Paul's tetrad chart

The chart of tetrads that Paul made for Blackjack and which Dave
Keenan revised is now posted as a short text file to the files area:

/tuning/files/Pehrson/

This is an extremely interesting document. However, I think it would
have been more productive to have arranged the tetrads according to
increasing complexity, rather than just as to their appearance as one
strikes the traditional Halberstadt keyboard.

Maybe I'll do that sometime.

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

/tuning/topicId_44307.html#44307

Just as a further clarification:

What I'm meaning is that, as one has the Blackjack *lattice* in front
of him, it's really pointless to list all the different possible
tetrads or chords, since one would readily see the same transposition
of intervals at other points of the lattice, and the same chord
really sounds pretty much alike even though it's at different pitch
levels.

And the idea of just cataloging by ascending Halberstadt finger
placement really isn't an *aural* organizing principle.

So, it would be better to make a graphic of increasingly dissonant
chords depending on their SHAPE in the lattice, getting more
dissonant, for the most part, as pitches get further from the basic
simple ratio just ones.

That would be a *very* valuable study, particularly if the chords
were to be shown graphically on the lattice. People are busy now,
though, so I doubt there would be any "takers" for this task...

In any case, that's pretty much the way I'm working with the lattice
now, anyway, but in a somewhat less systematic manner.

J. Pehrson