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Can someone explain why the visualizations are triangles, if the two axis are meant to represent similarity and time?
The horizontal axis represents musical time, from the beginning to the end of the piece, while the vertical axis shows how far the similarities persist into the higher-level structure of the piece.

If I understand this correctly, this means that the vertical axis goes from "similarity in large-scale structure" at the top to "similarity at the momentary scale" at the bottom, so the triangle is a sensible way to look at it.

I think it might be easier to look at the triangle from bottom-to-top; the "higher-level structures" build upon/are made up of the lower-level structures.

Or at least that's how this musicology-phile interpreted them.

Intersesting (and hackerish) side note on how the story finally broke:

"When Brian Ventura, a financial analyst from Mount Vernon, New York, put the recording of Liszt's Transcendental Etudes credited to Hatto into his computer, the Gracenote database used by the iTunes software identified the disc not as a recording by Hatto but as one by László Simon."

http://en.wikipedia.org/wiki/Joyce_Hatto#Recordings_unmasked

Other sources claim this was "almost certainly due to someone deliberately planting the information in the Gracenotes database" because "the track timings are too dissimilar for the software to pluck Simon's BIS recording out of the many 12-track CDs it holds" http://www.pristineclassical.com/HattoHoax.html

I wonder if the youtube audio fingerprinting algorithms would have picked this up, had these tracks been uploaded.
I wonder what the response is of the audiophiles who were claiming that these were original recordings? I know those types don't like to be debunked by 'science'. They seemed fairly adamant about this hoax being true and were somewhat insulting to anyone who thought differently.
We have no basis on which to speculate as to how this situation might have come about. It would, however, be very desirable for those who are in a position to clarify this to do so

Nicely put.