I often use mutes on the drums when teaching and practicing. Mutes reduce the overall volume of the drums for both hearing safety and ease of communication during class. They also protect the drum and allow me to use less-than-perfect bachi. We have two types at the institute, "muffin top" and standard.
Muffin-top mutes were made by LATI student, Tracey Oshiro. They are a feax-leather fabric with a band of elastic. Muffin-top mutes are quick to attach and remove, don't require any explanation, and don't have any overhanging edges to catch a bachi. These particular mutes are too thin, however, and they can't be rotated to reduce wear, so I tend to use them only when I need every mute I have.
The standard mutes are just a simple loop of thick fabric. The loop design is nice because it puts two layers of fabric over the head for the right amount of muting. As a bonus, the fabric can be rotated so that a different area of the fabric is exposed to the strike zone, dramatically lenghthening the life of the mute. The corners of the fabric can be tucked to better conform to the shape of the drum when necessary.
For the fabric, anything light-colored and wear-resistant should work. The mute pictured is made from upholstery fabric from the discount bin. To make it, I cut the fabric lengthwise, about 3" thinner than the diameter of the drum (about 14" pictured). The strip should be twice as long as the distance over the mimi, drum face, and opposite mimi, plus a few extra inches to sew the ends together to form a big loop (totaling about 4' for the pictured mute). The mute below was created for a 1.4 diameter taiko but works just fine on 1.3 drums with tucking of the excess, and 1.7 drums where the rope doesn't quite reach over the mimi all the way around the rim. The mute you see below has been in constant use for 2.5 years and isn't showing any significant signs of wear.
The rope should be soft to avoid scratching the body, somewhat elastic for a good hold, and large diameter so that knots can be easily removed. The kind you see in the photos is 1/2'' twisted cotton.