Dante Rosati's 21 tone JI scale

[Dante Rosati, TD 189.2]
>I have a page up now on my 21TJI guitar with a couple of pictures and a
>real audio file of a piece soas you can hear what it sounds like:
>http://www.users.interport.net/~dante/justguitar.html

Good one! Here's a 7-limit harmony lattice for it

10/9-------5/3-------5/4------15/8
/|\ /|\`. ,'/|\ / \
/ | \ / | \10/7 / | \ / \
/14/9-------7/6-------7/4 \ / \
/,' `.\ /,' \`.\|/,'/ `.\ / \
16/9-------4/3-----\-1/1-/-----3/2-------9/8
\ / \`. /,\/|\/.\ /,'/ \`. ,'/
\ / \ 8/7-/\|/\12/7-/---\-9/7 /
\ / \ | / 7/5 \ | / \ | /
\ / \|/,' `.\|/ \|/
16/15------8/5-------6/5-------9/5

So the 4:5:6:7:9 otonal pentad looks like

5
/|\
/ | \
/ 7 \
/,' `.\
4---------6---------9

and of course the 1/9:1/7:1/6:1/5:1/4 utonal pentad is the same shape
reflected thru a point.

So this 21 note tuning has 5 otonal and 5 utonal pentads. As with Lumma's
scale, the septimal kleisma (225/224, 7.7 cents) could be tempered out,
introducing only slow beats which are close to the limit of tuning accuracy
and increasing the available harmonies significantly. I haven't counted
them yet, but the idea is that 15/8 = 28/15, 5/4 = 56/45, 16/15 = 15/7, 8/5
= 45/28, 7/5 = 45/32, 10/7 = 64/45.

Maybe you already use these without worrying about distributing the errors,
but in case you're interested, minimum beat rates in all 4:5:6:7:9 chords
occur when the fifths are tempered 1.0 cent narrow, the major thirds 3.5
cents narrow and the 4:7's 1.4 cents narrow.

Regards,
-- Dave Keenan
http://dkeenan.com

>From: Dave Keenan <d.keenan@uq.net.au>
>

>So this 21 note tuning has 5 otonal and 5 utonal pentads. As with Lumma's
>scale, the septimal kleisma (225/224, 7.7 cents) could be tempered out,
>introducing only slow beats which are close to the limit of tuning accuracy
>and increasing the available harmonies significantly. I haven't counted
>them yet, but the idea is that 15/8 = 28/15, 5/4 = 56/45, 16/15 = 15/7, 8/5
>= 45/28, 7/5 = 45/32, 10/7 = 64/45.
>
>Maybe you already use these without worrying about distributing the errors,
>but in case you're interested, minimum beat rates in all 4:5:6:7:9 chords
>occur when the fifths are tempered 1.0 cent narrow, the major thirds 3.5
>cents narrow and the 4:7's 1.4 cents narrow.

Right now its nice to play with the just intervals and listen to the sounds
>they< like to make. Sometimes I catch my ear hearing something as a
distuned tempered harmony, but I'm finding it fruitful to try not do this
and let each new soundcolor speak for itself.

Like an obnoxious new convert to a religion, right now I am zealous for
justness (justice?). I'd much rather have some Swiss or German guitar maker
make me one with this just tuning nailed down to the cent. But maybe with
time I will moderate (modulate?).

It is definitely interesting, though, what you say about minimum beat rates.
One nice thing about JI is having some chords with no beats, chords with
painful beats and everything in between. I find it rather colorful after
decades of ET. Just like black and white photography allows depiction of
certain forms better than color, perhaps monochrome et takes the
sensuousness out of the sound somewhat so you can focus on the
note-relations better.

dante