The collection of Cesar Franck, commonly encountered under the misleading title "L'organiste," consists of a series of compositions in groups of seven pieces, bound together in a progressive ordering by semitone in major and minor tonalities. The series was composed, according to an original annotation on the autograph manuscript, for the harmonium. The importance of these "small" compositions is great, especially because they reveal a neat image of what music education and music composition could have meant for C. Franck during the last years of his life. They constitute a summa of his art of composing. Inside the ordering progress of these groups the composer exploits, in a methodical way, some of the most characteristic elements of music composition. He, therefore, presents techniques and rudiments related to the form and the content of music composition, and to performance practices. An illustrative presentation is the purpose of this article which will try to expose, in an analytical manner, the construction of the ordering of these pedagogical rudiments, aiming to shed new light on the importance and authenticity of this collection.