Bach composed the Inventions and Sinfonias while residing in the city of Köthen in Germany from 1717 to 1723. Even though they were not published or printed during his lifetime, the manuscript copies of the compositions were widely published by 1801 and used for teaching young musicians. When creating the compositions, Bach intended the compositions to allow the student to quickly transition from the stage of technical finger exercise to a more musical approach. The compositions also provide a method of finding and developing musical ideas for those studying composition.
The Inventions and Sinfonias include 15 inventions -- two-part, BWC 772 to 786 -- and 15 sinfonias -- three-part, BWC 787 to 801 -- for the keyboard. The series of inventions and sinfonias both begin with a C major and end in B minor. The musical pieces are arranged on an ascending chromatic scale with no duplication of keys. Both the two-part inventions and the three-part sinfonias use counterpoint, which is a musical relationship between two or more voices that are harmonically interdependent but independent in rhythm and contour. When the major and minor keys use the same note in the Inventions and Sinfonias, the major key is placed before the minor counterpart.
Bach's 15, three-part inventions are specifically called Sinfonias, or BWC 787 to 801. The key-system design of the sinfonias appears in the following order: C, c, D, d, E-flat, E, e, F, f, G, g, A, a, B-flat and b. Capitalized letters indicate a major key and small letters indicate a minor key. The sinfonias belong to a unique genre due to their key-system design and the way the bass line always accompanies the first entry in the upper part at the beginning of the piece. The sinfonias also follow the fugal style. The fugal style, which involves the counterpoint musical relationship, is found in all keys except number 5, or E-flat, and 11, or g. The 15 sinfonias use longer-breathing motifs than the inventions.
Bach's 15, two-part inventions are specifically called Inventions, or BWC 772 to 786. The key-system design of the inventions appears in the following order: C, c, D, d, E-flat, E, e, F, f, G, g, A, a, B-flat and b. Capitalized letters indicate a major key and small letters indicate a minor key. The inventions use a variety of counterpoint styles including strict canons, or c, F; fugal style, or G, b; and quasi-sonata form in binary structure, or E. The15 invention pieces use shorter-breathing motifs than the sinfonias.