Equal Temperament Tuning
Just Tuning. Very early keyboard instruments were tuned using a Just or Pure series of fifths.
Meantone and Well-Tempered tunings. Meantone tunings allowed for more keys to be used. So if a series of pure 5ths were tuned from C, C — G — D — A — E, the major third E in the C-chord would beat around 16.3 times a second. which is too fast to be pleasant, compared with the beat speed in today's ET - 10.38 beats per second.
The name meantone derives from the process of tempering the third by flattening it to beat equally with the tonic and the fifth. Different thirds were tempered in this way, to suit the requirement of the music being played.
Where a just tuning was almost useless, this meantone tuning allowed musicians to use more chords. If there was a change in key between pieces the musician at the keyboard would retune the instrument to suit. Numerous tuning methods were developed, with thirds ranging from pure or very slow-beating, to faster but acceptable, to too fast and unusable
Perhaps the culmination of these tuning temperaments was the Werkmeister II Well-Temperament, where the beat speeds of the thirds progress through a regular cycle of keys, with C-E beating slowest, then the thirds progressively speeding up through the keys G - D - A etc, in one direction, or through F - B♭ - E♭ in the other, with the key of C#/D♭ being the fastest.
The mood or character of the keys also progress from serene, to energetic to disturbed. Bach's Well-Tempered Klavier is thought by some to be a show-piece demonstrating the effectiveness of this or a very similar tuning.
By contrast, Equal Temperament, which progresses in beat speed by semitones, ranges from energetic to ... more energetic. It you transpose a piece and keep playing it higher, you may well speed up as you go. It is thought that the tempo of some Romantic music is tied in with the beat speed of the tonic third.