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A sequence is a musical idea that is repeated starting on a different pitch. Sequences are often both linear and harmonic, but can be one or the other. Common harmonic sequences often involve a circle of fifths progression involving a linear intervalic progression (LIP) of alternating intervals of 10-8 between the outer voices.
A harmonic sequence
Often times, a sequence occurs with alternating inverted chords (I IV6 viio III6 etc)
A sequence with alternating inversions
Chord functions are often disregarded, especially III and VII, in any harmonic sequence.
At times, the melodic sequence is not accompanied by a harmonic sequence.
A linear progression
A general rule of sequences is that they rarely continue past 3 repetitions, with the 4th repetion ending differently to get out of the sequence. It is considered boring to continue past 4. However, often another sequence might be started after one sequences finishes.