13-tone keyboard
Composing Xenharmonic Music

Composing Xenharmonic Music

A very important aspect of music composition is, of course, that of consonance and dissonance. Consonant chords sound clean and smooth, whereas dissonant chords sound harsher and generally have an audible “beating,” like a fast tremolo. Dissonance lends the feeling of an unanswered question (such as a dominant 7th chord), and consonance gives us the feeling that it has been answered (such as a major triad). This basic concept of various musical passages leading us through question-and-answer or tension-and-release feelings should be as valid in xenharmonic music as it is in standard twelve-tone music. But it’s a challenge!

Let’s begin with the fact that you can throw most of the harmony lessons you’ve ever had right out the window when composing xenharmonic music. We don’t necessarily hear standard concepts like “major” or “minor” or “dominant” in other tunings. Instead, each tuning is its own alien world ripe with unexplored territory, each with its own set of melodies, chords, and progressions waiting to be discovered and theorized. When we do stumble upon note combinations that remind us of standard chords, they may sound a bit “off,” or else the transition from one chord to another may feel slightly different than what we’re used to. That kind of push and pull on our traditionally trained music brains is what I personally enjoy.

You can throw most of the harmony lessons you’ve ever had right out the window when composing xenharmonic music.

Xenharmonic purists tend to focus on the mathematics of tunings, expressing tonal relationships as interval ratios. They generate beautiful mathematical charts, entropy maps, and latices, which deeply inspire xenharmonic composers, including those of us who aren’t purists! However, many xenharmonic musicians take the desire for pure ratios to an extreme, wanting everything to be perfectly in tune. This leads to an interest in “just tunings” (unequal temperaments based on pure ratios), or using a zillion-notes-per-octave or even “dynamic tunings” that offer a constant stream of perfect chords–as free as possible from any beating. The more pure the ratios (low number integer ratios are purest), the cleaner and smoother the sound.

Harmonic entropy plotted for triads.

Harmonic entropy is plotted for triads. See the original post on The Xenharmonic Alliance.

In my mind, however, the more important angle to consider is how we perceive one note or chord leading into the next. We hear music over time as a series of notes and chords, after all. Harmonic movement is where emotion and meaning comes alive in a composition. That is far more important to me than whether each individual snapshot in time is in tune or not. It is all a matter of taste and aesthetic, but I don’t usually enjoy music that is based on pure ratios throughout, because it sounds one dimensional to my ears. It misses the boat on dissonance, which is just as important as consonance. Yin and yang, light and dark, tension and release!

Dissonance is just as important as consonance.

Beating or not, partly what contributes to our sense of consonance and dissonance is simply what we’re used to. In the Western world we’ve heard our imperfect twelve-tone equal temperament all our lives, and therefore may perceive perfectly in-tune 3rds and 6ths as sounding worse than their tempered counterparts, which have more beating. That simple fact has sparked much curiosity and debate about how our brains actually perceive consonance and dissonance.

It may be a surprise to learn that modern research shows strong evidence that beating is not the best measure of whether chords and intervals sound pleasant or in tune (Edward Large et al.). Our brains don’t directly decipher in tune-ness from beating. What actually happens when we hear musical sound is that our neurons begin oscillating, and this “neural resonance” dynamically “pulls” intervals into tune, as long as the frequencies are within proximity to ratios of the harmonic series. In chaos theory speak, our neural oscillations become an “attractor.” In musician speak, if it’s close enough for rock’n’roll, it will sound in tune!

In musician speak, if it’s close enough for rock’n’roll, it will sound in tune!

I think this is good news all around. For one, the research shows that our sense of consonance is indeed driven by our preference for the harmonic series, and therefore all of our traditional musical ideas still stand. But more profoundly, it shows that our traditional harmony is a mere branch of something larger. With every new research paper in this field, we can begin to see the outlines of a universal harmonic theory, implying that we can develop unique but related “harmonic rules” for any tuning.

Now enter my world as an equal-temperament composer. I believe that music composition in equal temperaments is easier and simpler than using “just” tunings or other options and that it’s an entirely legitimate means of music composition. For me, personally, equal temperaments have offered decades of fascinating exploration—messy ratios and all. I prefer to fully explore equal-tempered tunings that have a very limited number of notes, such as 10edo, 16edo, 17edo, or 19edo, and discovering their particular “flavor”, as opposed to working with something like 53edo that has so many choices of frequencies that it doesn’t, in itself, offer a distinct flavor.

What are these flavors I speak of? In general, microtonal scales (smaller than half steps) offer a tenser vibe, and macrotonal scales (larger than half steps) have a more open and alien feel. Any tuning can just as easily sound ugly or exotic or beautiful. It really truly depends on how it is used. When I’m trying out a new tuning, it always starts off on the ugly end of the spectrum until I mess around for quite a while, eventually discovering chord combinations and nifty melodic lines, and what intervals to avoid.

Any tuning can just as easily sound ugly or exotic or beautiful.

It really helps to have a proper instrument to discover your new tuning on. Even if you aren’t a piano player, keyboard “controllers” (meaning no internal sounds–just keys) are a very flexible and relatively inexpensive way for anyone to get into xenharmonic composition or to expand the setup you may already have. And this goes hand in hand with the “virtual instrument” synthesizers I reviewed last week. I have collected several keyboards over the years and have rearranged the black/white keys for each of my favorite tunings.

The current trend is to use M-Audio Keystations (49, 61, or 88 keys), which can be had for anywhere from $50-$200 on eBay and other online stores. If you can afford it, buy more than one so that you will have extra keys. You’ll need them if you’re going to dive in and rearrange the keys! Some tunings will need extra black notes, and some will need extra white notes. It’s cheaper in the long run to buy extra keyboards rather than extra individual keys, which are usually marked way up in price.

Here is a video that shows how I remove and rearrange keys on an 88 note Keystation–in this case, for a 15-note tuning which requires lots of black keys! As you’ll see, you only need a screwdriver, needle nose pliers, and possibly a sander of some sort.

One deciding factor in choosing a tuning is the level of difficulty in building a keyboard. Scales that require a smaller ratio of white notes than normal are easier to put together. White keys have a wider area to contend with and trying to squeeze more of them on the keyboard causes a need for them to be thinner. I have sanded many white keys thinner in my day. It works but is not ideal, as pianists are used to uniformly sized white keys. On the other hand, using more black keys than normal results in gaps between the keys, and thus a wider spacing than normal.

I will show a few keyboard examples here along with music links for each, and perhaps you’ll see/hear something that attracts you. Then you can either build one yourself, or ask one of us to build one for you!

10edo is one of my all-time favorites, and yet it gets a bad rap for its impure ratios. Here is something I wrote in 10edo. The diatonic scale in 10edo has larger half and whole steps than 12edo, and the thirds are right in between Major and minor, lending to its alien feel. The diatonic scale has a harmonic minor vibe to it. In a perfect world, a ten-tone keyboard would look like this:

An idealized 10-tone keyboard

However, putting three white keys in a row would involve skipping some of the keyboard contacts where there would normally be a black note. One solution is to make the C a black note painted white. However, it would be a bit strange since C is the first note of the diatonic scale.

Otherwise, here is my “cheater way,” as I call it: Sawing off the wide part of the white keys allows any desired black/white key arrangement. For this style of keyboard, I remove the entire keyboard cover and build my own handle onto the back. It looks prettier than having a big gap where the white keys are chopped off, but fashioning the handle itself is work! I would not judge anyone who leaves it in the original casing.

10 tone


10 tone “Jupitar” Vertical Keyboard by Elaine Walker

19edo is highly recommended for anyone who feels a bit intimidated by xenharmonic music composition and would like to ease into it. It is a good “transition tuning,” as it offers something close to our 12-tone diatonic scale but with more pure 3rds and 6ths. Mind you, it has worse 4ths and 5ths–there is always a tradeoff. The experience of 19edo is like an exotic version of 12edo, with some extra black notes for ornamentation. Here is one of my 19edo songs from the ‘90s.

The most typical 19edo keyboard, however, requires doubled up black keys, which leaves unsightly gaps. But again, who’s going to judge? Not I! Simply play a whole step instead of a half step, and a minor third instead of a whole step, and you’ll see the relationship to 12edo!

19-tone keyboard

19-tone keyboard by Darren McDougall. Having more black notes than usual creates gaps between the white keys.

The 17edo keyboard is easy to make, as it has the same ratio of black:white keys as 12edo. It looks like a surreal piano. I thought 17edo sounded terrible until I got used to it, and now it is one of my favorites. 17edo is also a clear favorite in the xenharmonic community. Here is something I composed in 17edo.

17-tone

17-tone “Insanetar” Vertical Keyboard by Elaine Walker. The keys fit perfectly since it has the same ratio of white and black keys as a standard piano.

Here is a 13edo keyboard which has some white keys shaved thinner. 13edo music is neuron-bending since it is just slightly off from 12edo. Enjoy this 13edo music by Aaron Andrew Hunt. I would not suggest trying this at home. I mainly wanted to show this crazy keyboard with the squished white keys around the single black notes.

13-tone keyboard

13-tone keyboard by Elaine Walker. Having more white notes than normal causes them to not fit. Some white keys are sanded thinner.

When you start looking around The Xenharmonic Alliance and other websites, you will notice many other keyboard options, such as isomorphic keyboards, although they tend to be quite pricy and largely unavailable. My favorite of these is a specific type of hexagon keyboard, known as a sonome (which is like saying “hexagon piano”). If you can get your hands on something cool like this, do it! It will open up a world of xenharmonic improvisation that isn’t as easy on a regular keyboard. Having a five octave reach, seeing chords as “shapes,” and being able to transpose while maintaining the same fingering, can make xenharmonic composition a much smoother experience.

I suggest that you not worry about theory.

Whichever tuning or instrument you choose to compose with, I suggest that you not worry about theory and just improvise by ear for as much time as you can spare. Don’t fret over the specifics of your timbres beyond whether they sound good to you–that is, if you want to compose truly beautiful xenharmonic music. At some point you will want to see what theory is “out there” for your tuning, if any, and it will be interesting to compare it to what you come up with on your own. Share your music and findings with the xenharmonic community. It is always exciting when someone posts new music. Don’t be shy about asking questions. We’re all happy to help and we even build keyboards for each other.

I will leave you with some more informative links:

My page on microtonality
My FAU lecture on microtonality
The Xenharmonic Alliance
My personal website

Xenharmonic performance at Berklee

Xenharmonic performance at Berklee College of Music, 2010

NewMusicBox provides a space for those engaged with new music to communicate their experiences and ideas in their own words. Articles and commentary posted here reflect the viewpoints of their individual authors; their appearance on NewMusicBox does not imply endorsement by New Music USA.

2 thoughts on “Composing Xenharmonic Music

  1. Michael Robinson

    What a great resource this series of articles has been! Myself, I can attest to the excitement of exploring these concepts. While staying in Kula, Maui several years ago, the pure continuity of the truly black sky at night merging with the black sea in the distance, and the black contours of Haleakala, suggested melodic forms different from ragas I have used in the past, and I imagined three new melodic constructs immerging from shaping the saptaka (octave) into nine, eight, and seven equal parts for my composition, Nightmarchers, the three parts being Kula Midnight, Lahaina Midnight, and Hana Midnight. Here is a link for those who may be interested – http://azuremilesrecords.com/nightmarchers.html

    Reply
  2. Kyle Gann

    “I don’t usually enjoy music that is based on pure ratios throughout, because it sounds one dimensional to my ears. It misses the boat on dissonance, which is just as important as consonance.”
    If you had written *simple* rather than *pure*, I might have passed these sentences by. There’s plenty of dissonance available within pure ratios, and those of us who compose in just intonation take full advantage of it. As Harry Partch said, “Just intonation dissonance is a whole different serving of tapioca.” This is one of the misconceptions that the EDO people love to spread about just intonation. I wish I knew why.
    http://www.kylegann.com/JIreasons.html

    Reply

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