Often, getting up in the morning, I am attempting to make coffee and do all my other things too, like showering, shaving, dressing. It would actually save more time to first get fully dressed and then begin the water boiling for the coffee, since I am interrupting myself while getting dressed, etc... in order to follow the various steps of the coffee making process. I typically drip water over the floors running from the shower to pour the hot water into the French press coffee machine.
So what you want to do, as much as possible, is to avoid trying to save trivial amounts of time by doing two things, badly, at once. You might want to try some of the following.
*Don't listen to music while you work. Devote time later in the day specifically to hear music and do nothing else.
*Check and answer your email at certain designated times of the day, but do not leave it on in the background when you are not checking it.
*When you are eating, just eat (or talk with someone if you are not eating alone.).
*Generally avoid doing two things at once. You can make exceptions, like listening to music in the car or while running or cleaning. Or you can check out of a useless meeting by drawing or writing down lists of things to do later.