syndia3

Third 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 (¢)
135/128	92	135/128	92
9/8	204	16/15	112
1215/1024	296	135/128	92
5/4	386	256/243	90
675/512	478	135/128	92
45/32	590	16/15	112
3/2	702	16/15	112
405/256	794	135/128	92
27/16	906	16/15	112
225/128	977	25/24	71
15/8	1088	16/15	112
2	1200	16/15	112

Similar scales

File	Notes	Rotation	Max diff (¢)
qmean	12	1	10.3
duo101	12	1	10.9
bayes_alt12	12	2	12.3
duowell	12	1	12.5
syndwell3	12	3	12.5
PizarroJIapprox	12	1	12.8
strangeion	12	10	13.6
sc3_17_4	12	6	13.6
asbru	12	8	13.7
rainbow	12	3	13.7

Parent scales

File	Notes	Max diff (¢)
schisynch29	29	1.3
xen18-erlich-helmholtz-29	29	1.3
garibaldi24	24	6.3
xen07-chalmers-sixth-comma	19	10.8
xen18-erlich-augmented-15	15	15.6
choraled_scale	26	7.3
xen18-erlich-compton-24	24	8.8
dwarf27_7tempered	27	7.4
xen18-erlich-augene-15	15	16.3
xen18-erlich-helmholtz-41	41	1.3

Child scales

File	Notes	Max diff (¢)
xen09-wilson-marwa-03-03	7	0.0
xen09-wilson-marwa-09-05	7	0.0
xen09-wilson-marwa-09-06	7	0.0
xen09-wilson-marwa-09-07	7	0.0
xen09-wilson-marwa-09-08	7	0.0
xen09-wilson-marwa-09-09	7	0.0
xen12-wilson-09-4C2-hexany-04	6	0.0
lumma_wauchope-major	8	7.7
ninelim	5	7.7
Indonesia_Slendro_Tandak_Geroh	5	8.1

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

! 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
!
! 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