Hang Science

Two recent research paper releases from Felix and Sabina which were presented alongside their attendance at the ISMA (the International Symposium on Musical Acoustics) in Barcelona in September 07. They are presented here by kind permission of PANArt Hangbau AG. They are well-written and have saved me the job of rewriting the original research papers from 2000!!

HISTORY, DEVELOPMENT AND TUNING OF THE HANG
Abstract

The HANG is a new musical instrument, suitable for playing with the hands, consisting of two hemispherical shells of nitrided steel. It is the product of a collaboration among scientists, engineers and hangmakers, thanks to which we have been able to better understand the tuning process in all its complexity. Seven notes are harmonically tuned around a central deep tone (ding), which excites the Helmholtz (cavity) resonance of the body of the instrument. There are many ways to play the HANG. We show the different stages of its development over the seven years since its birth in 2000. We describe the tuning process and the musical conception of the HANG.

INTRODUCTION

The HANG was created in January 2000 by the tuners of PANArt Hangbau AG, formerly Steelpan Manufacture AG, Bern, Switzerland. It came out of twenty-five years of manufacturing the steelpan and research on its technology and acoustics. The youngest member of the family of acoustic musical instruments, the HANG is the result of a marriage between art and science. Five thousand HANG players worldwide and an ever-increasing demand show the deep resonance this instrument has with individuals. As we are only two hangmakers, our interest here is to invite scientists to continue working together to better understand this phenomenon.

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FROM STEELPAN TO HANG

PANArt Hangbau AG was founded in 1993 to give cultural and commercial support to the growing steelband movement in Switzerland. Europeans were fascinated by the“sweet sound of steel” from Trinidad, coming out of refashioned oil drums. The tuners of PANArt developed techniques to satisfy the great demand for steelpans and did intense research on different materials. The aim was to get instruments with both a high buckling resistance in the individual notes and a warm, harmonious sound. This research led to a new material, steel with a high nitrogen content. The higher rigidity of the material made it possible to develop other shapes of the clamped shallow shell. The PANArt tuners realized that a steelpan could now be manufactured with the help of a press. Instead of stretching the bottom of an oil drum with hammers to make it harder and stronger, they hardened a deep drawn hemisphere. As they now had a material of consistent thickness under their hammers, they started serious empirical research on optimizing the shaping to achieve their vision of sound.

The PANArt tuners met with physicists, engineers, metallurgists, and ethnomusicologists. The most significant input came from two physicists, Thomas Rossing and Uwe Hansen, who taught us to understand the vibration modes of resonating bodies and the recoupling effects in such complex systems.

We began to study the vibration modes of gongs, bells, all kinds of drums, bars, plates and shells. We experimented with our material to understand its laws and a large group of instruments came up called the PANG instruments.

Figure 1: The PANG instruments

Ping, peng, pong are steelpan-like instruments. Pung is a gong-like instrument, tubal is gamelan-like, pangglocke is bell-like and orage is cymbal-like.

The latest member of this family of nitrided steel instruments is the HANG.
It was born in the year 2000, when a percussionist demonstrated a ghatam to us and expressed the dream of having our PANG sounds in a resonating body that could be played with the hands.

PANArt had the know-how: the technology of deep drawing, the gas nitrided steel, the dome geometry of the notes, the octave-fifth tuning. The prototype had to be reduced in diameter from 60 cm to 50 cm to make it possible to be played on the lap.
The challenge was to bring the Helmholtz resonator, the central gong-like sound, and the tone circle, into a unified musical conception. Fewer notes could be tuned in, which meant that we would have to leave the chromatic scale behind and explore the large world of tonal systems. After one year the HANG was ready to be presented at the Frankfurt Music Fair.

To play harmonically tuned steel with the hands was a new dimension. That is the reason we called it the HANG, which means “hand” in the Bernese dialect.

In recent years PANArt has concentrated its energy on the HANG, and has discontinued building other steel instruments.

Figure 2: The HANG

Figure 3: The ding side

Figure 4: The gu side

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PROPERTIES OF THE NITRIDED STEEL

Thanks to the collaboration of engineers and metallurgists, PANArt was able to try out many different sheet metals from German steel mills, among them micro-alloyed, phosphorus and dual-phase steel. The change of the structure of the steel resulting from the diffusion of nitrogen was the only one of these alternatives that led to a better material for our technical and musical requirements, which included the following properties:
High Young`s modulus
High ratio of tensile strength to yield point
Low absorption
Surface layer with a non-metallic, somewhat ceramic behaviour
Corrosion protection equal to that provided by galvanization
High resistance to aging
Low cost and clean technology
Resistance to thermal fatigue
High internal compression

The high stiffness of the material, due to its thickness, forced us to experiment with shapes and edge conditions. A uniform thickness of 0.91-0.95 mm made it possible to shape symmetrical tone fields. An elliptical dome in the middle of the tone field led to a strong fundamental with two harmonic partials, an octave and a fifth. The higher modes came to lie around the third octave due to the stiffening effect of the dome. The notes now had soft edge conditions and were embedded in the stiff concave shell. With this favourable ratio of impedance the sound acquired a strong radiation.

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THE ART OF TUNING

There are no schools of tuning, and only a few tuners in University projects. Tuning is difficult to learn and to teach. Why?
As A. Achong claims (Achong, 2003), steelpan tuning is an art, because there are about fifty-seven parameters to consider in tuning a sound into steel. Each tuner has his/her style. We agree. Tuning a steel instrument is an intuitive task.
PANArt tuners developed a terminology for the tuning process. Nevertheless, it has not proven possible over the last few years to teach someone to build the HANG, and many a skilled steelpan tuner refused to collaborate.

Tuning is a knowledge based on daily practice, and on the internalization of the behaviour of the forces in the steel in relation to both resonance and pitch. Many questions remain unanswered and will require further research. (Rossing 2003).
We describe here, step by step, the different stages of the shaping and tuning of a HANG. We hope that further collaboration can help to clarify this non-linear dynamic system. Steelpan and HANG are complex shell structures. The Catalan roof and Gaudi`s work attracted our interest a number of years ago, and led us to the consideration of architectural thinking with respect to the HANG. We have more to learn from the shell constructions of engineers and architects like Frei Otto of Germany, Heinz Isler of Switzerland, and Buckminster Fuller of the USA.

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THE SHAPING AND TUNING OF THE HANG

Two shells (gu and ding) are deep drawn with a press from a common sheet.
The two shells are gas nitrided in an oven with an atmosphere of ammonia for a number of hours at a temperature of 600°C.
The playing surface of the ding shell (50 cm diameter with uniform thickness of 0.91-0.95 mm) is brushed with a brass brush (on an angle grinder, 3000 rotations/min.).

Seven elliptical domes are stamped around the ding, each with some blows of a hammer. Each dome is laid on a plastic ball (diameter 3-5 cm) that is covered with a rubber strip (2 mm thick). A specially shaped wooden block gets a blow of a heavy hammer in order to provoke a snap-through of the area around the dome.

The shell is annealed in the kiln for 15 minutes at a temperature of 400°C, with the following results:
Raising of the tensile strength by about 10%,
Increasing the hardness of the core,
Diffusion of the brass into the surface,
Relaxation of the introduced stresses.

The tuner starts his work with the ding side strongly clamped with a steel ring at its flange, which is 1 cm wide.
With a rounded wooden hammer, the hangbuilder stretches the areas around the domes. The introduced compressive in-plane stresses produce buckling phenomena like wrinkles in the note fields. These are reduced by upsetting the note with blows to the dome. Shaping a hyperbolic area around the dome leads to a frequency ratio of 2:3 of the (1,0) and (0,1) modes (octave and fifth). Strikes from both sides on the anticlastic ring (average curvature = 0) prepare the note to be lowered below the correct frequency (1:2:3). The tuner now forms the correct curvature around the note and at the same time eliminates stresses in the note field. This process will lower the fundamental and create a strong standing wave thanks to the right critical curvature. The note is now completely minimalized in stiffness and the impedance ratio between the convex note field and its concave neighbourhood is set. Some further strikes will be needed to raise the fundamental frequency to its correct place. The sound sculpture is now built. There are no external forces preventing it from vibrating, piston-like, and developing its mellow beauty.

Tuning is an art: dozens of parameters influence the quality of sound. Hangbuilders have to follow their own style intuitively, their own vision of a sounding sculpture.

They must master techniques that are unique in this art, such as ways to set the form, to smooth, to peen, to stretch and to upset the metal. They monitor the process by ear, observing the events on a chromatic strobotuner, along with the dance of quartz sand to check symmetry and vibration (Chladni patterns).

Figure 5: Quartz sand shows Chladni pattern

From the architectural and engineering point of view, the arch geometry of the concave shell as well as the geometry of the convex shell are changed into a new structure that generates bending movements under load (the impact of the player’s touch). The construction has an optimal utilization of forces in the concave supporting structure as well as in the tone fields, which should be free of external forces and can therefore develop their whole potential, which is given through the material PANArt created - a powerful high-energy sheet metal.
To test the correct construction, the whole shell is tempered at a temperature of 150°-180°C. It is retuned and tempered several times, depending on the degree of detuning.

The tuner doing the fine-tuning adjusts symmetrical nodal lines, checks the curvature of the edges, and brings the concave construction into its plastic beauty.

Tuning the gu involves stretching the area around the gu’s neck with a steel hammer, and smoothing the area with a rounded wooden hammer. The fundamental of the neck ring bell is lowered to D5, the (1,1)a to F5 and the (1,1)b to F#5.
The two shells are joined with a hybrid-polymer sealant. After one or two days, the flange protection ring (brass) is affixed. The playing surface of the HANG receives a coating of natural “hard oil”.
After a number of days, depending on the humidity and air temperature, the HANG is fine-tuned again. The tuner enters with a small steel hammer through the gu and makes the final blows. The relatively small detuning occurs through oval deformation, a spring back effect.
A final tuning is done after two weeks. The tuners sign their names and the instrument receives a serial number.

Figure 6: Tuning of the fundamental

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THE MUSICAL CONCEPTION OF THE HANG

Leaving behind the world of chromatic scales of the conventional steelpan, the PANArt tuners began to study tonal systems. They discovered a rich musical heritage among the world`s musical cultures, and tuned many different scales into the HANG. This ethnomusicological approach to musical conception came to an end in 2006 as the response from HANG players world-wide showed a marked preference for universal modes such as various pentatonic, and especially minor pentatonic modes.

Furthermore, there were some notes that resonated better than others. To make a step towards artistic freedom and higher sound quality, the tuners began to listen more carefully to their own responses and those of the HANG. We began to build in a kind of an acoustical cathedral, a space of sound based on the air resonance of the HANG played on the lap. This Helmholtz resonance (D2) became the fundamental of a new generation of HANG. The D2 received its octave D3 in the ding (central tone). The lowest note in the tone circle became A3, the fifth of the D3. The ding and its fifth got their octaves: D4 and A4. All HANG have this basic tonal structure.
The remaining four notes are tuned in with artistic freedom by the tuners.
The gu neck bell is tuned to a D5. The spectrum of the partials creates the somewhat mystical sound of a clay pot, similar to that of the ghatam.

The musical atmosphere can be described as a palette of intervals in a one octave range, which is suitable for all human voices. Sounds created by the hands in interaction with the playing surface are an important part of the musical expression of a HANG player. Realizing this fact, PANArt changed the quality of the surface by brushing it with brass to get a more well-integrated touch in the instrument.

CONCLUSIONS

The HANG is a new musical instrument. Individuals around the world appreciate it. There are two hangmakers worldwide. It is impossible to satisfy the growing demand. Further collaboration between art and science is needed to make it possible that other hangmakers may exist in the future.

REFERENCES

Achong, A. (2003). “The Theory of the Steelpan,” Proceedings of ICSTS 2000, Port-of-Spain, Trinidad, p 11.
Rossing, T. D. (2003). “Science of the Steelpan: What is Known and What is Not,” Proceedings of ICSTS 2000, Port-of-Spain, Trinidad, p 30.
Rossing, T. D. ; Hansen, U. J. ; Rohner, F. ; Schärer, S. (2001). “The HANG: A Hand Played Steel Drum,” Paper 2aMUR, 142nd meeting, Acoustical Society of America.

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ACOUSTICS OF THE HANG: A hand-played steel instrument

Thomas D. Rossing, Andrew Morrison, Uwe Hansen, Felix Rohner, and Sabina Schärer
Stanford University, Stanford, CA 94305 rossing@ccrma.stanford.edu
Illinois Wesleyan University, Bloomington, IL 61702 amorriso@iwu.edu
Indiana State University, Terre Haute, IN u-hansen@indstate.edu
PANArt, Engehaldenstr. 131, Bern, Switzerland


Abstract

The HANG is a new hand-played steel instrument developed by PANArt in Switzerland. We describe the modes of vibration, observed by holographic interferometry and the sound radiation from the instrument, observed by measuring the sound intensity in an anechoic room. A low-voice HANG is compared with a high voice-HANG.

INTRODUCTION

The steel pan or steel drum originated after World War II when the British and American navies left thousands of 55-gallon oil barrels on the beaches of Trinidad. Originally a rhythmic instrument, local musicians discovered how to transform the steel pan into a melodious instrument by conditioning the metal and dividing the playing surface into note area that could be tuned. Steel bands are now found all over the World, especially in the Caribbean countries, North America, and Europe.

Steel pans, known by such names as tenor, double tenor, double second, guitar, cello, quadrophonics, and bass, cover a range of more than 5 octaves. The end of the drum is hammered (“sunk”) into a shallow concave well, which forms the playing surface, after which the note areas are grooved with a metal punch. They are generally played with sticks wrapped with rubber. Most of the note areas sound at least 3 harmonic partials, tuned by skillful hammering [Rossing, 2000].

As steel bands became more sophisticated, several developments took place in steel instruments. Tuners preferred new barrels to used ones, and they selected barrels with the most desirable steel composition and gauge. Scientific studies of steel pans helped to guide the pan makers, and musicians, scientists and makers worked hand in hand to improve the instrument [Rossing, Hampton, and Hansen, 1996].

It was discovered that “nitriding” (surface hardening) the steel created a hard, durable playing surface with a softer core that could be readily tuned. The pang family of surface hardened steel instruments was created that included the ping, peng, pong, and pung [Rossing, Hansen, Rohner and Schärer, 2000; Rossing, 2001].

In 2000, PanArt created a new hand-played steel instrument, which they called the HANG. It consists of two spherical shells, fastened together. Like the pang instruments, it uses nitrided steel. It quickly became very popular with percussionists, who learned to create a wide variety of sounds. Another paper at this conference [Rohner and Schärer, 2007] describes the design, construction, and tuning of the latest version of the HANG. In this paper, we will discuss the acoustics of this popular instrument.

THE HANG

The HANG is shown in Figure 1. The top (DING) side has 7 to 9 harmonically-tuned notes around a central deep note, which couples strongly to the cavity (Helmholtz) resonance of the body. The HANG is usually played in the lap, although it can also be mounted on a stand. The bottom side has a large hole (GU) which acts as the neck of the Helmholtz resonanator. The resonator can be tuned by inserting a DUM into the hole, thus changing its diameter and neck length, or by varying the spacing of the player’s knees to change the acoustical “length” of the neck. A wide variety of bass tones can be achieved. Some playing techniques are illustrated in Fig. 2.

Figure 1: The HANG (DING side and GU side)


Figure 2: Some playing techniques for the HANG

The HANG can be tuned in a wide variety of scales. The high-voice HANG we report in this paper had 9 notes tuned to a pentatonic scale, as shown in Fig. 3. This is the same HANG describe in an earlier paper [Rossing, Hansen, Rohner, and Schärer, 2001]. Other scales are illustrated in Fig. 4. The low-voice HANG had 9 notes tuned to an Ake Bono scale with the lowest note at F3, one note lower than the Ake Bono scale shown in Fig. 4.

Figure 3. Tuning of high-voice HANG used in these studies


Figure 4: Other HANG scales (full list available here)

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MODES OF VIBRATION

Each of the notes on the HANG has three tuned partials with frequencies in the ratios of 1:2:3. Modal analysis can be done by several methods, but the finest resolution is obtained using holographic interferometry. An electronic TV holographic interferometer is shown in Fig.5. The object beam is projected on the HANG, and the reflected light is focused on the CCD array of a TV camera, while the reference beam is transmitted to the camera by means of an optical fiber. The resulting interference pattern is read out, pixel by pixel, and the holographic interferogram is constructed by a computer. Thus, an interferogram is created and updated at the TV frame rate (30 Hz in the United States). Figure 6 shows the high-voice HANG mounted on the air-supported optical table for holographic interferometry.

Figure 5. Apparatus for electronic TV holography


Figure 6. High-voice HANG mounted on holographic table

Five modes of vibration in the central G3 note area of the high-voice hang are illustrated by the interferogram in Fig. 7. In the (0,1) mode of lowest frequency, the entire note area vibrates with the same phase, while in the (1,1)aand (1,1)bmodes a nodal line bisects the note area. The nodal lines in the two latter modes are orthogonal to each other, so they represent normal modes. These three modes at 189 Hz, 390 Hz and 593 Hz have frequencies nearly in the ratio of 1:2:3. Also shown in Fig. 7 are the (2,1)aand (2,1)bmodes having two nodal diameters and frequencies 1418 Hz and 1543 Hz which are not harmonically tuned. The three lowest modes in the E4 note area, shown in Fig. 8, also have frequencies in the ratios 1:2:3, although the higher modes are quite different from those seen in the G3 mode.

Figure 7. Modes of vibration in the central G3 note area of the high-voice HANG

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Figure 8. Modes of vibration of the E4 note area of the high-voice HANG

The holographic interferograms in Figs. 7 and 8 serve as contour maps of the vibration amplitude. The “bull’s eyes” represent the points of maximum amplitude, and each fringe (light or dark) represents a decrease in amplitude equal to ¼ of a wavelength of the laser light used (532 nm in this case). Information about relative phase is not recorded except that adjacent areas generally differ in phase by 180o. To recover phase data, we modulate a second mirror with a signal at the drive frequency having an adjustable phase. Then it is possible to obtain a phase map [Engström, 1996]. Phase maps are useful in studying coupling between note areas.

Figure 9 shows phase maps of the D4 note area vibrating at its second resonance frequency (604 Hz) and the D6 note area vibrating at its lowest resonance frequency (also 604 Hz).

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Figure 9. Phase maps of the D4 note at its second resonance frequency (604 Hz) and the D6 note at its lowest resonance frequency (604 Hz) Color bars indicate phase in radians.

Holographic interferograms of the low-voice HANG driven at small and large amplitude at frequencies near the first three resonance frequencies of the central F3 note are shown in Fig. 10. The mode shapes of the (0,1), (1,1)aand (1,1)b, tuned in the ratios 1:2:3, are similar to those shown in Fig. 7. The coupling between various notes can also be seen. At 348 Hz, for example, the F4 note is strongly driven and the F4# is weakly driven, while at 520 Hz the (1,1)amode in the C4 note and the (0,1) mode in the C5 note show appreciable response.


Figure 10. Low-voice HANG driven at small and large amplitude at frequencies near the first three resonances of the central F3 note

In Fig. 11 the low-voice HANG is driven near the first three resonance frequencies of the F4# note. The (0,1), (1,1)a, and (1,1)bmodes are shown, along with coupling to the (1,1)amode of the C5# note.

Figure 11. Low-voice HANG driven at small and large amplitude near the first three resonances of the F4# note.

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SOUND INTENSITY

A convenient way to describe the acoustic field of a sound source is by accounting for the flow of acoustic energy outward from the source. The acoustic power density through a surface is called the sound intensity I. The instantaneous intensity is the product of sound pressure p(r,t) and acoustic velocity u(r,t). I(r,t) = p(r,t) u(r,t). The sound intensity can be written as the sum of the active intensity (AI) and the reactive intensity (RI), which are in quadrature: I(r,t) = A(r,t) + R(r,t). A(r,t) is associated with the component of u(r,t) in phase with p. The time-averaged form of the AI component is the power flux, while RI represents power stored in the near field. A vector field plot of AI shows vectors pointing in the direction of power flow, while RI vectors show the stored energy flux close to the sound source. The RI component of total intensity drops off as distance from the source increases, falling to zero in the far field [Copeland, Morrison and Rossing, 2005].

Intensity measurements of the sound field of the HANG were made in an anechoic chamber. A frame of aluminum tubing was suspended from the ceiling to support the instrument and the driving apparatus. An Ono Sokki CF-6410 sound intensity probe and a CF-360 FFT analyzer were used to measure the sound intensity at various planes near the HANG. The sound intensity probe consists of a pair of matched microphones with a spacing of 7 cm between them. A good approximation to acoustic velocity is obtained from the pressure difference between the microphones as they move in the sound field.

Active intensity measurements in a plane 8 cm above the top (G3 bass note) of the high-voice HANG are shown in Fig. 12. The A4 note was excited by a swept-sine signal (0 ≤ f ≤ 2000) and the intensity fields at the lowest three resonance frequencies were mapped over a 10x10 grid with 7 cm spacing between adjacent points.


Figure 12: Active intensity 8 cm above the center of the high-voice HANG

The active intensity maps show monopole radiation characteristics at the fundamental and second harmonic frequencies. The intensity field at the fundamental frequency exhibits a peak in AI directly over the note being driven. The intensity field at the second resonance frequency shows the largest active intensity region to be centered over the instrument and distributed over a large portion of the instrument. The intensity field at the third resonance frequency exhibits a dipole pattern.

Reactive intensity measurements in the plane 8 cm above the HANG are shown in Fig. 13. The reactive intensity fields show a circulatory pattern at all three resonance frequencies. The RI shown is the peak value per cycle. Half a period later, the vectors have reversed their direction. For the three modes measured, the RI aligns mostly in a circulatory pattern which suggests an exchange of energy between the front and back of the instrument.



Figure 13: Reactive intensity 8 cm above the center of the high-voice HANG

The intensity fields above the E4 and D4 notes were also measured and found to the similar to the intensity fields above the A4 note [Morrison, 2006].

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CONCLUSIONS

The HANG is a new hand-played steel instrument which has caught the fancy of many percussionists worldwide. Through experimenting with playing technique, performers have created many new sounds, and continue to do so. Understanding the modes of vibration and the sound radiation from the instrument help them to do so, as well as adding to our knowledge of the science of musical instruments.




REFERENCES

Copeland, B., Morrison, A., and Rossing, T. D. (2005) “Sound radiation from Caribbean steelpans,” J. Acoust. Soc. Am. 117, 375-383.
Engström, F. (1999) Small vibration amplitudes and phase of a baritone guitar (MS thesis, University of Luleå, Sweden)
Morrison, A. (2006) Acoustical Studies of the Steelpan and HANG: Phase-Sensitive Holography and Sound Intensity Measurements (PhD dissertation, Northern Illinois University, DeKalb, Illinois)
Rohner, F. and Schärer, S. (2007) “History and development of the HANG”, Proceedings of ISMA 2007, Barcelona.
Rossing, T. D. (2000) Science of Percussion Instruments (World Scientific, Singapore) Chapter 10.
Rossing, T. D. (2001) “Acoustics of percussion instruments: Recent progress,” Acoustical Science and Technology 22, 177-188.
Rossing, T. D., Hampton, D. S., and Hansen, U. (1996) “Music from Oil Drums: The acoustics of the steel pan,” Physics Today 49(3), 24-29 (March 1996).
Rossing, T.D., Hansen, U.J., Rohner, F., and Schärer. S. (2000) “Modal analysis of a new steel instrument: The ping,” (139thASA meeting, June 2000.
Rossing, T.D., Hansen, U.J., Rohner, F., and Schärer, S. (2001) “The HANG: A Hand-Played Steel Drum,” 142ndASA meeting, December 2001.

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