Suggested Learning Resources

Music Theory QuickThink:

- 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 1: 

            0 2 4 5 7 9 e

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

-              2 4 5 7 9 e

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

-                 2 3 5 7 9

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

-                    1 3 5 7

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

-                       2 4 6

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

-                          2 4

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

-                             2

-          Here is the resulting triangle chart

-          2 4 5 7 9 e

-             2 3 5 7 9

-                1 3 5 7

-                   2 4 6

-                      2 4

-                         2

-  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

Objective 50.1: Examples in Music: YouTube

https://youtu.be/hYLSmBcUO8E

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

1) YFIO

2) Video Lesson: How to find an interval class vector Ramsey Castaneda Channel

3) Online Reading: How to find the interval-class vector for a pitch class set http://aaron-rosenberg.wiki.uml.edu/file/view/ICvectors.pdf

4) Interactive Lesson: