Topic: four 'new' scales

4 scales

Thread (3 messages)

From: Carl Lumma (2004-01-06)
Subject: four 'new' scales

Though one of them (at least) is new like Corn Flakes.  Still,
it's a good time to "try them again for the first time".

Over on tuning-math, Gene is conducting a search of 12-tone,
5-limit pure JI scales that meet certain conditions for merit.
He's not done yet but we can play with these in the meantime.
Note Aaron Johnson.

Note also Kurt -- you said you had 25/16 in one of your scales...
Well, syndie.scl is a good way to have that.

-Carl

! syndie.scl
!
 81/80 and 128/125 Fokker block, Gene Ward Smith.
 12
!
 25/24
 9/8
 6/5
 5/4
 4/3
 45/32
 3/2
 25/16
 5/3
 9/5
 15/8
 2/1
!
! Also: Marpurg's Monochord No. 1 (1776).
!
! 6 major and 6 minor triads, strictly proper.
!
!        25/24---25/16
!         / \     / \
!        /   \   /   \
!       /     \ /     \
!     5/3-----5/4----15/8----45/32
!     / \     / \     / \     /
!    /   \   /   \   /   \   /
!   /     \ /     \ /     \ /
! 4/3-----1/1-----3/2-----9/8
!           \     / \     /
!            \   /   \   /
!             \ /     \ /
!             6/5-----9/5

///

! syndia4.scl
!
 81/80 and 2048/2025 Fokker block, Gene Ward Smith.
 12
!
 135/128
 9/8
 6/5
 5/4
 4/3
 45/32
 3/2
 8/5
 27/16
 16/9
 15/8
 2/1
!
! 4 major and 5 minor triads, strictly proper.
!
!                      5/4----15/8----45/32--135/128
!                      / \     / \     / \     /
!                     /   \   /   \   /   \   /
!                    /     \ /     \ /     \ /
! 16/9-----4/3-----1/1-----3/2-----9/8----27/16
!            \     / \     /
!             \   /   \   /
!              \ /     \ /
!              8/5-----6/5

///

! thirds.scl
!
 Major and minor 3rds paralleogram.
 12
!
 25/24
 10/9
 6/5
 5/4
 4/3
 25/18
 3/2
 8/5
 5/3
 125/72
 48/25
 2/1
!
! 6 major and 6 minor triads.  Not proper, but good stability.
!
!
!            125/72
!              / \
!             /   \
!            /     \
!         25/18---25/24
!          / \     / \
!         /   \   /   \
!        /     \ /     \
!     10/9-----5/3-----5/4
!        \     / \     / \
!         \   /   \   /   \
!          \ /     \ /     \
!          4/3-----1/1-----3/2
!            \     / \     /
!             \   /   \   /
!              \ /     \ /
!              8/5-----6/5
!                \     /
!                 \   /
!                  \ /
!                 48/25

///

! majsyn3.scl
!
 648/625 and 81/80 Fokker block, Gene Ward Smith.
 12
!
 25/24
 9/8
 6/5
 5/4
 27/20
 25/18
 3/2
 25/16
 5/3
 9/5
 15/8
 2/1
!
! 6 major and 6 minor triads, strictly proper.
!
! 25/18---25/24---25/16
!    \     / \     / \
!     \   /   \   /   \
!      \ /     \ /     \
!      5/3-----5/4----15/8
!        \     / \     / \
!         \   /   \   /   \
!          \ /     \ /     \
!          1/1-----3/2-----9/8
!            \     / \     / \
!             \   /   \   /   \
!              \ /     \ /     \
!              6/5-----9/5----27/20

///

From: wallyesterpaulrus (2004-01-06)
Subject: Re: four 'new' scales

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Though one of them (at least) is new like Corn Flakes.  Still,
> it's a good time to "try them again for the first time".
> 
> Over on tuning-math, Gene is conducting a search of 12-tone,
> 5-limit pure JI scales that meet certain conditions for merit.
> He's not done yet but we can play with these in the meantime.

Why did you choose these four to post here?

From: Carl Lumma (2004-01-06)
Subject: Re: [tuning] Re: four 'new' scales

>> Over on tuning-math, Gene is conducting a search of 12-tone,
>> 5-limit pure JI scales that meet certain conditions for merit.
>> He's not done yet but we can play with these in the meantime.
>
>Why did you choose these four to post here?

No reason.

-Carl