In music, counterpoint is the relationship between two or more voices which are harmonically interdependent yet independent in rhythm and melodic contour. In other words, one is balancing the vertical and horizontal sonic elements simultaneously, sort of the “warp and weft” used in weaving to turn thread or yarn into fabric.
A fugue is a contrapuntal compositional technique in two or more voices, built on a subject (a musical theme) that is introduced at the beginning then repeated at different pitches in each voice. A double fugue has two different subjects, introduced separately, which eventually are combined so they are presented together. This typically involves invertible counterpoint which is a process of presenting the subjects together so that the higher voice can become the lower voice and vice versa.
Fugues usually have three main sections: an exposition, a development and a final entry that contains the return of the subject in the fugue's tonic key. Some fugues have a recapitulation.
For my Double fugue the first subject is a perky little tune and the second subject is a slower, slithery motive.
As expected, expositions of the two subjects are presented separately in all voices and then combined above and below each other. Then the fun begins! In the development, also known as “middle entries,” I present both subjects in the minor mode, then in intervallic inversion, then combined in intervallic inversion, then rhythmic augmentation, then intervallic inversion and retrograde. The final entry presents both subjects in their original rhythms but one inverted and the other not with a stretto entry over a pedal point.