Partimenti are two things:
instructional bass lines designed to teach harmony and counterpoint
a method of learning composion and improvisation at the keyboard.
A little history
Partimenti – both the basses and the method – were developed and refined in Italy, particularly in four Neapolitan music conservatories. The conservatories in Naples were meant to conserve children, orphans, and teach them a trade, in this case music so they could make a living. The methods of conservatories were so succesful in teaching average child composition, improvisation, performance, and analysis that Naples trained musicians started to flood the churches and courts of Europe. Soon the Neapolitan conservatories began accepting paying students. After the French Revolution as the French Ministry of Culture set up the Paris Conservatory they imported Italian music teachers. Soon partimenti gained traction as a teaching method in Paris and in the conservatories around France. Though there was no central conservatory system in Germany many German musicians studied either with a student of the partimenti school or themselfs studied in Italy.
How do Partimenti work?
A partimento bass is composed with the expectation of other voices in counterpoint. To the trained partimentist analysis of a bass reveals how to realize the other voices.
The first tools in revealing a partimenti bass line are the Rule of the Octave and cadences.
The Rule of the Octave is a powerful tool and can be used to modulate as well.
Sequences are another tool.
As you learn partimenti technique the partimentist learns to analyze a bass line looking for moves from the Rule of the Octave, cadences, modulations, and sequences.
Partimenti arn’t just harmonic exercises using block chords. As your vocabulary of partimenti playing expands you can begin to add diminution to the melody and various textures and answering voices to the upper voices.
A performance of an advanced partimenti is almost inditinguishable from a piece of 18th century music.
Imagine the possibilities as an improvisor, composer, and a performer if you have this much musical craft at your finger tips.