Computer-based investigations in harmony


A quantitative study of the quality of ‘harmonic tension and relaxation’


How does a composer take care of vertical events? How do different musical lines interact harmonically? These have been two of my main questions ever since I became acquainted with post-tonal music.


Among other qualities of chords, it is the concept of ‘harmonic tension and relaxation’ that has always been of great importance to me. To explore this quality of chords comprehensively, I wrote a piece of software that performs massive amounts of calculations, based on given criteria, to create and sort a collection of chords according to their level of tension and relaxation. In fact, one of the main parts of this inquiry is to find the criteria that play critical role in our aural perception of this quality of chords. After examining various hypotheses, I have come to the conclusion that the most important factor is the presence and voicing of specific tense trichords in the structure of complex chords. This is discussed in detail in my dissertation document.



Classification of microtonal harmonies based on Middle-Eastern modes


To take this to the next level, I decided to explore the qualities of chords that are not based on western pitch collections, in particular chords made of microtonal pitches found in Middle-Eastern modes. Using aural perception as the main guide and with the help of computer analysis, I have listed and categorized all the microtonal trichords of this music, based on their aural qualities. This catalogue of sorted trichords can be utilized to analyze complex microtonal chords that contain a mixture of these trichords. The results of this investigation will be used in my next composition projects.


It is worthy to mention that Middle-Eastern music, including Iranian music is mostly monophonic or heterophonic. I believe the results of this investigation can be used as a theory of harmony that can potentially add to the richness and diversity of this music.



Algorithmic composition


To take my ideas on computer-assisted analysis of chords further, I designed a software module that generates chord progressions based on the fluctuations of harmonic tension and relaxation. These chord progressions follow a soprano-bass framework that is itself generated by another software module that creates melodic lines based on interlocking tri-chords.


Expanding even further on this idea, I wrote a code that creates transforming rhythmic lines based on given rhythmic cells, and based on that, I wrote another module that creates diverse musical textures using the computer-generated chord progressions. These musical textures in MIDI numbers were then written into MIDI files readable in any notation software. I used the outcome of these series of software modules as a basis for the instrumental pitched material of some of my recent compositions. You can find these software modules at the link below:



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