harmonizations: modulations
One of the most important principles of a prelude is that it ends in the same key as it started. This does not prevent the pianist from performing modulations within the prelude itself. However, there is also another type of prelude that has a specific function, called a modulating prelude or simply modulation. This type of prelude is used to make a connection between two pieces of repertoire with different keys.
In his publication The Art of Preluding, Op. 300 (1833), Carl Czerny (1791-1857) provides various modulating chord progressions:
Carl Gottlieb Hering (1766-1853) provides almost a thousand 'Ausweichungen' in his Praktische Preludierschule (ca.1812).
MODULATION SYSTEMS
Rather than relying on ready-to-use chord progressions to modulate to a new key, one can benefit from understanding the 'systems' of modulation. In his publication Modulations (ca.1888), Bernhard Rollfuss (1837-1904) gives a clear view on some of the possible modulation systems, for example modulation by a diminished chord:
Some more interesting publications regarding modulations:
Carl Philipp Emanuel Bach (1714-1788)
Versuch über die wahre Art das Clavier zu spielen (vol.1&2) (Berlin, 1753 part I, 1762 part II)
=> p325 Von der freien Fantasie
Antonio Soler (1729-1783)
Llave de la modulacion y antiguedades de la musica (Madrid, 1762)
Wolfgang Amadeus Mozart (1756-1791)
Modulierendes Präludium (1776-77)
Joseph Georg Vogler (1749-1814)
Tonwissenschaft und Tonsetzkunst (1776, Mannheim)
Betrachtungen der Mannheimer Tonschule (1778-81, Darmstadt?)
Johann Samuel Petri (1738 - 1808)
Anleitung zur Praktischen Musik (Leipzig, 1782)
=> Zehnte kapitel, Abschnitt vier, pp. 249-282
Ludwig van Beethoven (1770-1827)
2 Preludes, Op.39 (Leipzig, 1789)
Emanuele Imbimbo (1765-1839)
Gamme ou Echelle Musicale (ca.1810)
Friedrich Starke (1774-1835)
Wiener Pianoforte-Schule (vol.1) (1819) pp. 21-23
John Field (1782-1837)
Exercise modulé dans tous les tons majeurs et mineurs, H 33 (London, 1820)
Johann Christian Heinrich Rinck (1770-1846)
Ecole Pratique de la Modulation Op. 99 (Paris & Anvers, 1831)
Friedrich Wilhelm Kalkbrenner (1775-1849)
Traité d'Harmonie du Pianiste (Paris, 1849) pp. 36-40
John Hiles (1810-1882)
A catechism of harmony, thorough-bass, and modulation, with examples (London, 1882)
Bruno Zwintscher (1838-1905)
Technical Exercises for the Pianoforte (1887) see p. 32
Bernhard Rollfuss (1837-1904)
Modulations (ca.1888)
Oscar Beringer (1844-1922)
Tägliche Technische Studien (1889) see p.118
Salomon Jadassohn (1831-1902)
De Kunst zu Modulieren und zu Präludieren (1890)