syndia5
Fifth 81/80 2048/2025 Fokker block = pipedum_12.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 |
| 75/64 |
275 |
25/24 |
71 |
| 5/4 |
386 |
16/15 |
112 |
| 4/3 |
498 |
16/15 |
112 |
| 45/32 |
590 |
135/128 |
92 |
| 3/2 |
702 |
16/15 |
112 |
| 405/256 |
794 |
135/128 |
92 |
| 5/3 |
884 |
256/243 |
90 |
| 16/9 |
996 |
16/15 |
112 |
| 15/8 |
1088 |
135/128 |
92 |
| 2 |
1200 |
16/15 |
112 |
Similar scales
Parent scales
Child scales
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
! 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
!
! 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