Reciprocal Graphs. Duration of a piece of music from its tempo.
If a piece of music is played faster, it takes less time to perform it!
In other words, there is a reciprocal relationship between musical tempo (measured in crotchets or quarter notes per minute) and duration of music (measured in seconds). As the tempo gets bigger, the duration gets smaller. If the tempo is doubled, the duration is halved.
This demonstration graph plots tempo on the x-axis with values from 0 to 500. Of course, in practice a tempo of zero means the music has stopped, so the duration reaches for the sky above the top of the Y-axis! The duration in seconds is calibrated from 0 to 400 seconds on the Y-axis.
The formula for this graph is y = a/x where a = 3600. For example, a tempo of 60 crotchets per minute means each crotchet will last exactly one second. There are 15 bars, each with 4 crotchet beats, so the elapsed playing time will be 15 times 4 = 60 seconds. You can use the cross-hair to verify this result on the demonstration chart. If the tempo is increased to 180 crotchets per minute, the graph will show a playing time of 20 seconds.