One of the things that makes playing the trumpet (or cornet or trombone) interesting is that accessory called the "mute". Sometimes also described by members of the trumpet section in my band as "pots and pans". But really, what is a mute, what does it do and what varieties are there?
Simply, a mute is a "thing" inserted into, attached to or held in front of the bell of the trumpet (cornet, trombone) for the purpose of changing the timbre and/or volume of the sound of the instrument. Mutes appear in many different shapes and sizes, and are usually made of metal (most commonly aluminum or copper), fibre, plastic or rubber. The shape, size and material a mute is made of has a significant effect on the sound it produces. More on that later.
When shopping for any mute, there are several factors to keep in mind. The band you play in might have guidelines as to which brand of mute you must use. This might be done for visual effect so as to avoid a trumpet section with several different looking mutes, or to ensure a proper "blend" of the sound. This last factor is something you might want to keep in mind even if your band doesn't prescribe a particular mute: different brands of mutes will sound slightly differently. The material the mute is made of will also make it sound different. Different sounding mutes might cause the trumpet section not to "blend" properly. Another factor is cost. How much do you want to spend on your mute? A rule of thumb: the better the quality and the sound, the more expensive it will be. You figured that one out yourself, right? So, which options are there?
The mute most frequently called for in sheet music is probably the straight mute. The name could be confusing since the straight mute is rarely "straight". It is usually more or less pear shaped, although Humes & Berg (the red and white ones) produces a cone shaped straight mute. The straight mute will usually be the first mute a student trumpet player buys. Straight mutes are available in plastic, fibre and metal. The plastic ones are cheap and in my opinion should be avoided. They don't sound very good, and unless you really know what you are doing and need one for a specific purpose, try to go for something a bit better. The next step up is the fibre mute. A fibre straight mute will probably be a Humes & Berg red and white cone-type straight mute. These sound a lot better than the plastic ones, and have the advantage of being quite rugged (the metal ones tend to dent and scratch). If you are thinking about buying a fibre mute, I would suggest at least trying one of the metal mutes. These metal mutes (the largest variety of straight mutes) have a "brighter edge" to them. If you don't know what I mean, try one and compare it to the fibre (or plastic) mute, you should hear the difference. Also, not all brands of (metal) straight mute sound the same. This is mostly a matter of taste. The metal in straight mutes is usually aluminum, although you can get copper and brass (bottom) straight mutes. Jo-Ral makes all-aluminum, copper bottom and brass bottom straights. The copper and brass causes the sound to be a bit "darker" or "warmer". Compared to the Jo-Ral aluminum straight the difference isn't like night and day, but you can hear it. I myself own both an aluminum and a copper bottom Jo-Ral straight, and the copper does sound sweet. However, be aware that copper and brass as metals are between 3 and 4 times heavier than aluminum. When you hold it in your hand it might not feel all that heavy, but hang it 20" away from your face at the end of a trumpet and it becomes heavy quickly. Copper and brass bottom straights are definitely more expensive than the regular aluminum ones. One feature of straight mutes is that they tend to sound "sharp". In other words, a note played with the straight mute will sound slightly higher than the same note played without the straight mute. You may want to keep an ear out for this when choosing a straight mute. Whichever straight you decide upon, I recommend you try out as many different ones as you can. Most vendors will have a booth or room where you can sit and play undisturbed, and won't mind you trying out several different models. It should help you form a better idea of what the different models sound like, and what you yourself prefer. If nothing else, it's fun to do!
The next most common mute is the cup mute. A cup mute resembles a straight mute with a cup stuck to the bottom of it, with the open side of the cup facing toward you. They sound quite different from the straight though. Cup mutes are more frequently used in jazz and popular music, rarely in symphonic music although this is just a generalization. The first time I played a cup mute it reminded me of the 40's big band sound. Cup mutes are also available in plastic, fibre and metal. As with the straight mutes, try to avoid the plastic ones. Contrary to with straight mutes, in cup mutes the fibre (especially the red and white Humes & Berg) cup mute is much more common. It has a softer, more mellow sound to it as opposed to the metal cup mutes which have a brighter edge. In my experience the intonation of fibre cup mutes becomes difficult below a trumpet's lowest regular C (C below staff) and becomes almost impossible at F# (lowest normal note on a trumpet). Metal cup mutes don't show this behavior. On the other hand, how often do you play down to F#? Cup mutes tend to sound a bit "flat": a note played with a cup mute will sound slightly lower than it would without the cup mute. In metal cup mutes this is not quite as pronounced as in fibre cup mutes (translation: metal cup mutes tune better). Like fibre straights, fibre cup mutes are more rugged than metal ones. It is entirely possible that you will eventually choose to have both a fibre and a metal cup mute, for different purposes. Just as with the straight mute I recommend you try as many different types as you can. As with the straights, different brands of cup mute will probably sound slightly different. Denis Wick has a (metal) cup mute with an adjustable cup (it slides in and out over a "straight mute"-like base). By moving the cup closer to or further away from the bell you can get different "colors" of sound from the same mute. Jo-Ral's tri-tone cup mute (also metal) has padding that can be inserted into the cup for different effects. Inserting the padding makes it both softer (less loud) and takes the bright edge off the sound. Cup mutes are usually aluminum, but are available with copper cups from some maufacturers.
The plunger mute. Really, the simplest of mutes but no less fun. In it's basic form it is a toilet plunger (without the handle) which you hold in your hand and move in and out in front of the bell of the trumpet. You can buy specialized plunger mutes, but the easiest type is probably the rubber plunger you buy to unclog your drain (small one for trumpet or cornet, regular size for trombone). It's cheap and very effective (and indestructible). I have heard that it is best to make a small hole in the center to let the sound escape more easily. It is up to you whether or not you do that (I myself haven't, so far)
The last of the most common mutes goes by different names. Harmon mute. Bubble mute. Wah-wah-du-all. Although they look somewhat different they are really all the same thing. Most commonly they are referred to as harmon mutes. The name apparently comes from the Harmon company which first came up with this type of mute. Essentially a harmon mute is a sphere or cylinder of which one end (yes, I know a sphere doesn't have an "end") inserts into the bell of the trumpet without letting sound escape from the side as is the case with the straight or cup mute. The other side has a hole in it through which a tube slides with a small cup at the end. They can be used with or without the tube inserted. With the tube inserted you can move your hand in and out from the small cup to produce a duck-like sound (hence "wah-wah"). When the score calls for a "harmon mute" the tube is always removed. Ever heard Miles Davis? That's what it sounds like without the tube. These mutes reduce the volume of the instrument most (by about 20dB), so you might not be able to hear yourself when playing in a group. Be careful not to exceed your lips capabilities. Generally the harder it is to get "the buzz" out of one of these (in other words, the more air it needs), the better the sound will be. This is related to the weight of material; a thin-walled harmon will buzz quickly. These mutes are only available in metal. Usually aluminum, but Jo-Ral (at least) also makes a harmon mute (or bubble mute as they call it) entirely of copper. The copper here has the same effect as it does on straight mute, making it "darker" or "warmer". These apparently are much preferred for jazz. However, as noted before since copper is a lot heavier than aluminum, these all-copper bubble mutes will soon start to feel like a brick hanging from the end of your trumpet. I am told Jo-Ral bubble mutes, both copper and aluminum, sound great but (therefor) require a lot of air. Using a harmon mute without the stem might sound like a good idea to use as a practice mute. Don't. Although you should practice with all your mutes now and then, using one of these all the time for practice might set your embouchure such that it will be hard to play correctly without one. Like the straight and cup mutes, the harmon also tends to change the pitch: harmon mutes sound sharp (higher).
One other kind of mute you might run across occasionally is the bucket mute. Perhaps the most common type is the (again red and white) Humes & Berg bucket. It is a fibre "bucket", the diameter of the bell (about 5" on a trumpet), open on the end facing the bell of the instrument with cotton wadding on the inside (the stuffing is kept in with a net over the end). It clips on to the bell. Jo-Ral makes a bucket mute which could be described as the top of a harmon mute, fitting inside the bell, closing it off and a bottom consisting of a cylinder with wadding inside and 2 or 3 large holes drilled in the side. It is available entirely in aluminum or aluminum with a copper bottom. Again, the copper bottomed one is described as being very heavy. These Jo-Ral bucket mutes are said to sound quite different from the traditional bucket, but not unpleasant. I have never heard or played one, so I couldn't say. Some say the advantage of it is that there is no risk of the clips damaging the bell. Regular (Humes & Berg-style) bucket mutes make a trumpet sound more like a flugelhorn.
There are of course many other different types of mute. Take a look at a Humes & Berg brochure to get an idea of the variety. But these are the most common ones. When shopping for a mute, always try as many different ones as possible. One vendor might not have all brands, so visit different vendors. There is no shame in owning several different mutes of the same type (straight, cup) for different purposes. So go out and have fun!