# The Statistical Mechanics of Machine Learning

I recently gave a presentation on the statistical mechanics of machine learning.  This talk covers deep learning neural networks and how they are inspired by the physics of magnetism.  Specifically, how the spin glass and Ising model are applied to study the hidden layers of deep neural networks. Here is the presentation: deepLearning

# 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[…]

# Composing with Complementary Cycles

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.

# Machine Language for Music

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 Read more about Machine Language for Music[…]

# Composing with the Thue-Morse Sequence

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 Read more about Composing with the Thue-Morse Sequence[…]

# Using the Properties of Fractals to Compose Music

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 Read more about Using the Properties of Fractals to Compose Music[…]

# Quantum Cellular Automata

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 Read more about Quantum Cellular Automata[…]

# 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[…]

# luna Nightlight

luna NightlightTM is a captivating nightlight application for the iPhone and iPad that will capture your imagination, and put you right to sleep by playing your favorite music.  luna NightlightTM is comprised of beautiful spheres dropping from the sky, calmly floating down, and mysteriously disappearing into the night.  Or, turn the phone upside down and watch Read more about luna Nightlight[…]