Since my abstract thoughts seems not to be well appreciated, here is a

"concrete" challenging problem having goal only to introduce my definition

of _Sonance degree_ in my next post. If I have no feedback, I could so have

illusion that it's not only by lack of interest :-)

Could you calculate an approximative "sonance" value for any interval

represented by a coordinate vector

(x0 x1 .. xN)*

in a primal basis

<p0 p1 .. pN>

where only p0 is known, say as the prime 2?

As such that question would have no sense, but with a given coherent set of

unison vectors defining a system, this problem has a deep sense : the first

coordinate (the power of 2) retains IN A COHERENT SYSTEM sufficient

information to obtain this well-approximated value for the "sonance".

More concretely. Let U = {(-4 4 -1)*,(-3 -1 2)*} a such set of unison

vectors defined by its coordinates. Without using the fact that these

vectors would represent 81/80 and 25/24 in <2 3 5>, it is possible to

easily calculate a numerical value which is the _sonance degree_ in this

system for any interval represented by (x y z)*, say (-1 1 0)* and (-3 1

1)* which would be 3/2 and 10/9 in <2 3 5>.

My definition of _Sonance degree_ simply generalises that.

Pierre