Background: P. D. Q. Bach is a fictitious composer invented by musical satirist "Professor" Peter Schickele. Schickele developed a five-decade-long career, performing the "discovered" works of the "only forgotten son" of the Bach family. Schickele's music combines parodies of musicological scholarship, the conventions of Baroque and classical music, and slapstick. The name "P. D. Q." is a parody of the three-part names given to some members of the Bach family that are commonly reduced to initials, such as C. P. E., for Carl Philipp Emanuel Bach.
Context: Schickele divides P. D. Q. Bach's fictional musical output into three periods: the Initial Plunge, the Soused Period, and Contrition. During the Initial Plunge, P. D. Q. Bach wrote the Traumerei for solo piano, an Echo Sonata for "two unfriendly groups of instruments", and a Gross Concerto for Divers Flutes, two Trumpets, and Strings. During the Soused (or Brown-Bag) Period, P. D. Q. Bach wrote a Concerto for Horn & Hardart, a Sinfonia Concertante, a Pervertimento for Bicycle, Bagpipes, and Balloons, a Serenude, a Peruckenstuck (literally German for "Hairpiece"), a Suite from The Civilian Barber (spoofing Rossini's The Barber of Seville), a Schleptet in E-flat major, the half-act opera The Stoned Guest (the character of "The Stone Guest" from Mozart's Don Giovanni), a Concerto for Piano vs. Orchestra, Erotica Variations (Beethoven's Eroica Variations), Hansel and Gretel and Ted and Alice, an opera in one unnatural act (Humperdinck's Hansel and Gretel and the 1969 film Bob & Carol & Ted & Alice), The Art of the Ground Round (Bach's The Art of Fugue), a Concerto for Bassoon vs. Orchestra, and a Grand Serenade for an Awful Lot of Winds and Percussion.  During the Contrition Period, P. D. Q. Bach wrote the cantata Iphigenia in Brooklyn (Gluck's Iphigenia in Aulis, etc.), the oratorio The Seasonings (Haydn's The Seasons), Diverse Ayres on Sundrie Notions, a Sonata for Viola Four Hands, the chorale prelude Should, a Notebook for Betty Sue Bach (Bach's Notebook for Anna Magdalena Bach and Buddy Holly's "Peggy Sue"), the Toot Suite, the Grossest Fugue (Beethoven's Grosse Fuge), a Fanfare for the Common Cold (Copland's Fanfare for the Common Man) and the canine cantata Wachet Arf! (Bach's Wachet auf).  A final work is the mock religious work Missa Hilarious (Beethoven's Missa Solemnis) (Schickele no. N2O - the chemical formula of nitrous oxide or "laughing gas").
Question: Who was the composer ?. Whats the answer?
Schickele divides P. D. Q. Bach's fictional musical output into three periods: