Topic: The Six Syndia Scales

5 scales

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