A temperament is a tuning scheme for a piano, or any stringed instrument. Historically, pianos were tuned in various ways as a kind of palette for the composer. Many of the great composers actually invented their own way of tuning their piano. Tuning their piano was necessary because the pianos were not built strongly enough to withstand the tension. In the process of tuning, they would create a different sound for each individual key signature. This is the reason they specified a particular key signature for each composition.
If you play an interval, like a third, you will hear a vibrato or beating of the two notes when sounded together. If you were able to tune the strings yourself, you would notice that the beating speed changes as you flatten or sharpen the notes. Using this phenomenon of beat speed, the composers would create a key signature with a vibrato (beat) that would complement the composition. For example, if they wanted to write something soothing, like a love-song, they would choose a slow vibrato. Similarly, if writing a piece with a lot of tension in it, they would use a key that had a faster vibrato.
There are many historical temperaments created by composers in the past, some of which were quite wild. In fact, some key signatures were not used because the beating was obnoxious and sour. They were called “wolf” notes, for good reason! By the law of physics, creating octaves and intervals within it requires a certain amount of fudging and massaging to allow all the different key signatures to exist simultaneously. When you sharpen or flatten a note within the octave, the inverted interval is also affected, so if one moved a particular note too far, the complementary note would become a wolf note, and the key signature that it was associated with would not be usable.
Nowadays, almost all tuners use the modern “equal temperament” in which all the notes are spaced equally. The advantage is that one can transpose to any key signature without changing the vibrato. The pitch frequencies for each note are equally spaced within the octave. If one wanted to try a special temperament on his or her piano, if the effect is found to be unacceptable, one would have to pay to have another tuning to revert it back. Many modern keyboards have a switch which will simulate the sound of an historical temperament, which is an easy way to get the feel of the way the composer intended the piece to sound.
For more information on this and other subjects, please contact me.
Paul
