[tuning-math] Re: 38 linear 7-limit temperaments compatible with 12-et
- From: "genewardsmith" <genewardsmith@xxxxxxxx>
- To: tuning-math@xxxxxxxxxxxxxxx
- Date: Fri, 19 Jul 2002 00:59:04 -0000
--- 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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