Can someone give a mathematical definition of accelerando and ritardando in music? Are these exponential, linear phenomena?

Any hints is appreciated!

  • I'd have called this a duplicate, except this asks for accelerando, too. – Dekkadeci Nov 25 '18 at 15:43
  • Yes - this counts as a dupe. The answers are equally as applicable. – Doktor Mayhem Nov 25 '18 at 18:28

There is no mathematical definition, as they can depend on different composers, conductors or orchestras.

So you cannot state it is linear or exponential or anything fixed or defined. Please listen to as many recordings or performances of works which include accelerando and ritardando and learn for yourself how variable they are as concepts.

The only correct answer (like many things in music) is:

It depends.

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