0c: Modulating Canons with the diminished Fifth / augmented Fourth

The diminished fifth resolves in simultaneous contrary motion by semitones into a major third. Its lower tone has the syllable Ti and moves up to Do. Its upper tone has the syllable Fa and moves down to Mi.

The augmented fourth resolves in simultaneous contrary motion by semitones into a minor sixth. Its lower tone has the syllable Fa and moves down to Mi. Its upper tone has the syllable Ti and moves up to Do.

If one alters the resolution interval Do-Mi (or Mi-Do) flatwards, it doesn't change the notes, but it changes the syllables to So-Ti (or Ti-So). Moving the So one step down to Fa, yields a new instance of the "devil interval".

If one alters the resolution interval Do-Mi (or Mi-Do) sharpwards, it doesn't change the notes, but it changes the syllables to Fa-La (or La-Fa). Moving the La one step up to Ti, yields a new instance of the "devil interval".

In the result one obtains two modulation two-bar canos, modulating after each bar.

The Melodies are:

| Ti Do (b) | So Fa Mi (b)| for flatward modulation

and

| Fa Mi (#) | La Ti Do (#)| for sharpward modulation

In view of the circle of fifths order of the seven syllables one may easily understand how the canons work.

Flatward modulation:

Sharpward modulation: