Exercise 5-1. Set transposition and transpositional equivalence of sets

 

Sets are transposed by equally transposing all the pcs in the set. Remember that, by convention, the Tn operation is measured "ascending" (clockwise), so "n" is a number of semitones that you add to each pc in the set. For instance, T5 of set [3,5,8] is
  3 5 8  
+    5  5  5  
=  8 10 1      set [8,10,1]

 

  1. On a printout of this page or on a separate sheet of paper, transpose the following sets by the values indicated. Write the resulting sets in normal form. Be careful -- some of the resulting normal forms may surprise you!

    Click on the lines beside the sets to reveal the correct answers. Pressing the Reload button will remove the answers. You can also read comments on most answers.

    1.    T7 of [2,3,6,8]
    		 
    2. T5 of [9,10,1,3]
    		Comment
    3. T4 of [1,2,5,6,9]
    		Comment
    4. T3 of [0,2,4,6,8,10]   
    		Comment
    5. T6 of [5,6,11,0] Comment

If, when you transpose all of the pcs of a set by a certain interval, they map onto those of another set, then the two sets are said to be transpositionally equivalent to each other. They are considered to be the same type of set -- to belong to the same set class.

  1. Below are some pairs of sets. Tell whether or not the two sets in each pair are transpositionally equivalent. (Find the Tn level at which the initial pc of the first set maps to the initial pc of the second set. Then see whether the rest of the pcs map.)

    Click on the lines beside the set pairs to reveal the correct answers. Pressing the Reload button will remove the answers. You can also read comments on the answers.

    1.   [2,4,5,8,10] [5,7,8,11,1]       Comment
    2. [4,5,7,8,9,10,0] [0,1,3,4,5,7,8]       Comment
    3. [0,4,7] [6,10,1]       Comment
    4. [6,7,11,0] [1,2,7,8]       Comment
    5. [3,5,6,8,9,10,11,0]    [11,1,2,4,5,6,7,8]          Comment

 

Page last modified 25 July 2001 / GRT

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