I don't understand that. How could the time signature stay the same if "what gets the beat" changes? I'm a bad boy. I didn't study your lesson on this Bart.
Once you make the shift, assuming you are staying there and really performing a
metric modulation, you can still be in 4/4 because the new "what get's the beat" has been established and can be thought of as the quarter-note.
Let's say I'm playing a groove, it's in 4/4 and
90 bpm. This means the quarter-note gets the beat; 90 quarter-notes in a minute. When I shift, performing a metric modulation, let's say I'm going to let the dotted-eighth-note get the beat. When I do this, the ratio is 3:4; the quarter-notes occur in the span of 4 dotted-eighth-notes. At this point, I'm still thinking 4/4 because I'm just emphasizing or implying where I'm shifting or modulating to. There's still 16 sixteenth-notes in the bar.
Once you do this, if you maintain it, the ear hears a new pulse. We can use some good ol' Algebra to see what the new tempo is ...
Doing the math, we find that if I shift from quarter-note pulse to dotted-eighth-note pulse, the new tempo is
120 bpm.
Since I have shifted, performing the metric modulation, there's no need to relate it to the old meter or tempo. I've established my new pulse, and can notate it in 4/4 or any new meter you want ... but rather than 90 bpm, I'm now at 120 bpm.
In my audio example from the 5-Minute Lesson, I stayed in 4/4, but performed a metric modulation by first letting the dotted-eighth be my new implied pulse, then actually shifting to it permanently, making it equal to my old quarter-note ... time signature wise.
And who says high school Algebra is a waste of time?!
