Warping along a line

Suppose I have a piece in four-part, mostly 5-limit harmony in
porcupine, and another such piece in meantone. Suppose I take each
part in the porcupine piece, calculate the generator, and add it to
the generator of the meantone piece, then consider this to be a
generator of something in tetracot, and find a suitable octave to go
with the generator to get a note somewhere in the region of the
average of my other two notes.

What does this give us? If the two chords are major triads and the
root, thirds and fifths correspond for the two pieces, then the result
will be a major triad with the same arrangement of root, thirds and
fifths. The same is also true if both chords are minor triads. If one
chord is major and the other is minor, then the result will be the
neutral thirds triad which is one of the features of tetracot. If the
chords are in a different inversion, then results will vary, but an
alternative approach would be to match root, third and fifth before
doing the addition.

This is an example of what sort of warping could be done; a mutant
tetracot piece obtained by crossing a porcupine with a meantone piece.
I think it has possibilities.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> Suppose I have a piece in four-part, mostly 5-limit harmony in
> porcupine, and another such piece in meantone. Suppose I take each
> part in the porcupine piece, calculate the generator, and add it to
> the generator of the meantone piece, then consider this to be a
> generator of something in tetracot, and find a suitable octave to go
> with the generator to get a note somewhere in the region of the
> average of my other two notes.
>
> What does this give us? If the two chords are major triads and the
> root, thirds and fifths correspond for the two pieces, then the
result
> will be a major triad with the same arrangement of root, thirds and
> fifths. The same is also true if both chords are minor triads. If
one
> chord is major and the other is minor, then the result will be the
> neutral thirds triad which is one of the features of tetracot. If
the
> chords are in a different inversion, then results will vary, but an
> alternative approach would be to match root, third and fifth before
> doing the addition.
>
> This is an example of what sort of warping could be done; a mutant
> tetracot piece obtained by crossing a porcupine with a meantone
piece.
> I think it has possibilities.

Maybe we should ask for volunteers to compose the two pieces in
question, and get an agreement on the length of the piece and its
overall structure. Presented nicely, such a request might generate
interest on makemicromusic or tuning.