Perfect Sound Forever

3rd Bridge Helix

30-05-2008, Primavera Sound Festival, Barcelona

From Experimental Punk to Ancient Chinese Music &
the Universal Physical Laws of Consonance
by Yuri Landman
(December 2008)

This article is an excerpt of my lecture that I gave at the Primavera Sound Festival in Barcelona about my self-built musical instruments. I explained what kind of instruments I make, why I make them and for which bands I make them for. I showed the audience my models and played the instruments. Additionally, I gave a more extensive explanation about one particular instrument I have created, the Moodswinger.

After finishing this, I discovered that this was not only a musical instrument, but also an educational measurement instrument which shows a universal system of consonant values based on simple physical laws. I discovered that all musical scale systems all over the world are derived from this basic system, including the worst inharmonic, deviated tuning system of all of these variations- what we know as our Western 12-tone logarithmic equal tempered scale.

The Beginning

I bought my first guitar and bass guitar when I was 18. I always had a fascination for direct and simple punk rock structures instead of the highly practiced virtuoso guitar playing used in symphonic rock and hard rock. In line with this aesthetical rule, I refused to take traditional guitar lessons from a jazz or blues teacher. I took notice of some chords and knew where to put my fingers for a C7 or minor D-chord, but I have never practiced long enough to play them well. I cannot even play Nirvana's "Polly" properly for instance. I developed my playing technique in a different direction.

The band I appreciate the most for their color of sound is Sonic Youth, especially their first recordings. Derived from the noisy droning soundscapes of Glenn Branca, Sonic Youth developed a new path of experimental punk rock, mainly focused on untraditional playing techniques on customized guitars with drumsticks and screwdrivers put under the strings and heavily detuned string combinations. I knew Branca's name from a short biography in the Dutch ‘86 Pop Encyclopedia, describing his guitar symphonies and mentioning his self-made 'mallet guitars'; table shaped string instruments with a large amount of strings with rods between the strings and hit with drumsticks. Unfortunately, I had never seen the instruments close up.

For years, I worked with prepared guitars, placing objects under the strings and mainly playing them on the other side (opposite of where the string are), where the pick-up is not taking up the string attack directly. Like a tuning fork the opposite string part resonates on the attacked string side. When placed on the middle of the string, both sides have an equal tone and the resonation is optimum. When placed on another position however, the tone is much more interesting, because the resonation then causes a strange clock-like, multi-phonic tone.

Zoppo & Avec-A

Together with my school friend Cees, I started a band called Zoppo. We recorded songs on a Tascam 4 track and put out albums and singles. I played bass and odd prepared guitar arrangements and took care of the sound quality. Although limited in possibility with only 6 strings during the recording process, this prepared guitar technique gave us quite good results because of their sometimes unexpected aleatoric moments and it was just searching for a few hours and modifying the tuning until it fit into the already-recorded guitar lines which formed the song structure.

Originally, we were a two piece studio band, but after two albums, we started playing live and the reconstruction of the arrangements became a problem for me. Most of the time, I remember how I prepared my guitars, but when recording, along with the preparation, there were many other parameters too. It can be very dissimilar from playing the guitar traditionally- the sound can be 100% different and impossibly inharmonic with only the slightest deviation from any of the parameters like EQ, distortion, tuning and the third bridge positioning. And additionally, when you stand up on a stage wearing the guitar on your shoulders, the screwdriver slips off because of the gravity and it moves while you are playing a song because the strings are vibrating.

Because of my increasing annoyance at not getting my sound under control with a normal guitar, I started creating a custom built instrument.

This was around 2000. I quit Zoppo and started a less-professional band, Avec-A with Valentijn. Because I was mainly focused on creating suitable instruments for sound enhancement at the time, I was not making music anymore at all. So my career as a musician dried up. The final and current result from my experimentalism has become not the music, but the instruments themselves to create music with.

Building for other bands

At one time, there were almost 20 wooden string instruments lying in my attic, not used at all. Then came the idea to approach international bands to collaborate on my project. The plan: I created a string system for experimental guitarists to offer them more sound possibilities. In return, this would lead to increasing attention for my work, maybe turning it into a commercial business.

I first approached Liars who had just released Drum's not Dead. After meeting them in Utrecht at a gig in Ekko, they accepted my offer and let me decide what to make for them. I had made a few third bridge guitars and decided to make for them an improved version of an earlier prototype. This became the Moodswinger. I made two exact copies, so I wouldn't regret giving my instrument away.

After Liars, I approached Lee Ranaldo of Sonic Youth and created from some of his ideas- a sympathetic, 18 string, bi-headed droning guitar. For Jad Fair, I created a 2-string instrument with 12 additional plucking thumbs. I also approached Amadeo of Blonde Redhead, for whom I still have to build something for- hopefully soon, I will be able to fulfill my promise to him. Recently, I made a 3-way stereo guitar for the band Blood Red Shoes.

From left to right: The Springtime for Laura-Mary Carter, the Bachelor QS for Jad Fair,
the Moonlander for Lee Ranaldo and the Moodswinger for Aaron Hemphill.

Back to the Moodswinger

Afterwards, the Moodswinger had a strange side effect on my musical perception, which is the subject of this article. The instrument contains the most worked-out third bridge scale until now. I haven't seen any other third bridge instruments with this type of string division scaling. One predecessor is good to mention, because it formed my ideas; the Pencilina, made by a guy from New York called Bradford Reed. Bradford's Pencilina comes the closest to my instrument, but is more individualized in its approach. He can play the instrument very well, but he had to train a long time for it. My main goal was to create an instrument on which every guitarist could easily play a tune. I was trained as a chemical analyst, studying math, science and physics, so I understood what was actually happening with the third bridge technique. But for Liars, I had to develop a system that they would understand too. My English was very bad around then, so my work had to be understood in the instrument.

Bradford's Pencilina, which has 1/4, 1/2 and 3/4 on the upper neck and 1/4, 2/5, 3/5, 2/3 and 3/4 on the lower neck.

This lead to my current research on string resonance, physics and microtonal scaling. I didn't know Aaron Hemphill (from Liars) had studied microbiology, so it was pretty easy to explain him how the instrument worked. He immediately understood what happened. On the Internet, I found a site about a slide instrument called the Analude, made by a mathematician named Steven Rowat, which contained a color dotted system indicating microtonal harmonic positions. Around then, I didn't understand how Rowat had constructed his colored scheme.

He based it mainly on the just intonation theory of Harry Partch, using commonly used ratio's like 16/15, 9/8, 6/5, 5/4, 4/3, 3/2, 8/5, 9/5, 15/8, 2/1, etc.. Later on, I discovered that these are frequency ratios instead of string ratios. I work mainly with string lengths because it is much easier to understand the relationship between the several string positions. The string ratios are the inversion of frequency ratios. For 6 months, I developed a sort of color-dot system which explained the tonal cohesion of all of the rich tonal positions on my instruments. This was clearly better suited for myself than the double-colored system which Rowat worked with. With the color dots, I created families of tones, so the 1/2 position is grey for instance, the 1/3 and 2/3 positions are the red dotted family, 1/4 and 3/4 orange, 1/5, 2/5, 3/5 and 4/5 are yellow, etc.. I was just following the colors of the rainbow.

I discovered the left side of the octave middle was a mirror image of the right on the scale. So, the idea I came up with was to put two more scales on the neck of the instrument as well as on both sides of the string division scale. There would be the normal logarithmic scale used on guitars and a logarithmic scale going in the opposite direction. With these two logarithmic scales, I could read out the attack tone and the complementary humming tone coming from the opposed string part.

The Ancient Chinese Guqin

I still didn't see any relation between my overtone scale and the logarithmic scale on the guitar. This has always surprised me. Why aren't they equal to each other? Then one day, I was looking at the irregular pattern on the neck of the Moodswinger and suddenly, I remembered the Turkish Saz (a stringed instrument) that my old friend Cees had once bought on a vacation trip. The Saz has, as opposed to European instruments, an irregular fret positioning. I wondered if perhaps this system had a similarity with my scaling system. The Saz has a lot more frets in the first octave, so this was too difficult to compare with. After searching a bit on Internet, I found something else- an ancient traditional Chinese instrument called the Guqin. Although the two instruments are played in a totally different way, I had unconsciously recreated something very similar.

That was strange. Apparently, I discovered something which had already been discovered 4000 years ago. Everett M. Rogers wrote a book about the diffusion of innovations, giving one group the name ‘Laggart,' which is the ones that always come after everybody has been there. This is the opposite of the more widely known term 'early adopter.' I was a little late with this rediscovery, making me probably the biggest Laggard of all time. I did research on other Non-Western Instruments and suddenly, I recognized on almost all string instruments all over the world exactly the same positions, all derived from the scale I had worked out on the Moodswinger. Sometimes, a few positions were left out, and on other instruments some different pitches were put in, but always the 2/3, 1/3, 1/2, 1/4, 3/4, 4/5, 3/5, 2/5 ratios appeared on the scales. So this cleared-out musical scaling was not traditionally formed but instead, it was traditionally modified slightly from a basic universal physical system. This struck me deeply. I had always thought it was only people who had made something up and agreed with each other about cultural and traditional rules concerning what sounds good and what sounds bad. This is untrue. Simple physical rules mainly stipulate what sounds good, not only subjective normative rules. That's the difference between an objective falsehood and a subjective falsehood.

I compared the Moodswinger scale with pictures of other instruments and discovered the similarity in scaling on almost every other traditional instrument from all places on Earth. From top to bottom: The Moodswinger, the Russian Bailalaika, the Chinese Dan Gnuyet, the American Appalachian Dulcimer and the Iranian Tar.

Western Musical Evolution

In most Western books about musical tuning Pythagoras, the Greek mathematician of A2 + B2 = C2, is mentioned as the inventor of the harmonic relations between tones and string lengths as well as a system called Pythagorean tuning. In reality, he wasn't the inventor of the system- Babylonian texts of 3500 B.C. also described this tuning system. And he also didn't invent the relation between string length and consonant tone combinations. Besides the Babylonians, the Chinese had already made this discovery 1000 years earlier. Anyway, let's give Pythagoras some credit although he didn't invent it- he was surely very busy calculating otherwise.

Pythagoras did his musical thinking with the help of an instrument called the Monochord and developed his Pythagorean tuning which led to a huge development in transposable music, one of the key signatures of Western Music. My Moodswinger, I later discovered, follows a certain level of the same principles as the Monochord and the Guqin- that's why I had this rediscovery without knowing anything about Pythagoras or the ancient Chinese scaling system.

After Pythagoras, the musical tradition of the Middle Ages of church choirs bent his system slightly back to the physical just major scale and an alternate just scale called the minor scale. Bach worked with a new mathematical tuning system which repositioned these major and minor scales to a transposable system again, but he was not improving consonance compared to the physical system. The true physical harmonic values only can relate to the fundamental tone, but never among all tones mutually. Later on, other alternative tunings were used, but every other made-up mathematical system is a compromise. Under the influence of the colonization at the end of the 19th century, Eastern music came to Europe and Debussy integrated that- odd intervals returned again in Western music.

Meantone (a similar temperament to Pythagorean tuning) was no longer the solution to use when playing these tones, so Western music took refuge once again: the logarithmic equal tempered scale, abbreviated 12-TET, currently used in almost all pop music, leading to an increasing false tonal relationship between the tones. In Europe, this option had already been known for 400 years, but it was always rejected because other systems sounded better and were more physically consonant. But the increasing tonal freedom forced Western music to use this tuning.

Strangely enough, listening tests have been done among Western audiences and the conclusion was that the audience mainly preferred this inharmonic structure of today's logarithmic scale. It was not because it sounds better but they got used to this false system, describing it as rich or colorful and describing the just tuning as boring, cold or empty. However, a test from 1948 in Holland done by A.D. Fokker had a contradictory conclusion. The audience were mainly trained musicians and they didn't prefer the 12-TET at all. I assume Eastern people probably would consider it also ‘messy,' ‘nervous' and unsilent (which it is physically). That's why we consider Eastern music sometimes relaxing or empty, depending on how you interpret their works. It was not very strange that this test had different results, because it took place before mass recorded pop music, mainly written in 12-TET, and daily radio and television broadcasting became an unconscious indoctrination, stipulating the esthetical norm of what sounds good.

Modern Noise Rock

Back to punk rock experimentalism now. For a very long time, I've wondered why the sound of Sonic Youth is atonal and full of noise but also atmospheric, sweet, and silent at the same moment. Sonic Youth used screwdrivers to play their guitars and this is perhaps considered to be a punk statement mainly, but instead of creating atonal noise, they created pure consonant tones. They weren't aware of it in 1980, but I think Glenn Branca knew about the physical background of it because he is also very interested in and inspired by the work of Partch. When I showed Ranaldo my Moodswinger, he told me that Branca's third bridge instruments were far more primitive. They were just fields of strings with a rod in between them and he probably used it in an aleatoric way with coincidental tone combinations. But I doubt if he used it so randomly. Branca also built a double-body guitar which, similar to the screwdriver technique, looks like an artistic and humoristic dada statement, but in fact this also contained some truth about consonance.

Glenn Branca with his double bodied siamese twin guitar

The Moodswinger scale, based on the same values Harry Partch worked with, is a mirror image. Branca's guitar is a mirror image too. So probably, Branca knew quiet well what was happening and his double bodied instrument is not a joke at all. It has to do with harmonic truth of two opposed string parts- the natural overtone series and their complementary series which are the basics for musical tuning systems. Branca and Sonic Youth went back to the more physical harmonic rules. And of course, many sound patterns used in experimental rock are deviations from the major and minor scale and therefore lesser consonant, but there is a paradox. Out of the swamp of dissonance, new primitive creatures come alive and climb out of the lake. These primal creatures may sound odd but when watched closer they share the harmonic physical values for consonant sound with Chinese traditional music. Pop music is false in its solid pattern, because it is off key in relation to the physical just intervals. Experimental rock instead is, in a certain way, less false than pop music, because this kind of music does not solidly stick to the false 12-TET tuning, but slightly bends the tones to more consonant values.

The third bridge system provides proof for this, but I can also explain a similar situation about amplifier feedback related to overblowing, which is following the same rules of the natural overtone series. Heavy distortion enhances the overtone range of a string vibration, also returning back to those physical laws. That's why heavy metal is played on only one or two strings instead of all six. The natural overtone series doesn't match the off-key inharmonic 12-TET tones of the other strings which complete the chords. I assume that a similar phenomenon is present in electronic equipment which is used in an altered way, like circuit bending or the overdriven Roland 303 used in acid house music. The Velvet Underground used alternate tunings often tuned in unison or in octaves, which also leads to a 'quiet' driven sound. On Sonic Youth's album Sister, I hear guitars which almost remind me of the sound of a trumpeting elephant. This is no coincidence, but the result of physical forces.

So my conclusion is all these extended techniques used in experimental rock lead to a more natural just harmonic structure compared to the traditional techniques used in mainstream pop music, which is harmonically off the road, instead of the assumed middle of the road.

Besides the harmonic truth in extended playing techniques, I also assume tube amplification swallows atonal inharmonic values to make a better harmonic structure similar to the light fields in a plasma lamp. And similarly, I also believe tape compression used in recording restructure the musical pattern. But I cannot prove this with measureable results and this assumption is too far from my work as an instrument builder, so I leave this research to other people. But this is why I believe that people are still using old equipment- because it sometimes physically sounds better and not because musicians are necessarily nostalgic.

The Helix of Consonance

Finishing this text, I hope it explains the atmospheric sound of Velvet Underground, Sonic Youth, Polvo, Yo La Tengo and many similar bands who are working with altered techniques mentioned above. Their loud walls of noise sound chaotic at first, but behind this field of noise, there is a certain silence too. Now I won't go as far to declare that the experimental rock bands mentioned are making similar music as the Chinese did. That's not true, because this only counts for the structure of the sound, not for the chord progressions. But with the extended playing techniques, there are just borders being crossed to the 12-TET and those crossing borders bend backwards to long-ago discovered basic physical laws. I would like to compare this development of modern art rock with a helix shape. The first string sound was created by primitive people, then this sound was constructed in its most pure intervals, leading to the invention of the Guqin. This is the first cycle in the helix, taken up to the first level. Then the Pythagoras deviations were used and bent back to the second level of consonance during the Middle Ages. Bach went off the road again with calculated false pitches. Other tuning systems went back and forth on the helix every time a step further shifting between physics and math for the best possible solution. With electricity, it became possible to arrive at a new level of physical consonance, the result being the formation of experimental rock with its variety of extended playing techniques.

The harmonic values taught in Western musical lessons are deviated values and are a subjective normative value and not a physical consonant truth at all. The old ancient physical laws are pushed away by a simplistic 12 tone scheme which allows many possible solutions within the system, but fails when you go outside the system. I considered flattening the color of sound with a logarithmic 12-TET-tuning, but it became nothing more than painting with numbers.

Creating music by following the rules of the logarithmic scale used on guitars and keyboards is like working with just 12 slightly polluted colors and without even knowing that yellow and blue generates green. The origin of 'pretty sounds' has largely faded away in Western musical training. If I had known this when I was 18, I would have approached a nice harmony with more attention instead of rejecting it. Fortunately, experimental rock took hold, with the help of electricity and extended playing techniques in its own specific way, bringing the music up to a next level in the helix of physical consonance. I am curious what the next helix level will sound like.


Further reading about the relationship between physics and music:

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