Name: Christopher Otto
Nationality: American
Occupation: Composer, violinist
Current Release: Christopher Otto's rag’sma for 2-3 string quartets, recorded with his fellow members of the Jack Quartet, is available at greyfade.

If you enjoyed this interview with Christopher Otto, visit the official Jack Quartet website. He also has a personal homepage with more detailed information on his compositions and a bandcamp account.

Was there a particular event or experience that made you realise that there might be more outside of the realm of music we take for granted? When did you first start getting interested in the world of alternative tuning systems?

I had a transformative experience when I was around 10 or 11, having played violin since I was 8 and piano since I was 5.

I got to play in a performance of John Cage’s Twenty-Three, for 23 strings, at the University of Illinois in Champaign. In the 23-minute piece I had a total of 2 notes to play, each of which could be anywhere from a few seconds long to over 10 minutes. Having mostly studied music from the “classical” tradition, the piece’s sense of open-ended possibility and endless combinations of sustained harmonies was a revelation. Also on that concert I heard a performance of Iannis Xenakis’s Analogique A+B, for 9 strings and tape, which I found hilarious and utterly fascinating.

When I was around 15 or 16, Jeff Gibbens, a former student of Ben Johnston, introduced me to the central concept of just intonation, the idea that pitch can be organized in terms of ratios of frequencies. He showed me a lattice of pitches, with fifths going to the right and major thirds up, that explained a paradox of tuning that came up in my violin studies.

(I wrote an article that goes into some of this.)

I always liked math, and from then on I’ve been interested in exploring different connections between math and music, often through just intonation.

What artists working with alternative tuning systems are you personally interested in? What approaches do you find inspiring?

I’m very inspired by the music of Catherine Lamb, La Monte Young, Eliane Radigue, James Tenney, Ellen Fullman, Marc Sabat, and Wolfgang von Schweinitz (among many others). The Extended Helmholtz-Ellis JI Pitch Notation by Sabat and Schweinitz has been very helpful for me in translating between ratios and traditional pitch notation.

[Read our Ellen Fullman interview]
[Read our interview with Michael Robinson about La Monte Young, Tuning & Indian Classical Music]

Terms like consonant and dissonant are used in school, but mostly with very limited understanding of what they mean. How has your own idea of these terms changed over time and how do you see them today?

Hermann von Helmholtz, James Tenney and William Sethares have influenced my definitions of consonance and dissonance, and my approach continues to evolve.

For me it’s not about pleasant vs unpleasant, but more akin to smoothness vs roughness. This sensation of roughness comes from the speed and prominence of beating - interference between close frequencies. We can think of a sonority as relatively complex (more dissonant) if the ratios approximating it involve bigger numerators and denominators (as 9:8, the major second, is more complex than 3:2, the fifth).

In my violin octet I thought of consonance as simply the frequency of the implied fundamental. Accordingly a just triad in a high register is more consonant than the same triad low (which makes sense to me). But then any sonority with irrational intervals, like equal temperament, would have a fundamental of 0 Hz - infinitely low.

The trajectory of my violin octet is from higher fundamentals to lower and lower ones - going from 42 Hz to 21 Hz to 14 Hz (now no longer a pitch but a rhythm) and eventually approaching 0 - unison. Thus in a way the dissonance is decreasing, but it ends up approaching maximum consonant. So this is a kind of paradox, leading to a looser definition of consonance that takes into account fuzziness.

Around each ratio is a fuzzy region of frequency space that approximates or points to the exact ratio. In this way the dissonance curve for a pair of frequencies could be a fractal, infinitely nested with local minima for the ratios and nearby frequencies.

In rag'sma I thought of the 3rd quartet as trying to find the best-fit, or most consonant, fundamental for the notes generated by the other 2 quartets, which follow their own independent logics. In this way consonance and dissonance function as a linearization of the multidimensional space of harmony.

What were some of the most interesting tuning systems you tried out and what are their respective qualities?

I’ve been most interested in various forms of just intonation, with different pieces using different subsets of the infinite space of rational numbers. I find that each prime factor imbues a certain character or quality to the ratio - so for example traditionally with major and minor triads you’re using primes 2, 3, and 5, but I also like the 2, 3, 7 space, where the major thirds are wider and minor thirds narrower. (You can hear this in La Monte Young’s Well-Tuned Piano.)

In rag'sma I use the 2, 3, 5, 7 space for quartets 1 and 2, but re-interpret more complex ratios of these primes as simpler ratios with higher primes that are nearby, thus blurring the boundaries between different systems.

Do different tuning systems suggest different kinds of music? Would you say that different tuning systems are capable of expressing different, and potentially unique emotional states?

I think tuning is integral to music, so changing the tuning changes the music. For me the ratios give the clearest expression of distinct qualities, which can correlate with specific feelings. It’s fascinating to me how a very small change in pitch can totally transform the character of an interval.

What challenges does playing in different tuning systems present to you as a performer? If you're performing a piece in a different and new-to-you tuning, how will you approach this?

The most immediate challenge confronting me as I try new tunings is simply how to hear whether it’s in tune. For the rational intervals of just intonation there are clear mathematical predictions of what difference and combination tones should be produced, and which harmonics should align - then it’s a matter of listening, noting what I’m actually hearing, and figuring out how it matches the prediction. Sometimes it’s a specific pair of harmonics for which I want to slow down the beating, and sometimes it’s more of a generalized sensation. Understanding the math can help guide the ear.

In learning a piece with new tunings, usually I slow down the tempo or freeze on certain harmonies, and gradually the processing time it takes me to imagine, listen to, and perform the tuning speeds up. The longer a harmony is sustained, the more precise the tuning can be, so in speeding up you allow more fuzziness.

How, if at all, has performing in a different tuning system changed your creative practise?

Thinking about the infinite ways to model pitch relationships has opened me up to so much as a performer, composer, and listener. Rather than visualizing only a closed circle of 12 pitch-classes, or a linear low-to-high frequency space, I can embrace the full multidimensional nature of harmony.

So far, the focus with regards to alternative tuning systems has mainly been on harmony. But melody is affected, too. How do you personally understand melody and what changes when it becomes part of a new pitch environment?

I like to treat harmony as extending over all time scales, so pitches are just faster vibrations and rhythms slower ones.

Melody for me is the unfolding of harmony in time, but since harmony itself is made of time, it’s all integrated, a mapping of time to itself across different scales.

With electronic tools, playing and composing in just intonation has become a whole lot easier. Do you find this interesting?

Yes, it can be fruitful to use electronic tools to explore tuning in different ways. For rag'sma I made a mockup of the first two quartets with sine tones, and then created a function to model how my mind might find the best-fit fundamental. I also use a tuner or listen to sine tones on headphones to lock in quicker, but of course this only supplements listening to the actual sound.

In composition I use mathematical programming languages to create structures, and sometimes to create sound directly. For example, for my piece MAW I recorded a bunch of straight tones on violin and bass and used algorithms to construct a pathway through harmonic space and edit the files to create a mix that I could immediately listen to. This certainly made it easier for me to make compositional decisions based on the sonic results.

For interested readers, what are books, websites, articles or other sources of information you recommend for them to educate themselves on the topic?

I would highly recommend checking out plainsound.org for a lot of just intonation and microtonal resources, as well as Catherine Lamb’s website. I’m working on a website, christopherotto.space, to share my work and hopefully there will be more resources there in the future.

Helmholtz’s On the Sensations of Tone is a classic, and Harry Partch’s Genesis of a Music has an intriguing and idiosyncratic approach. I’d also recommend William Sethares’s Tuning, Timbre, Spectrum, Scale, Jan Haluska’s The Mathematical Theory of Tone Systems, and John Chalmers’s Divisions of the Tetrachord.

There are also interesting apps and programs coming out for alternative tuning systems, for example Khyam Allami’s Apotome and Leimma, which allow users to select preset tunings and create their own. Wilsonics is an app that allows you to explore the tunings and geometric diagrams of Erv Wilson. Many people are working in alternative tunings - the possibilities are limitless.