My Experience at MCM 19 -- a small blog by Matt Klassen


It was a great privilege for me to attend the conference MCM19 in Madrid this summer. In this short blog I will mention some of the highlights of my experience at this conference, and invite others to continue the conversation.

Thank you to the organizers!

First of all, thanks again to the organizers of this fantastic conference! Great work to all of you, and I am already looking forward to the next one! They are all listed here: https://mcm19.etsisi.upm.es/sponsors

Who am I?

In case I didn't get to chat with you, I am from Redmond, Washington, USA. I gave a talk on Wednesday called: Constraint-Based Systems of Triads and Seventh Chords, and Parsimonious Voice-Leading. I am pictured below trying out some Ramirez guitars near Puerta del Sol in central Madrid, and also in the last session at MCM19 seated (on the right) next to Alexandre Popoff, and Moreno Andreatta.

Matt plays Ramirez Matt with others

Collaborative talks

Here is something I really loved to see at the conference: Collaborative talks of many kinds! One of my favorites was the talk by Jason Yust and Dmitri Tymoczko, Fourier Phase and Pitch-Class Sum, which was a really genuine effort by two leading researchers to come together and see how their approaches to similar concepts could enlighten and complement each other. This is a great service to the research community, and a great model to follow! Another one was the talk by Thomas Noll and Karst de Jong Embedded Structural Modes:Unifying Scale Degrees and Harmonic Functions. This was a great example of collaboration between musical and mathematical elements, with live illustrations on the piano, always a great plus!

A question on constraint-based systems

After my talk on Wednesday, Thomas Noll asked me a very good question: "Did you use the constraint-based definition of triads in the proof of the structure theorem for the group of transformations?" My answer was: No, not explicitly, however it is something that I was thinking about for the larger systems. In fact, as I worked on this, on the way home, I was able to extend the proof to the constraint-based system of seventh chords, in a way which does leverage the definition. The basic idea is that because of the constraint-based approach, the chords in the system have lots of connections to other chords and the paths which are used to produce the group elements are easy to construct in an organized way. So thanks for asking, Thomas!

Music Theorists doing Mathematics, or Mathematicians doing Music Theory?

Before coming to this conference, I was not sure if there would be more Music Theory Ph.D. researchers, or more Mathematics Ph.D. researchers attending. I find the cross-over subject matter very appealing and I am happy to say that I found both types! I am technically of the latter type, although I have been a serious musician since about age 16, before I found an interest in mathematics.

Discussion of the Efficacy of Mathematical Abstraction in Music Theory?

This is a topic which I would love to see discussed more deeply. Since my paper involved group theory, I will pick on this one topic here. When I originally saw the paper "Musical Actions of Dihedral Groups" by Crans, Fiore, and Satyendra, in the American Mathematical Monthly, I was struck by the beauty of this mathematical description of

Music composition using a Hamilton path of seventh chords

Since time was short for the presentation, I neglected to play a musical example which is relevant. The example is a composition for piano by Bruce Stark, my colleague at DigiPen in Redmond. This piece utilizes a portion of the chord sequence which was quoted in my talk, pictured below. The link to Bruce's performance is here: Prelude No.6 by Bruce Stark. Also, the chord sequence in the composition is referenced here: chord sequence , and more compositions of Bruce Stark are here: Bruce Stark's Page

Hamilton Path of Seventh Chords

Theorbo video

A few people said that they would like to see the whole video (of which I played a short excerpt in my talk) so here it is: Tocatta Arpegiatta


Since I am somewhat new to the subject of Mathematics and Computation in Music, it was a great experience for me to prepare a paper, to receive very helpful comments from reviewers, and to begin to catch up on a mountain of reading in this very interesting field! Additionally, I would like to thank all of the participants at MCM19 for making this a very welcoming experience.

Matt Klassen