CHARM has another page which describes the visualization techniques more fully: http://www.mazurka.org.uk/ana/timescape/

If you read that, you’ll see that these triangular plots are means of visualizing the correlations of all the subsequences of two (or more) sequences of data. The data being compared in the original article are analyses of musical recordings (not the recordings themselves) — things like tempo, phrasing, harmonic structure, etc.

The bottom of each triangle shows how the analysis of the first piece compares to the analysis of the second piece (or the analyses of the other pieces, depending on the total number involved), by comparing the smallest possible subsequences. If two piece analyses are being compared, then the colors represent the degree of correlation between them; if one piece analysis is being compared to many, then the colors represent which piece best correlates to the first.

The second row, working up, compares slightly larger subsequences, and represents the results in color in the same way. The third row up again compares larger subsequences, and so on, until you reach the top row (the apex of the triangle), in which case the comparison is between one entire sequence (the largest possible subsequence, in other words) and another.

If you represent each comparison as one block of color, then you have a decreasing number of blocks per row, moving upwards, and thus a triangle makes sense.

The page linked to above also contains these “hierarchical correlation plots” in bell and rectangular shapes, but I’m not sure why you’d want to use either form. The correlation plot seems to naturally be a triangle.

They even provide an online tool to generate your own “scape plots”: http://www.mazurka.org.uk/software/online/scape/

Of course, I just read all this now, so no promises about my accuracy. :)

“During his doctoral studies at Stanford, Sapp developed a means of representing harmonic structure through what he called keyscapes: triangular figures in which the base corresponds to the moment-to-moment course of the music, with successively higher layers showing averaged values based on the layer below, with the apex of the triangle consisting of a single value representing the average value for the piece as a whole.”

Yeah, I don’t completely get it either… maybe if I knew more about music..

I don’t agree that they ‘pussyfoot around.’ They are music researchers. I thought they did a nice job of presenting their argument, evidence, and conclusion.

“An unanticipated outcome of this work was the discovery that the Concert Artists recording of the Mazurkas issued in the name of Joyce Hatto was in fact a slightly modified version of the recording by Eugen Indjic; this was the first proof of the infamous Hatto hoax, which became generally known in February 2007.”

http://www.charm.rhul.ac.uk/projects/p2_3.html

That seems fairly unambiguous.

Also, ignoring the hoax, CHARM has a page that discusses the visualization tools themselves:

http://www.charm.rhul.ac.uk/analysing/p9_4.html

They explain the triangular visualizations, created by Craig Snapp at Stanford, as follows:

“Sapp developed a means of representing harmonic structure through what he called keyscapes: triangular figures in which the base corresponds to the moment-to-moment course of the music, with successively higher layers showing averaged values based on the layer below, with the apex of the triangle consisting of a single value representing the average value for the piece as a whole. The result is to provide a visual impression of the strength of particular hamonies at particular points in the music at both a local and global level.”

That makes sense to me, and seems useful. And quite possibly applicable to other fields besides music.

Craig Sapp: http://ccrma.stanford.edu/~craig/

Two papers of his on this keyscape technique and its applications:

http://portal.acm.org/citation.....34.1095544

https://ccrma.stanford.edu/~craig/papers/01/

The ultra-academic tone of the article shouldn’t surprise much: it was, after all, produced by an musicological think tank whose participants were drawn from several universities and research groups. Perhaps it was a sop to the music world’s sensitivities that they rehearsed the entire background of Joyce Hatto’s life in such detail and ended the article in such studied neutrality.

Once they got to discussing their analytical method, with examples showing how Rubenstein’s own performances of the same piece could vary over time, and how only a direct reissue of a recording could be virtually identical to another, I thought the case was closed.

The visualizations demonstrated that her performances were impossibly identical to someone else’s, with “the small markings at the bottom of [the figures] merely reflect[ing] limitations in the accuracy of data capture.”

From what I remember the guy only ever admitted patching recordings to cover-up his wife’s moans of pain. Not wholescale copying..