On Temperament and Tempering
By REIKO YAMADA
As a composer from Japan trained in the Western musical tradition, I sometimes have uneasy feelings about composing music in European styles. At the same time, I am also uncomfortable with the appropriation and exploitation of Asian cultural traditions, such as the traditional tuning systems (for example, Raga in Classical Indian Music or the pentatonic scales of Japanese Shakuhachi or Gagaku music), by both European and Asian composers. A recent project focused on artistic research and creation using the digital organs at the Zentrum für Orgelforschung der Kunstuniversität Graz gave me the opportunity, twenty years into my career, to reassess these relationships and examine the very foundation of Western music by exploring its historical tuning systems. This exploration, in turn, led me to draw inspiration from an aesthetic principle that originates in the Japanese musical tradition yet remains entirely within the vocabulary of Western music.
For centuries, Western musicians and scholars have tried to define the pitch relations within an octave by dividing it into twelve equally-spaced notes. A set of pitches that produce mathematical proportions between the fixed tones, or intervals, is known as a tuning system. However, splitting the octave into exact, equally-spaced steps while, at the same time, producing interval relations that are harmonically in tune is impossible. Thus, throughout the history of music, the complexity of this problem has bothered physicists, composers and music theorists, many of whom have proposed compromised solutions prioritizing either pure harmonic relations or equal distance between the twelve tones.
For example, just intonation is one of many historical Western tuning systems that focuses on purity as a way of preserving the harmonic order found in the natural world. This type of tuning involves arranging the main intervals as whole-number ratios (i.e., 3:2 or 4:3). Nonetheless, in just intonation, the pure sonorities of some intervals come at the cost of creating great discrepancies in others, hence producing so-called “wolf” intervals. A wolf interval is an interval that is notably sharper or flatter than the size of the corresponding justly-tuned interval (the result of tuning other intervals to be harmonically pure), and is therefore exceedingly dissonant, which sounds quite unpleasant. Countless variations of such tuning systems were developed by placing wolf intervals in various locations based on musical trends and ideological beliefs. The practice of tuning in harmonically pure intervals by one method or another, whether just intonation or meantone temperaments,[1] flourished during the Renaissance and Baroque periods. Some of these systems continued to be used throughout the nineteenth century, alongside other, newly invented tuning systems.
In contrast, a system such as the twelve note equal temperament, developed in the eighteenth century and the most widely used tuning system in Western music today, does not prioritize the preservation of pure intonation. Instead, it proposes that an octave be divided into twelve equal semitones, avoiding the shocking wolf tone by slightly reducing all the intervals. However, this solution makes all intervals impure. Today, practically all Western instruments with fixed pitches are tuned using equal temperament.[2]
Figure 1. Excerpt from the project sketchbook by Reiko Yamada
In practice, absolute and true equal temperament[3]—or any system, for that matter—is technically unattainable. Circumstances preventing its achievement include the infinite variety of physical factors affecting an instrument’s sonic production, such as the quality of the air (temperature, humidity), and the distracting effect of timbre and harmonic contents on human perception. The notion of pure intonation, which the Pythagoreans championed as inspired by the purity of the soul or the movements of celestial bodies, no longer enjoys currency. Seeking to preserve historical tuning systems is no longer a matter of sacred beliefs or a search for a pure acoustic phenomenon, yet there is growing interest in historic Western temperament, particularly with the recent development of technologies such as user-friendly tuning apps.[4]
Far more than a strictly musical choice, this popular interest in alternatives to the relatively simple standard twelve-note equal temperament system seems to connect to a much broader postmodern phenomenon of questioning the basic assumptions underlying society, politics and the economic system under which we live. Factors far beyond musical aesthetics have been invoked as justification for the use of historical music systems; for some, their use signifies returning to a kind of natural order, whereas accepting equal temperament involves compromising ideals for practicality. For example, Terry Riley, discussing composer La Monte Young’s use of just intonation, states that Young’s work is “crafted in such an original profound manner as to make us feel that it is the product of a large unknown tradition, aged and mellowed over peaceful centuries of development and of whose shamanic wisdom he is the sole heir.”[5] Riley continues, “Here, for the first time in Western music, we experience the full-blown metaphysical archetypes of the Far East that infuse the high classicism of Bali, Java, India, and China, borne aloft on a separate ray, a genuine new breath of devotion […] this is truth”. In Harmonic Experience, musician and theorist W.A. Mathieu concludes that “pure harmony is hard-wired,” that “The forces that govern the production of overtones govern our ears also, and our ears’ responses.”[6]
* * *
The study of historical tuning systems in the West has traditionally been the domain of a small number of academics and enthusiasts. Most people in the field of music are content to ignore the issue entirely, assuming equal temperament as the standard tuning of the Western twelve-note chromatic scale. Yet among those who do pay attention to it, debates are strikingly heated. Within a relatively niche group of early music theorists and, particularly, interpreters and historians, heated discussions rage on issues ranging from the legitimacy of well-known scholarly works (such as those of Jorgensen)[7] to the theory and practice of applying various tuning systems to actual instruments.[8]
Until well into the nineteenth century, several tuning systems coexisted in various parts of Europe, their respective merits and drawbacks heatedly debated. Theorists and instrumental makers built keyboards with 19, 27, or 32 keys per octave with split keys, a movable keyboard, or between two and six rows of keyboards in order to preserve pure intervals. Some theorists and composers invented multiple tuning systems and used them for various instruments, sometimes adopting different systems for each composition. It was only after a lengthy struggle against strong ideological resistance that equal temperament gradually became accepted as the universal system. What supporters of equal temperament claimed, and what critics in turn feared, did indeed happen: human ears and minds adapted to the imperfect and impure intervals of modern-day equal temperament.
Composers are naturally quite attuned to these concerns and many have explored alternative tuning systems. Most of their interest in recent decades has centered around the use of microtonality based on equal temperament or non-Western systems. However, composers such as La Monte Young, Harry Partch, Lou Harrison and Wendy Carlos are known for working with alternative tuning systems, including historical Western ones.
Interestingly, a similar interest also animates an unexpected group of non-specialists. Among the new age and alternative music communities, some call for tuning instruments to A=432 Hz instead of the generally accepted reference frequency of A=440 Hz, claiming that this non-standard system has “healing” properties and that the standard system is part of a broader conspiracy against the people.[9] More relevant to the present article is the fact that proponents of this view show a growing interest in and appreciation for pure or just intonation.
Figure 2. Excerpt from the project sketchbook by Reiko Yamada
With the recent development of easy-to-use tuning apps, several historical tuning systems containing pure intonations, previously effectively reserved for practitioners of so-called Early music (repertoire from Medieval, Renaissance and sometimes Baroque periods), suddenly became fashionable among non-academic musicians. Whether or not the definition and execution of historical tuning systems in the context of the new tools is historically accurate—or even properly implemented—is another question. In this context, equal temperament represents a powerful metaphor of an ideal compromised for the sake of practicality.
* * *
Up until recently, I had mostly refrained from using alternative tuning systems, especially non-Western tuning systems, for one very simple reason: as an Asian composer, I wanted to avoid the cliché exoticism associated with non-Western tuning systems. I felt uncomfortable witnessing, over and over, the appropriation of Asian cultural traditions in various media in the West, the use of Asian tuning systems, such as those found in Japanese shakuhachi and gagaku music, by both European and Asian composers. Furthermore, as in many other Asian countries, Western music and the Western musical education system are now overwhelmingly dominant in Japan. Almost all my musical education was based on the Western music system. The desire to counteract the disconnection this creates is what drove me, in 2016, to start exploring and reconsidering my relationship to European music in a radical way by deconstructing its very foundation, its tuning systems, and to do so at a European music institution.
While I was an artist-in-residence at IEM (Institute for Electronic Music and Acoustics), I started a project at the Zentrum für Orgelforschung der Kunstuniversität Graz (Center for Organ Research at University of Music and Performing Arts, Graz). The Organ Institute hosts, among other instruments, organs, keyboard and digital organs equipped with the Haptwerk and DynTune systems.[10] The DynTune system is a tool that allows organ players to switch the tuning system in real-time using a foot pedal. One of the organs equipped with the DynTune system was a hybrid organ developed by the company Rodgers Organs using a technology that combines a pipe organ with a digital organ, incorporating sample sets of historic pipe organs and offering cutting-edge digital capabilities. This instrument can be connected to loudspeakers using 24.2 channels instead of only sounding through the organ pipes.
Moreover, as a fixed-pitch instrument often found in churches, the organ has always been a focus of discussion among music scholars, theologians, and philosophers as they debate the broader implications of pure intervals. In an instrument that allows tuning changes in real-time, therefore, I found nothing less than the perfect battleground on which conflicting ideas surrounding tuning systems could be implemented. Thus I began a journey into recognizing my uncomfortable, yet fitting relationship, given my long-standing interest in aesthetic imperfection, with historical tuning systems.
Figure 3. Excerpt from the project sketchbook by Reiko Yamada
The word “tuning” acquires new meanings when we move beyond the setup of musical instruments. In the study of soundscapes, particularly in R. Murray Schafer’s seminal book The Tuning of the World (1977), the term “tuning” refers not only to a specific adjustment of musical pitches but also, and more generally, to one’s attitude towards an overabundance of acoustic information. More specifically, whereas the verb to tune has traditionally meant “to adjust with respect to resonance at a particular frequency” and “to make more precise, intense, or effective,”[11] Schafer uses it instead in relation to his empirical method of soundwalking. The practice of soundwalking consists of exercises in hyper-attentive listening, in the sense of tuning into the world by classifying and selecting the sounds around us in a sensitive, discriminating way. When we think about constructing a tuning system, most of us imagine selecting and adding pitches in order to divide an octave. Schafer’s perspective on the sound world suggests tuning as a subtractive method, beginning with the acknowledgement of the ever-lingering presence of unselected frequencies in the background.
While performances that faithfully reproduce historical repertoire necessarily require attention to specific historical temperaments, as a new music composer, I am more interested in what historical tuning systems mean to us today. Indeed, my composition 1/12 of Comma for E-Organ Solo[12] recognizes the cacophony of the world by selecting a set of frequencies from historical tunings and, as these appear and disappear, using multi-channel spatialization to reveal new sets of pure perfect fifths. Keeping pure perfect fifths in temperaments such as just intonation always has the downside of creating incorrect intervals elsewhere. This particular composition, being full of pure perfect fifths, therefore reveals those unavoidable discrepancies. The constant, clustered cacophony that this produces, fading in and out, reminds the audience that an unlimited number of other frequencies are always present in the background.
Just as the debate over temperament has historically been about more than just musical aesthetics, this composition is not only about musical notes. The piece is a stand against prioritizing one system over all others, and exhibits the messiness of the balancing act between the practical and the ideological that arose with the development of temperament. Much as it may look, on the surface, as though these debates have been resolved by settling on the twelve-note equal temperament system, anyone who learns even a little about temperament is struck by the fact that a problem such as preserving the simple ratios from natural overtones (which many would consider extremely important) has never really been resolved. 1/12 of Comma for E-Organ Solo explores the struggle to select one compromised system over another, leaving the messy consequences of such a choice on full display to the audience. After all, the debates about temperament seem to be an effort to bring order to a muddled world. With this piece, I reject the imperative that insists on solving an unsolvable problem by imposing a single system, rather than presenting several possibilities that simply take turns.
Figure 4. Aleksey Vylegzhanin performing 1/12 of Comma for E-Organ Solo June 6, 2018 at Orgelfrühling Steiermark ©Fabian Czernovsky
The story of historical tuning systems is the story of our struggle to accept imperfection. The very notion of organizing sounds into tuning systems was a losing battle from the beginning, as a scale formed entirely of pure intervals cannot be contained within the space of an octave. In their search for a solution, music scholars and instrument makers have tried countless variations of temperaments, modified instruments, and produced philosophical and psychoacoustical explanations only to end up abandoning all perfect natural proportions (ratios) in favor of today’s equal temperament. We know that equal temperament has proven its practicality and set the stage for the development of a sophisticated musical repertoire and the ensemble performances we now enjoy. The adjustments are small enough that their effects are as subtle as those of fluctuating temperature and humidity or tuning techniques, yet discussions about temperament are frequently met with uneasiness, and disagreements on this topic quickly flare up. In that respect, responses to this subject echo responses to other life situations where we have selected the most practical from among a series of fundamentally imperfect options, and made the chosen solution so ubiquitous that our senses have become used to it and we have forgotten all other possible choices.
In my composition 524288=531441 for Violin and E-Organ[13], I wanted to confront the uneasiness and insecurities associated with this topic. Obviously, in musical performance, we typically consider uneasiness and insecurity to be the opposite of what one expects from a good performance. Without the courage and open-mindedness of my collaborators, violinist Barbara Lüneburg and organist Aleksey Vylegzhanin, the project would not have been possible. In this work, the tuning of an organ, traditionally an instrument of fixed tuning, is made “unfixed” via the use of the DynTune pedal. The score is written in such a manner that the two instrumentalists are constantly in and out of tune with each other, making the performers genuinely insecure and forcing them to struggle with tuning on stage. For the organ part, I used Pythagorean and meantone 1/4 syntonic comma[14], combined with the traditional rules of functional harmony to create an environment where perfection and imperfection coexist.
The score excerpt (fig. 5) shows a four-voice chorale-like texture following an otherwise simple constant harmonic progression. However, a change in the tuning triggered by the tuning pedal introduces a complex recurring transformation.
Figure 5. Excerpt of the organ part from the score 524288=531441 for Violin and E-Organ by Reiko Yamada
While the relationship between the four organ “voices” is vertically consistent, the organist provides an irregular and subtle series of changes by adopting varying tempo and an imprecise live operation of the pedal. The result is a mixture of pre-programmed multi-part superimpositions constantly changing in relation to each other, with the organist’s musical judgment (through timing changes) coming into play in real time. This process forces the other musician, a violinist, to constantly adjust her intonation in front of the audience.
Figure 6. Excerpt from the project sketchbook. by Reiko Yamada.
Essentially, I aimed to create something similar to the effect of sawari, a noise maker built into certain Japanese instruments, delicately adjusted to create a flawed effect following the traditional aesthetic concept of imperfection. However, I also wanted to remain entirely within the Western music vocabulary, without copying Japanese practices. Rather than creating this effect within a single instrument, I implemented it within the relationship between two instruments on stage. The organist moves between just intonation and meantone tuning (using the new MIDI tools) and the violinist tries constantly to be in tune with the organ. This is not, in other words, the expression of a Japanese alternative to Western models, but rather an exploration of Western music’s own internal problems, using parallels with Japanese principles, to create new aesthetic effects.
* * *
Figure 7. Excerpt from the project sketchbook by Reiko Yamada
Tempering pitched instruments and, in turn, ensembles, forces us to determine what our priorities are when we use sounds. In this world full of nuance, perhaps one way to approach this is to try deselecting the default option and continuing to explore the issue while recognizing its unsolvable nature. Deciding to upset the established order to revisit our priorities and alternatives could help us acknowledge the richness of the nuanced world, and to accept our imperfect capabilities.
I recognize that all my research and creation during my residence at a European research institute were made possible by the advancest of modern digital technologies. Only in this environment, where resources are abundant, and I was far from my homeland, was it possible for me to come to terms with the delicate and complex issues of comfort and discomfort, perfection and imperfection, and to mirror my discomfort by making a compromise with the solution of equal temperament (itself a compromise) in order to search for my own solutions to this quandary. Only then was I able to advocate for non-Western approaches to the Western historical tuning system.
Figure 8. Excerpt from the project sketchbook. by Reiko Yamada
In conclusion, I present another example of a radical solution to the issue of temperament in 7:8 for performer and fixed media.[15] The work, full of samples from various organ sources in a variety of tunings, was put together as a fixed media work, thereby entirely avoiding the limitations intrinsic to acoustic fixed-pitch instruments as well as the problem of ensemble playing with multiple players in multiple tuning systems. Both the performer’s movements and the musical motifs are inspired by the mechanics of the organ. However, the performer never “plays” the organ but instead evokes through their movements the ever-imperfect adjustments of the organ’s mechanics to temperaments as compromised, imperfect solutions to an unsolvable problem. This collaborative creation strives to find as yet unnamed connections in the subtle intermedia between the sounds and movements in the organ space, and to suggest a radical role for the performer in this context. To find a way out of the unsolvable problem of temperament might require rethinking and reframing some unquestioned standards of the musical performance tradition, perhaps going as far as to reimagine the very role of the musical performer.
Figure 9. Co-creator and performance artist Christina Lederhaas during the premiere of 7:8 for performer and fixed media. June 6, 2018 at Orgelfrühling Steiermark ©Fabian Czernovsky.
Acknowledgements
The author would like to thank Nicolas Trepanier, Brian Cherney, Wendy Gan, Marko Ciciliani and Barbara Lüneburg for valuable discussions and suggestions on the manuscript, as well as the Rainbow Coalition at Radcliffe and Antoine Reserbat-Plantey for the inspiration to write this text. Special thanks to the editor, Alejandra Cardenas, the proofreader, Kirstin Cameron and the team at Radical Sounds of Latin America, without whose assistance and keen insights, this article would not have been possible. The author is supported by ICFO (Institute for Photonic Sciences) and the artistic research described in this article was supported by St.A.i.R. (Styria Artist in Residence Scholarship).
[1] To put it simply, while just intonation seeks to maintain the purity of the fifths, meantone tunings narrow the fifths in order to maintain the purity of the common thirds.
[2] A “fixed-pitch” instrument refers to an instrument on which the pitches are prepared beforehand and cannot be altered in the moment (i.e., piano, guitar) unlike, for example, the human voice or the violin.
[3] A temperament is a tuning system that compromises on pure intervals to accommodate other musical requirements, such as the capacity to modulate to multiple keys.
[4] Popular tuning apps such as Airyware Tuner, APTuner, and Cleartune have come to include presets of dozens of historical tuning systems in recent years.
[5] In the liner notes of “The Well-Tuned Piano” by La Monte Young (1987).
[6] Mathieu, William Allaudin. 1997. Harmonic experience: Tonal harmony from its natural origins to its modern expression. Simon and Schuster.
[7] Jorgensen, Owen H. 1991. Tuning: containing the perfection of eighteenth-century temperament, the lost art of nineteenth-century temperament, and the science of equal temperament, complete with instructions for aural and electronic tuning. Vol. 4. East Lansing, MI: Michigan State University Press. Some scholars have criticized Jorgensen for the limited sources and his eccentric terminology used.
[8] There are several journals and online communities dedicated to discussions on tuning theory, composition, instrument building, software development and information about tuning-related events around the world, such as Xenharmonikon: An Informal Journal of Experimental Music (Frog Peak Music) and 1/1 The Journal of the Just Intonation Network (the officers of Other Music, Inc., 1985-2007). In academic journals such as Early Music (Oxford University Press), temperament and tuning systems are recurring subjects.
[9] Leonard G. Horowitz provides a good example of such conspiracy theory: “The monopolization of the music industry features this imposed frequency that is ‘herding’ populations into greater aggression, psychosocial agitation, and emotional distress predisposing people to physical illnesses and financial impositions profiting the agents, agencies, and companies engaged in the monopoly. Alternatively, the most natural, instinctively attractive, A=444Hz (C5=528Hz) frequency that is most vividly displayed botanically has been suppressed. That is, the ‘good vibrations’ that the plant kingdom obviously broadcasts in its greenish-yellow display, remedial to emotional distress, social aggression, and more, has been musically censored.” ( Horowitz, Leonard G. 2015. “Musical Cult Control: The Rockefeller Foundation’s War on Consciousness Through the Imposition of A=440Hz Standard Tuning” in Medical Veritas 7.
[10] DynTune, developed by Jan Ročnik, allows performers to make real-time modifications of organ temperament using a foot pedal.
[11] Merriam-Webster, s.v. “tune (v.),” accessed June 14, 2021 https://www.merriam-webster.com/dictionary/tune.
[12] The title, “1/12 of Comma” refers to the resulting distance between pure intonation and the equal temperament in the interval of a perfect fifth.
[13] The numbers 524288 and 531441 together refer to the Pythagorean comma, one of the discrepancies in pure intonation tuning.
[14] Pythagorean tuning makes all the fifths perfectly consonant, and as a result, all the major thirds and major sixths are too wide. In quarter-comma meantone system, the perfect fifth is flattened by one quarter of a syntonic comma in order to obtain justly intoned major thirds.
[15] The simple acoustic ratio of 7:8 falls in-between major second and minor third, unable to fit in the conventional Western twelve-note tuning system.
References
Carlos, Wendy. 1987. “Tuning: At the Crossroads.” Computer Music Journal 11, no. 1: 29-43. Accessed June 23, 2021. https://doi.org/10.2307/3680176.
Isacoff, Stuart. 2009. Temperament: How music became a battleground for the great minds of Western civilization. New York: Random House, Inc.
Schafer, R. Murray. 1977. The Tuning of the World. New York: A.A. Knopf.
Reiko Yamada is a composer and sound artist, originally from Hiroshima, Japan. She composes concert works, creates sound art installations, and works with interdisciplinary collaborators. Her work explores the aesthetic concept of imperfection in a variety of contexts. Yamada holds a D.Mus. in composition from McGill University and is a recipient of numerous prestigious awards and fellowships including a Fellowship at the Radcliffe Institute for Advanced Study of Harvard University in 2016-16. She is currently a postdoctoral researcher at ICFO (Institute for Photonic Sciences) and composer-in-residence at the Phonos Foundation in Barcelona.