Modulation through the Great Diesis
This chapter deals with “deceptive tonicizations” and some interesting modulations or key changes. The strangest one is below, in this example.
The most interesting 12-eq comma is the Great Diesis, and modulation combined with a Great Diesis comma has enormous affective power. In 53-eq, the 41-cent leap of the Great Diesis is well approximated by a two-step move, say, from E1 to F2b. Here is the relevant part of the lattice for this modulation:
Figure 13-3b Great Diesis and modulation
. C – G
.D1b — A1b
Now let’s do a sudden modulation from C Major to D1b Minor:
C – E1 – G to D1b – F2b – A1b Figure 13-3b with sound [bass line C e1 D1b]
I encourage you to also play this modulation on the piano (the E and the Fb on the piano are of course the same note, which makes this modulation palatable). However, the only note these two keys have “in common” in 53-eq are E1 and F2b, the comma of the Great Diesis in 12-eq. In Johnny Reinhard’s notation, that’s E-21 to E +24. We’re taking a 45-cent microtonal jump, almost a quarter-tone away! In my example above, I’ve put the E1 and F2b right on top so everyone can hear it. At first, you may think it’s closer to a half-step, like Eb to E, but it actually is closer to a quarter-tone. It may take some time for our collective ears to decide if this is even a valid harmonic leap in 53-eq. In 12-eq, the E remains the constant pitch holding these two distantly-related chords together. Play it on the piano; it sounds mysterious but acceptable to the ear. We’ve heard this kind of modulation in classical music for over 130 years now. But with the 45-cent microtonal leap now made obvious in 53-eq, there are no notes in common between the two chords at all. This harmonic leap can be evoked in 12-eq, but how much more intense or even jarring it is when you can hear it for exactly what it is! I’m not sure it works very well in 53-eq. As I’ve mentioned before, it is also possible to hide the E1 – F2b transition in a middle voice where the transition is less obvious. It can work better if the transition is “buried” in a middle voice and maybe with a little vibrato or glissando thrown in. Check out pages 424-425 of Mathieu’s Harmonic Experience for a more detailed description of these modulations with commas.
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