User nemosyn asked me an interesting question, and requested this writeup, namely an explanation of why these instruments exist AT ALL.
After all, a C melody saxophone exists, there is a C pitched trumpet, and so forth. In theory, if we simply made all instruments concert pitch we would literally only need ONE "part" for a given piece of music, and have everyone play from the same sheet.
First off, concert pitch has not been standard throughout history. It's been changed before and might change again. In fact, some orchestras have a "gimmick" of playing pieces in instruments tuned for former pitch to show you "what it sounded like when it was written".
But fair enough, the real meat of the question is why a trumpet reads "C" and plays a "B flat" and a bass clarinet is actually pitched an entire major 9th lower than "C".
To be fair, many instruments play concert pitch. A piano does. So does a violin, viola, oboe, bassoon, trombone, and tuba.
There are many other instruments that play a perfect octave lower or higher but are in the same pitch, so a C and concert pitch C are in unison- the double bass and guitar sound an octave lower than written, as does the contrabassoon. A piccolo is an octave higher than written. The decision was made in these cases to write the music an octave higher to prevent having to write everything on the bass clef, or in the case of the double bass, have the artist have to read sheet music where everything is extended with lines well below the bass clef. Imagine being a piccolo player and having to try and work out what six lines above the top of the treble clef actually sounds like all the time. Pitching that down an octave puts it in the clef and makes it easier to read.
But when we look at the culprits we find woodwinds. Clarinets, saxophones, trumpet, French horn, and English horn. And therein lies the aggravation for many people.
Keep in mind that these instruments are many many hundreds of years old and were made well before any idea of standardization of pitch. But the decision was made to notate them in a common way in terms of reading music so that a player could more easily move from one instrument from another.
If I grab the clarinet on my wall, and finger it with the octave key down the first three holes plugged with my fingers, the note produced is written as G. If I grab my alto saxophone off the wall and use the octave key and the first three keys, it's written as G. Should I ever figure out how the hell to get the embouchure right to play the flute and decide to give jazz flute a try, if I was to grab a flute and mash down the octave key and the first three keys... you're about to guess right, that is indeed notated as a G. The recorder, that horrible sounding cheap woodwind that young children everywhere are given to learn the basics of music on, the first three holes and the thumb hole is.... G.
The practical upshot is, I can grab any of a number of related woodwinds and with only minor variations of Boehms' flute key system (Klosé for the clarinet, etc.) stand a really good chance of quickly learning or even sight-reading music using a variety of them. They may not sound the same, but the point is I can easily make those notes happen.
That's all very well and good, TheAnglican, but if they could standardize fingering, why not standardize pitch as well?
I'm glad that you asked.
Watch a guy tune a drum, it's a pretty interesting process. They'll remove the bottom head with a key, put the top head on and stretch it, and then they'll slowly raise the tension on the head, testing the tension at every lug point and trying to equalize it. What you'll hear is that the drum sounds off and dissonant, with audible "beats" in the tone where the sound interferes with itself. You get it where the drum sounds clear, but it's meh. And then you get to a specific frequency, and the damn thing comes alive and rings out with a beautiful, clear tone. Unless the drummer wants a muddy sound (and death metal guys do) you'll typically find drummers try to tune their instruments so that they ring out beautifully.
I'm sure you've also had the experience where you have a piece of music playing at volume in the living room on the good stereo and when a certain note comes on forcefully you hear a chiming, rattling sound as all the good wine glasses start to vibrate in sympathy. That's how you shatter a crystal wine glass, by the way, find the frequency at which it starts to vibrate in sympathy and sing that at it forcefully.
Where I'm going with this is that most instruments have an acoustic quality. An innate one. A modern electric guitar is basically a plank with some pickups on it and it matters very little how that's shaped or even the quality of the wood, unless you're talking about a semi-acoustic or hollowbody guitar. This explains the wild designs of the 1980s where things were lime green and shaped like a collection of spikes. It didn't matter at all, the magic was in the pickups and strings. But as for a clarinet, or a saxophone, these are basically tubes that ring out optimally when they have a specific shape, a specific length, and a specific mass.
And that doesn't always jive with concert pitch C.
Consider that a Selmer Mark VI is a legendary instrument with beautiful tone that is highly coveted by musicians and collectors alike. As for the C melody saxophones of the 1920s, they're a novelty put together so that you didn't have to buy two pieces of sheet music so your other daughter could play from the hymnal with the daughter that played the piano because sheet music was scarce in Iowa, and designed and marketed as such.
Instrument makers have spent hundreds of years defining, refining and perfecting instrument families, and for many, many, many reasons have standardized on B flat, E flat, and so forth. We've tried to make playing in those families somewhat sane by notating them in the same way for the same fingering. The only person that hates his life is the composer that hears a particular note in his head, and then has to think about how to pitch it up, down, an octave up, or what have you.
But it beats the alternative of telling a woodwind player that if he wants to play C on the alto saxophone it's one strange combination of keys, and C on the clarinet, another strange combination of keys, and so forth. With straightforward notation, teaching the instrument is much easier. I can't imagine trying to teach a small child "Au Clair De La Lune" with instructions not to lift and then lower an adjacent key, but to do two completely unrelated versions of a CTRL-ALT-DELETE hand movement.