syndia6

Sixth 81/80 2048/2025 Fokker block

Open in Scale Workshop Scala analysis Download scl

Properties

Notes12
Period1200.0 ¢
Just5-limit
Source Mailing lists
Referencehttps://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_8328.html#8328
Thread5 scales
Tone Tone (¢) Step Step (¢)
135/128 92 135/128 92
9/8 204 16/15 112
6/5 316 16/15 112
5/4 386 25/24 71
4/3 498 16/15 112
45/32 590 135/128 92
3/2 702 16/15 112
405/256 794 135/128 92
27/16 906 16/15 112
16/9 996 256/243 90
15/8 1088 135/128 92
2 1200 16/15 112

Similar scales

FileNotesRotationMax diff (¢)
sc3_17_1 12 0 6.8
werckmeisterIV_variant 12 7 7.2
werck4 12 7 7.8
kirnberger2 12 9 10.8
kirnberger3 12 2 10.8
kirnberger1 12 9 10.8
Sp_refi_Ki_3 12 2 10.8
kb2_118 12 9 10.9
secorwt08 12 9 11.4
Sp5LimDodek 12 9 11.4

Parent scales

FileNotesMax diff (¢)
indians 22 1.1
indianred 22 2.0
indiansouth 22 2.0
xen02-wilson-indic 22 2.0
jsmith24 24 2.0
indiang 22 3.5
schis24 24 3.5
schisynch29 29 1.0
xen18-erlich-helmholtz-29 29 1.1
xen03-wilson-positive-29 29 2.0

Child scales

FileNotesMax diff (¢)
synmav4 7 0.0
synmav5 7 0.0
xen09-wilson-marwa-03-03 7 0.0
xen09-wilson-marwa-03-07 7 0.0
xen09-wilson-marwa-03-10 7 0.0
xen09-wilson-marwa-04-10 7 0.0
xen09-wilson-marwa-09-08 7 0.0
xen09-wilson-marwa-09-09 7 0.0
xen09-wilson-marwa-09-14 7 0.0
xen09-wilson-marwa-09-15 7 0.0
Mailing list post 
From: Gene Ward Smith (2003-12-30)
Subject: The Six Syndia Scales

These are the six possible Fokker blocks, up to transpositional 
equivalence, which can be obtained from the 81/80 (SYNtonic)
and 2048/2045 (DIAschismic) commas. Since midpoints between numbers 
of the form i/12 are numbers of the form n/24, I took all offsets
n/24 for n ranging from -12 to 12 to obtain these, though in fact 
taking only odd n should suffice. The first two are self-dual, or 
whatever the word is (and if there isn't one, there should be) for a 
scale transpositionally equivalent to its inverse. Then 3 and 4, 5 
and 6 are inversionally related pairs. When a name already existed in 
the Scala archives, I used that form of the scale, otherwise I just 
picked one of the 12 which looked nice. All of these on reduction by 
meantone lead to Meantone[12].

! syndia1.scl
First 81/80 2048/2025 Fokker block = ramis.scl
12
!
135/128
10/9
32/27
5/4
4/3
45/32
3/2
128/81
5/3
16/9
15/8
2

! syndia2.scl
Second 81/80 2048/2025 Fokker block
12
!
16/15
256/225
6/5
32/25
4/3
64/45
3/2
8/5
128/75
9/5
256/135
2

! syndia3.scl
Third 81/80 2048/2025 Fokker block
12
!
135/128
9/8
1215/1024
5/4
675/512
45/32
3/2
405/256
27/16
225/128
15/8
2

! syndia4.scl
Fourth 81/80 2048/2025 Fokker block
12
!
135/128
9/8
6/5
5/4
4/3
45/32
3/2
8/5
27/16
16/9
15/8
2

! syndia5.scl
Fifth 81/80 2048/2025 Fokker block = pipedum_12.scl
12
!
135/128
9/8
75/64
5/4
4/3
45/32
3/2
405/256
5/3
16/9
15/8
2

! syndia6.scl
Sixth 81/80 2048/2025 Fokker block
12
!
135/128
9/8
6/5
5/4
4/3
45/32
3/2
405/256
27/16
16/9
15/8
2
Full thread (1 messages) 
From: Gene Ward Smith (2003-12-30)
Subject: The Six Syndia Scales

These are the six possible Fokker blocks, up to transpositional 
equivalence, which can be obtained from the 81/80 (SYNtonic)
and 2048/2045 (DIAschismic) commas. Since midpoints between numbers 
of the form i/12 are numbers of the form n/24, I took all offsets
n/24 for n ranging from -12 to 12 to obtain these, though in fact 
taking only odd n should suffice. The first two are self-dual, or 
whatever the word is (and if there isn't one, there should be) for a 
scale transpositionally equivalent to its inverse. Then 3 and 4, 5 
and 6 are inversionally related pairs. When a name already existed in 
the Scala archives, I used that form of the scale, otherwise I just 
picked one of the 12 which looked nice. All of these on reduction by 
meantone lead to Meantone[12].

! syndia1.scl
First 81/80 2048/2025 Fokker block = ramis.scl
12
!
135/128
10/9
32/27
5/4
4/3
45/32
3/2
128/81
5/3
16/9
15/8
2

! syndia2.scl
Second 81/80 2048/2025 Fokker block
12
!
16/15
256/225
6/5
32/25
4/3
64/45
3/2
8/5
128/75
9/5
256/135
2

! syndia3.scl
Third 81/80 2048/2025 Fokker block
12
!
135/128
9/8
1215/1024
5/4
675/512
45/32
3/2
405/256
27/16
225/128
15/8
2

! syndia4.scl
Fourth 81/80 2048/2025 Fokker block
12
!
135/128
9/8
6/5
5/4
4/3
45/32
3/2
8/5
27/16
16/9
15/8
2

! syndia5.scl
Fifth 81/80 2048/2025 Fokker block = pipedum_12.scl
12
!
135/128
9/8
75/64
5/4
4/3
45/32
3/2
405/256
5/3
16/9
15/8
2

! syndia6.scl
Sixth 81/80 2048/2025 Fokker block
12
!
135/128
9/8
6/5
5/4
4/3
45/32
3/2
405/256
27/16
16/9
15/8
2

Raw file

! syndia6.scl
Sixth 81/80 2048/2025 Fokker block
12
!
135/128
9/8
6/5
5/4
4/3
45/32
3/2
405/256
27/16
16/9
15/8
2
!
! https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_8328.html#8328
!
! [info]
! source = Mailing lists
! file = tuning-math/messages/yahoo_tuning-math_messages_api_raw_7445-9944.json
! topic_id = 8328
! msg_id = 8328