Harmony: Diminished Triads, Secondary Dominants, Chromaticism.

The modulation I7 - IV suggests a key a fifth lower and the modulation II - V suggests a key a fifth up. We should name them V7/IV and V/V. We could repeat these modulations in each new key whether we go up or down, successively altering notes so that we get new keys. For example we could do I II V VI II III VI using successive dominates or go in the reverse I I7 IV flat-VII flat-III etc. These are called Circle of Fifths Modulations that even have a form in written music of the bass part having a see-saw appearance using the root tones of the chords while the top parts often move move chromatically down. A passage in the second movement of Mozart's Jupiter Symphony #41 in C K 551 comes to mind.

The history of music involves shortcutting the preparation for these modulations as listeners become familiar with and expect them. This evolves into the music of Wagner and his successors. One avenue to this is to consider what happens when you construct a minor triad on all the scale degrees to which you add a diminished seventh. These so-called diminished seventh chords have an interesting property. If you chromatically alter any note, you stretch one of the intervals by a minor second, you get a dominant seventh chord of a new key. Since you can do this for any of the four notes of the diminished seventh, you can get four different dominant seventh chords. This is what Wagner does in his operas, especially in the "Ring" cycle. In the wonderful finale of Act One of Mozart's lesser known opera of 1791, La Clemenza di Tito, this chromaticism is foreshadowed by his use of diminished chords that interrupt excepted cadences but also resolve into distant keys chromatically on one or two occasions, this wonderful Sextet is highly recommended listening.