Rhythm
Musashi refers to the fact that there are rhythms in everything in life and that these are particularly important and relevant to exponents of the sword. The accomplished practitioner should be aware of these rhythms and how to match and also disrupt them. This holds true for the modern fencer as without a concept and awareness of both your own rhythm and that of your opponent you will not be able to dictate the fight and close to a distance where you can make a valid hit. All to often I see fencers plodding up and down the piste in a predictable rhythm and then wondering why a) they cannot make a hit or b) why their opponent can hit them so easily. Rhythm and footwork need to be viewed as another weapon in a fencers armoury and like any weapon there are times when it is appropriate to deploy different styles and times when it is not.
Matching Rhythm
Matching rhythm is appropriate where you wish to employ more complex compound attacks, particularly those that involve feints or deceptions to confuse your opponent. A matching rhythm allows your opponent to see your feint and react to it, thus allowing your compound attack to succeed. Complex blade movements are difficult to execute when you and your opponent are not synchronised. A matching rhythm is also useful to lull your opponent and makes a sudden rapid attack or change of rhythm more upsetting to them.
Disrupting Rhythm
Disrupting an opponents rhythm is useful when you wish to attack on their preparation or do beat attacks etc. You can disrupt an opponents rhythm by using varied footwork styles such as cross steps, ballestras and appelles etc, leaving them in such a state of confusion that you can make your attacks with greater chance of success.
It must be noted that you should not exclusively concentrate on your rhythm as this will narrow your perspective too much, rather your rhythm should be natural and easy to maintain. Like all things in fencing a seemingly simple concept can be deceptively difficult to execute. However, there wouldn't be any fun otherwise would there?!