Stretched octaves on piano

Now that we are recording the piano for my realization of Ives's Universe
Symphony, I have had to okay that octave will be stretched, even as the
tuning is based on untempered extended Pythagorean tuning. As some of you
have obviously already surmised, the piano won't sound like a piano if the
octaves are not slightly stretched.

The conservative stretching yields a 25 cents eighthtone at the top, more
typically at 35 cents and 45 cents. Everything will be pure inside the
octave, to itself. This is a fascinating calculation because the whole piece
is based on the theory of an eighthtone dieses in both the Pythagorean comma
and in 48-tET (which is used for 2 measures of 5 trumpets).

Wish us luck heading to Michael Harrison's studios in Brooklyn. This is the
new downtown.

Peace, Johnny