A comparison of Partch's scale in RI and Hemiennealimmal

RI:

edges: 18, 32, 64, 88

connectivity: 0, 0, 0, 2

Hemiennealimmal:

edges: 64, 106, 159, 219

connectivity: 0, 0, 0, 4

The numbers are edges/connectivity in the 5, 7, 9 and 11-limits. I conclude that a great deal is gained by tempering in this way, and nothing significant is conceded in terms of quality of intonation. Of course, 72-et would do much better yet, but then some concessions will have been made.

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> RI:
>
> edges: 18, 32, 64, 88
>
> connectivity: 0, 0, 0, 2
>
>
> Hemiennealimmal:
>
> edges: 64, 106, 159, 219
>
> connectivity: 0, 0, 0, 4
>
>
> The numbers are edges/connectivity in the 5, 7, 9 and 11-limits. I
conclude that a great deal is gained by tempering in this way, and
nothing significant is conceded in terms of quality of intonation. Of
course, 72-et would do much better yet, but then some concessions will
have been made.
>

I totally agree. With the discovery of microtemperaments like this, an
insistence on strict RI starts to look more like a religion than an
informed decision.