A remarkable subgroup temperament

The 5-7-9 triad on Igs' list is in the 2.9/5.9/7 subgroup, and it can be tempered via a remarkable temperament tempering out the landscape comma, 250047/250000, with mapping [<3 3 2|, <0 -1 -2|]. If you tune it to 7287edo, for example, you won't be able to tell it from JI, yet it is of low complexity, with a period of 1/3 octave and a generator 10/9. MOS of size 6, 9, 15, 21, 27 etc.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> The 5-7-9 triad on Igs' list is in the 2.9/5.9/7 subgroup, and it can be tempered via a remarkable temperament tempering out the landscape comma, 250047/250000, with mapping [<3 3 2|, <0 -1 -2|]. If you tune it to 7287edo, for example, you won't be able to tell it from JI, yet it is of low complexity, with a period of 1/3 octave and a generator 10/9. MOS of size 6, 9, 15, 21, 27 etc.

Here is a 12 note scale (so not a MOS) which I give in just tuning. It has six 1-7/5-9/5 triads and six 1-9/7-9/5 triads if you are willing to count the three off by a landscape comma. Since that is less than a third of a cent, I'd count them. Of course you could always temper.

! terrain.scl
JI version of generated scale for 63/50 and 10/9
! effectively 250047/250000 (landscape) tempering in 2.9/5.9/7 subgroup
12
!
50/49
10/9
500/441
63/50
9/7
7/5
10/7
100/63
81/50
441/250
9/5
2/1

Thank you - saved.

I'm busy with a bunch of 12 equal stuff at the moment - but I will be
getting to the backlog.

Do you happen to have a scala file representation of Godzillia? I seem to
have missed that one.

Chris

On Wed, Mar 9, 2011 at 7:18 PM, genewardsmith
<genewardsmith@...>wrote:

>
>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> >
> > The 5-7-9 triad on Igs' list is in the 2.9/5.9/7 subgroup, and it can be
> tempered via a remarkable temperament tempering out the landscape comma,
> 250047/250000, with mapping [<3 3 2|, <0 -1 -2|]. If you tune it to 7287edo,
> for example, you won't be able to tell it from JI, yet it is of low
> complexity, with a period of 1/3 octave and a generator 10/9. MOS of size 6,
> 9, 15, 21, 27 etc.
>
> Here is a 12 note scale (so not a MOS) which I give in just tuning. It has
> six 1-7/5-9/5 triads and six 1-9/7-9/5 triads if you are willing to count
> the three off by a landscape comma. Since that is less than a third of a
> cent, I'd count them. Of course you could always temper.
>
> ! terrain.scl
> JI version of generated scale for 63/50 and 10/9
> ! effectively 250047/250000 (landscape) tempering in 2.9/5.9/7 subgroup
> 12
> !
> 50/49
> 10/9
> 500/441
> 63/50
> 9/7
> 7/5
> 10/7
> 100/63
> 81/50
> 441/250
> 9/5
> 2/1
>
>
>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:

> Do you happen to have a scala file representation of Godzillia? I seem to
> have missed that one.

! godzilla9.scl
!
Godzilla[9] in 19et tuning (4\19 generator)
9
!
189.47368
378.94737
442.10526
631.57895
694.73684
884.21053
947.36842
1136.84211
2/1

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> If you tune it to 7287edo, for example, you won't be able to tell it from JI, yet it is of low
> complexity, with a period of 1/3 octave and a generator 10/9. MOS of size 6, 9, 15, 21, 27 > etc.

Of course, there's also 33-EDO and 39-EDO which only miss JI by a couple cents. And 27-EDO's definitely passable.

;->

-Igs

Thank you Gene!

On Wed, Mar 9, 2011 at 7:47 PM, genewardsmith
<genewardsmith@...>wrote:

>
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> > Do you happen to have a scala file representation of Godzillia? I seem to
> > have missed that one.
>
> ! godzilla9.scl
> !
> Godzilla[9] in 19et tuning (4\19 generator)
> 9
> !
> 189.47368
> 378.94737
> 442.10526
> 631.57895
> 694.73684
> 884.21053
> 947.36842
> 1136.84211
> 2/1
>
>
>
>