Der Rufer is a composition I wrote for the Bremer Schlag-zeugensemble directed by Professor Olaf Tzschoppe and premiered in Theater Wrede (Oldenburg, Germany) in Sept 2021. This composition is the first result of a planned, long-term collaboration between Lund University/Malmö Academy of Music and the European Spallation Source (E.S.S.). The E.S.S. is a multi-disciplinary research facility based on the world’s most powerful neutron source, whose goal is to enable scientific breakthroughs in research related to materials, energy, health and the environment, while addressing some of the most important societal chal-lenges of our time. In the first step of this cooperation, I collaborated with J.G. Weisend II, a Deputy Head of Accel-erator Projects at E.S.S. looking at the issues surrounding Superfluid Turbulence. Specifically focused on a property of cryogenics, known as superfluid helium (He II), we in-vestigated ways to transmit processes used in cooling superconducting magnets used for MRI machines and particle accelerators, to organized sound by loosely mod-eling phenomena found in He II.

  What is Superfluid helium (He II)?

He II is a phenomenon from quantum mechanics (the branch of physics that deals with the behaviour of matter and light on a subatomic level) which may be modeled as the flow of fluids that is independent of one another. For example, in figure one we see a normal fluid flowing to the right, while a superfluid stream flowing to the left (see figure 1).

Figure 1. Independent flow in Second Sound.

In He II, the fluid component consists of fluctuations in the density of particle-like thermal (temperature) excitations. These fluctuations occur in regions in which the density of particles are densely to sparsely packed (see Figure 2). However, since it has no viscosity, superfluid flows are unaffected by fluctuations in particle density of normal fluid flows. With He II the propagation of temperature waves is known as second sound.

Figure 2. He II may present fluctuations of particle density, from tightly to loosely packed.

  Second sound

Second sound in He II can be understood by considering sounds in our everyday experience. Whether in the office or playing in the park, the sounds we hear involve changes in the density of air, water or even helium. These changes in density are caused by pressure changes, so that molecules packed at higher densities produce regions of higher pressure, while those molecules that are less densely packed produce lower pressures.

In He II we have two types of flows: the normal fluid flow and the superfluid flow. Even though considered to be different flows, the total density in He II is the sum of these two components. Since superfluid flows have no viscosity (energy), those regions dominated by superfluid component will be cooler than those regions rich with normal fluid flow. When regions are dominated by either normal or superfluid components, the overall effect they carry will be of temperature change. These temperature variations are known as second sound.

To compare, first sound is created when pressure changes the density of normal flow, while second sound is created by the alternation of heat pulses or oscillations between hotter and cooler regions in He II. The speed of second sound in He II is roughly 20 m/s which can be compared to the speed of first sound in He II ~ 200 m/s.

  Influences of second sound and other properties of He II

In 2020, second sound came full circle.

Inspired by sound, conceived within physics and then re-turned to music in Der Rufer, second sound became a central influence in this first cooperation of a planned, long-term exchange between Lund University and the European Spallation Source (ESS).

In Der Rufer, eight principles from ultra-cold physics influenced the composition, including:

(1) ANISOTROPY, which is the property of substances to exhibit variations in physical properties along different molecular axes, or in other words, looks different from different perspectives(Donelly 1988) (see fig. 3).

Figure 3. anisotropy.

(2) ISOTROPY, which is the property of substances to exhibit uniformity in all orientations(Misner 1968) (see fig. 4).

Figure 4. isotropy.

(3) VORTEX, which is the property of fluids to form a spiral. In fluid, a vortex revolves around an axis line, which may be straight or curved. Vortices may be seen in a cup of coffee, or while draining a bathtub. Vortices can move, stretch, twist and interact in complicated ways and are important in turbulence. The velocity within a vortex is greatest next to its core and decreases with distance from its center(Wikipedia) (see fig. 5).

Figure 5. vortex.

(4) VORTICES, BEND AND TWIST, which Feynman proposed that superfluids rotate in more complicated ways than normal fluid(Feynman 1955) (see fig. 6).

Figure 6. vortices bend and twist.

(5) BIFURCATION (quantum leap), in quantum mechanics, an atom must occupy only one energy level. As the atom moves about, it can only acquire energy in set amounts. In order to move to a higher energy state, only a relatively high energy disturbance may drive the atom into a higher state(Williams 2020) (see fig. 7).

Figure 7. bifurcation.

(6) MUTUAL FRICTION, occurs when normal fluid and superfluid are coupled, where velocity and temperature are higher6. As friction expands beyond normal fluid to affect superfluid flow, the superfluid begins to extract energy from normal fluid and grow in amplitude(Putterman/ Rudnick 1971) (see fig. 8).

Figure 8. bifurcation.

(7) TURBULENCE, PAST AN OBSTACLE. In normal fluid, turbulence often occurs past an obstacle, like large boulders in a rapids, in the manner of eddies, whirlpools and all manner of vortices. Turbulence decays downstream of the obstacle (see fig. 9).

Figure 9. turbulence.

(8) SECOND SOUND, is a quantum mechanical phenomenon which propagates through superfluid helium as a temperature wave rather than as a dispersal of energy. It is known as second sound because the wave motion of heat is similar to the wave motion of sound, which consist of fluctuations in the density or pressure of molecules in air. Similarly, second sound consists of fluctuations in the density of particle-like thermal excitations in superfluid.

Another important property of second sound is that superfluid helium consists of two fluid elements that can flow independently of one another. Normal fluid and supersound flow in opposite directions and thus “flow through each other”.

At low temperatures, viscosity disappears in superfluid, contrary to normal fluid where viscosity increases as temperature decreases. Some of the interesting effects from superfluid helium include a fountain that may flow forever due to thermomechanical properties of superfluid with no viscosity; that superfluid helium may climb up the sides of a bucket, and; that in a two-fluid experiment, that normal helium can be trapped by a plate with micro-holes while when cooled to a superfluid, helium can pass through the micro-holes.

Even though the regions of high and low density of normal fluid and superfluid change over time, the overall density remains the same(Balibar; Univ. of Innsbruck; Donnelly 2009; Pellam)(see fig. 10).

Figure 10. second sound.

  How was He II represented in music?

In Der Rufer I loosely modelled these eight principles in the following ways.

1. ANISOTROPY. That a property will look different from a different perspective, was seen in Der Rufer, when a single rhythmic series served as the object viewed from different perspectives. One perspective involved a contradiction; in which active, expressive gestures played over large physical distances on marimba and vibraphone, are muted to lessen the sense of pitch almost completely. The instruments decouple slightly from the monophonic rhythmic series, mirroring entropic processes, which at the end of this first section appears in retrograde (see fig. 11 and sound 1).

Figure 11. anisotropy.
Sound 1. Edgerton. Der Rufer, anisotropy.

2. ISOTROPY. Exhibiting uniformity in all orientations I developed material where the performers are asked to perform sustained tones by rubbing a handheld cymbal with drumstick. Referencing orchestral string performance practice, the percussionists are asked to exactly synchronize rubbing patterns similar to synchronized bowing by orchestral string sections, changing up- or down-bow simultaneously. As well, the players are asked to uniformly produce timbral changes on the cymbals that include playing pure tones, increase/decrease of roughness, vary pressure and scrape, changing direction of rub, etc. (see fig. 12 and sound 2).

Figure 12. isotropy.
Sound 2. Edgerton. Der Rufer, isotropy.

3. VORTEX. The idea of a fluid forming a spiral was assisted by an evolving cone-like phenomena seen in whirlpools and tornados, etc. (see fig. 13).

Figure 13. nodes on vortex.

Scored for vibraphone and marimba, each with supplemental metal or wood sticks, these vortices produced the most complicated pitch and rhythmic structures in the entire piece (see fig. 14 and sound 3).

Figure 14. vortex in marimba and vibraphone.
Sound 3. Edgerton. Der Rufer, vortex.

Table 1 shows a nonserial matrix of integers used to generate non-determinative rhythms. These numbers were derived from the physical distance between nodes of a vortex. The measurements were taken at a descending series of nodes, for example the distance between point A and point B equaled 14.5 cm; while the distance between point B and point C equaled 13.8 cm, etc. In total there were 17 points, producing 16 lengths (see fig 15). In order to build in variation and develop scaling that would allow for intuitive control, I transposed this initial integer series downward, so that there were 21 integer series in total.

Table 1. nonserial matrix.

Five three-dimensional vortices were modelled and then mapped upon a two-dimensional space, where the relative height of each point was translated into pitch. However, for time and rhythm, I did not develop a new matrix for each vortex, as it was important to build in as much redundancy as possible, while still retaining a certain level of real-world complexity (see fig. 15).

Figure 15. mapping of distance between nodes.

How did I translate numbers into rhythm? Below I show one example. It was important for me that the process allowed for intuition and not mechanical reproduction. If we look at table one, I chose to interpret the matrix beginning with a descending series (not inversion in the classical 12-tone matrix)(Scheonberg 1995) at 4.14 moving to 3.94, then to 3.68, etc. Then to interpret each number sequence, I followed the general process:

How did integers become rhythms?

I. Generally, the first integer defines the division/subdivision or iteration of the allotted timespan, then
II. the second integer defines the division of any sub-unit, then
III. the last integer defines the closing of the gesture

Figure 16 presents an interpretation of 3.94.

The first number (3) identified a division or iteration of the time span allotted to the figure. For example, in fig 16 the numbers used were 3.94. As we can see the overall length of the timespan is divided by a triplet.

Next, the second number (9) is asked to control one of the pre-final sub-units. In figure 16 we see that the first pulse is a single half-note. This is followed by 9-tet (9:2) spanning the second and third elements of the triplet.

Then, the third number (4) defines the closing part of the gesture. In this example, the final number becomes a 4:3 tuplet (see fig 16 and sound 4)

Figure 16. application of integers to rhythmic notation.
Sound 4. Edgerton. Der Rufer, integer to rhythm.

4. VORTICES, BEND AND TWIST. Feynman proposed that superfluids rotate in more complicated ways than normal fluid. So, in Der Rufer, I focused on the idea that normal and superfluid flows can bend and twist vortex cores if/when they come within a critical bandwidth. In Der Rufer, there are three appearances of this influence, which were musically interpreted as unusually sustained legato gestures pairing marimba and vibraphone with voice (see fig. 17 and sound 5).

Figure 17. interpretation of bent vortex.
Sound 5. Edgerton. Der Rufer, vortices, bend and twist.

When the voice appears, it is playing the role of Der Rufer. The voice should be nasal and pressed. In the first appearance of this material, the voice should be in a moderately high tessitura as it mimics the gestures of the vibraphone. In the second appearance of this material, the voice is to mimic the marimba which is played arco-rub with a superball mallet, which will produce pitch contours in a considerably lower tessitura than when vib is rubbed with drumstick. While mimicking the instruments, the voice performer is asked to sing a Greek text (notated with IPA symbols) which could be the sort of thing a stentor would intone to his troops on the way to battle. The texts, written by me in Greek, are translated into English below:

“send young man on foot into holy sea, away from war with truth”
“fear not child”
“fear not death”
“work with God”
“write with truth”.

In the final section, the voice reappears, again in a higher tessitura and this time accompanying him/herself with a large tom-tom to emphasize and reinforce the strong nature of the message s/he is sending. At the end of the piece, all instruments, including the voice become softer. However, the performer is asked not to lose energy, as the idea here is that the sounds become softer due to distance, as if the soldiers were marching further away in the distance (see fig. 18 and sound 6).

Figure 18. vortices, bend and twist.
Sound 6. Edgerton. Der Rufer, idea of stentor.

5. BIFURCATION (Quantum Leap). Here, I focused on the idea that in quantum mechanics an atom must occupy only one energy level, and that only high energy disturbances can drive fluid into a higher state. Based upon energy change, these quantum Leap gestures are accompanied by a change of tempo and dynamic. Then, since a high energy disturbance is needed to drive the fluid to a higher level, I produced energy changes using cresc/decresc with the sustained rubbing of the Tibetan cymbal or tam-tam (see fig 19 and sound 7).

Figure 19. quantum leap.
Sound 7. Edgerton. Der Rufer, bifurcation.
Sound 7b. Edgerton. Der Rufer, bifurcation on steriods.

6. MUTUAL FRICTION. In mutual friction, I focused on the idea of attachment between normal fluid and superfluid, so that they drag each other around.

In this material, superfluid is represented by arco-rub on handheld cymbals, while normal fluid is represented by rhythmically active pizz and arco gestures on the other instruments. Representing friction, I’ve asked the performers to produce timbral changes to the arco rub motions on the handheld cymbals (see fig. 20 and sound 8).

Figure 20. mutual friction.
Sound 8. Edgerton. Der Rufer, mutual friction.

7. TURBULENCE, PAST AN OBSTACLE. Focusing on the idea that turbulence which occurs downstream of an obstacle progressively decays over time, I wanted to build in a quasi-narrative structure in which laminar flow is interrupted by a loud crash, imitating an obstacle in a stream. After this obstacle, turbulence is represented by soft rattles, scratches, tremolo and all manner of eddies and whirlpools, all which decay over time (see fig. 21 and sound 9).

Figure 21. Turbulence past an obstacle.
Sound 9. Edgerton. Der Rufer, turbulence, past an obstacle.
Sound 9b. Edgerton. Der Rufer, turbulence, to an obstacle.

8. SECOND SOUND. I set up a process in which a wavelike phenomenon features alternating regions of tightly and loosely packed normal fluid molecules, while the superfluid remains unaffected since S has no viscosity.

In these sections, Superfluidity is represented by arco-rub on handheld cymbals, while normal fluid is portrayed by pizz and arco production within their corresponding multipercussion setups (see fig. 22 and sound 10).

Figure 22. second sound.
Sound 10. Edgerton. Der Rufer, second sound alternation of tightly and loosely packed fluid.

The materials were organized around four principles that were mixed and matched including: (1) tightly packed normal fluids, (2) loosely packed normal fluids, (3) normal fluid, featuring high viscosity, (4) superfluid featuring low/no viscosity. A final controlling principle in these gestures are that the overall density must stay constant. In general, the character of the second sound material features heterogeneous textures of rhythmically active + tightly packed motion versus more static + loosely packed motion (see fig. 23 and sound 11).

Figure 23. second sound.
Sound 11. Edgerton. Der Rufer, overall density stays constant whether heterogenous or homogenous texture.

  The title, “Der Rufer” refers to what?

The title, “Der Rufer”, refers to a sculpture in Bremen by Gerhard Marcks that refers to a Greek Herald from Homer’s Iliad (see fig. 24).

Figure 24. Sculpture Der Rufer by Gerhard Marcks in Bremen, Germany.

On the base of the sculpture is written:

Der Rufer von Gerhard Marcks (1889 –1981)
Der Rufer ist der Figur des Stentor nachempfunden, der mit gröherziger und ehernen Stimme so laut rief wie fünfzig Männer. (Homer, Ilias, 730 v. Chr.)

Der Rufer is modeled on the figure of the stentor (Herald, bard, or crier) who shouted as loudly as fifty men in a generous and brazen voice. (Homer, Iliad, 730 BC)

Die drei Meter hohe Bronzeskulptur wurde 1967 von Gerhard Marcks im Auftrag von Radio Bremen geschaffen. Am 25 November 2007 wurde der Rufer vor dem Neubau von Radio Bremen an der Weser aufgestellt.

The three-meter-high bronze sculpture was created in 1967 by Gerhard Marcks on behalf of Radio Bremen. On November 25, 2007, Der Rufer was placed in front of the new Radio Bremen building on the Weser river.

  Conclusions

In conclusion, we show how concepts and ideas from the advanced physics of cryogenics was useful for the creation of a new artistic work. Specifically, this involved translating eight principles from ultra-cold physics into sound, including: anisotropy, isotrophy, vortices, vortex rotation, bifurcations, mutual friction, turbulence past an obstacle, and second sound. Each of these principles were loosely modeled into music in ways that translated an active process across modalities. One such example was that of Anisotropy, or the idea that something will look different from a different perspective. When translated into sound, one interpretation was that an active rhythmic gesture was heard from different perspectives by varying the intervals of a fast-moving passage from a stepwise motion into passages with large leaps thrown in, while continuing to play fast; or by damping the bars of vibraphone and marimba nearly completely, so the effect of extreme amplitude difference become holes within a flowing stream of corrupted information. In this paper there is no claim regarding the effectiveness of method in this transference of ideas and/or processes from science to art. There is no attempt to posit any grand narrative, while Der Rufer on the surface bears resemblance to modernist narratives, my feeling is that there is something else at work here; which, while not having any overt resemblance to nature, still does retain some percept to real life.

European Spallation Source. ESS, based on the world’s most powerful linear accelerator, is one of the largest users of He II in Europe. At ESS, He II cools the superconducting RF cavities that provide the bulk of acceleration for the proton accelerator that drives what will be the world’s brightest neutron source. Research using neutrons at ESS will enable scientific breakthroughs in a wide range of fields including: materials, health, energy, the environment and engineering. More information on ESS may be found here: https://europeanspallationsource.se

  References

Baggaley, A./ Laurie, J./ Laizet, S. (2014). “Numerical simulations of thermal counterflow in the presence of solid boundaries”. Powerpoint Presentation. University of Glasgow.

Balibar. S. (2017). “Laszlo Tisza and the two-fluid model of superfluidity”. Comptes Rendus Physique 18: 586-591.

Donnelly, R.J. (1988). Superfluid Turbulence. Scientific American 259/5: 100-109.

Donnelly, R.J. (2009). “The Two-Fluid Theory and Second Sound in Liquid Helium”. Physics Today 62/10: 34-39.

Feynman, R. P. (1955). Progress in Low Temperature Physics. North-Holland, Amsterdam.

Misner, C. W. (1968). The Isotropy of the Universe. Astrophysical Journal 151: 431.

Pellam, J.R. (1953). “Second Sound Propagation in Liquid Helium”. Physics Today 6/10: 4-9.

Putterman, S.J./ Rudnick, I. (1971). ”Quantum Nature of Superfluid Helium”. Physics Today 24/8: 39-47.

Schoenberg, Arnold. (1995). The Musical Idea and the Logic, Technique, and Art of Its Presentation, ed. and tr. and with a commentary by Patricia Carpenter and Severine Neff. New York: Columbia University Press.

University of Innsbruck. (2013). ”Observation of second sound in a quantum gas”. ScienceDaily (15 May 2013). www.sciencedaily.com/releases/2013/05/130515131508.htm.

Wikipedia contributors. Vortex. Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 10 Jun. 2020. Web. 18 Jun. 2020.

Williams, M. (2020). “Excitons form superfluid in certain 2-D combos”(2020 June 15). Retrieved 19 June 2020 from https://phys.org/news/2020-06-excitons-superfluid-d-combos.html.

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