syndia2

Second 81/80 2048/2025 Fokker block

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-math/topicId_8328.html#8328
Thread	5 scales

Tone	Tone (¢)	Step	Step (¢)
16/15	112	16/15	112
256/225	223	16/15	112
6/5	316	135/128	92
32/25	427	16/15	112
4/3	498	25/24	71
64/45	610	16/15	112
3/2	702	135/128	92
8/5	814	16/15	112
128/75	925	16/15	112
9/5	1018	135/128	92
256/135	1108	256/243	90
2	1200	135/128	92

Similar scales

File	Notes	Rotation	Max diff (¢)
qujus1	12	3	7.7
parizek_ji1	12	10	7.7
smith-exotic1	12	1	10.5
jubilee12sym	12	10	11.4
werckmeisterIV_variant	12	8	12.4
brac	12	6	12.6
AlexMalcom1721	12	10	12.8
aaron	12	6	12.8
asbru	12	6	13.1
sc3_17_4	12	11	13.6

Parent scales

File	Notes	Max diff (¢)
sentdia	21	7.7
xenoga24	24	7.7
xen18-erlich-helmholtz-41	41	1.0
perz	27	7.7
sensidia	27	7.7
tenn41c	41	2.2
partch-29-av	29	7.7
48temp	48	0.9
mean24rat	24	11.6
xen18-erlich-catler-24	24	11.9

Child scales

File	Notes	Max diff (¢)
xen03-wilson-negative-07	7	0.0
xen09-wilson-marwa-04-09	7	0.0
xen09-wilson-marwa-06-02	7	0.0
xen10-wilson-purvi-02a-01	7	0.0
xen10-wilson-purvi-02a-02	7	0.0
xen10-wilson-purvi-02b-01	7	0.0
xen10-wilson-purvi-02b-02	7	0.0
xen10-wilson-purvi-09c-03	7	0.0
xen12-chalmers-tritriadic-dm-5-3-1	7	0.0
xen15-gilson-ptolemy-diatonic-syntonon	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

! 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
!
! 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