Well, before the keyboard instruments were well tempered [think of the Well-Tempered Klavier], it was impossible to play in tune (i.e. with good intonation) in certain keys. And by the old system it would be impossible to do the annual (or semi-annual) tuning in such a way as to be able to play all keys in tune.
Modern string players still have this problem, albeit to a much lesser extent. When I'm tuning my cello, say I start by choosing an appropriate A, and then tune the first fifth (A and D) to a very exact fifth. So far so good. If I then forget all about the A and tune the next fifth (D and G) in an isolated way, to be a very exact fifth, and then do the same thing with the last fifth (G and C), ignoring the other strings, I will have a problem when I try to get certain chords and intervals in tune. [Each individual fifth was very pleasing, but over the whole range of the instrument, one quickly discovers that this untempered way of tuning the instrument results in unresolvable contradictions.]
My solution is to tune the instrument as follows:
- Match my A to whatever has been given
- Tune the D to the standard exact fifth below the A
- Make the next fifth a hair on the small side
- Make the last fifth a little smaller still
Now I have a structure I can work with pretty well.
I have read descriptions in a viola forum that were rather similar in procedure, with much the same final result.
[The result is slightly skimpy fifths. Taken out of context, each of these fifths is a little smaller than it should be, strictly speaking. However, this is what prevents me from getting some unavoidably ugly results.]
[Through this tuning procedure, I am trying to achieve consistency. I can adjust all the stopped notes (i.e. the fingered notes), but I can't adjust the open strings. So, this tuning procedure results in a set of compromises that creates many tiny intonation problems, for the sake of avoiding a small number of large intonation problems. Just as tempering the keyboard instruments did.]
Intonation is a subjective thing. I am a string player. However, I took a couple of semesters of voice lessons. My [voice] teacher sometimes remarked that my "string player style intonation" would not fly in the vocal world -- as an example, my leading tones were too high for vocalists' taste -- but she recognized that I was not alone; the whole breed of string players play their leading tones higher than many other musicians.
[As a string player, for a leading tone to sound pleasing to my ear, and "in tune," I need to bend it quite close to the tonic, i.e. I need to get it very, very close to the tonic. I feel that I am milking that leading tone for all it's worth. I feel that if I did not do that, it would be like when someone is telling a joke and just as he's about to pronounce the punchline, someone comes in and distracts the listener with some unimportant but very distracting interruption. When the joke teller tries to pick up where he left off, it's not the same -- and the punch line doesn't satisfy.]
*[What I'm talking about in this section is the effort, and the satisfaction, of getting a series of individual notes to be in tune with each other, within a particular tonality (=key). (This is possible because of the tempered way I tuned the instrument.)
Edit, responding to your comment checking your understanding:
So (testing my understanding) given a desirable (pure) musical pitch, tempering represents a divergence from it in the name of compromise.
Yes, I think we are on the same page here, except that intonation, for me, is always relative to something. Having played the first note, I now will listen very carefully and adjust as needed so that the second note will be in tune with respect to the first. (I'm not sure a person with perfect pitch would feel the same as I do about this....)
Intonation is the striving towards realisation of pitch regardless whether pure or compromised.
Not sure what you're saying here, so I'll skip this sentence.
As we tend for historical reasons to associate intonation with purity -rather than simple realisation- of tone, it has become more or less synonymous with just tunings, which can be misleading.
I don't think I agree with this sentence.
In particular, the terms temperament and intonation cannot be interchanged.
I think I agree. Having a well-tempered instrument makes it feasible for us to play in tune in any arbitrary key.