Temperament and music

The temperament and tuning of electronic musical instruments is a subject that receives relatively little attention. Most of the synthesizers on the market today do not allow precise tuning of each note. When these synthesizers have a keyboard, they generally adopt a traditional design of the sort that can be found on most instruments of the same family (e.g. piano, organ), and use equal temperament as a general rule.

In equal temperament, the octave is divided into 12 equidistant tones. What notably results from this mathematical division is friction when playing a root note and a fifth together, or when playing a root and a major third together. With equal temperament, the fifth is not pure—it is exactly 1.96 cents away from purity. As 1.96 is a low value, it does not turn the combination of such notes into a result that sounds wrong. On the other hand, when it comes to the major third, the discrepancy is much more marked (+13.69 hundredths) and produces a clearly distinguishable effect to the trained ear. This may also be why, compared to the major triad, the minor triad was perceived as more stable and was so popular during the Romantic period. While the diff

La découverte des proportions musicales par Pythagore selon Franchino Gaffurio, From the collection of: Swiss Museum & Center for Electronic Music Instruments (SMEM)
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However, the abstract beauty of simple ratios producing consonances soon collided with a physical reality: polyphony and the crafting of string instruments. In monody, the singer can seek perfection by moving to the fifth or third at any time, since the notes follow on from one another. In musical instrument making, the fortepiano, or its successor, the grand piano, represents a typical example of the problems raised by temperament. A piano can be tuned, but what temperament should be chosen? While a number of different temperaments have co-existed in the history of keyboard instrument making, it is indisputably the equal temperament clavier that prevailed. One of the main reasons for this is its flexibility. While a well-tempered clavier can perform miracles in some keys, the same tuning can be disastrous in others. For this reason, a clavier intended for flexible usage needs to be a clavier with equal temperament. 

While musical instrument making tended toward the use of this model from the late 17th century and imposed it almost universally during the 18th century, some avant-garde composers in the 20th century sought to distance themselves from it. For example, in his piece, The Well-Tuned Piano La Monte Young tuned a grand piano using principles from a just intonation system. This system is notable for allowing him to play a pure fifth (3/2). In his system, while some intervals tend toward purity, others move away from it—as is the case with the major third. Other great temperament trailblazers can be found in the realm of microtonal music, where all kinds of temperament are used—equal or otherwise. The story of how a split in temperament emerged in the West (post-antiquity) often includes Debussy's discovery of Javanese music at the Exposition Universelle in Paris in 1889 (as a result of which he wrote Pagodes, using a pentatonic key). Although that particular case didn't involve a new temperament, the discovery of new systems for dividing the octave opened a door for others to walk through. During the 20th century, a number of composers continued to dig away at this infinity of intervals—including Harry Partch and Adriaan Fokker, to name but a few.

Apart from some isolated figures, equal temperament remained omnipresent in 20th century music. It is worth remembering that equal temperament is a compromise that attempts to reconcile acoustics (the physics of sound), mathematics, and the process of making musical instruments. 

But when it comes to synthesizers, what options do users have for creating music in alternative temperaments? As a general rule, the answer is simple: very little. That said, the early years of synthesizer production got off to a good start. Several synthesizers from the early 20th century allowed users to control the pitch of notes. The theremin is not limited only to certain notes (and therefore certain temperaments), and the same can be said of the ondes Martenot when the instrument is played using its ring. Meanwhile, the trautonium has a controller that allows musicians to vary the pitch of a note just using their fingers, without any mechanical constraint. The first modular instruments, such as the Buchla 100, didn’t restrict users’ choice of pitch either. All these instruments have something in common: they either had no keyboard, or they had an additional system for selecting the pitch. While Robert Moog was not the first person to build a synthesizer with a keyboard, he was the first to successfully put one into mass production, with his Moog Minimoog Model D in 1970. The rest is history. Numerous brands and models later, the keyboard still reigns supreme among the various types of synthesizer available. According to Bruno Spoerri (in his smem talk), Robert Moog was fully aware of the limitations of this method of control, and for the rest of his life he continued trying to change or replace the keyboard, but did not succeed. It is clear that adding a keyboard to synthesizers diminishes them, because the instrument’s wonderful ability to control values continuously is then turned into a discrete system. The 1970s, 80s, and 90s saw little in the way of innovation by manufacturers regarding the options for controlling their instruments. Instead, they focused on developing digital synthesizers, MIDI, and user-friendliness.

Thomas Bloch Ondes Martenot 

Fortunately for people who like to experiment with microtonal sound, change is afoot. In terms of hardware, the limitations of equal temperament can now be bypassed completely thanks to the outstanding instrument known as the Haken Continuum. This instrument does not have a keyboard, but rather a continuous surface that detects all changes of position and pressure. A digital synthesizer, the Haken Continuum comes with the EaganMatrix Sound Engine, a software program that allows all these movements to be interpreted. The Haken Continuum reuses a principle that was already employed in the Trautonium in the early 20th century, but considerably expands on its possibilities to create an instrument that lives up to contemporary standards. The Doepfer Ribbon Controller is another instrument that allows this kind of control, but in an extremely basic way; the Doepfer model does not produce any sound by itself, and functions solely as a controller. 

Haken Continuum Fingerboard, From the collection of: Swiss Museum & Center for Electronic Music Instruments (SMEM)
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Some manufacturers have opted for a different approach, seeking to expand the possibilities offered by a traditional keyboard. The best-known controller, the Seaboard, is produced by Roli (which is also the developer of the Juce platform). Its keyboard is a soft version of a traditional keyboard. The keys haven't disappeared, they're just less pronounced.The instrument also has an area that you can use to play a glissando. A recent arrival, Expressive E, the manufacturer of the Touché controller, is currently developing the Osmose keyboard. The Osmose also uses some of the possibilities offered by the Seabord, but in the form of a traditional keyboard. However, these instruments cannot be put in the same category as the Haken Continuum. They don't try to offer significant microtonal possibilities, but rather to provide additional means of expression. Modular synthesizers also allow a more flexible use of pitch. However, when it comes to setting the rules for this, the options are few and far between: you have to use either a quantizer or a microtonal-friendly sequencer. Fortunately, Tubbutec recently developed a tool that fills this gap: the µTune module, which is a quantizer dedicated to microtonal music.

Expressive E - Osmose, From the collection of: Swiss Museum & Center for Electronic Music Instruments (SMEM)
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In terms of software, there is one application that allows you to do pretty much anything: the Scala. With this software, you can prepare your own temperaments for use with either hardware or software synthesizers. Unfortunately though, few existing synthesizers support this standard as yet. There are developers that incorporate this possibility into all their instruments, such as U-He and TAL, for example. However, this system does not resolve the controller problem for people who want to play using their hands, so a suitable controller is still needed.

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Some iPad apps allow you to use certain microtonal standards. For aficionados of special temperaments, downloading the Wilsonic app is a must. This tool allows users to create their own temperaments through different mathematical models. They can then be used in a variety of apps, like AudioKit Synth One, for example.

All in all, the possibility to modify a synthesizer's temperament is of limited interest to manufacturers and developers. That's because the number of users interested in these possibilities is minimal, too. It's a shame, because microtonal music allows you to unlearn what you've learned. It forces musicians to listen to the friction that exists between two notes, or between two frequencies, and decide whether they sound well together. Personally, having learned the piano as a child and then rubbed away on instruments without a predetermined scale, I find it striking just how much most young musicians don't listen (just as I also didn't listen)—instead, a piano's keys are pretty much seen as switches whose pressure is guided by the score. It seems to me that we need to rediscover harmony through experience, and microtonal instruments are an excellent tool for doing just that.

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