**Pitch-Set Transformation**

The next topic to discuss is **Pitch-Set Transformation**.

This topic starts as a follow-on from the Contiguous and Non-Contiguous Segmentation topics. Once a segment has been extracted from the row using either of these segmentation techniques, the resultant segment can be manipulated using pitch-set transformations.

The general idea is that **(a)** you extract a segment (pitch-set) from a row, then **(b)** apply a pitch-set transformation to that segment (pitch-set) transforming it into a different pitch-set, then, optionally, **(c)** apply another transformation to the second pitch-set to create a third pitch-set, etc. This allows for the creation of more content.

In my usage, Pitch-Set Transformations will typically be used in a manner analogous to Sequence (described above) in that it provides a method of generating content based on only some of the pitches of a given row independently of the remaining pitches of that row. The main difference between a Sequence and a Pitch-Set Transformation is that a Sequence will repeat the same relative pitches in the same order on differing transpositional levels, while a Pitch-Set Transformation will modify the pitches using the various transformational processes.

For my purposes I will not make use of *all* of the possibilities of pitch-set transformations. This is primarily due to the fact that making use of the full possibilities of this technique will take one into the realm of free atonality. For my purposes, I do not wish to go that far.

The pitch-set transformations which I will make use of are:

**Complementation**

The complementation transformation involves transforming a pitch-set into its literal complement.

**Inversion**

The inversion transformation involves transforming a pitch-set into its literal inversion.

**Pitch**

The pitch transformation involves modifying one of more pitches of pitch-set-1 resulting in pitch-set-2.

**Subset**

The subset transformation involves extracting some of the pitches from pitch-set-1 resulting in pitch-set-2 which has a smaller cardinality than pitch-set-1.

**Superset**

The superset transformation involves adding one or more pitchs to pitch-set-1 resulting in pitch-set-2 which has a larger cardinality than pitch-set-1.

**Vector**

The vector transformation involves transforming pitch-set-1 into pitch-set-2 which will be a pitch-set whose interval vector is similar to that of pitch-set-1. In my usage there are three levels of vector relationships. From strongest to weakest they are: **(1)** when the two vectors are exactly the same (Forte called this the **Z** relationship), for example, the vectors for both sets are [013202], **(2)** when there is only one vector different between the two vectors, for example, [124310] and [114310], or **(3)** when the difference is that two of the vector values have been switched, for example, [231041] and [131042].