Gordon, the tuning issue you mention is really quite sophisticated.
In an ensemble, such as a choir, a string quartet, a band, or orchestra the musicians listen and tune to each other.
However, a keyboard instrument such as a piano, is tuned in advance and the notes do not tune to each other interactively.
Pythagorus studied this -- he tuned a perfectly-in-tune 5th (called a perfect fifth or P5 for short), and then tuned that fifth to the next one, and so on... clear around all the notes and discovered that he didn't end up where he started. Yep, Mother Nature decided to arrange the perfect intervals in a spiral rather than a circle! This "extra" space between where we ended up and where we started is called the "Pythagorean comma".
Keyboard temperaments, then, are specifications for distributing the comma between the notes. Some temperaments keep certain keys "perfectly" in tune at the expense of other keys being "way out" of tune. "Equal temperament" distributes the comma equally per note such that everything is not-quite-exactly in tune but is in-tune-enough to be playable.
You will notice that in piano concertos, for the most part, the orchestra plays, then the piano plays, then the orchestra... back and forth! Individual instruments or small groups may play along with the piano (because they can tune to match the piano!) however you rarely hear a bunch of instruments and the piano all going at once? And the reason is the very tuning issues that you mention.
In an ensemble, such as a choir, a string quartet, a band, or orchestra the musicians listen and tune to each other.
However, a keyboard instrument such as a piano, is tuned in advance and the notes do not tune to each other interactively.
Pythagorus studied this -- he tuned a perfectly-in-tune 5th (called a perfect fifth or P5 for short), and then tuned that fifth to the next one, and so on... clear around all the notes and discovered that he didn't end up where he started. Yep, Mother Nature decided to arrange the perfect intervals in a spiral rather than a circle! This "extra" space between where we ended up and where we started is called the "Pythagorean comma".
Keyboard temperaments, then, are specifications for distributing the comma between the notes. Some temperaments keep certain keys "perfectly" in tune at the expense of other keys being "way out" of tune. "Equal temperament" distributes the comma equally per note such that everything is not-quite-exactly in tune but is in-tune-enough to be playable.
You will notice that in piano concertos, for the most part, the orchestra plays, then the piano plays, then the orchestra... back and forth! Individual instruments or small groups may play along with the piano (because they can tune to match the piano!) however you rarely hear a bunch of instruments and the piano all going at once? And the reason is the very tuning issues that you mention.