Basis change for monzos, vals and wedgies

For whatever insight it may bring, here is an example. Suppose instead
of 2,3,5,7 as a basis for 7-limit, we use 27/25, 21/20, 2401/2400 and
4375/4374. Then the corresponding basis for vals is
<19 13 19 24|, <0 2 3 2|, <-1 -2 -3 -3| and <4 6 9 11|. The
definitions for bimonzo, bival and compliment are the same, giving a
new basis there as well. We have

441-et: <49 31 0 0|
612-et: <68 43 0 0|

ennealimmal: <<1 0 0 0 0 0||

This can aslo be computed from

2401/2400: |0 0 1 0>
4375/4374: |0 0 0 1>

For miracle, we have

225/224: |-5 8 -2 -1>
1029/1024: |-5 8 -1 -1>

miracle: <<1 0 8 0 5 0||

We could also have used, for instance

72-et: <8 5 0 0|
175-et: <19 12 0 1|

I'm fond of 12-et in this system:

12-et: <1 1 1 1|

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> For whatever insight it may bring, here is an example. Suppose
instead
> of 2,3,5,7 as a basis for 7-limit, we use 27/25, 21/20, 2401/2400
and
> 4375/4374.

Paul Hj., this would interest you.

Then the corresponding basis for vals is
> <19 13 19 24|, <0 2 3 2|, <-1 -2 -3 -3| and <4 6 9 11|. The
> definitions for bimonzo, bival and compliment

Why, thank you :)

> are the same, giving a
> new basis there as well. We have
>
> 441-et: <49 31 0 0|
> 612-et: <68 43 0 0|
>
> ennealimmal: <<1 0 0 0 0 0||
>
> This can aslo be computed from
>
> 2401/2400: |0 0 1 0>
> 4375/4374: |0 0 0 1>
>
> For miracle, we have
>
> 225/224: |-5 8 -2 -1>
> 1029/1024: |-5 8 -1 -1>
>
> miracle: <<1 0 8 0 5 0||
>
> We could also have used, for instance
>
> 72-et: <8 5 0 0|
> 175-et: <19 12 0 1|
>
> I'm fond of 12-et in this system:
>
> 12-et: <1 1 1 1|