Brass Instruments

This question has many parts:

What is a mute? A mute is a device that changes the sound of the instrument it is used on. It is not a device, necessarily, for making an instrument quieter, although that may be a by-product of the change.

How are they used on Brass instruments? Primarily, mutes are objects which are placed in the bell of a brass instrument. Some mutes block the passage of certain frequencies, others improve the coupling between the bore and the air for certain frequencies (causing them to lose less energy, therefore sound stronger). Some pass the sound from the instrument through resonating chambers which modify the sound. Some add a "port", which the player can close or partially-close with their hand, making a wah-wah sound. The variety of mutes is great, and some even choose to make their own. They vary in materials, shapes, porting, resonances, etc.

How does it affect the sound? This can be answered very simply, for instance, as appropriate to an elementary-school student, or in very complex mathematical terms. I'll attempt to strike a middle-ground here.

First, you need to understand how a brass instrument makes sound. The instrument appears to be quite simple: a brass tube with a bell at one end and a "landing pad" of sorts where the player's lips can vibrate. In reality, the bore of brass instruments are complex, the mouthpiece is acoustically complex, and the bell, although easy to describe, is still anything but simple. All together, these elements combine to cause the brass instrument to act like the double-reeds, acoustically. All this means is that brass instruments can resonate on each of the harmonics of a complex tone at the fundamental pitch, which is determined by the length of the instrument. To play different notes, the player switches from harmonic-to-harmonic and changes the length of the horn, either by a valve or telescoping tubing. The odd limit is that the actual fundamental is harder to play than the double reeds (and other 'stopped conical pipe' instruments). The availability of the instrument to resonate at many harmonics also affects its tone: brass instruments have them all, so the sound is bright and even metallic.

To get a different tone, the brass player can use a filter, resonator or coupler. These three devices, in acoustic terms, reduce or block ranges of frequency, use an acoustic structure to increase the power of certain frequencies (often by scavenging the power from other frequencies) or changes the impedance of the bell to make some frequencies get from the bore to the air (where the audience can hear it) with less loss of energy, respectively. All of these types are performed with mutes, and they are all placed into the bell of the instrument.

One exception to this description is the French Horn. In the case of the horn, the player's hand is placed in the bell, and used in all but the most exceptional cases. But rather than simply modifying the tone of the instrument, a skilled player can 'stop' the horn (by nearly blocking off the bell's coupling to the air with their hand) and get a pitch one semitone higher than the normally-placed hand. This was used to get chromatic pitches with the 'natural' horn, which had no valves. Derived from the hunting horn, the Natural Horn was still in use in Beethoven's day (his Horn Sonata, for instance, was written for such a valveless horn). The stopped note is very different in tone from the normal sound of the horn, so this is a form of muting, and composers took advantage of the different tone for emotional effect.

This question has many parts:

What is a mute? A mute is a device that changes the sound of the instrument it is used on. It is not a device, necessarily, for making an instrument quieter, although that may be a by-product of the change.

How are they used on Brass instruments? Primarily, mutes are objects which are placed in the bell of a brass instrument. Some mutes block the passage of certain frequencies, others improve the coupling between the bore and the air for certain frequencies (causing them to lose less energy, therefore sound stronger). Some pass the sound from the instrument through resonating chambers which modify the sound. Some add a "port", which the player can close or partially-close with their hand, making a wah-wah sound. The variety of mutes is great, and some even choose to make their own. They vary in materials, shapes, porting, resonances, etc.

How does it affect the sound? This can be answered very simply, for instance, as appropriate to an elementary-school student, or in very complex mathematical terms. I'll attempt to strike a middle-ground here.

First, you need to understand how a brass instrument makes sound. The instrument appears to be quite simple: a brass tube with a bell at one end and a "landing pad" of sorts where the player's lips can vibrate. In reality, the bore of brass instruments are complex, the mouthpiece is acoustically complex, and the bell, although easy to describe, is still anything but simple. All together, these elements combine to cause the brass instrument to act like the double-reeds, acoustically. All this means is that brass instruments can resonate on each of the harmonics of a complex tone at the fundamental pitch, which is determined by the length of the instrument. To play different notes, the player switches from harmonic-to-harmonic and changes the length of the horn, either by a valve or telescoping tubing. The odd limit is that the actual fundamental is harder to play than the double reeds (and other 'stopped conical pipe' instruments). The availability of the instrument to resonate at many harmonics also affects its tone: brass instruments have them all, so the sound is bright and even metallic.

To get a different tone, the brass player can use a filter, resonator or coupler. These three devices, in acoustic terms, reduce or block ranges of frequency, use an acoustic structure to increase the power of certain frequencies (often by scavenging the power from other frequencies) or changes the impedance of the bell to make some frequencies get from the bore to the air (where the audience can hear it) with less loss of energy, respectively. All of these types are performed with mutes, and they are all placed into the bell of the instrument.

One exception to this description is the French Horn. In the case of the horn, the player's hand is placed in the bell, and used in all but the most exceptional cases. But rather than simply modifying the tone of the instrument, a skilled player can 'stop' the horn (by nearly blocking off the bell's coupling to the air with their hand) and get a pitch one semitone higher than the normally-placed hand. This was used to get chromatic pitches with the 'natural' horn, which had no valves. Derived from the hunting horn, the Natural Horn was still in use in Beethoven's day (his Horn Sonata, for instance, was written for such a valveless horn). The stopped note is very different in tone from the normal sound of the horn, so this is a form of muting, and composers took advantage of the different tone for emotional effect.