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13/3: Deceptive Tonicization and Modulation

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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


.              E1

.               |

.              C    –    G

.               |

.D1b —  A1b

.               |

.             F2b


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.

If you would like to learn much more about this chapter, “Deceptive Tonicizations and Modulations”  in 53-equal tunings, you can buy the entire book, The Grand Unified Theory of Music, in pdf form for $25 with hundreds of embedded musical examples of scales and chords from all over the world.

A free introduction to what The Grand Unified Theory of Music offers is on this website and includes both text and a few musical examples from each webpage. If you would like to learn more about this chapter and the full contents of this entire e-book, you can buy The Grand Unified Theory of Music for $25, with hundreds of embedded musical examples of scales and chords from all over the world — and ideas for how to set up your computer system —


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Next Page: 13/4 – Modal Modulation