Equal Temperament Tuning.

Very early keyboard instrument were tuned using a Just or Pure series of fifths ...

Meantone tunings allowed for more keys to be used. So if a series of pure 5th were tuned from C,
C > G > D > A > E, the major third E in a 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, with the key of C# being the fastest.

Bach's Well-Tempered Klavier is thought by some to be a show-piece demonstrating the effectiveness of this or a very similar tuning.

...... etc

Next:  Temperament, 1

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