Driftwood - a 2.3.7.13/10 limit temperament

So start with the "ultramajor" version of blackwood, in which you
start with a chain of 5-equal and then create another 5-equal chain
that is offset by a 10/13, rather than a 5/4. Sounds like blackwood,
but you get the colorful ultramajor triads instead of the normal major
ones. Pretty straightforward.

It also makes a lot of sense here to eliminate 91/90, thus equating
13/10 and 9/7, since the "subminor" version of the ultramajor chord
that this tuning generates is a pretty decent 6:7:9, albeit with a
sharp fifth. In fact, it's probably the most successful tuning that
eliminates 91/90 that I've seen so far. 10 out of 30 works well for
this.

I was thinking we could call it "driftwood" to keep with the island
feel that I think that subgroup temperaments prioritizing 13/10 have.
But, I think this might screw up the naming convention if we call the
676/675 temperament the island temperament, so that's a pretty
tentative name.

There is one more interesting thing about this tuning. Let's say
you're in 30-tet, and you map 9 differently than you map 3*2 - you end
up with very consonant 4:7:9 triads and 4:7:8:9 tetrads over 5 of the
roots. And furthermore, wherever you go, you can move by fifth, since
we're within the blackwood framework. This is a beautiful sound,
although much more intense and resonant than the usual "island" vibe I
get from these tunings. But this is an inconsistent temperament, so I
guess it isn't regularly mapped at all.

Here's the 30-tet version:

! driftwood_30.scl
!
Driftwood - 10 out of 30
10
!
200.00000
240.00000
440.00000
480.00000
680.00000
720.00000
920.00000
960.00000
1160.00000
2/1

-Mike

thanks - grabbed and on the list to try.

On Tue, Jan 18, 2011 at 12:31 AM, Mike Battaglia <battaglia01@...>wrote:

>
>
> So start with the "ultramajor" version of blackwood, in which you
> start with a chain of 5-equal and then create another 5-equal chain
> that is offset by a 10/13, rather than a 5/4. Sounds like blackwood,
> but you get the colorful ultramajor triads instead of the normal major
> ones. Pretty straightforward.
>
> It also makes a lot of sense here to eliminate 91/90, thus equating
> 13/10 and 9/7, since the "subminor" version of the ultramajor chord
> that this tuning generates is a pretty decent 6:7:9, albeit with a
> sharp fifth. In fact, it's probably the most successful tuning that
> eliminates 91/90 that I've seen so far. 10 out of 30 works well for
> this.
>
> I was thinking we could call it "driftwood" to keep with the island
> feel that I think that subgroup temperaments prioritizing 13/10 have.
> But, I think this might screw up the naming convention if we call the
> 676/675 temperament the island temperament, so that's a pretty
> tentative name.
>
> There is one more interesting thing about this tuning. Let's say
> you're in 30-tet, and you map 9 differently than you map 3*2 - you end
> up with very consonant 4:7:9 triads and 4:7:8:9 tetrads over 5 of the
> roots. And furthermore, wherever you go, you can move by fifth, since
> we're within the blackwood framework. This is a beautiful sound,
> although much more intense and resonant than the usual "island" vibe I
> get from these tunings. But this is an inconsistent temperament, so I
> guess it isn't regularly mapped at all.
>
> Here's the 30-tet version:
>
> ! driftwood_30.scl
> !
> Driftwood - 10 out of 30
> 10
> !
> 200.00000
> 240.00000
> 440.00000
> 480.00000
> 680.00000
> 720.00000
> 920.00000
> 960.00000
> 1160.00000
> 2/1
>
> -Mike
>
>