Linear recurrences for generators

If the characteristic polynomial of a linear recurrence has a single
root with the maximum absolute value, and if this root is positive, we
can use the corresponding linear recurrences much in the manner golden
meantone. If the coefficients of the polynomial are confined to
{-1,0,1} this is particularly nice.

I find there are exactly 800 polynomials between degree two and eight
which are irreducible and have the above property. I've uploaded a
file to the files section listing the maximal root and the polynomial,
with url

/tuning-math/files/Gene/polly

We find for example that using a fourth as generator, and requiring
our meantone forth to be between the 31 and 50 et fourth, gives us

x^8-x^6-x^3-x^2-x+1

We get a meantone fifth for the same range from

x^8-x^7-x^6+x^5-x^3-x^2+1

We can find a 2/secor between the 103 and 113 et values from

x^8-x^7-x^6-x^5-x^3+x^2-x+1