The brass family is one of the oldest families of musical instruments. In the broadest sense the term brass does not even imply that the instrument is made of brass, whereas saxophones, although made of brass, or at least some other metal, belong to the woodwinds. In fact, an 'alphorn', which is a quite common folklore instrument in the European Alps, or the Australian didgeridoo, which is a quite fashionable 'world music' instrument nowadays, is a brass instrument, although made entirely of wood. The same thing applies for conch shells or real 'horns'.
To decide whether a wind instrument belongs to the brass family you have to look at the method of tone production.

Overview: Wind instruments

Wind instruments are characterized by the fact that the tone is produced by oscillation of an air column. The pitch is determined by the length of that column.

There are three different families of wind instruments¹: "flutes", "reeds" and "brass". They differ from each other by the way the tone is created:

• Flutes (in the very broadest sense) create a tone by guiding a stream of air over a sharp edge. This can be done by blowing into the instrument (recorders, ocarinas, ...) or by blowing over the instrument (transverse flutes, panflutes, ...).
• Reeds have a little piece of solid material (wood or reed, hence the name) that vibrates in the air flow, thus producing an air vibration within the instrument. There are double reed instruments (oboe, bassoon, english horn) which have two vibrating reeds tied together, and single reed instruments (clarinets, saxophones) which have only one vibrating reed attached to a mouthpiece.
• Brass Instruments create their tone by the vibrating of the player's lips at the mouthpiece.

Brass Instruments - a closer look

The first brass instruments (which were not even made of brass, but of horns or conch shells) had a fixed lentgh. The player had only a very limited choice of tones to play, all of which are harmonics. To understand the concept of harmonic notes a little physics and a little mathematics is needed. All the following calculations are simplified as much as possible, but the principle should shine through the formulas. Most of them are also valid for reeds and flutes.

First question: Are tube length and frequency range somehow correllated?

Yes, they are. The longer the tube, the deeper the sound. Sound travels at a speed of app. 1,000 ft/sec². If a tone has a frequency of 440 cycles/sec, or 440hz, the wavelength of this tone is calculated as follows: 1,000 ft/sec divided by 440 cycles/sec = 2.272727... ft.

Tubes do not create a sound, they just enforce it. Unfortunately it is not possible to enforce any random frequency with any random tube. There has to be a exact ratio of tube length / wave length. Brass instruments are open tubes, i.e. they are open at both ends. The calculation for open tubes would be tube length x 2 = fundamental wave length, or the other way round: fundamental wave length / 2 = corresponding tube length. If a frequency of 440 hz has to be enforced by a tube, the length of the tube is determined as follows: Speed of sound / frequency = wavelength ; wavelength / 2 = tube length. Insert the numbers: 1,000 ft/sec / 440 hz = 2.2727.. ft; 2.2727.. ft / 2 = 1.13636.. ft. This calculation neglects some factors like the width of the tube or its bore (cylindrical, conical, ...), but they have only linear influence on the calculations.

Second question: How is it possible to produce different pitches without changing the tube length?

Take a fictional open tube with a lentgh of 5 ft. Its basic tone would have a frequency of (1,000 ft/sec divided by 5 ft) / 2 = 100 hz. If you trigger³ the air in that tube with a frequency of exactly 100 hz, the resulting wavelength is exactly the same as the double length of the tube, so the wave fits exactly or 'stands' in the tube. If the frequency of the sound source is gradually raised, the resulting wave length will be shorter, no longer fitting exactly. The waves within the tube are no longer 'standing', but floating back and forth, interfering with each other and thus extinguishing themselves. When the sound source reaches a frequency of 200 hz, the wavelength will be 5 ft. Two of those waves will fit exactly ('standing') into the tube, which means that the first harmonic⁴ of that special tube has been found. Raise the pitch to 300 hz and get a wavelength of 3.333... ft, which stands in the tube three times, and so forth.

Third question: Why are these correllated pitches called 'harmonics'?

If two of the harmonic pitches are played simultaneously, they tend to sound good together, whereas two non-harmonic pitches tend to sound bad. Example: a 100 hz tone and a 200 hz tone have an interval of exactly one octave and sound absolutely harmonic. Lots of untrained ears will not even notice that they hear two different tones. A 200 hz and a 300 hz tone form a perfect fifth, which is also one of the pure intervals. A 300hz and a 400hz tone form a perfect fourth which is still a quite harmonic interval, and so on ...
These notes form an array of tones like a ladder or 'scale', the so called natural harmonics scale. This scale starts with a really big step (one octave), followed by a smaller one (a fifth), again a smaller one (a fourth), again a smaller one (a major third), and so forth. This scale follows a logarithmic pattern. This means that no matter what frequency you start with, the corresponding octave will always have twice that frequency, the corresponding fifth will always have 3/2 times the frequency, .... The following table shows frequency ratios and the corresponding intervals:

There is only one little, but big problem: These ratios do not fit exactly into our twelve tone scale. A little calculation example will show the problem:
Take the tone A, two octaves below the standard 440hz-A. It has a frequency of 110hz. If we stack a major triad on top of this tone we first add a major third (110hz x 5/4 = 137,5 hz) to get a C#; then we add a minor third to that C# (137,5 x 6/5 = 165hz) to get the fifth; then we add a fourth to that E (165hz x 4/3 = 220hz) to get the next A. If we control the frequency, we divide the 220hz by 2 to go down one octave, and we have the original 110hz again q.e.d.

What happens if we build one octave from identical intervals? In our dodekaphonic system three major thirds fit exactly into one octave: We start from the A (110hz) and go up one major third (110 x 5/4 = 137,5hz) and we get a C#. Another major third brings us up to the F (137,5 x 5/4 = 171,875 hz), and the last major thrid takes us to the A again (171,875 x 5/4 = 214,84375 hz ???). Comparing the "perfect" octave with this "composed" one, we see that the latter one is flat significantly. Unfortunately our ears are well able to hear these little differences, and playing the 220 hz and the 214,8 hz simultaneously will cause one's toenails to curl up.

The solution to this problem was to dispense with the natural harmonics and to use a weighted average twelve tone scale instead. The standard half tone interval was defined to have a "well tempered" frequency ratio of 1:2^1/12. Starting from the 110hz tone mentioned before, we get the following tone scale:

This well tempered tuning offered the possibility to introduce a standard tuning to all instruments, as only one fixed tone needed to be defined, and all other tones were derived from that focal point. The forementioned Chamber Tone A (440hz) is this center tone. Sometimes the tuning of a whole orchestra is shifted up slightly to get more tension on the strings, which causes a brighter tone. To finetune that pitch shift, some definition like A=445hz has to be made.

Fourth Question: How can all the other notes which are not in the harmonic scale be played?

Before the invention of valves or slides (as used with the slide trombone) the answer was quick and simple: They can't. This was an enormous drawback both for composers and musicians. The key to the other notes was the length of the tube. Instead of changing to another instrument (with different tube length and different natural scale) in the middle of a tune, which would have required artistic skills, valves which opened some extra tubes were invented. The modern standard trumpet, first built around the year 1815, has three valves, which allow the player to shift the whole natural scale down for one to six semitones⁵. As the trumpet's usable tone range starts not at its theoretical base tone, but at the first harmonic (first octave), the next natural tone is one fifth (i.e. seven semitones) higher. If the player shifts that tone down for all available six semitones, he is only one semitone above the first harmonic, and there's no tonal gap.

The following table shows the fingerings for a chromatic scale, played on a Bb-trumpet, which is the standard today:

Brass Instruments

Trumpet

Trumpets are the highest pitched brass instruments. Their tube has a standard length of 4 1/2 ft. The sound of a trumpet can be martial or festive, but also very subtle when played with a mute. There are two basic types of trumpets, one with rotary valves, the other one with piston valves.

Cornett

The cornett is very often mistaken for a trumpet. The differences are in fact very small. The cornett has a wider bore which causes a slightly softer tone. One of the best known cornett players was 'Satchmo' Louis Armstrong, who is nevertheless referred to as one of the most influential trumpet players.

Flugelhorn

Even the flugelhorn is sometimes mistaken for a trumpet. The differences between the flugelhorn and the trumpet are obvious, however: The flugelhorn has a wider bore, which makes the instrument significantly larger in size. The tube length, however, is still the same ( app. 4 1/2 ft.) as the trumpet's. To be exact, the flugelhorn should not be seen as a wider trumpet, but as a soprano tuba, as its conical bore is typical for the tuba family.

French Horn

The french horn is related to the signalling horns that were and still are used for hunting. It has inherited the typical round form, but it has been equipped with a sophisticated set of valves. Today's standard french horns are double horns, which means that they can be turned from a F-instrument into a Bb-instrument at the touch of a valve. They have, of course, the standard set of three, sometimes four valves. It's the only brass instrument where the valves are operated with the left hand⁷. The right hand is stuffed into the muzzle of the horn, which contributes to the soft, mellow sound.

Tenor horn, Baryton, Euphonium

These three instruments are very closely related. They are sometimes mistaken for 'little tubas', which is, however, exactly what they are. Lots of instrumental families come in a set of four voices from soprano to bass (soprano sax, alto sax, tenor sax, baritone sax, or violin, viola, tenor violin⁸, bass violin or violoncello⁹). Barytone or tenor horns form the baritone or tenor voice of the tuba family.

Tuba

The tuba is the lowest brass voice. It comes in different shapes (tuba, helikon, sousaphone) and tunings (F-tuba, Bb-tuba, C-tuba).

Trombone

The trombone is the only chromatic brass instrument which doesn't usually have valves. The length of the tube is changed by a slide at the bottom of the instrument. Sometimes a valve trombone is seen, too, which has a regular set of valves instead of a slide. Trombones come in different voices. There is even a soprano trombone which has the tonal range of a trumpet (experts say that it's in fact a slide trumpet). The most common one is the tenor trombone which has the tonal range of a tenor horn. Some trombones have additional valves ('triggers') which are operated with the player's thumb. These valves can change the tuning of the trombone, similar as with the (double) french horns.

'Wooden' Brass Instruments

The Australian didgeridoo is just a long, more or less straight wooden pipe without any moving parts. The tone is created by the players lips, along with some singing and grunting into the instrument. This causes the specific, magic sound of the 'didge'.

The European 'alphorn' is a really long straight wooden tube with a curved up muzzle. Typical alphorns have a length of 15 ft and more.

Brass Instruments made of animal horns or Chonch shells

Sometimes animal horns or conch shells are used as wind instruments. As their length and hence their pitch is a freak of nature, they hardly fit into a standard musical context. Some players, esp. Mr. Steve Turre, have pushed the conch shell perfomance beyond the limit of what was imaginable before.