Equal and Historic Temperaments Illustrated

Here are three examples of the same piano tuned in different temperament

Pythagorean Temperament is shown below.  The octaves are pure, but only about half the notes are useable.  The intervals will be different in the different key signatures.  The values in the tuning charts show the deviation from the theoretical sharp or flat.


Well-Temperament from the 18th century is shown in the example below.  This was an improvement as more notes were available for composition i.e. more major thirds sounded bearable.  Again the octaves are tuned pure and so are the major fifths.


Equal Temperament from the 20th century is shown below.  Notice that the graph is smooth.  All notes are useable. In order to get the intervals to fit into the octave, the major fifths are slightly contracted and the major fourths are slightly expanded.  That's why neither of these is called "perfect".  All of the major thirds in the scale are useable.