This is the Necker cube:
You can see it with the lower-left face being apparently closest to you, or it can flip so that the upper-right face is closest to you. Sometimes (not often, and not for long) I can even see it as a bunch of line segments on a flat plane. What you can't do is see more than one interpretation at a time.
There are a lot of these sorts of perceptual rivalry demonstrations, some of which you can find on Jack Pettigrew's page. Some (like the Necker cube) switch back and forth with a sort-of characteristic period of a second or two; some might go minutes without switching.
It's also possible to have auditory rivalry. The following sound alternates between a high and a low note, with each note lasting 0.25 seconds. But it's possible to hear it as mostly the low note, briefly interrupted each beat by the high note, or the other way round. Probably I heard something similar during a talk given by Pettigrew, but I also associate this example with the "Do not cross" warning signals at Brisbane level crossings.
Here I am trying to play Comptine d'un autre été : l'après-midi, mostly following this extended version of Yann Tiersen's original (with a bit extra at the end):
And then my right forearm fell off. My play is a bit ragged (and a lot faster than it's supposed to be...), but I had the small victory of being good enough to trip YouTube's automated detection of copyrighted material.
The best bits are in amongst those long series of sixteenth-notes. I usually hear the melody line as the lowest notes, like this:
The other notes just add colour and make the whole thing sound pretty. But there's a bit of perceptual rivalry, and I can latch my brain onto hearing the highest notes (I don't hit the notes at the right time in the following – breaking a bar up into 16 pieces and hitting a note on the 3, 6, 9, and 12 isn't a skill I've mastered):
In the following, I repeat that section for a minute, playing all the notes (too quickly). I can hear the low notes, or the high notes, or follow the melody up and down. I haven't managed to get my brain to isolate the middle notes.
Something sort of related happens in the second-last phrase. The lowest in each set of three sixteenth-notes alternates between a G and a B during the Em and G chords, between F# and B during the Bm chord, and between F# and A during the D chord. Usually when I play this or hear it in MIDI form (as below), I only specifically hear the G's and F#'s, until the last bar, when suddenly these A's start sounding and it's as though I'm playing a very fast game of Pong. It's really quite distracting to me when I play. On the other hand, sometimes I do hear the B's and so the rhythm feels consistent. I have no idea how anyone else hears this:
(Since recording the video, I fiddled with the last four notes of each bar, so it's not quite the same as what I play in the video, or even what I would have played if I could keep anything like regular time during this passage.)
I don't have any grand theory of melody perception to tie these observations into. I initially thought that for me, there might be some threshold pitch around the B5 note above which rapidly played notes become background to a melody line below the threshold. As evidence for this, if I play the whole thing an octave lower, I always hear the B's playing Pong with the G's and F#'s. But I've tried transposing up or down a couple of semitones, and the pattern I hear is usually the same as the one I first described. So I think my melody perceptions are some complicated function of absolute pitch and relative intervals and surrounding notes, and I haven't come up with a simple rule that describes it.
The "core" part of Comptine d'un autre été (the first two minutes of the video) scores very highly on the metric of "how good it sounds" divided by "how hard it is to play". I've seen comments from better pianists that it's simple enough to sight-read; I... was not able to sight-read it, but I had a decent grasp of how it all fit together after about eight hours of practice, which I thought was a surprisingly short time.
Unlike for Music Box Dancer, I didn't make regular progress recordings, my improvement being obvious enough that I didn't need a record of earlier play to convince me that it was worth persevering with. (Perhaps with more frequent progress recordings I could have stopped myself from playing it all too quickly.) I'd guess that I spent the first two hours getting the hang of the left-hand pattern and easy part of the melody, another two hours trying to work out how the sixteenth-note section made any sense, and (once the melody I knew did start to pop into my headphones) another few hours making it sound coherent together.
Each extra phrase in the extended version of the piece took a few hours to get used to, and overall about 40 hours of practice went into the video. In the middle there's a bit where the right hand plays chords up and down the melody line, and I found this surprisingly difficult, both to get the rhythm right (many of the notes fall on weird fractions of beats) and also because I apparently struggle to play E minor chords with my right hand (?!?).
The long section at the end is quite taxing on my right forearm, and I usually need to rest for a bit after playing it, or at least relax with something less challenging to the muscles. This made developing muscle memory harder than it otherwise would have been, since I couldn't just drill it for half an hour.
Anyway despite some obvious room for improvement, I'm pretty happy with how this is going.
Written and posted 2014-12-20; recorded 2014-12-19.