Fourth Species Counterpoint and the Klein Four-Group

We are going to compose a short piece of music, then extend the music by adding symmetry relations. This will allow us to create a tonal-atonal-tonal structure.  In particular, we will be using a Klein four-group, from the field of group theory.  The Klein four-group has some very interesting properties that can be directly applied Read more about Fourth Species Counterpoint and the Klein Four-Group[…]

Transformational Model for Voice Leading

This video explains voice leading with respect to atonal music.  There are two models for atonal voice leading: Transformational and association.  We will discuss the transformation model in detail and give an example of how this particular voice leading works.  The transformation model focuses on pitch-class counterpoint, which is created by transposition and inversion of Read more about Transformational Model for Voice Leading[…]

Using Uniform Triadic Transformations to Map Out Chord Progressions

Transformational music theory involves the study of how musical objects, such as chords and rhythm, can transform from one to another.  The music theorist Hugo Riemann (1849 – 1919) studied transformations of chords through operators that formed a group, these operators were defined by their voice leading properties.  Voice leading is essentially how individual notes Read more about Using Uniform Triadic Transformations to Map Out Chord Progressions[…]


     LUMA is a software tool designed to perform algorithmic composition using set theory and associated techniques to help create melodies and harmonies that you may not otherwise have been able to create.