11.2

The beginning of the introduction to the final movement of Ludwig van Beethoven's Piano Sonata in C, op. 53 ("Waldstein," composed in 1804), played in Thomas Young's temperament (1800), which he designed to make "the harmony most perfect in those keys which are the most frequently used," hence making the more infrequent keys less "perfect" in harmony. Note that this example begins and ends in the rather common key of F, in between visiting more unusual harmonies via a bass line that descends chromatically from F to C (measures 1–6). You may want to compare the effect of the more consonant harmonies (such as at the beginning and the end) and those more dissonant (the Italian sixth chords in the second halves of measures 1 and 4).

11.3

The same passage played in equal temperament, in which the octave is divided into twelve equal semitones so that all keys, whether "frequently used" or not, have the same degree of (im)perfection of their harmony. Compared to Young's, equal temperament spreads the imperfection over all keys equally.