Embellishments are created by involving the surrounding notes of chord notes. The example below from Czerny's Pianoforte-Schule Op.500 (1839) shows a broken C-chord embellished with the semitones below the chord notes.

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Often the diatonic note above the chord note is involved as well, as shown in the example below from Montgeroult's Cours complet pour l'enseignement du forte piano (composed 1788-1812).

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An endless number of combinations can be made with embellishment notes. Despite the fact that these embellishment notes in broken triads are very often found in written-out preludes, piano methods rarely provide specific exercises for this. Instead, one may find exercises where the principle of a lower semitone is practiced in a scale exercise, as in the example below from Adam's Encyclopédie du Pianiste Compositeur (1840).


Exercises for studying common embellishment patterns around a C-chord can be found here.