Audiences at Iganz Schuppanzigh’s 1820s quartet concerts in Vienna would have expected a string quartet to be a weighty, four-movement work with an emphasis on a sonata form, thematische Arbeit (motivic working) between parts, and an overall tonal plan based on one or two primary key areas. Beethoven no doubt had such connoisseur listeners in mind with this work, but was pushing far beyond that traditional idea of the string quartet. Op. 131 is full of all sorts of different kinds of writing. The chapter explores the quartet in terms of fantasia, a word found frequently in connection with Op. 131, starting with a discussion of the free fantasia as a work exhibiting apparently chaotic musings over a highly logical ground plan. As Carl Philipp Emmanuel Bach pointed out in his influential discussion of the subject, there is method in the seeming madness of the free fantasia, especially as regards harmonic links. The chapter considers the entire work as a fantasia, exploring the clever linkage of seemingly disparate ideas within and between movements. The fantasia form might seem the opposite of the formalized string quartet genre as it was starting to be understood by Beethoven’s time, but in one important respect it was not. The free fantasia was a work for the connoisseur: as Carl Friedrich Michaelis noted in his article on music and humor of 1807, the free fantasia, in particular, reveals to the connoisseur listener the soul (or inventive repository) of the composer.