Jan 15, 2008 13:54
Super fun twelve-tone puzzle
1) Assign order numbers to a twelve-tone row, such that 0 refers to the first tone, 1 refers to the second, … e refers to the last note of the row.
So, <0,1,2,3,4,5> refers to the row’s first hexachord (whatever the pitch classes happen to be) in its original order and refers to a retrograde of the row’s second hexachord.
2) Create a twelve-tone row with the following property:
Every other note (starting with the second one) is T1 of the row’s first hexachord and every other note (starting with the first one) is T1 of the row’s second hexachord.
More formally:
T1(<0,1,2,3,4,5>) = <1,3,5,7,9,e> and
T1(<6,7,8,9,a,b>) = <0,2,4,6,8,a>
See how long this takes you! It's kind of easy if you work it through step by step...