What is a mute?

A mute is a piece of equipment that affects the volume, but mainly, affects how a brass instrument sounds by changing the timbre of the instrument.  The mute is inserted into the bell of the instrument and fits snugly into place using cork and friction. How the sound quality is changed is primarily determined by which mute is being used.

Mutes are used in a wide variety of musical genres and styles, mostly used in classical or jazz repertoire.  Modern day classical music (symphonic and wind band works from the 20th century to modern day) and jazz music have composers featuring muted brass instruments for desired effects in their music.  Classical works mostly use the straight mute while jazz music has a wider range of mutes that are used such as the straight mute, Harmon mute, cup mute, and even a plunger.  Brass musicians will sometimes use mutes when accompanying a vocalist so they don’t overpower the performance.

Materials Matter

Cardboard ("Stonelined") or Plastic
Several well-known mute makers have a line of mutes aimed at students that offer a lower price point. These mutes do a decent job but don't last as long (sometimes the moisture blowing through the instrument can weaken the carboard or the glue holding the corks on). If you're building a collection of mutes and don't foresee a lot of use from a mute, this will do just fine. 

Metal
A large step up from cardboard without breaking the bank, many working professionals and amateurs alike choose metal mutes. Certain mutes (like the Wah-Wah) are only available in metal due to the desired sound effect. Metal mutes can take a tumble and still sound great. 

Wood
Looking for a custom made mute that is equal parts craftsmanship and beauty? A wooden mute may be what you want. 

Carbon Fiber
A mute material that is extremely durable and lightweight, and looks like its straight out of the matrix. 

Straight Mute

The most common mute.  Nine times out ten, if a piece just says “mute” or “with mute” this is the mute the composer is asking for.  A straight mute is attached to the instrument with thick pieces of cork that leaves a gap between the mute and the instrument itself.  The cone design allows for the sound to be distributed between the inner chamber of the mute as well as escaping through the sides of the mute.  This achieves a quieter volume and a more muffled or subdued timbre.
Suitable for trumpet, French horn, trombone, euphonium/baritone, tuba

Cup Mute

A cup mute resembles a straight mute with a bowl affixed to the end.  The bowl is designed to bounce the sound back away from the audience.  This creates a very muted and dark tone quality, much more than that of the straight mute.  Some cup mutes have an adjustable cup that gives more control over how muted that sound will be.
Suitable for trumpet, trombone, euphonium/baritone, tuba

Bucket Mute

Attached to the bell of the instrument, a bucket mute is essentially a bucket filled with a sound absorbing material that helps reduce the high frequencies of the instrument. This particular mute produces the most reduced/muffled sound quality of all the mutes.  Some modern bucket mute designs resemble that of a large straight mute with cotton or foam filling the inner chamber of the mute.
Suitable for trumpet, trombone

Plunger

As the name suggests, a plunger mute is literally a plunger with the wooden handle removed (make sure to use a brand new plunger!).  A plunger gives the musician the ability to open and close the mute while playing.  The plunger being closed over the bell sounds similar to that of a cup or bucket mute while open just sounds like the instrument without a mute.  Moving the mute open and closed creates a “wah-wah” effect similar to the wah-wah mute or solotone mute. 
Suitable for trumpet, trombone

Wah-wah Mute

Also known as a Harmon mute or bubble mute, a wah-wah mute is a large cylindrical or spherical mute that is made up of two parts (the mute itself and a removable piece called the stem). Pieces that call for this mute will inform the musician whether or not the stem will be used.  When inserted into the instrument, the wah-wah mute completely seals off the bell so all sound is filtered through the mute itself.  This creates a very nasally almost metallic tone quality. The name ‘wah-wah’ comes from the sound that is produced when the musician moves their hand open and closed over the end of the mute while being played, similar to that of a plunger.
Suitable for trumpet, trombone

Solotone Mute

A solotone mute consists of two cones that are attached together by a tube running down the center.  The sound quality is similar to the wah-wah mute but has been described as a more intense version of that sound.  This mute was very popular between 1930 - 1950.  Nowadays, it has fallen out of favor but composers will call for this mute if they want to emulate the tinny/raspy quality of 1920s, 30s, or 40s radio.
Suitable for trumpet, trombone

Stop or Stopping Mute

‘Stopping’ is a French horn technique that has the musician sealing off the bell of the horn by wedging their hand into the bell.  This creates an effect similar to the nasally quality of the ‘wah-wah’ mute.  Due to the shortening of the air passage within the horn, players have to play each note ½-step down in order to achieve the correct pitch.  A stopping mute was eventually developed to eliminate the need to use your hand.  A stopping mute comes in transposing models or non-transposing models.
Suitable for French horn

Practice Mute

Practice mutes are designed, as the name implies, for practice.  These mutes are similar in shape to a straight mute but are filled with a sound dampening material as well as nearly sealing off the bell of the instrument.  Due to this, this mute allows very little sound to leave the instrument.  This allows the musician to practice without disturbing those around them.
Suitable for trumpet, French horn, trombone, euphonium/baritone, tuba

Silent Brass

Developed by Yamaha, Silent Brass is an electronic version of a practice mute.  The mute contains a built-in microphone with a 3mm jack on the end of the mute.  The player can plug headphones into the jack and hear themselves better than what a standard practice mute allows.
Suitable for trumpet, French horn, trombone, euphonium/baritone, tuba

A note about woodwinds:

Due to the way a woodwind instrument is designed, mutes have very little or no change to the way the woodwind instrument sounds.  Over the course of many years, people have tried to mute woodwinds in various ways but nothing has caught on. Attaching or inserting objects into the woodwind instrument can change the lowest pitches of the instrument (since all of the holes are covered) but would not mute the instrument in a way that a mute does for a brass instrument.