, in the right hand, the notes going upwards and the notes going downwards, thus:
D E F# G A B C# D C# B A G F# E D
While the left hand, starting on the same note, goes downwards, and then upwards, thus:
D C# B A G F# E D E F# G A B C# D
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The other main example of a contrary motion scale is a contrary motion chromatic scale, which includes all the black and white notes in any given scale. Using a D contrary motion chromatic scale, over a single octave, the right hand would play:
D D# E F F# G G# A A# B C C# D C# C B A# A G# G F# F E D# D
While the left hand would play, starting on the same note:
D C# C B A# A G# G F# F E D# D D# E F F# G G# A A# B C C# D
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