Composers know that the outline of a melodic line can be reproduced at a higher or lower pitch to induce excitement or prolong and help bring out all the life and beauty that's inherent within the notes that precede or follow it.
This is called a sequence.
Sequencing is very commonly used to help create new material for the extension of a work, and it should come as no surprise that it sounds very natural; sequencing is in fact a phenomenon in the living world that's involved with the replication of DNA in the reproduction process of all natural life as we know it (photo).
Not every piece of music has sequences written into it, but many do, and they lend interest and additional life and movement to any passage that has them.
Longer, more extended fugue subjects invariably employ sequences and derive much of their charm from them.
Any of the larger musical forms require the repetition of material in different keys, and sequences often play a major role in that.
This is yet another time-honored compositional tool that can be applied to virtually any style of music, but it comes in particularly handy in shaping longer subjects and working bridge passages and episodes in fugues.
For some examples of sequences and how they work, the scores of this author's Fugues from Op. 6, 10, 13, 18, 19, 20, 21, 26, and 31 may be consulted.
This author's d minor Op. 10 Fugue, for example, is ripe with sequences, starting with the subject, which is long; they're not only written into the episodes (modulating passages between entries) but also into the links connecting the 3rd and 4th entries in the exposition.
Every episode to be found in the A Major Op. 13, D Major Op. 18, e minor Op. 24, a minor Op. 25, b minor Op. 26, and D Major Op. 28 Fugues -- EVERY LAST EPISODE in all 6 Fugues -- is built upon a sequence!
The A Major Op. 13, a minor Op. 25, and b minor Op. 26 Fugues also have long subjects employing sequences, as do all 3 Postludes from the Op. 29-31 collection; Op. 31 also contains a 4 voice modulating bridge section which links the exposition with the 1st entry in the relative key; this bridge passage is constructed entirely around an ascending sequence which builds in excitement as it approaches the cadence in the relative key.
There are also sequences in the development sections of the Op. 5, Op. 25, and Op. 28 Preludes which will repay careful study.
Sequences like this when judiciously used can stir interest in a development, create a fugue episode out of virtually nothing, infuse a longer fugue subject with melodic motion, or lend a special charm to a modulation, injecting it with a sense of energy and life.