Doublemint temperament

By this I mean the planar temperament, sans 5's, with Margos commas
<352/351, 364/363, 442/441> as a basis. We get 2058/2057 and
10648/10647 for free, incidentally.

This temperament can be defined by the mapping

[[1, 0, 0, 7, 12, -13], [0, 1, 0, -4, -7, 9], [0, 0, 1, 1, 1, 1]]

where the generators are the approximate 2, 3 and 7. The odd primes (sans 5) up to 17 have rms values

1904.031656 3370.499213 4154.372587 4442.277617 4906.784117

The septimal comma 64/63 is mapped to 21.437474 cents, and one way to work Doublemint would be two keyboards, each with a fifth generator of
size 704.03 cents, separated by this comma.

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:

> The septimal comma 64/63 is mapped to 21.437474 cents, and one way to work Doublemint would be two keyboards, each with a fifth generator of
> size 704.03 cents, separated by this comma.

If we use 2, 3/2, 64/63 to represent primes rather than 2,3,7, the mapping to primes becomes

[[1, 1, 4, 7, 9, 0], [0, 1, -2, -6, -9, 7], [0, 0, -1, -1, -1, -1]]

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
>
> > The septimal comma 64/63 is mapped to 21.437474 cents, and one way to work Doublemint would be two keyboards, each with a fifth generator of
> > size 704.03 cents, separated by this comma.
>
> If we use 2, 3/2, 64/63 to represent primes rather than 2,3,7, the mapping to primes becomes
>
> [[1, 1, 4, 7, 9, 0], [0, 1, -2, -6, -9, 7], [0, 0, -1, -1, -1, -1]]

We can also add 5 to Doublemint if we like, extending the above mapping to

[[1, 1, 7, 4, 7, 9, 0], [0, 1, -8, -2, -6, -9, 7],
[0, 0, 1, -1, -1, -1, -1]]

The rms fifth now is 704.071479 cents, and the keyboard separation becomes 20.733799 cents.