Suggested Learning Resources

1) YFIO

2) Video Lesson:

3) Online Reading: Transposition OpenMusicTheory.com http://openmusictheory.com/transposition.html

4) Interactive Lesson: 

Music Theory QuickThink:

How to recognized and label two pitch-class-sets that are related by transposition...

- Arrange both sets in their ascending form that is most compact (around a clock face)

- Subtract each integer of one set from its corresponding integer in the other set (mod12)

- If the difference of each subtraction is the same, then the sets are related by transposition

- Example: consider set X {2,0,t,e,9} and set Y {9,7,5,6,4}

          - First arrange these in most compact ascending order.  Set X becomes {9,t,e,0,2} and set Y becomes {4,5,6,7,9}

          - Now subtract (mod12) set Y from set X        {9,t,e,0,2}

                                                                                      - {4,5,6,7,9}

                                                                                         5,5,5,5,5

- These two sets are related by transposition of 5 half steps

- We label this relationship in the following way   X=T5Y   

- The T stands for 'transposition' and the 5 is the pitch-class-interval of transposition between the two sets

- It is sometimes helpful to read the label backwards for clarity.  "Y, transposed by 5 results in X"

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How to find the index number and label two pitch-class-sets that are related by inversion...

- Arrange both sets in their ascending form that is most compact (around a clock face)

- Reverse the order of one of the sets

- Add each integer of one set to the corresponding integer in the other set (mod12)

- If the sum of each addition is the same, then the sets are related by inversion, and the 'distance/transposition' of the inversion is the resulting summed integer

- Example: consider set X {8,t,9,e,1} and set Y {t,9,7,e,0}

             - First arrange these in the most compact ascending order. Set X becomes {8,9,t,e,1} and set Y becomes {7,9,t,e,0}

             - Reverse the order of one of the sets and add the other... (we'll reverse X) {1,e,t,9,8}

                                                                                                                                               + {7,9,t,e,0}

                                                                                                                                                   8,8,8,8,8

             - These two sets are related by inversion, and the distance of the inversion is 8 half steps.... 8 is called the index number

             - We label this relationship in the following way, X=T8IY

             - I stands for 'inversion' and the T stands for the index number of 8

Objective 53.1: Examples in Music: YouTube

https://youtu.be/KgELJOpLNaE

Objective 53.1: Correctly label sets related by transposition with a Tx number, and correctly label sets related by inversion with an index number