Mason Williams, who wrote Classical Gas, was also the Smothers Brothers' head comedy writer; he also essentially created The Smothers Brothers Comedy Hour. He created the "Pat Paulson for President" campaign, and won an Emmy award for his comedy writing on the show in 1968.
In addition, he helped launch the career of Steve Martin by hiring him as a writer on the Smothers Brothers' show. Initially, Williams paid Martin out of his own pocket.
Here he is performing the song: Classical Gas.
Here's someone a little cuter playing it: Classical Gas - Gabriella Quevedo.
And here she is was someone a little less cute playing it:
https://www.youtube.com/watch?v=vcKPiQPcT9o
It's a TE standard.