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why is the chromatic scale written differently going up and down!

Because it is chromatically written. There are lots of different types of scales in music. Some have seven notes, some have five, some sound happy and some sound sad. But, there is one type of scale that uses all twelve pitches in western music called the chromatic scale.

Explanation:

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i'm not sure i completely understand your question, but i will do my best.

i think the answer you are looking for is sequence. (see below)

a repeated melodic fragment would be best defined as repetition, while repeated chords (different or the same) could be a chord progression. however, you then mentioned the chord and melodic fragment beginning on higher or lower pitches, in that case, the answer could be best defined as a sequence. the definition of a sequence is as follows: "the restatement of a motif or longer melodic (or harmonic) passage at a higher or lower pitch in the same voice."

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