two new acoustic microtonal instruments

should anyone be interested,I've uploaded pictures of my two new
microtonal instruments to the photos files

I'd like to post a brief bit about my two new microtonal instruments.
They're both acoustic instruments; one is a tenor ukulele and the
other is a 6-string banjo, or a banjotar. Chris Shaffer did the work
on both of these instruments, and without his enthusiasm and
generosity they'd still exist only in my mind—so THANKS Chris!

The tenor ukulele is fretted as a maximally even 8-out-of-13 in
thirteen-tone equal temperament. Thirteen-tone equal temperament is
almost exclusively mentioned in tuning theory with a negative
connotation, as a sort of pinnacle of atonality and discordance. But
sometimes things need a different perspective, and trying to compare
12TET and 13TET is really quite counterproductive. There are many
truly beautiful scales and subsets in 13TET, and this 8-out-of-13
contains a wonderful 7-tone scale:

0, 2, 3, 7, 8, 10, 11, 13

The banjotar retains the standard 12TET fretting but adds 5 just
intonated notes:

33/32, 7/6, 11/8, 14/9, 7/4

This gives a 17-tone octave, and this arrangement represents three
separate one-dimensional planes of 3, 7 and 11 limit ratios. It also
rather nicely approximates a 3, 5, 7 and 11-limit grid and the banjo
resonator wonderfully melds the otherness of the new notes to the
standard 12-TET arrangement.

--- In tuning@yahoogroups.com, "daniel_anthony_stearns"
<daniel_anthony_stearns@y...> wrote:
> should anyone be interested,I've uploaded pictures of my two new
> microtonal instruments to the photos files