31-tone guitar

The 31-tone guitars around the Fokker organ

The 31-tone guitar is one of the other microtonal instruments owned by The Huygens-Fokker Foundation. Or rather, 31-tone guitars, since there are multiple instruments, both acoustic and electric. Instead of the usual twelve-tone system per octave, as found on standard guitars, the 31-tone guitar is based on a tuning with 31 tones per octave. This system, known as the 31-tone system, offers a rich palette of sounds and harmonies that would not be possible on a 12-tone guitar.
The origin of the 31-tone system dates back to the 16th and 17th centuries, when the Italian composer Nicola Vicentino and the Dutch scientist Christiaan Huygens proposed dividing the octave into 31 tones in order to preserve the pure thirds of meantone temperament while still being able to modulate to all keys. This idea was later further developed by the physicist Adriaan Fokker, who in the 20th century advocated for the construction of instruments capable of realising this tuning. A well-known example of this is the 31-tone organ, built in 1950 by organ builder Bernard Pels on commission from Fokker and installed in the Teylers Museum in Haarlem.

Even before that time, Adriaan Fokker had a 31-tone guitar built to support his lectures with musical examples. It was probably in 1941 (or no earlier than 1939) that Fokker acquired a jazz guitar from the Dutch firm Amka, whose brand name consisted of the first letters of the forenames of the Veneman family. The company had moved from Haarlem and Amsterdam to The Hague to produce violins and, slightly later (1938), guitars. It is unclear, however, whether Fokker commissioned Amka to build a guitar with 31 frets per octave, or if the addition of the many frets was subcontracted to another instrument maker. What is known is that by 1941, Adriaan Fokker already owned this 31-tone guitar, as evidenced by a lecture he gave that year in which the instrument was discussed.
Below is a quotation from the texts (page 481) of the lectures that Adriaan Fokker (1887–1972) and his colleague Balthasar van der Pol (1889–1959) gave at the Teylers Museum in Haarlem on 20 and 27 December 1941:
“It is crucial to become truly acquainted with the tones. To this end, I had a guitar made with thirty-one frets per octave, at the distances calculated according to HUYGENS. It is not easy to play, because one must place the fingers much more precisely than on a regular guitar, but one can still play many chords. Thus, I can let you hear a chord of E major, E-G#-B-E. If I play Ab-B-E, you will hear that it is out of tune. That difference I cannot demonstrate on the piano. Once again, I play a minor third chord G-B-E. If you play b and e each a semitone higher, Cb and Fb, it is again out of tune. Now a chord with the harmonic seventh. I hope that when I play G-B-E#, you will find it satisfactory, and that you agree it transitions nicely into G- C- E. But now I play G-B-F. Compare that with G-B-E#, and it is clear which chord is better: the latter. If I play B-F and add Ab, so Ab-B-F, the chord is again correct. We can hear how the interval B-F resolves into Bb-Gb. That is correct. Here we find what HUYGENS noted confirmed: the tritone B-E# (5:7) resolves into the third C-E, its complement, the diminished fifth, B-F (7:10) resolves into the sixth Bb-Gb.”
The lecture, centuries after Vicentino’s 31-tone music, possibly presented the very first acoustic demonstrations of the 31-tone system in the Netherlands and beyond, nearly a decade before the construction of the 31-tone organ (Fokker organ). This makes the Amka 31-tone guitar a historic instrument, even though the frets have partially pressed into the wood over the years and the instrument is no longer professionally playable.

The Huygens-Fokker Foundation also owns 31-tone guitars that are used in the concert series centred around the 31-tone organ. These are played by the resident 31-tone guitarist, Stefan Gerritsen. In 2010, the foundation acquired a fine, conventional acoustic Spanish guitar (model 3A) from the Amsterdam guitar maker Otto Vowinkel, which was later refretted from 12 frets per octave to 31 frets per octave by Sebastian Nuñez, an Argentinian maker of early string instruments now living in Utrecht. The guitar features a spruce top, a wood renowned for its exceptional resonance qualities. The back and sides are made of light and durable Indian rosewood, which also has excellent tonal properties. The fingerboard of this guitar was designed by the prominent microtonal thinker Siemen Terpstra (born 1948), a Dutch Canadian residing in Amsterdam, who has himself built numerous microtonal guitars and designed microtonal fingerboards. The spacing of the individual frets was calculated with precision by Terpstra. All the guitar’s fret spaces are painted in different colours (colour-coded) by Siemen Terpstra to help maintain orientation. Because the frets are much closer together than on a conventional 12-tone guitar, the 31-tone guitar is significantly more challenging to play. Guitarist Stefan Gerritsen is a specialist in playing this unique (left-handed) 31-tone guitar. He was also the one who, in 2018, acquired a (likewise left-handed) electric guitar from the Fender brand (Stratocaster series), with the aim of using it for the microtonal ensemble Ensemble SCALA. To achieve this, it had to be possible to detach the neck from the body. In 2019, for this purpose, the Huygens-Fokker Foundation commissioned instrument maker Sjaak Pronk from Broek op Langedijk to create a 31-tone guitar neck, suitable for both left- and right-handed players, thus enabling the construction of an electric 31-tone guitar. The fret positions were again calculated by Siemen Terpstra.

Regarding his Integrated Color-Code for Microtonal Guitar Fretboards (in the spaces between the frets on the fingerboard), Siemen Terpstra once wrote in an article: “The first time that I visited Ivor Darreg (in 1981) he was living in Glendale, California. I was impressed by his amazing array of experimental instruments, but what grabbed me most was his re-fretted guitars. He had a large collection of them, guitars that he had carefully altered over the years. There were so many that it was a veritable feast to me! I had never played re-fretted guitars before, and it was almost overwhelming. Many of his guitars were pretty trashy – Ivor was not a wealthy man, but his dedication to the exploration of alternative tunings was quite impressive. A handful of them were pretty good – I think that I played all of them for a few minutes that unforgettable day. He had guitars in 19-ET, 22-ET, quarter-tone, 17-ET, and other odd divisions, but the sweetness of the 31-ET guitar impressed me most. It was also right at the `edge’ of the possible, or so it seemed to me. There were so many frets, so close together, how could you possibly put more frets on a guitar? Some years later I played a 34-ET guitar, and it largely confirmed the sentiment. From that day forward, I had an interest in 31-ET guitars.
Although I could `noodle’ my way around the fretboard, I soon found that it was almost impossible to play because I would invariably get lost. What fret am I on, and what chord is this? I then realized that the problem could be solved if some colour-cocle would be painted onto the neck for visual guidance. Ivor had a colour-code (rather complex) for his megalyra steel-guitar, but his `normal’ guitars were generally unmarked. On standard guitars, we generally use an inlay dot at the 5th, 7th, and 12th frets as the `colour-code’, and arguably this is adequate for 12-ET, but 31-ET is so complex (rich) that this traditional system no longer proves adequate. I began several years of experiment with alternative colour-codes trying to come up with an optimal design.
In fact, I caught the `guitar-altering bug’ from Ivor, and when I was back in Canada I acquired a semi-trashy electric guitar which seemed perfect for `experimentation’. (What is there to lose?) I had never done a guitar fret job before, so I assumed that the results would be pretty bad. To my surprise, the scale turned out to be pretty close to accurate, there was only a minimum of `buzzes’, and I now had my own 31-ET guitar! At this point, my irnerest in colour-codes intensified. By 1984, I had several designs which arguably have some consistent logic underlying them. The purpose of this little article is to lay out the reasons for my chosen design. Here is why I ended up with this particular pattern.” The electric 31-tone guitar with colour coding by Siemen Terpstra was acquired by the Huygens-Fokker Foundation in 2013 and was used in concerts until 2018.

A microtonal guitar frequently used in the concert series of the Huygens-Fokker Foundation is the beautifully sounding 31-tone guitar designed by Bert Terpstra (not related to Siemen Terpstra) and built by Dirk Janssen. On this instrument, however, only a subset of 17 of the 31 tones can be played. Compared to the piano keyboard, this corresponds to the seven white keys and twice the five black keys (for both five sharps and five flats). This makes the instrument easier to play than a full 31-tone guitar and produces a more pleasing sound, as there are fewer frets on the fingerboard that might alter the tone. Furthermore, by modulating from the key of C, almost all classical keys can be reached. For much early music in meantone temperament and even many pieces in the 12-tone equal temperament, this subset of the 31-tone system is sufficient, while still allowing enjoyment of the pure thirds the system offers. Bert Terpstra has written about his guitar: “My guitar is a good classical acoustic guitar. I did not choose the 31-tone system to play microtonal music, but precisely to play 16th-century Renaissance music (Dowland) and 17th-century Baroque music (Bach). The 31-tone system was already devised in the 16th century. For that kind of music, you do not need all 31 tones. That is why I left out all the tones on my guitar that are unnecessary for this music. Hence, you can see that my guitar has an incomplete set of frets. This makes it relatively easier to play. And yet it is still quite challenging to play Bach on this guitar.” This (left-handed) guitar is also played by the regular 31-tone guitarist Stefan Gerritsen.

Building a 31-tone guitar requires a thorough redesign of the traditional instrument. The fret layout on the neck must be adjusted so that 31 equal intervals fit within an octave. This means the distances between frets are significantly smaller than on a standard guitar, requiring greater precision in string adjustment and intonation to produce the correct microtonal steps. The playability of a 31-tone guitar differs substantially from that of a conventional guitar. The closely spaced frets demand a new technique for playing chords and melodies, as traditional fingerings are not directly applicable. Additionally, due to the many frets on a 31-tone guitar, there can be a slight loss of tonal quality. One of the main advantages of a guitar based on the 31-tone system, however, is the ability to play purer intervals. Moreover, the system provides access to intervals such as the harmonic seventh, which are absent in standard equal temperament. The 31-tone guitar has now attracted the interest of musicians and composers seeking new sound possibilities and wishing to acquire a relatively affordable 31-tone instrument. Since 2011, the Huygens-Fokker Foundation has had the expertise of guitarist Melle Weijters, a skilled performer in the field of microtonal guitars, who has become a regular participant in Fokker organ concerts and other musical activities.