Introduction

This repository is based on the paper "Using Variable Order Markov Model in Measuring Temporal Dynamics of Melodic Complexity in Jazz Improvisation" by Philip Pincencia (2024).

Project sturcture:

VOMM-MEL-COMPLEXITY
│   README.md
│   gui.py
│   
└───Paper_and_Conference_Slides
│   │   Paper.pdf // Coming Soon
│   │   Conference_Slides.pdf
│
└───Supplement
│   └───Harmony_Score
│       │   Hscore_general.py
│       │   file112.txt
│       │   ...
│   └───Chroma_Vector
│       │   chroma.py
│       │   file112.txt
│       │   ...
│   
└───examples
│   │   ... // song names
│   
└───src
│   │   midi_rep.py
│   │   createdistribution.py
│   │   vomm_ppm.py
│   │   sliding_window.py
│   │   chord_parser.cpp
│   │   chord_parser.exe

Details

Here I detail the steps of each of the approaches

Variable Order Markov Model (VOMM) Approach

I used the VOMM algorithm called Predict by Partial Match (PPM), which is implemented as a Multiway Trie. This is based on the paper "On Prediction Using Variable Order Markov Models" by Ron Begleiter, Ran El-Yaniv, and Golan Yona in the Journal of Artificial Intelligence Research 22 (2004) 385-421.

To learn the PPM model consists of several steps:

1. Convert to training sequence: xml file is parsed by midi_rep.py

#

2. Instantiate an object of the appropriate class. Example:

import vomm
my_model = vomm.ppm()

3. Learn a model from the data.

import vomm
my_model  = vomm.ppm()
my_model.fit(training_data, d=2)

Internals

Denote $q$ as the training sequence.
Learning a model consists of

1. Construct the set $S$ consisting of contexts of length at most $D$ in the training sequence. Precisely, $S={s\in q ||s|\leq D}$.
2. Building the Mutliway Trie $\mathcal{T}$
3. Estimating the probability distribution $\hat P(\sigma|s)$ for each context $s$ and symbol $\sigma$ in the alphabet.

After creating an object $x$ of whichever class you chose and fitted to the training data, the object $x$ will have several attributes of which 3 are important:

• pdf_dict -- this is a dictionary with key context $s$ and value the probability distribution $Pr(|s)$.
• logpdf_dict -- it's similar to pdf_dict, but the value is the log of the probability distribution.
• context_child -- this is a dictionary with key context $s$ and value the set of possible longer children contexts ${ xs }$ which are in the set of contexts recovered in step 1. This dictionary speeds up finding the largest context $s$ which matches the tail end of a sequence of symbols.

Future Implementation

• Develop a web server to let users drop in an xml file and the associated chord changes pasted from WJazzDatabase
• Animate the sliding window analysis to better understand the how the measure behaves
• Convert music21-independent python files to C++ to speed things up.