[tuning-math] Re: 38 linear 7-limit temperaments compatible with 12-et

--- In tuning-math@xxxx, Gene W Smith <genewardsmith@xxxx> wrote:

> Here's a microtemperament for multi-keyboard enthusiasts:
> [3, -24, -54, -58, 94, -45]   [[3, 0, 45, 94], [0, 1, -8, -18]]
> 
> comp   31.51783075   rms   .1469057415   bad   145.9322934

Let's see how this one might work. We can change the mapping given above to the 
equivalent

[12 3]
[19 5]
[28 5]
[34 4]

The generators for this are well approximated by 14/171 and 1/171, and we can 
use this as a keyboard system for the 171-et, with the 12-note keyboards tuned 
to semitones of size 14/171 ocatves, and the keyboards separated by 1/171. This 
non-ocatave tuning (12*(14/171) = 168/171, a comma less than the octave) can be 
modified to one which tunes each rank of 12-note keyboards slightly unevenly, 
to the 14/171 MOS, namely [14 14 14 15] repeated three times. Of course this 
gives four different patterns for chords, but you pays your money and you makes 
your choice.




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