Suggested Learning Resources
Remember: Pitch Intervals means number of half steps, Ordered-Pitch-Intervals means
with + or - , Pitch-Class-Intervals means y-x mod 12.
You can tell if two Pitch-Class Sets are related by inversion if you (1) analyze
their Pitch-Class-Intervals, and determine if the pitch-class-intervals of the two
sets each add up to 12.
For Example consider the two pitch-class-sets {8,t,0,e,1} and {2,0,t,e,9}
|
|
Set A
|
Set B
|
|
|
{8,t,0,e,1}
|
{2,0,t,e,9}
|
|
Pitch-Class Intervals
|
2,2,e,2
|
t,t,1,t
|
Notice above that each corresponding pitch-class intervals add up to 12. These two
sets are related by inversion.
Creating an inverted set - there are several methods
Method 1 - Find the the inverse of each pitch-class in the set
- Analyze the numbers in the set, and then make a new set with corresponding numbers
that add to 12 with the original set
- Example {8,t,0,e,1} would result in {4,2,0,1,e}
Method 2 - Find numbers on the opposite side of the clock face
- The inverse of each number is on the opposite side of the clock if you make a horizontal
line
- For {8,t,0,e,1} 4 is straight across from 8 on the clock... 2 is straight across
from t on the clock... etc
NOTE: You can also transpose the resulting inverted set, and you will still have
an inversion relation to the original set. If you do this, it is very important
INVERT FIRST and then TRANSPOSE, else it will not work.
Method 3 - ascending using the rainbow method for inversion
- For sake of analysis and discussion, it is often helpful to have both a pitch-class-set
and its inversion set arrange in ascending order
- First, place your original set in ascending order {8,t,0,e,1} becomes {8,t,e,0,1}
- Now start with the last number, and find the number that adds to 12, placing it
as the first number of the new set
- The second to last number corresponds with the second number of the new set and
so on.
- Example {8,t,e,0,1} ---> {e,0,1,2,4}
https://youtu.be/KgELJOpLNaE?t=2m15s
Objective 51.2: Calculate the inversion of a pitch-class-set