Peter Davies provides this diagram for his keyboard layout:
Sunday, June 30, 2013
Remapping the Harmonic Table
I am amazed and delighted to discover that
Peter Davies
came up with a hexagonal keyboard layout very much like mine.
He makes keyboards with this layout, as do the folks at
C-Thru-Music.
This layout can be remapped to a kleismatic microtonality in very much the same way that my layout can be.
Note that the pattern of repeated notes in this kleismatic microtonal mapping is not the same as in the conventional mapping. This is where the musical potential for this alternate tuning lies.
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The strangest feature of this tuning is definitely the treatment of fifths. In this keyboard layout, hexagons vertically adjacent are related by a fifth. Looking e.g. at the rightmost column, there is a vertical series -20, 11, 42, 75. The intervals are 31, 31, and 33. That pattern is repeated, two fifths of 31 followed by one of 33. 31 steps is extremely close to a just tuned perfect fifth ratio of 3/2. 33 steps corresponds to a ratio of 192/125, which is very sharp - one interval table calls it a diminished sixth.
ReplyDeleteWhile this tuning will open up new musical possibilities, it will definitely make some traditional possibilities very problematic!
The wikipedia article says a diminished sixth is the classical "wolf tone".