Groven ex machina: The Evolving Technology of Tuning
- Side: 44-56
- Publisert på Idunn: 2004-05-14
- Publisert: 2003-05-14
It is seventy-five years since Eivind Groven wrote his thesis Naturskalaen (The Natural Scale), and first set forth the goal of creating a keyboard instrument capable of playing all possible scales - from idiomatic folk music scales to extended just intonation. Pursuit of this goal led him to experiment with both piano and organ and eventually to the development of his famous renstemte (or pure-tuned) organ. It is ironic, even contradictory, that this supposedly 'natural' instrument would need such sophisticated use of technology to imitate the simple scale of the seljefløyte. However, it was not the desire to imitate just one scale that constantly pushed Groven to the cutting edge of technology and music, it has always been possible to tune a piano or an organ to a particular scale. What Groven sought was an adaptive instrument-an automatic tuning machine capable of switching effortlessly back and forth between a multiplicity of scales. Groven and others wrote a great deal about the tuning systems and scales themselves (see for example Groven, 1948, 1968; and Code, 2001), so in the present article I trace the development of the tuning device, Groven's "renstemningsautomat", through four stages of technology: from his early experiments with piano in the 1920s, through switchboards and circuitry, to the computerized upgrade taking place today by NoTAM (Norwegian Network for Technology, Acoustics, and Music).
Version 1.0: piano prototype
In 1929, two years after the publication of Naturskalaen, Groven received a grand piano from a generous benefactor, Anders Backer Grøndahl. The gift was intended for experimental
use in developing an ideal piano capable of playing in pure tuning, or just intonation, in every key. Within a year, Groven demonstrated to Grøndahl and a colleague, O. M. Sandvik, that his prototype for an electronic mechanism was capable of automatically retuning a piano string at the touch of a button. Grøndahl found the invention extremely interesting, but added that it would be expensive to implement. In the following years, Groven sought and received patents in America, England, Germany and France and made contact with numerous piano manufacturers in the hope of capturing their interest in his project.
The problem Groven set about to tackle in 1929 was centuries old. Keyboard tuning is a compromise arising from the intersection of multiple (often opposing) influences: acoustic ideals, musical goals and physical constraints (to name three). The primary physical constraint is that every pitch must have its own key - its own button. In contrast to a violin or the human voice, for example, a piano must have a finite number of pitches. And specifically how limited this needs to be is closely related to a simple practical matter: the number of fingers on our hands. Too many buttons makes it unwieldy to play. Attempts to produce keyboards with a large number of keys required performers willing to learn a new, sometimes awkward, playing technique, and thus never gained widespread popularity. If the number of buttons is limited, however, a choice has to be made in relation to which pitches to include and which to leave out depending on the requirements of the music. Historically, there has been a balancing act between wanting to have acoustically pure triads and needing to be able to play in any particular key. Using a standard keyboard, however, any fixed tuning in just intonation (i.e. with pure chords) is essentially limited to one tonality. In other words, when there are only twelve pitches with which to work and the primary triads of one key are made acoustically pure most other keys become unusable. To accommodate this, one must either retune the instrument for each new key or temper (i.e. adjust) the pure intervals to minimize the number of unusable ones. Although the former was at one time common performance practice, it was time-consuming and precluded the use of multiple tonalities within the same piece (or even the same concert).
As such, tempering became the more commonly employed practice. Tempering provides a wider range of available keys, but at the expense of the purity of the intervals. The first temperaments were unequal, and some of the intervals were still acoustically pure. The goal was to render each key usable, but not necessarily identical. In the standard used today, 12-tone equal temperament (12-ET), all keys are identical: none of the triads are acoustically pure, but neither are they so far out-of-tune as to be unusable. It is a common misconception that 12-ET is the best solution for keyboard tunings because it is the most recent. The fact is that 12-ET is not better (nor the most recent); it simply maximizes certain musical characteristics at the expense of others.
In his attempt to balance the equation, Groven refused to sacrifice the purity of intervals. He did not want the pianist to have to learn a new playing technique, so he rejected
both tempering and expanding the number of notes on the keyboard as options. He was left with only one variable: retuning. He needed to decrease the time it took to retune the strings enough to make it a viable alternative during performance. This was a technological problem. In the same year that he received Grøndahl's gift of the piano, Groven began collaborating with technicians such as Jon Chr. Skeie at the Institute for Physics in Oslo to develop a mechanical solution. They first measured the amount of force required to increase and decrease the tension of a piano string by a specified amount. Next they experimented with different types of levers capable of redistributing this force to minimize the effort required. They settled on the lever shown in Figure 1, with two arms attached to the fulcrum, or pivot point (labelled 4), perpendicular to one another: one very long (5), the other very short (3). (This figure is adapted from a drawing included in Groven's patent.)
Figure 1. Retuning lever.
In this design, one end of a piano string is anchored down (2), while the other end is fastened to the short arm of the lev
The movement of the long arm is controlled by a rotatable electromagnetic wheel. The lever is connected by means of a link to the rotating core, which in turn is attached to an arc by a radial arm. The wheel can rotate (within a range of about 60 degrees) by means of an electric current to specific contact points, at which time a "brake" locks the wheel in place. The effect of this elaborate device is that the tension of the piano string can be automatically adjusted to any of four discrete settings. Theoretically, the spacing between the contact pins would be calculated to produce four precise and repeatable tunings of the string within a range of about plus or minus 1/8th of a half-step, or plus or minus 16.5 millioctaves (or 20 cents). (Note: The millioctave is a unit of measurement for pitch intervals: an octave equals 1000 millioctaves; an equal-tempered half-step equals ca. 83 mo.)
On Groven's proposed piano, each string would have its own specially calibrated retuning mechanism with at least three settings, possibly as many as five. These would be placed in a sound-insulated chamber above the strings (see Figure 2).
Figure 2. Overhead view of proposed piano.
The levers would be mounted on the piano frame at the front end of the instrument. It is unclear from either his description or his sketches how (or if) he intended to include the normal tuning pins. Since the retuning device is only a fine tuner, the normal tuning pins would still be required for installing and setting the base tuning for the strings. If the levers were in front, it looks as if the tuning pegs would have to be moved to the back. This, of course, would make it virtually impossible for one person alone to tune the piano.
The electronic retuning mechanisms, however, were to be controlled by a second keyboard manual, about 2 octaves in length, within easy reach of the performer. In some sketches this retuning keyboard is placed in front of the playing manual (as in Figure 2), while in other sketches the reverse is the case. The performer does not select a setting for each string individually (which could require a bank of over 400 retuning keys), but rather selects from one of 23 preset tonalities. In other words, pressing a single retuning key sends an electric current to an appropriate contact pin on every string. The retuning key for D, for example, would not only set the tuning for D in every octave, but all of the other scale degrees as well, in relation to D as the base. In his patent, Groven does not elaborate on the particular tunings that would be assigned to each of the 23 presets. Based on the indications of his theoretical work as whole, I believe that he planned to include some presets in historical just scales (with parallel majors and minors combined) and some based on specialized scales found in Norwegian folk music.
With Groven's design one could switch the tuning of the entire piano automatically and virtually instantly. The press of a single button would set in motion 88 levers pushing
or pulling on the strings by exact amounts in various combinations. In theory, the change of tuning could even be in the middle of a piece modulating from one key to the next. In practice, however, Groven's proposal was not without its problems. Even the demonstration of the prototype for Grøndahl and Sandvik in 1930 was only a partial success. It didn't move fast enough because of both friction and insufficiently high voltage. Perhaps more alarmingly, the electromagnet gave off sparks, making it a fire hazard. Nevertheless, everyone in attendance felt that, in spite of these "minor" technical glitches (such as the possibility of burning the piano down), Groven had, at least in principle, solved the problem.
However, while Groven may have succeeded in inventing a device which could deliver a specified level of force with precision, there was no guarantee that the effect of this force on the tension of a piano string would result in precise and predictable tuning. The notion that tightening a string by 'x' amount would raise the pitch of the string by exactly 'y' cents every time is implausible. Real-life strings are extremely temperamental (no pun intended). Their tuning can be altered merely by changes in the temperature or humidity of the room. The response of a string also changes with age. Moreover, a string takes time to adjust to a new level of tension. The rapid and fairly significant changes in tension performed by Groven's retuning device would probably make the string unstable and incapable of holding the new tuning. According to piano technician George Booth (1996, 124), "[raising] the pitch of an instrument by just one hertz is enough to destabilize [it]." A string on Groven's piano could be altered by as much as 10 Hz.
Additionally, in order for the pitch to remain stable, the amount of tension had to be equalized. When the pitch of a string is raised, the part of the string nearest the side at which the tightening takes place will carry more tension than the rest of the string. When the string is subsequently played (i.e. struck by the hammer), this increased tension will be redistributed and the string will be even sharper. This can recur each time the note is played until the tension is finally equalized across the entire length of the string. The converse occurs when the pitch is lowered. In order to set the string (i.e. firm the pitch), a piano tuner will play the note loudly and repeatedly while turning the tuning pin, thereby equalizing the tension. This practice would, of course, be musically unacceptable if one were attempting to retune in the middle of a piece (even if it were physically possible for the pianist to repeatedly strike all 88 keys simultaneously). Failing to set the strings, however, would likewise compromise the performance by leaving the strings out-of-tune.
Groven would have been aware of the physical problems inherent in tuning piano strings described above. According to his memoirs (1971), he tuned pianos on various occasions and thus must have experienced the difficulties first hand. Furthermore, his primary instrument, the hardingfele, is notorious for its instability of pitch: usually each string must be tuned more than once, because it is common for one string to be out-of-tune as a result of tuning another string. Although Groven does not write about it, the
unreliability in retuning strings must have been a major concern of piano manufacturers and a fundamental reason for Groven's eventual abandonment of his piano project. His final word on the matter was simply that "it did not lead to any results." (1971, 60)
Version 2.0: Telephonic organ
In leaving the piano behind, however, Groven did not give up on his quest toward the ideal keyboard instrument. He shifted his attention instead to accomplishing the task with the organ. Rather than attempting to vary the tuning of an organ pipe in real-time through the use of some sliding extension, Groven opted to triple the number of pipes to 36 tones per octave. He sites as a precedent John Haywood Compton's 1933 British patent, which describes a 24-tone 'enharmonic' organ with a second set of equal-tempered pitches 11 mo. (14 cents) below the first which could be inserted when necessary to produce more favourably tuned thirds and sixths. In Groven's organ, there are three variants of each pitch (e.g. 3 C's, 3 C#'s, 3 D's etc.) each tuned approximately 1/8th of a half-step apart. At any given time, only one variant of each note is actually connected to the organ manual, so Groven still maintained the standard 12-note keyboard on which the organist could play. Similar to his piano design, the performer can manually select which pipes (i.e. tuning) to use from a control box next to the keyboard. In addition, however, Groven developed an ingenious device that allowed the tuning to be switched automatically during performance - 'on the fly' as it were - without requiring any additional tasks for the organist.
At first, Groven dismissed the idea of a self-tuning organ as merely wishful thinking. Then one night in 1939 he describes the following moment of inspiration:
"I woke up in the middle of the night at 2 o'clock. It was a light summer night. I felt so clear-headed it was as if the sun shone straight into the folds of my brain, and suddenly there stood the answer crystal clear before me: the keys could do the job themselves! ... like dialing a number on a telephone."
Groven's 'Eureka!' was to use automatic telephone switchboard relays to connect the organ manual to the pipes. Needless to say, this was a highly innovative application of what, at the time, was new technology. He actually enrolled in a course at the telephone company to learn how to solder the relays and was able to obtain some used switchboard equipment to make his device, the renstemnings automat, or the pure-tuning automaton (see Figure 3).
Figure 3. Groven soldering relays in the renstemnings automat.
The original version required over 300 separate relays. With the automaton, however, playing the organ manual was literally like placing a telephone call to the pipes. A C major triad, for example, would be routed by the switchboard to the particular pipes needed to produce a purely tuned chord. A subsequent F minor triad would be a new 'telephone number' and might require a different set of pipes to be connected. All dialling and switching took place in real-time without any appreciable delay in the performance. Not only did the tuning of the organ change depending on what was being played, the automaton took into account what had already been played. In other words, a C major chord wasn't always tuned the same way, but was dependent on the musical context. The music that preceded a given chord acted as a kind of area code which had the effect of routing the same telephone number to different geographic locations.
Delayed by the German occupation of Norway during World War II, Groven finally completed the automatic tuning device in 1947. The pipe organ was completed in 1953, when it was installed in the Trinity Church in downtown Oslo (as a second organ). It was here, one year later, that the little organ received its most prominent visitor, Albert Schweitzer, who was in Oslo to receive the Nobel Peace Prize. Taking ill, he was forced to cancel all his engagements except the award ceremony and a visit to Groven's organ. Upon playing it, Schweitzer proclaimed it the fulfilment of a lifetime dream and said to Groven: "This is science - You make the wine, and I drink it."
Version 3.0: Transition to transistors
In the 1960s, Groven carried his work forward into the age of solid-state electronics. Along with Ragnar Bogstad, he built an electronic organ-the first in Norway-completed in 1965. This instrument had the advantage of producing 33 different timbres, including specialized imitations of folk instruments like the seljefløyte. (The acoustic pipe organ had only one voice.) In addition, the electronic organ utilized a 43-tone scale and newly built renstemnings automat. The closet of telephone switchboard relays was replaced with a considerably smaller version of the automaton using electronic transistors built by Bjørn Raad at the Central Institute for Industrial Research, Oslo, Norway. The logic for these circuit boards was based on the schematics of the original switchboard relays and is detailed in Groven's book, Renstemningsautomaten, published in 1968. While Groven's book comprehensively describes his adaptive tuning system, it was not identical to the final version of the physical renstemnings automat. In reality, there was no final version. Groven continued to rethink and revise his musical system of dynamic tuning, each change necessitating a modification to Raad's transistor device. Prior to his death in 1977, Groven left designs for yet another, more streamlined tuning schematic which was never implemented. Throughout his life, Groven's musical experimentation continued alongside his technological developments.
The pipe organ was eventually moved to its present location, the Organ House, on Groven's estate in Ekeberg (on the outskirts of Oslo). Both the pipe organ and a newer electronic organ were connected to Raad's transistor automaton and were still used frequently for performances and recordings over a decade after Groven's death. The 'new' renstemnings automat eventually began to show signs of age. Although the organ could still be played by replacing the pipes with the manual control box, the real-time tuning feature was no longer fully functional. This problem became particularly worrisome in the late 1990s as preparations were underway to commemorate Groven's centennial year in 2001. While there were numerous other Groven accomplishments to commemorate, the celebrations would be incomplete without the inclusion of his pure-tuned organ. It was determined, however, that the organ needed to be repaired, refurbished, or entirely rebuilt, but there was neither the time nor the funds to accomplish this before the centennial.
Version 4.0: Software upgrade
The solution presented itself with yet another transference of technology, this time to computers. Beginning in the 1980s, interest in Groven's work led to the development of computer programs which simulated aspects of his renstemnings automat. Written by Jørn Arvidsen (1982) and Lars Frandsen (1995), these programs were not intended for real-time performance. However, Knut-Einar Skaarberg (1995) adapted Groven's tuning logic into a program which controlled the MIDI pitch-bend function of an electronic
synthesizer in performance (with polyphonic textures using multiple MIDI channels). Following their lead, I began working on a similar program for use with a network of specially-tuned Yamaha Disklavier pianos. This has come to be called the Groven Piano. At the time, I knew nothing of Groven's early experiments with the piano; my intention was to create a substitute for the organ for use in the centennial commemorations.
The Groven piano comprises a network of three acoustic pianos, a control keyboard and a computer interface running the tuning software, called Groven.Max. As with Groven's organ, the pianist plays on a standard keyboard which, instead of producing a sound, sends a MIDI signal to Groven.Max. MIDI, or Musical Instrument Digital Interface, is a protocol for exchanging musical information between electronic instruments and computers. The Disklavier series are acoustic pianos equipped with internal mechanisms that operate the keys and hammers in response to a MIDI signal. The control keyboard (the instrument which the pianist actually plays upon) does not produce a sound, but instead sends a MIDI signal to the computer with the exact timing and dynamics of each note played. This signal is analysed by the computer program and rerouted to the three acoustic pianos in accordance with the desired tuning. These three pianos - designated Blå, Gul and Rød - replicate the actions of the performer with virtually no perceptible delay. The pianos, donated for the premiere by Yamaha Scandinavia, were each tuned differently, thus providing 36 strings per octave to match the organ's 36 pipes. Thus, unlike Skaarberg's program, Groven.Max does not send pitch-bend or system exclusive commands to retune the instruments dynamically, but simply reroutes the MIDI signal for each note played to the piano with the desired tuning for that pitch (similar in function to Groven's renstemnings automat). The premiere took place on 19 April 2001 at Norges musikkhøgskole in Oslo, Norway with support from Yamaha Scandinavia, Norsk Kulturråd, the Eivind Groven Institute for Just Intonation, the US-Norway Fulbright Foundation and the University of Oslo. Photographs and soundclips of the premiere can be found at http://www.wmich.edu/mus-theo/groven. The North American premiere of the Groven Piano took place in 2002 at the Irving S. Gilmore International Keyboard Festival in Kalamazoo, Michigan with instruments on loan from Yamaha USA.
Following the success of the Groven Piano, my attention returned to Groven's retuned organ. Rather than attempt to repair the almost 40-year-old transistor device, it was time for another technological upgrade. A project was undertaken along with NoTAM (the Norwegian Network for Technology, Acoustics and Music) to replace the old electronic interface with a computer-operated system. Henrik Gunnar Sundt from NoTAM has been chiefly responsible for constructing the hardware, while I look after the software side of things. The electronic relays for each individual organ pipe have been reconnected to a custom-made MIDI-controlled device, which is now connected to a Mac computer running a modified version of my Groven.Max software. Groven's original
custom-made organ manual has been replaced by a Kurzweil synthesizer for the control keyboard.
The software user-interface (shown in Figure 4) preserves all the functions of Groven's previous control box in addition to many new features.
Figure 4. Control panel for the new pipe organ interface.
On the left-hand side of the screen there is a pitch-box displaying the current tuning of the organ. When a button is highlighted, all octave registers for that pitch-class are output to the corresponding tuning variant. Individual pitches are selected by clicking on a pitch button in the blue, gold or red shaded regions of the pitch-box (i.e. the 12 upper, 12 middle or 12 lower pitch buttons, respectively). Additional preset scales are available from the pull-down menu at the upper-right corner of the pitch-box. This feature is similar to the semi-automatic system proposed in Groven's original piano patent. Most of the current presets are tunings used for specific compositions and arrangements of Norwegian folk music. The 'Auto-tune' button is clicked to engage the real-time tuning function. When auto-tune is first engaged, the default settings are shown underneath (pitch-field 3, standard size), and a default C-just scale is set in the pitch-box. The pitch-field or size can be changed using the pull-down menus or the alternative set of 'orgel knapper' which replicate the old control box. (For a detailed musical explanation of these automatic tuning functions, see Groven, 1968 or Code, 2002.)
The new software-based control does much more than merely replicate the actions of Groven's original hardware. A one-octave display keyboard in the middle of the control panel monitors the incoming notes being played on the synthesizer keyboard. Another feature allows the incoming notes to be transposed up to twelve half-steps up or down to facilitate vocal and instrumental accompanying. The use of a MIDI-controlled system also creates new modes of performance and recording. A live performance by an organist can be captured and saved as a MIDI data file. This MIDI file can later be
played by the computer software alone (without the keyboard) to recreate the same acoustic performance with the organ or any other MIDI instrument. This feature would be useful for providing direct comparisons of the same performance in different tuning systems, including 12-tone equal temperament. These MIDI performances can be used as demonstrations for visitors to the Organ House and can assist the Eivind Groven Institute in producing future audio recordings.
While many organs have multiple sets of pipes producing a wide variety of different timbres, Groven's pipe organ has only one voice. With this computerized system, however, it is possible to expand the number of timbres by mixing sampled organ sounds stored in the computer together with the acoustic pipes. In essence, this restores the capabilities of Groven's now defunct electronic organ. Moreover, the synthesizer, computer and software can be used as a stand-alone system that can be transported to concert venues outside the organ house and allow Groven's work to reach a much larger audience. It is even possible to connect the organ to the Internet for live remote performances. Organists from around the world can perform on remote MIDI keyboards and be heard live by audiences at the organ house. Likewise, organists in Norway can have their performance transmitted over the Internet to be simultaneously realized by a MIDI instrument at another location, such as the Groven Piano installed at Western Michigan University in the United States. Groven's work has come full circle - from a local network of telephone switchboard relays to the global network of the Internet.
Finally, with this latest version of the renstemningsautomat researchers can continue Groven's musical and scholarly work with adaptive tuning. As stated above, Groven himself was constantly revising and refining his system, experimenting with different scales (e.g. a 43-tone just scale) and different tuning criteria. Each change necessitated physically rewiring the hardware and consequently displacing the previous system. By contrast, the new software-based system can easily be modified. We can realize the alternate tuning-logic left by Groven prior to his death, in addition to testing new tuning strategies. All of these can coexist side-by-side, permitting performers to choose from among multiple systems of interactive performance.
From levers to telephone relays to transistors and now to computers, Groven's keyboards have been in a continual state of evolution - utilizing the technology of the day in the service of a musical and aesthetic vision. What is perhaps more evident to us with this latest software incarnation is that, in addition to music and technology, Groven worked in what we would now call artificial intelligence. The renstemnings automat is specialized artificial intelligence representing a fairly comprehensive musical system of consonances and dissonances. Via the keyboard, the renstemnings automat receives input from the real world, processes it and makes decisions about how the music should be performed based on its knowledge of tuning, tonality and harmony. The process is intended to simulate the intuitive choices of intonation made by human performers,
such as those in a string quartet or vocal ensemble. More specifically, the intelligence embodied within the core of the organ's brain is none other than Eivind Groven's. It is, after all, Groven who methodically anticipated all the possible combinations of pitches which could occur in a piece of music and wired the first renstemnings automat with his solution of how each should be tuned. His vision and aesthetic sense quite literally provide the technology with the musical soul behind the retuned organ.
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_____. "Acting Natural: Eivind Groven's Naturskalaen and the Renstemtee Organ." Norsk Folkmeusikklags skrifter 15 (2001).
_____. "Groven.Max: An Adaptive Tuning System for MIDI Pianos," Computer Music Journal, 26(2), 2002.
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Den norske komponisten, musikkforskeren og folkemusikeren Eivind Grovens (1901-1977) var alltid åpen for eksperimenter og fornyelse. Ett av hans store kunstneriske mål var å konstruere et tasteinstrument som var befridd fra den begrensing 12-tempereringen innebærer. Et instrument som både kunne gi akustisk rene intervaller i alle tonearter og som kunne gjenskape de unike skalaene som opptrer i autentisk folkemusikk. Idet han ville realisere sin store musikalske og estetiske visjon, anvendte han dagens nyeste teknologi. Artikkelen vil følge utviklingen av Grovens automatiske omskjaltingsinnretning gjennom fire teknologiske stadier: fra hans tidlige eksperimenter med klaver i 1920-årene, gjennom bruk av telefonsentralbord-releer og deretter elektroniske transistorer knyttet til orgler,
frem til den oppgradering basert på moderne datateknologi som idag finner sted i Grovens orgelhus i Oslo i regi av Eivind Grovens institutt for renstemming og NoTAM (Norsk nettverk for teknologi, akustikk og musikk), Universitetet i Oslo.
David Løberg Code er professor i musikk ved Western Michigan University i Kalamazoo, MI, USA, der han underviser i musikkteori. I 2001 var han Fulbright-stipendiat og gjesteforsker på avdeling for musikkvitenskap ved UiO. Han er oppfinner av Groven-pianoet som hadde verdenspremiere på Norges Musikkhøgskole 19.april 2001. Code er opprinnelig klassisk bratsjist; spiller også norsk folkemusikk og danser bygdedans.