Do you sleep Gene? :)

Gene wrote:
Try 1/1--2700/2401--5/4--4/3--3/2--5/3--2401/2400--2/1
Paul wrote:
2401/2400 is not between 5/3 and 2/1, gene!
Gene wrote:
OK, so be picky about it. :)

2401/1280 is, though. I intended to put up a slightly modified version of
1--9/8--5/4--4/3--3/2--5/3--15/8--2, with the 9/8 adjusted down by 2400/2401
and the 15/8 adjusted up by the same amount. Since h7(2401/2400) = 2,
this throws a spanner in the works.
You conclude from there, your presumed counterexample is not epimorphic. I hope I don't
need to show that that CS implies EPIMORPHISM as I shown that. However you have
doubts and believe it's not epimorphic with your definition.

You're wong!

Using your words I say there is a val h such that if qn is the nth scale degree, then h(qn) = n.

I don't say h(qn) = 4n which would be true even with the false way you represent it. No, there
is a true val such that h(qn) = n.

It was not bad to try to show off with your spanner, but it would have been better to try to
understand what you were doing.

You simply forgotten to reduce the basis before wedging. You used the basis <2 3 5 7> while
there exist a dependance about 7. The minimal basis is <2 3 5 2401>. Using the false one,
you introduce inappropriate lattice points, so the corresponding val would be [28 44 64 78].

It's the type of error where modifying unwittingly the representration you attribute the thing to
the represented object. There is no problem with that CS and epimorph scale, but with your
way to described it with a spanned primal basis, where the octave periodicity 7 appears 28,
for each block is filled with supplement lattice points never used.

In the basis <2 3 5 49>, the val would be [14 22 32 78] while in the minimal basis, the val is
[7 11 16 78] and your example is perfectly epimorph.

Pierre