Could someone provide a simple (for beginners) answer to the question, "What is concert pitch?" I understand that different brass and reed instruments play at different pitches and that a C played on one is not necessarily a C played on another. I further understand that it is obviously a pitch that a total orchestra can tune to. But what is the proper definition?
The problem you appear to be running into is that there are two different definitions for the term "concert pitch":
The pitch as described using a non-transposing instrument, such as a piano. Sometimes the word "pitch" is replaced with a specific note name to describe the exact note, e.g. Concert B♭.
The frequency and pitch name that a band or orchestra is tuned to. The most common example is A440, which means that a non-tranposing instrument will be tuned so that the pitch A above middle C is 440 Hz.
While these are accurate definitions, a beginner would likely also want to know what a transposing instrument is.
Many instruments have multiple versions that play higher or lower pitches. To make it easier to switch between them, the sheet music for these instruments will often be transposed so that the same fingerings correspond to the same notes, no matter how high or low the instrument. Such instruments are called "transposing instruments."
Examples include the B♭ Trumpet and B♭ Clarinet, where their C sounds like a Concert B♭. They have have to play D to play a Concert C.
For transposing instruments (like much of the brass family and some of the wind family), the written note does not correspond to the sounded note. Concert pitch is the sounded pitch.
For a B♭ trumpet, to play a concert pitch C5, it needs to play a written D5. For a guitar, to play a concert pitch C5, it typically needs to play a written C6 (alternatively, be explicitly written with an octave transposing clef, a violin clef with an 8 underneath, a practice that is only slowly taking hold). A soprano recorder has a concert pitch of C6 for a note written as C5. Horns tend to be off by a fourth.
When coordinating with other musicians playing different instruments, the communication about pitches is usually done in concert pitch as a "common language". The conductor usually talks in concert pitch as well. There may be some exceptions, like octavating (contra) bass instruments: that they are sounding an octave lower than written tends to be an "implementation detail" of the bass group they are a part of. But since it is rare to talk about octaves anyway, this rarely is an issue.
if you look at the saxophone family each instrument produces a different note when playing a C fingering.
Tenor saxes are B♭ instruments. So if you play a C fingering on a tenor you will hear concert pitch B♭.
Alto sax is an E♭ instrument. So if you play a C fingering on a alto you will hear an E♭ concert.
This is a problem if you say play a C and each instrument plays a C fingering producing different notes.
If you say please play C concert the tenor will play D and the alto will play A and they will both sound like C!!
You may be asking yourself, well why!? The reason is that you may play 4 different saxes and transposing in your head would be very difficult. Especially if you are switching instruments in the same concert or even the same song. But if you are reading and the composer transposed for you you can just play the fingering that is indicated and the note will sound correctly. Just make sure you are reading the correct score because now as you can see the alto score and tenor scores will be written differently even if they are playing the same pitches.
I'm mainly providing an answer to address some comments about Wikipedia not providing adequate sources and the idea that "concert pitch" is supposedly not used to refer to a pitch standard (but rather only in the transposing instrument sense). There has also been speculation that dictionary writers just made the first meaning up. Apologies to OP if this is not a "simple answer" for beginners, but as there seems to be some controversy in answers and comments, I thought it might be helpful to provide background.
The original meaning of "concert pitch" in English referenced emerging pitch standards in the 1700s. Merriam-Webster notes this sense of an international pitch standard from ca. 1735 (though, admittedly, their definition of "international pitch" doesn't give the historical variance in that definition, which wasn't 440 Hz in the 1700s).
The Oxford English Dictionary gives an example of this internationalization from 1772:
Concert or Opera Pitch, for a Vocal Performance &c. from which all other notes may be proportioned.—The Lombardy, and Venice Pitch, is a Tone higher than ours, or theirs at Rome.
The development of the tuning fork in the early 1700s was instrumental in this concept, hence a dictionary from 1783 can claim that a "pitch fork" (i.e., tuning fork) can be
a device for tuning musical instruments to concert pitch
This meaning continued as the primary one in common use throughout the 1800s. Usually ensembles tuned to a particular reference pitch. From an 1848 dictionary:
Concert pitch, the pitch, or degree of acuteness or gravity [highness or lowness], generally adopted for one given note, and by which, consequently, every other note is governed.
When Alexander Ellis, perhaps the greatest English-language authority on pitch standards of his day, wrote his series of articles on The History of Musical Pitch (1880), he employed the term concert pitch in this manner.
As noted by other answers, in modern musical practice the term concert pitch is also used more generally to refer to the sounding pitch of a transposing instrument. This meaning likely comes out of the German tradition that differentiated Kammerton ("chamber pitch," sometimes translated as concert pitch) and Chorton ("choir pitch," which was generally higher and corresponded to the pitch of the organ). As organs lasted for centuries and were much more difficult (if not impossible) to move to another pitch standard, there needed to be a way to convert the pitches of the other instruments (which followed current standards) to the organ (which was unchanging in its pitch standard) to allow various instruments to play together.
The English term concert pitch gradually acquired a related sense to those German terms, perhaps because it was frequently used as a translation of Kammerton when discussing the tuning of old organs. (Bruce Haynes, in A History of Performing Pitch: The Story of 'A' (2002) makes reference to the English phrase chamber pitch occurring perhaps as early as the 17th century as a translation of Kammerton, but he gives no references that early.) The concert pitch was thus not only the standard tuning of instrumental ensembles (as Kammerton was in German-speaking lands), but also the way of navigating between instruments pitched at various levels, i.e., what we now think of as "transposing instruments."
Around the time of Ellis's aforementioned study, one begins to see more discussions of the term concert pitch used specifically in reference to other transposing instruments. For example, from 1874:
A B flat cornet is one on which the "open" notes, though bearing the names C E G sound B flat D F; that is, a whole tone lower than they do on a C cornet; and it is called a B flat cornet to denote that it is a whole tone below concert pitch, and that consequently, to enable it to harmonize with any instrument that is at concert pitch, the music for it must be written a whole tone higher.
One also begins to see the emergence of the usage to refer to specific pitches as "concert X" when they are transposed to the standard pitch scale, as in the following excerpt from the same page:
I might put it on to the printer that I am made to ask, "If the B flat of the cornet is concert C," instead of "is the C of the cornet concert B flat;" [...]
I don't know how much earlier that last usage might go, but that was the first I was able to locate in a quick search on Google Books.
With the international pitch standard settled around A4 = 440 Hz in the 20th century, the term concert pitch sometimes just refers to that pitch standard today. It is also still used frequently in the original sense as the pitch standard to which an ensemble (usually a large instrumental ensemble) tunes, whether A440 or something else. But the specific meaning referencing the relationship of transposing instruments to their absolute pitches in the non-transposed scale has probably become the most common meaning among practicing musicians, unless they frequently play with ensembles the employ various differing pitch standards.
Concert pitch is a concept that is useful when dealing with transposing instruments. It denotes the pitch system of non-transposing instruments, which you can think of as a common language. This is in contrast to "written pitch," which is each instrument's own language, as it were.
If you are talking about a horn part, and you mention the pitch C♯, it's ambiguous: you might mean the written C♯ that is the same pitch as the trombone's F♯, or you might mean the written G♯ that is the same as the trombone's C♯. To indicate that you're naming pitches as they are written in the part, you prefix the pitch names with the word "written," as in the previous sentence. To indicate that you're naming pitches as they sound (that is, in the pitch system used by nontransposing instruments), you use "concert" instead.
Suppose an orchestra is playing an E-major chord. You want to discuss the tuning of the root. The clarinet part is written for clarinet in A and has a written G. The tenor sax has a written F♯. The alto sax has a written C♯. The horn has a written B. It's much easier just to say "everyone playing a concert E here, tune your octave with the tuba." But if you're just speaking to one player, it's usually easier if you use the written pitches.
Before writing this answer, I found that many dictionaries claim that "concert pitch" means that A is 440 Hz, but I've never heard it actually used in that sense. I think some dictionary writer was stuck trying to squeeze an explanation of transposing instruments into a definition of "concert pitch" and hit on the pitch standard as a way to define it without having to explain how transposing instruments work. Being unaware that some orchestras use an A that is other than 440 Hz, they were also unaware that they were thereby inventing a new sense that nobody actually uses.
There is no actual pitch that is concert pitch. That's why we refer to it as concert pitch. It's whatever pitch is decided that the whole orchestra - all musicians - will tune to in order to be 'in tune' with each other
Often it happens to be A=440Hz, but that's not actually what's known as 'concert pitch'. It may be so in some parts of the world, but it ain't necessarily so. Many years ago, it could be much lower. Many years before that, it was whatever everyone tuned to and it really didn't matter too much - as long as everyone actually tuned to the same thing!
There is a second definition, too. A lot of instruments are transposing instruments. That is, their music is written out in a key that is different from that of non-transposing instruments, i.e. piano. The problem here is that, say with a B♭ trumpet, its music is written out a tone above 'concert pitch'. When a trumpet player sees a C note on the music, the note blown comes out as a B♭. Here, the B♭ is called 'concert B♭', but when discussing the music - the dots, the note is referred to as a C.
“Give me an A!”
But which A? Different violinists would provide different A, from instrument to instrument andfrom orchestra to orchestra, from land to land, from town to town, from time to time ... if not orchestras worldwide would have in unison defined a standard pitch.
And this is not so long ago. You can imagine what problems musicians would have in our time when they are jetting around the world if there wouldn’t be this standard pitch (which is still differing today and not so stable as and definitely fixed as it would be desirable.
I add this link first to make clear that there are international attempts to define c.p. = 440 Hz.
The other problem you are mentioning (not all instruments are tuned in C) is quite different but can be solved by fine tuning if they’re constructed near orchestra pitch. They are transposing instruments and their voice part is adapted to their difference to the C instruments.
To come across the critic of phoog I‘m posting these 2 quotes:
In 1939, an international conference recommended that the A above middle C be tuned to 440 Hz, now known as concert pitch. As a technical standard this was taken up by the International Organization for Standardization in 1955 and reaffirmed by them in 1975 as ISO 16. The difference between this and the diapason normal is due to confusion over the temperature at which the French standard should be measured. The initial standard was A = About this sound439 Hz, but this was superseded by A = 440 Hz, possibly because 439 Hz was difficult to reproduce in a laboratory since 439 is a prime number.
Despite such confusion, A = 440 Hz is the only official standard and is widely used around the world. Many orchestras in the United Kingdom adhere to this standard as concert pitch. In the United States some orchestras use A = 440 Hz, while others, such as the New York Philharmonic, use A = 442 Hz. The latter is also often used as a tuning frequency in Europe, especially in Denmark, France, Hungary, Italy, Norway and Switzerland. Nearly all modern symphony orchestras in Germany and Austria and many in other countries in continental Europe (such as Russia, Sweden and Spain) tune to A = 443 Hz.
In practice most orchestras tune to a note given out by the oboe, and most oboists use an electronic tuning device when playing the tuning note. Some orchestras tune using an electronic tone generator. When playing with fixed-pitch instruments such as the piano, the orchestra will generally tune to them—a piano will normally have been tuned to the orchestra's normal pitch. Overall, it is thought that the general trend since the middle of the 20th century has been for standard pitch to rise, though it has been rising far more slowly than it has in the past. Some orchestras like the Berlin Philharmonic now use a slightly lower pitch (443 Hz) than their highest previous standard (445 Hz)