## Melodic similarity - a theoretical and empirical approach

#### L. Hofmann-Engl

##### Keele University (UK)

PhD thesis, 2003

Paperback: 316 pages

Publisher: LAP Lambert Academic Publishing, 2009

ISBN-10: 3838310462

ISBN-13: 978-3838310466

## Abstract

*(taken from the thesis)*
This thesis investigates melodic transformations and melodic similarity from a theoretical,
cognitive and empirical angle. In this context melodic transformations are not only seen as an
independent entity unrelated to melodic similarity, but melodic similarity is based upon the
concept of melodic transformations. However, before melodic transformations are introduced,
the relevant parameters are established based on a concept of intentionality.
There, melotonic (pitch related), dynamic (loudness related) and chronotonic
(related to duration) values are introduced and defined. Subsequently, melotonic,
dynamic and chronotonic transformations are developed based on reflections and translations.
The algebraic structure of these transformations is investigated via reflection and translation matrices.
It will be shown that mapping two melodies (chains) onto each other via a reflection chain, provides
information about how closely two chains are inversions to each other.
Based on two specific reflections, the similarity and interval vectors will be defined,
which are to form the conceptual framework of melodic similarity. This is, the length of the
similarity vector delivers information about how close two chains are in absolute terms
(e.g. In the context of melotonic similarity how much two chains are transpositions of each other)
and the interval vector delivers the information about how similar two chains are in terms of shape.
The similarity and interval vectors are to form the basis for a variety of similarity models fashioned
for specific contexts. The melotonic and chronotonic similarity model will be put to their test in three
experiments. As will be shown, the experiments are in support of this approach.

Chameleon Group of Composers © 2003