 |
|
 |
| Exercise
11-3. Set symmetry. |
Sets that map wholly onto themselves under Tn (other than
T0) and TnI operations do so because their interval
patterns feature inherent symmetries. The greater the degree of such symmetry
a set has, the more levels of Tn and TnI will produce
complete invariance, and the fewer distinct sets will make up a set's
class. The fourth column in the table
of pc set classes indicates the number of Tn and TnI
levels under which sets in each class remain invariant; it is thus a guide
to set symmetry.
Below are sets that exhibit various levels of symmetry. List the Tn
and TnI levels at which each set remains invariant and the number
of distinct (variant) sets in the set's class.
| 1. |
[5,7,10,0] |
 |
| 2. |
D-F#-A# |
|
| 3. |
[3,4,5,9,10,11] |
|
| 4. |
[5,6,7,8,0,1] |
|
|
| Page last modified 10
July 2001 / GRT
|
|
|
