“And so forth through all the keys” – What Beethoven Meant

This phrase, often found in Beethoven’s sketchbooks, typically follows a short musical idea—such as a theme, a harmonic progression, or a contrapuntal figure—written in one or two keys. By writing “così via per tutte le tonalità” (“and so forth through all the keys”), Beethoven signaled his intent to transpose or modulate the material systematically across the entire circle of fifths, either as a compositional exercise or as part of a broader contrapuntal or harmonic exploration.

Such annotations reflect Beethoven’s deep engagement with tonal architecture, and his desire to test the structural resilience of musical ideas when subjected to modulation and transposition. This approach is especially evident in his fugue sketches, variation sets, and pedagogical exercises, where thematic material is often reimagined in multiple tonal contexts.

In modern terms, this phrase could be seen as an early example of algorithmic thinking in music, where a rule or pattern is applied iteratively across a defined system—in this case, the twelve major and minor keys.