Dicot and "Number 56"

This pair has the same problem as Pelogic and Hexidecimal.

Number 23 Dicot

[2, 1, 6, -3, 4, 11] [[1, 1, 2, 1], [0, 2, 1, 6]]
TOP tuning [1204.048158, 1916.847810, 2764.496143, 3342.447113]
TOP generators [1204.048159, 356.3998255]
bad: 42.920570 comp: 2.137243 err: 9.396316

Number 56

[2, 1, -4, -3, -12, -12] [[1, 1, 2, 4], [0, 2, 1, -4]]
TOP tuning [1204.567524, 1916.451342, 2765.076958, 3394.502460]
TOP generators [1204.567524, 355.9419091]
bad: 66.522610 comp: 2.696901 err: 9.146173

With the TOP tuning for Number 23, the [4, -4] approximation of 7:1
(3390.59 cents) is better than the [1, 6] approximation. Because the [1,
6] approximation is 26 cents flat, the 4-cent sharp octaves actually
make the 7:4 worse.

I'm wondering why "number 56" and "hexidecimal" are so far down the
list, if they're clearly better than the ones labeled "dicot" and
"pelogic"? Try tuning these up in Scala; it's clear that the "number 56"
and "hexadecimal" mappings are better. The "4:5:6:7" in number 23
mapping actually sounds more like a "1/6:5:4:7"!

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> I'm wondering why "number 56" and "hexidecimal" are so far down the
> list, if they're clearly better than the ones labeled "dicot" and
> "pelogic"?

They are more complex. What happens is that for these low-complexity
temperaments you don't go out very far before running into the
terminus of the Miller-consistent region.