TR, with respect to loudspeakers, is a measure of how quickly the speaker system reacts to an electrical impulse, and of how quickly the sound stops once the input stops. Poor TR is a form of distortion that is seldom quantified in product literature / specifications / advertising, even though good TR is required for high fidelity.

Where the TR is poor, sounds are less sharp (have poor attack), and are mooshed together (have poor decay - so often the first sound will not fade away before the next one begins). This is less noticeable when playing continuous tones, but is quite obvious on transient sounds (hence the name, duh!)

Certain speaker drivers are more capable of good TR than others. It's basically due to their power-to-weight ratio. For 'normal' or dynamic drivers, the best TR is achieved where the magnet is powerful (i.e. expensive) and the cone is very light. The voice coil is the interface between the two, and it needs to be good for both factors - lightweight (since it is part of the moving mass) and with many turns of wire within the field of the permanent magnet. This is why funky coils are used in some premium drivers - aluminium rather than copper for weight, and flat or hexagonal wire rather than round, to fit more wire in the same space.

There are a couple of exotic drivers that have outstanding TR, ribbon drivers and electrostatic panels. These drivers have very low moving masses - with no voice coil. The diaphragm itself acts as a voice coil, and the entire area is driven, rather than just the centre. Sadly, they are generally only usable for midrange and treble duty, as the amount of diaphragm movement is limited.

The enclosure that the driver is fitted into also has a large effect on TR. The obvious offender is flimsy enclosures, where the walls vibrate, and add to the soud produced by the driver. These vibrations add a droning sound to the reproduction, and add to the decay time of the system - when the electrical input ceases, the sound of the box walls resonating takes a few moments to die away to nothing.

The other way enclosures detract from TR is where the air that is resonating within the enclosure contributes to the sound output. These resonances take a little time to build up and die away. To illustrate this, consider an acoustic guitar - what happens when you strum it, wait a second, and then put your hand on the strings to stop them moving? The note can still be heard for a few moments before it dies away. This is mostly the sound of the resonating air in the sound box.

Bandpass and Bass reflex enclosures thus suffer poor TR - a driver will always have better TR in a well made sealed enclosure than in the best ported design. Transmission line, open baffle and infinite baffle designs offer the best TR.