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[…]
This page contains the supplemental material, both sheet music and mp3, that is associated with the YouTube video I made titled, “Composing Music with Complementary Cycles”. The following music is derived from the complementary cycles of the P8/I1 dyad.
Binary numbers allow for the representation of any number using only two digits, 0 and 1. This piece of music is derived from taking a set of integers, in this case, multiples of 6, and converting these integers into their corresponding binary representation. For each binary number the 1’s are summed to create an integer[…]
The Thue-Morse sequence is a binary sequence and was first used by Eugene Prouhet in 1851 by applying this sequence to the study of integers. However, it was Axel Thue in 1906 that used this sequence to create the field of study called, “combinatorics on words”. In 1921 Marston Morse applied the sequence to differential[…]
I’m not sure if they knew it at the time, but composers such as Johann Sebastian Bach and Ludwig van Beethoven composed music notes that obeyed the principals of fractals, and in particular, a power law function. Hsü et al (1) reported in 1990 that log-log linear plots can be used to determine if a[…]
Cellular automata (CA) is a discrete system using simple rules and used to model complex systems. Historically, the initial major contributor to CA was John von Neumann. von Neumann was trying to find a model of self-replicating systems, a system that could produce exact copies of itself. Fast forward to the 1980s where Stephen Wolfram[…]
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[…]
Since I drink so much coffee when I work, I thought it might be a cool idea to talk about the merits of the, very interesting, coffee bean. I not only enjoy the smell and taste of coffee, it is amazing what coffee does to me when I drink it. We have all experienced this[…]