Tempo markings should always be placed at the top of every part and score using a metronome marking. Many writers use words such as "Fast", "Moderately", or "Slow" to indicate a tempo. Exact tempos can only be indicated with a metronome marking, which is why using the metronome marking is the only method recommended here.
Exact tempos are crucial when creating music written for video or exact commercial lengths for jingles and such. Tempos using metronome markings can give you a calculation to insure the desired length of time the music needs to play is achieved.
Metronome Tempo Marking. You want to supply this using the meter of the composition. When the pulse is a quarter note, indicate your tempo Marking with a quarter note equals. If cut time, then half note equals, and so on.
Changing the Time Signature but keep the same beat pulse. This indicates a quarter note in the first tempo (example, 4/4) is equal to a dotted quarter when the pulse changes from 4/4 to 6/8. Meaning if your quarter note = 100, when you get to the 6/8 time signature, you want the pulse to remain at 100, but now the pulse is a dotted quarter (in 6/8) instead of a quarter (as it was in 4/4). This can be any pulse to any other pulse.
Changing the Speed of the Tempo. Changing tempos in the middle of a score or chart can be very effective, but requires a bit of planning to pull it off cleanly. The absolute best approach to this is the change the tempo in the bar preceding where the listener hears the tempo change using a "held note". The held note(s) gives the conductor or drummer one bar to establish the new tempo BEFORE notes are played at the new tempo.
Here is an example of how to change the speed of a tempo using a held note:
Rubato or Free Tempo. The absence of a strict tempo such as we have looked at thus far. Rubatos must be conducted by someone, and any Rubato areas should be written as smoothly as possible. You want to avoid busy notes and especially syncopated rhythms (rhythms on the upbeat). It is also a good idea to indicate held notes as tied notes equal to the notes which have movement.
Here is an example of how to write a Rubato or Free Tempo:
Notice the use of tied half notes instead of whole notes to help the musicians follow the pulse being conducted.