Two more Japanese papers

Here is a brief account of the other two papers John sent me.

The first is another by Kazuo Kondo. Here he decides to construct the periodicity block for the kleisma and the schisma, and seems to want to detemper it into 53 equal or something of the sort. However, he somehow manages to convince himself the PB has 54 tones, even though it should have 53, so he completely wigs out and removes a corner from the block, and then treats it as if it was a problem in chemistry concerning imperfect crystals. He produces a lot of nonsense about non-Riemannian geometry and screw dislocations, which may be describing his mental processes, and he ends by an unattributed quotation saying that tempering out commas is a good idea.

The second paper is non-Kondo, and makes more sense than anything Kondo seems capable of. The author, Nobuyuki Otsu, takes sixteen temperaments, such as meantone, Kirnberger 1-3, Werckmeister 1, C and 3, and so forth, and subjects them to various kinds of statistical analysis designed to show relationships. A cluster analysis gives a dendrogram, (sometimes called cladogram) of the relationships in the form of a tree. Factor analysis sorts of methods, involving eigenvalue decomposition, are also applied, and he shows diagrams of the projections onto the first few eigenspaces. He also applies the same analysis to the tones themselves, so that you caan find out if C would rather hang with G or with F#. The results, unsurprisingly, tell us that meantones are like other meantones, and well-temperaments like other well-temperaments, but the details might interest someone.