Rank 2 temperaments in which two consecutive generators form a simple otonal triad

I find these temperaments to be particularly awesome, because they
help to create the sensation for me that the generator is this magical
thing that encodes harmonic information. Some examples:

1) Meantone - 8:9:12
2) Porcupine - 10:11:12
3) Machine - 7:8:9
4) Glacial - 8:9:10
5) Semaphore - 6:7:8
6) Mavila - 10:11:15
7) Negri - 12:13:14

Also, here are a few in which the generator chain forms consonant
tetrads or better

1) Porcupine - 9:10:11:12
2) Glacial - 8:9:10:11
3) Mavila - 10:11:12:15:16 (eh...)
4) Negri - 12:13:14:15:16(:17:18:...)

Anyone know of any others?

What would be really, really, unbelievably awesome would be to come up
with a "triadic chord" from all of this, in which every triad in the
chord is consonant, rather than every dyad.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Anyone know of any others?

Mohajira/migration/mohaha/hemififths, myna and orwell all do a much better job of this than those you list.

On Tue, Jan 3, 2012 at 12:31 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Anyone know of any others?
>
> Mohajira/migration/mohaha/hemififths, myna and orwell all do a much better job of this than those you list.

How do two consecutive generators of any of those temperaments yield a
simple otonal triad? They'd all yield a non-otonal essentially
tempered triad.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> > Mohajira/migration/mohaha/hemififths, myna and orwell all do a much better job of this than those you list.
>
> How do two consecutive generators of any of those temperaments yield a
> simple otonal triad? They'd all yield a non-otonal essentially
> tempered triad.

Ah, out of tune otonal is better than in-tune essentially tempered! Sorry, I didn't know things had to be otonal, and it's a restriction which makes your quest pretty hard to realize.

On Tue, Jan 3, 2012 at 12:40 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > Mohajira/migration/mohaha/hemififths, myna and orwell all do a much better job of this than those you list.
> >
> > How do two consecutive generators of any of those temperaments yield a
> > simple otonal triad? They'd all yield a non-otonal essentially
> > tempered triad.
>
> Ah, out of tune otonal is better than in-tune essentially tempered! Sorry, I didn't know things had to be otonal, and it's a restriction which makes your quest pretty hard to realize.

In tune otonal would be ideal, but the reason I'm looking for otonal
is because otonal generalizes the property of dyads which activates
some virtual fundamental. So if dyadic chords are nice, then triadic
chords would probably be even better. Chords like that would probably
sound like stained glass.

-Mike