thirds

Major and minor 3rds paralleogram.

Open in Scale Workshop Scala analysis Download scl

Properties

Notes	12
Period	1200.0 ¢
Just	5-limit
Source	Mailing lists
Reference	https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_51116.html#51116
Thread	4 scales

Tone	Tone (¢)	Step	Step (¢)
25/24	71	25/24	71
10/9	182	16/15	112
6/5	316	27/25	133
5/4	386	25/24	71
4/3	498	16/15	112
25/18	569	25/24	71
3/2	702	27/25	133
8/5	814	16/15	112
5/3	884	25/24	71
125/72	955	25/24	71
48/25	1129	3456/3125	174
2/1	1200	25/24	71

Similar scales

File	Notes	Rotation	Max diff (¢)
wreck_a	12	3	11.6
12_class	12	4	13.8
wilson_class	12	9	13.8
starrc	12	4	14.5
wilcmarv7	12	4	17.7
wilcmarv11	12	4	20.1
classr	12	4	21.5
diadiaschis2	12	11	23.5

Parent scales

File	Notes	Max diff (¢)
kleis	19	0.0
xen07-chalmers-mandelbaum-1	19	0.0
xen18-erlich-hanson-15	15	3.8
limx15	15	4.1
xen18-erlich-keemun-15	15	5.7
scj22_a	22	0.0
xen18-erlich-hanson-19	19	3.8
ramx15	15	8.1
precata19	19	5.3
madagascar19	19	5.5

Child scales

File	Notes	Max diff (¢)
fivecrys1	7	0.0
xen09-chalmers-tritriadic-3-4-5	7	0.0
xen12-chalmers-tritriadic-mt-3-5-15	7	0.0
xen15-chalmers-triadic-diamond-5-4	7	0.0
xen18-ayers-table-41-42	7	0.0
xen15-chalmers-triadic-diamond-8192-6561	7	2.0
Vietnam_Bac	5	6.6
xen15-chalmers-triadic-diamond-64-51	7	6.8
Cambodia_Pentatonic_02	5	7.6
xen15-chalmers-triadic-diamond-56-45	7	7.7

Mailing list post

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

///

Full 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 [email protected], 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

Raw file

! 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
!
! https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_51116.html#51116
!
! [info]
! source = Mailing lists
! file = tuning/messages/yahoo_tuning_messages_api_raw_50001-52481.json
! topic_id = 51116
! msg_id = 51116