Suggested Learning Resources

- INTERVAL-CLASS-VECTOR – usually written in square brackets [ ] lists the number
of intervals from a pitch-class-set that fit into each interval-class.

- Since there are 6 interval classes, there are always 6 numbers within each interval
vector. Interval-classes are listed from left to right.

- A set with no elements in it at all would have an interval-class-vector of [0,0,0,0,0,0]

- A set that had two interval-class 1's three interval-class 2's and one interval
class 6 would have an interval-class-vector of [2,3,0,0,0,1]

--------------------------------------

To calculate an interval-class-vector...

There is a formula we can apply to determine all the possible intervals that will
occur between the pitches within a given set.

It is called making a triangle chart. Here's how to do it.

- Step 1: List the pitches in the set, and underline the list.

- Step 2: Subtract the first element from the remaining elements to derive
a second row.

- Step 3: Using the second row, subtract its first element from the remaining
elements to create a third row.

- Continue the process until all rows have been exhausted.

- Finally count the number of interval classes and tally them from left
to right, beginning with interval class 1

- EXAMPLE Taking a major scale: C, D, E, F, G, A, B, -- we convert this
to integers 0, 2, 4, 5, 7, 9, e

- Step 2: (subtract 0 from each subsequent element)

- Step 3: (subtract 2 from each subsequent element)

- Step 3: (subtract 2 from each subsequent element)

- Step 4: (subtract 1 from each subsequent element)

- Step 5: (Subtract 2 from each subsequent element)

- Step 6: (Subtract 2 from each subsequent element)

- Here is the resulting triangle chart

- Within the triangle chart above, count up how many numbers match into interval-class
1 (all of the 1's and e's) Answer = 2

- How many match interval-class 2 (2's and 10's)? Answer = 5

- How many match interval-class 3 (3's and 9's)? Answer = 4

- How many match interval-class 4 (4's and 8's)? Answer = 3

- How many match interval-class 5 (5's and 7's)? Answer = 6

- How many match interval-class 6 (6's)? Answer = 1

- List those number from left to right in square brackets to show the Interval-Class-Vector
[2,5,4,3,6,1]

“Equivalent sets” usually share the same INTERVAL CLASS VECTOR… they are related
either by transposition or inversion

https://youtu.be/hYLSmBcUO8E

Objective 50.1: Define and calculate the interval-class-vector for a given set