Hi! Let's talk tempo!
1) Let's try finding examples of these in the music you listen to! Ritardandos will probably be the easiest to find, since they're a pretty common way to end songs. Beyond that, try to think of songs you know that might have double time or half time switches in them, then listen to it and count along to see if it really is. If not, is it a different sort of metric modulation? See what you can find!
2) Now let's try playing metric modulations. You can do this on an instrument, or just tap a table. Find a comfortable tempo, then start tapping along. Once you're feeling it, try switching to double time. After that, try half time. Once you've got those down, maybe even try more advance modulations, like the triplet. It'll be tricky, but there's really no substitute for actually trying these things hands-on!
3) Let's get philosophical for a second. One thing I left out of the video was the observation that our perception of double time works kind of like our perception of the octave. Exactly doubling the pace seems to create a sort of equivalence, where we hear them as almost the same thing. Why do you think that is? Is that similarity even noteworthy? I'm not really sure, but I'd love to hear your thoughts!
And that's it! We'll see you next week!
About 3): Well, it's pretty much the same phenomenon, right? Just us being comfortable with frequencies that are related by a factor of two. The only difference is that in the context of pitch, we detect the frequencies without hearing each individual cycle.
ReplyDeleteAs to why we "like" frequencies that are related by a factor of two (or, for that matter, frequencies that are related by a small integer factor), I think it is because when such pairs of frequencies show up in nature, they likely have a common source, so we probably evolved to group them together and experience them as a single sound. Vi Hart has a wonderful video on this: https://www.youtube.com/watch?v=i_0DXxNeaQ0
I love that video! And yes, I agree, it's kind of the same phenomenon. What's interesting to me, though, is that in pitches we can identify it harmonically (That is, the overtones are detectable) which means we can draw those relationships more effectively. Two frequencies an octave apart aren't just double the frequency, they also have many of the same overtones. That lets us draw some interesting parallels between overtones and rhythmic subdivisions. I'm not entirely sure what that means yet, though...
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