Have you ever known someone who is never quite happy, no matter what you do to please them? And even when you think you've done everything the way they want, they change the parameters and you're back to square one?
Well, that's what pitch is all about. It's like balancing on the top of a ball. You're never able to relax and just be. You have to adjust constantly.
But there's often no time to adjust, especially in a moving line. In a chorale, where each note is held a bit, the chords carry the line. But a melody is mostly passing tones of some sort, so one has to act on the fly. You have to just feel how to fit in with those around you. And pray, and sweat, and pray some more, and bite and honk. If you're lucky, you'll get a bit more than half the notes in tune. That's why I feel like slapping people when they say "Oh, it must be such a JOY to play music!!!".
In an orchestra, the oboe sets the pitch. Uppity oboe! "My way or the highway." No really, oboe is limited in pitch variation, so that's why they tune us. Oboists are fine as people, but nicer when drunk. These days all oboists use electronic tuners to be sure they are right on. Most orchestras tune to 440, which is the number of vibrations per second in the note "A". But some orchestra's, like Saint Louis and Boston, tune to 442. It's only a hair higher, but it makes a world of difference. If I played in either of those orchestras, I'd have to adjust all my equipment to be comfortable at that pitch level.
OK. So I've spent hours at home with a tuner checking each note on my instrument, learning which notes are a little or a lot sharp or flat, and finding ways to adjust those accordingly. Now remember, tuners are giving you a "tempered" reading, based on the "equal temperament scale". That means each pitch is equidistant from the next. But if a singer sings a major scale starting on "A", for example, the third note in the scale, C#, would probably be sung a bit low to a tuner. That's because in any particular "key" the third is usually "felt" low.
There's a good reason for this. It's called "just intonation", meaning each pitch is tuned to "blend" best in it's function in that particular key. Are you still with me? So the singer sings the C# quite low because it is more mellow in that key. If someone sings or plays an A and another plays a C#, those notes will clash until the C# is lowered, 26 cents low to be exact. A cent is 1/100th of a half tone.
That's just one example of "just intonation". Each note of the scale is slightly different in its needs in order to sound "right" in that scale. Now throw in different keys, especially minor keys, and things get really complicated.
Once in awhile I'll hear someone joke about how their instrument came "tuned at the factory". In the case of wind instruments, it's true. A well made instrument will have a fairly even "tempered" scale, so each note is fairly well pitched and can be adjusted by the player's embouchure to meet the needs of the music. But even the best clarinets have tuning flaws. For example, when I try a new instrument, I check for skewed 12ths, the interval the clarinet jumps in the second octave. The upper 12th is usually high.
So, back to tuning in real life. I've prepared my piece at home, and tuned my instrument and prepared fingerings to adjust for problems. I get to rehearsal and start playing, and I'm out of tune. Why? Many reasons. My reeds may be different in the hall, which is dryer and warmer. The reed may stiffen, raising the pitch. My instrument will also tune higher in warm conditions. I may blow harder in the context of the other instruments, lowering the pitch. It turns out that clarinet goes flat when it plays loud, and sharp when it plays soft. And all the other woodwinds go the opposite way. So the clarinets are left in the dust while everyone else tunes merrily along. Grrrr. What happened to tuning at the factory???
Remember, in the woodwind section there are four completely different instruments playing together. The oboe, a double reed instrument with limited pitch flexibility and dynamic range, and a very dense tone; the bassoon, another double reed with a much lower range and extremely complex acoustical layout, the flute with no reed but with a radically different sound production, and the clarinet, which is acoustically alien to all the others. It's like the United Nations; We all pretend we get along, but blame the others for all the problems.
So how do we ever sound good together? My section has been together 16 years, and we know each others playing, temperaments, habits, weaknesses, strengths. With lots of trust, intuition, experience and ten tons of concentration on the moment, we often manage to sound like one instrument. At least during the tuning note. Then the concert begins and it's each for himself.