Pareidolia I, a 31-edo etude (2023)

About the Piece

Firstly, I need to say that this piece (and the next Pareidolia that I am currently working on) is originally intended to be played on a lumatone , but I still haven't been successful on finding a lumatone player. That being said, I also don't own the instrument so some chords my change in the future, once I get someone that can try to perform the piece and give me some feedback.

This piece is my first exploration of 31-edo. It is called Pareidolia because I attempted to create a system which had rules that I personally understand as the foundations of tonality, and the result is a piece that resembles something familiar, but it is not at all what it seems.

All of these "foundational rules" relate to the concept of tension and resolution. In simple terms, the most important interval that creates this dichotomy in tonal music is the tritone, which gets resolved as the interval of a third that belongs to some chord. Another important characteristic of tonal music is the leap of a fifth that happens melodically (often in the lower voice if we are talking about a text-book, simple harmony case) when the harmony moves from a dominant to a tonic chord. I attempted to translate these (and other) rules to a 31-edo system, which allowed me to create strong "tonal" centers and therefore reuse other well-known concepts such as modulation and some traditional counterpoint rules.

Why 31-edo?

For this project, I chose to divide the octave into 31 equal parts because that is still a manageable number of notes for a performer, and the smallest interval possible, the diesis, is still very perceptible. Additionally, the fact that I could work with five different interval qualities of a third allowed me to generate beautiful new colors in my experimentations, especially when using the near just major third, which is just 1 cent shy of a perfect 5:4 third.

31-edo is versatile enough for me to keep expanding on this system in the future, re-using patches and any acquired knowledge, since eliminating some of the 31 notes provides an infinite number of options for new systems, scales and colors.

As an example, Pareidolia I uses a quartal harmony, and Pareidolia II (still in the works) will use a triadic harmony, but both pieces will follow the exact same rules of harmony and counterpoint, only having different scales. This is much harder to do on the regular 12-edo system.

Pareidolia's Harmonic System

The first problem I had to solve on this project was the tritone resolutions, especially taking into account that 31-edo has two tritone sounding intervals (the augmented fourth and the upaugmented fourth). I soon realized that if you resolve the augmented fourth as one would normally solve a tritone, but moving each note by a dieses in contrary motion instead of a semitone, the resulting interval is a perfect fourth (or fifth, if inverted). This resolved interval is present both on quartal and triadic chords, which means that this tritone resolution is highly versatile.

Then, through experimentation I found scales that fulfills the following rules:

• With the exception of the dieses used to solve the tritone (pitches 31 to 1, and pitches 14 to 13 of the 31-edo), every other step should be variation of a second (to keep the similarity with 12-edo music, or the "pareidolia").
• A perfect fifth above the tonic (pitch 18 on the 31-edo) needs to be present, so the aforementioned polarizing dominant-tonic jump is possible. A quartal harmony should also make it possible for me to have a chord that unites the perfect fifth with the tritone (that is, pitches 18, 13, and 30 of the 31-edo need to fit into a chord based on the interval of fourths, just like in triadic chords in 12-edo).

Most scales that fitted these rules had 9 notes. I chose the one with the following pitches: 0, 4, 8, 13, 14, 18, 22, 26, and 30.

This scale also had the benefit of, when in a quartal harmony context, provide a chord in which the root is one dieses below the tonic, and said root has an interval of a tritone with another note of the chord, similar to the seventh degree of a tonal major harmonic field, which I found quite charming. I now also had a chord that functions as a dominant without its root.

The next step was to plan modulations. I wanted to experiment with different types of modulation but I especially wanted to try very smooth, prepared and imperceptible changes of harmonic field. To achieve this, I analyzed and compared each of the 31 possible transpositions of my scale and compared the number of similar notes between them (something similar to finding neighbor tones). Once I found my target "new key", I planned for different types of modulations based on the quartal chord similarities.

Finally, I want to note that this system also allowed me to use secondary dominants and the sonic results were very satisfying.