Prodigy[12]

Rolling along with these 11-limit 12 note hobbits, I come to the rather peculiar temperament prodigy. What makes it peculiar is that it tempers out 225/224 and 441/400, but good tunings for it shrink 243/242, 1024/1029, 384/385 and 2400/2401 to the same tiny interval, and tempering this out also leads to miracle. But don't discount prodigy, as constructing scales for it, such as this hobbit, leads automatically to a corresponding interesting miracle scale. Below I give a miracleized version, tuned to 72 equal. Now you can do miracle on your good old trusty Halberstadt keyboard!

! prodigy12.scl
Prodigy[12] 225/224&441/440 hobbit, 72et tuning
! As a miracle scale, [-8, -7, -6, -2, -1, 0, 1, 2, 5, 6, 7, 8]
12
!
116.66667
233.33333
266.66667
383.33333
500.00000
583.33333
700.00000
816.66667
933.33333
966.66667
1083.33333
1200.00000
!
!! preprodigy12.scl
! Prodigy[12] 5-limit transversal
! 12
!!
! 16/15
! 256/225
! 75/64
! 5/4
! 4/3
! 45/32
! 3/2
! 8/5
! 128/75
! 225/128
! 15/8
! 2/1

thanks!

On Tue, Jan 11, 2011 at 12:12 AM, genewardsmith <genewardsmith@sbcglobal.net
> wrote:

>
>
> Rolling along with these 11-limit 12 note hobbits, I come to the rather
> peculiar temperament prodigy. What makes it peculiar is that it tempers out
> 225/224 and 441/400, but good tunings for it shrink 243/242, 1024/1029,
> 384/385 and 2400/2401 to the same tiny interval, and tempering this out also
> leads to miracle. But don't discount prodigy, as constructing scales for it,
> such as this hobbit, leads automatically to a corresponding interesting
> miracle scale. Below I give a miracleized version, tuned to 72 equal. Now
> you can do miracle on your good old trusty Halberstadt keyboard!
>
> ! prodigy12.scl
> Prodigy[12] 225/224&441/440 hobbit, 72et tuning
> ! As a miracle scale, [-8, -7, -6, -2, -1, 0, 1, 2, 5, 6, 7, 8]
> 12
> !
> 116.66667
> 233.33333
> 266.66667
> 383.33333
> 500.00000
> 583.33333
> 700.00000
> 816.66667
> 933.33333
> 966.66667
> 1083.33333
> 1200.00000
> !
> !! preprodigy12.scl
> ! Prodigy[12] 5-limit transversal
> ! 12
> !!
> ! 16/15
> ! 256/225
> ! 75/64
> ! 5/4
> ! 4/3
> ! 45/32
> ! 3/2
> ! 8/5
> ! 128/75
> ! 225/128
> ! 15/8
> ! 2/1
>
>
>