ComposerTools.com / Theory / Pitch Class Sets / 4.  Interval Vectors

4         Interval Vectors

An "Interval Vector" is a list of six numbers which summarizes the interval content in a PC Set. With a little experience, you will be able to get a sense for how a PC Set sounds when you see its interval vector. Further, once you know the interval content of a PC Set, you will also be able to manipulate the sound of the PC Set by inversion and octave displacement of pitches to emphasize certain intervals over others.

4.1          Pitch Intervals

                                                    A3 to D5   =      Perfect 11th  ascending        =      +17 half steps
                                                    D5 to A3   =      Perfect 11th descending       =      -17 half steps

                                                    A3 to D5   =      Perfect 11th                             =      17 half steps
                                                    D5 to A3   =      Perfect 11th                             =      17 half steps

4.2          Interval Classes

4.3          Interval Vectors

 


How to compute an interval vector:

o        Step 1:    Go through all pairs of pitches in your PC Set.

        If your PC Set has:           It will contain:
                2 pitches                        1 interval
                3 pitches                       3 intervals
                4 pitches                       6 intervals
                5 pitches                      10 intervals
                6 pitches                      15 intervals

Overall, the formula for computing the number of intervals (Ni) from the number of pitchs (Pi) is:
                               Number of Intervals  =  ( N*(N-1) ) / 2

o        Step 2:    For each pair, subtract the smaller number
from the larger number.

o        Step 3:    Take the result of step 2 and increment
the appropriate slot in the interval vector
using the following chart:


 

Copyright 2004 by Paul Nelson, all rights reserved.