Acoustics and physics

• 1: Helmholtz resonance and the shell
• 2: How a note works
• 3: Tuning theory and measurement

1 - Helmholtz resonance and the shell

PHY-09What is Helmholtz resonance in plain terms?#

beginner

The mechanism is a mass on a spring, and nothing more complicated than that. Push the plug of air in the neck inward and it compresses the air inside, which pushes back. The plug overshoots outward, the inside air is now rarefied and pulls it back, and the oscillation continues at whatever rate that particular mass and that particular springiness produce. The steel is not vibrating in this mode at all. It is the air doing the work.

The frequency is given by

f = (c / 2π) × √( A / (V × L) )

where c is the speed of sound in air, roughly 340 m/s, A is the cross sectional area of the port, V is the volume of the cavity and L is the effective length of the port neck. The effective length is a little longer than the physical neck, because air just outside and just inside the opening moves along with the plug; the usual correction is about 0.6 times the radius at the outer end and about one radius at the inner end.

Read off what the formula tells you. A bigger cavity gives a lower frequency, which is why a deep shell has a deeper gu tone than a shallow one of the same diameter. A bigger port gives a higher frequency, because more air mass moves per unit of pressure change. A longer or narrower neck gives a lower frequency, which is why makers curve the neck of the gu inward or outward.

It is a general phenomenon, not a handpan speciality. A guitar body and its sound hole form a Helmholtz resonator, typically tuned near the second lowest string. Car cabins do it when you open one window at speed. Bass reflex loudspeaker ports are deliberate Helmholtz resonators.

See also: PHY-10

PHY-10How does the gu port create the deep bass whoosh?#

beginner

Strike a tone field and it does not only push air outward into the room. It also pushes air inward into the cavity. That inward push is a broadband impulse, and it contains energy at every frequency, including the cavity’s own. The cavity picks out its resonance from that impulse and rings on it, driving the plug of air in the port in and out. Because the port is a large, well coupled opening firing into the room, the resulting low frequency radiates efficiently despite being a small share of the total energy.

The measured figures are consistent across makers, with the expected variation. PANArt found the Hang’s cavity resonance at about 85 Hz, which is close to F2, and stated that it could be detected in all spectrums of the instrument’s sound. Saraz report a general handpan range of about C2 to G2, with their own instruments typically landing between E flat 2 and F2 depending on shell size and port design. Since it varies with cavity volume and port geometry, expect any given instrument to sit somewhere in that band rather than at a fixed value.

Two things follow from this that players notice quickly.

It is always there. You do not have to do anything to hear the whoosh. It sits under every note as a warmth and a body that the instrument would sound thin without. This is a big part of why a handpan sounds much larger than its physical size.

It moves. Anything that changes the effective port area or neck length changes it. Resting the instrument on your thighs partly covers the port and lowers it. Sitting it flat on the floor obstructs it more. Lifting it clear raises it and lets it project. Makers exploit this too: covering the port or adjusting leg position is a standard way of bending the gu tone during play.

See also: PHY-11, PHY-13

PHY-11What is the gu tone and how do I play it?#

intermediate

Playing a tone field excites the cavity indirectly. Playing the gu excites it directly: you use your hand as a piston at the mouth of the port.

The basic technique is to reach under the instrument, or tilt it, and strike the area around and over the gu with a relaxed cupped or flat hand. Aim for a slap that momentarily seals and then releases, rather than a hard hit on the steel. The steel around the port is not tuned and hitting it firmly does nothing useful; the sound you want is the air moving.

Variations worth practising:

• Open slap. Hand strikes and leaves immediately. Gives the fullest, most open gu tone at its natural frequency.
• Closed or muted slap. Hand strikes and stays, partly covering the port. Lengthens the effective neck and shrinks the effective opening, so the pitch drops and the decay shortens. This is the classic bass bend.
• Continuous modulation. Hover a hand over the port and move it while notes ring on the top shell. Because the Helmholtz resonance is present in everything you play, moving your hand sweeps the low end of the whole instrument. It is subtle, and it is very effective in a recording.
• Knee and leg control. How you sit changes the port coverage continuously and without occupying a hand. Many players use this without ever thinking about it.

PANArt built explicit variations on this idea. On the Integral Hang, partially blocking the gu produced a sympathetic D2. Their later Gubal replaced the central ding with a hand wide inwardly curved opening and made the deep cavity tone a primary voice, with a gung bass note at roughly 78 Hz, close to E flat 2.

The main practical caution is ergonomic rather than acoustic. Reaching under a four kilogram instrument on your lap for extended periods is awkward, and playing the gu is much easier on a stand or with the instrument tilted on one thigh.

See also: PLA section

PHY-12How does the air cavity couple the two shells?#

advanced

There are two coupling paths between the shells and it is worth separating them.

The structural path is the rim. Bending waves in the top shell can in principle travel round the flange into the bottom shell. In practice this path is deliberately weak, because the rim is stiff, massive and damped by the adhesive joint. That is by design; see ANA-07.

The air path is the one that matters. Because the cavity is enclosed, any inward motion of one shell raises the internal pressure everywhere in the cavity almost instantly at low frequencies, and that pressure acts on every internal surface, including the whole of the other shell. Below the first standing wave frequency of the cavity, the air behaves as a single lumped spring and the coupling is essentially uniform.

The consequences:

The bottom shell is part of the instrument even though nothing is tuned on it. It is a large, relatively compliant plate that the cavity air drives. It radiates, and it stores and returns energy. Instruments with bottom notes make this explicit, but it is true even of a plain gu shell.

The cavity loads every tone field. A tone field pushing inward against an air spring behaves slightly differently from one radiating into free air. This is why sealing the port entirely raises the pitch of the notes and kills their sustain: the cavity becomes a stiff sealed spring with nowhere for the air to go.

Damping one shell damps both. Anything that touches the bottom shell, your legs, a cushion, the floor, adds mass and damping to a component that the whole system leans on. This is a real and audible effect, not a marginal one.

Above the frequency where the cavity’s own dimensions start to matter, the lumped spring model breaks down and standing waves take over. See PHY-13 and PHY-14.

PHY-13Why is a handpan louder when I lift it off my lap?#

intermediate

Take the two separately.

Damping. Flesh is an excellent absorber. Where your thighs contact the bottom shell they add mass and, more importantly, convert vibration into heat rather than reflecting it. Since the cavity air couples the bottom shell to everything else, damping it removes energy from the whole system, not just from the part you are touching. Notes get quieter and shorter, and the loss is concentrated in the low end where the bottom shell is most active.

Port obstruction. Your legs, and often a cushion or a strap, partly cover the gu. That does two things. It reduces the effective opening area, which lowers the Helmholtz frequency, and it restricts the airflow, which reduces how much bass energy actually reaches the room. Together they make the instrument sound smaller and duller.

This is why the same instrument can seem transformed on a stand. A good stand contacts the rim, which is already acoustically dead, and leaves the whole bottom shell and the port free. Players comparing instruments in a shop should insist on hearing them the same way, because lap versus stand makes a bigger difference than many of the differences they are trying to judge.

Some practical corollaries:

• If you play on your lap, a thin foam ring or a proper lap cushion that supports the rim rather than the dome preserves much more of the sound than resting the shell directly on your thighs.
• Sitting the instrument flat on a hard floor is the worst case: near total port obstruction plus a large damped contact area.
• Conversely, lap damping is a legitimate expressive tool. Lifting one thigh during a phrase opens the instrument up audibly, and some players use exactly that.

None of this is unique to handpans. Guitarists notice the same thing when a body is pressed against a chest, and the mechanism is the same: the resonator needs to be free to move and the port needs to be free to breathe.

See also: PHY-12, REC section

PHY-14How do shell geometry, standing waves and crossover shape the sound?#

advanced

The Helmholtz resonance treats the cavity air as one lumped spring, which is a good model only at low frequencies. Higher up, sound waves travelling across the cavity begin to reflect off the internal surfaces and reinforce or cancel at particular frequencies determined by the path lengths. Since path lengths are fixed by shell diameter and depth, so are those frequencies.

Saraz have published the most concrete measurements available and they map cleanly onto that model. Their primary interference band, described as the most intense and extending over roughly 150 cents, tracks shell diameter directly:

Larger shell, lower affected note, exactly as longer path lengths predict. They also identify a secondary, much subtler band producing 3 to 12 cents of instability, again shifting with diameter.

On their 21 inch instruments they describe B flat 4 as the worst case in their range: no matter how well the note is tuned, there is typically 20 to 50 cents of wobble in the sustain, particularly when it is the fundamental of a note. That is a large number, and the honest conclusion is that it is a geometric property of the instrument, not a tuning fault.

Temperature and humidity shift these frequencies because they change the speed of sound. Saraz note that A4 on a 21 inch chamber sounds good at around 27 degrees Celsius but becomes problematic below about 16.

What makers do about it: build several shell diameters so a problem note can be moved to a different shell, avoid offering scales that put an important note in the worst band, and experiment with internal baffling. Saraz report that closed cell foam and neoprene reflect rather than absorb and are modestly effective at particular positions, but rarely eliminate the interference.

Going deeper: the rim and the dome. The two pieces of geometry that are not tone fields do more than hold the instrument together. The rim is deliberately stiff, massive and damped by its adhesive joint, which makes it an acoustic termination: bending waves arriving there meet a large impedance mismatch and are absorbed rather than reflected back into the shell as whole-instrument modes. It also seals the cavity, which is the precondition for any Helmholtz behaviour at all, and its diameter fixes the internal path lengths that put the crossover bands where the table above shows them. The dome, meaning the overall convex curvature of each shell, is what makes thin sheet stiff. A curved plate resists bending far more than a flat one of the same thickness, which is what lets a 1 mm shell hold a tuned note without flopping. Curvature also varies across the shell, falling away sharply near the rim, and that gradient is part of why tone fields cannot be placed in the outermost band and why the fields nearest the rim behave differently from those near the ding. Locally, the small dome or dimple at the centre of each tone field applies the same principle at small scale: PANArt called their version dome embossment, discovered in 1997, and described the resulting saddle form prestress as the Rohner and Schärer buckling. It stiffens the middle of the field, sets its boundary conditions and suppresses some harsh high modes.

See also: PHY-03, ANA-07, PHY-17

2 - How a note works

PHY-01How does a single tone field produce a pitch?#

beginner

Nothing is attached and nothing is tensioned in the way a string or a drum head is. The tuner is working with three variables in the metal itself: the area of the field, its thickness, and its curvature together with the residual stress locked into it. Larger and thinner lowers the pitch; more curvature and more prestress raises it. Every hammer blow moves some combination of the three, which is why tuning a handpan is a slow iterative process rather than a single adjustment.

When you strike the field, you deform it briefly. The steel’s elasticity pushes it back, it overshoots, and it oscillates. Because it is a two dimensional plate rather than a one dimensional string, it can oscillate in many different spatial patterns, called modes. Each mode has its own frequency and its own map of where the steel moves most and where it barely moves at all.

The untuned steel around the field is what makes this work. It is thicker, stiffer and differently curved, so it presents a large impedance mismatch at the edge of the field. Vibration reaching it is largely reflected back into the field rather than escaping across the shell. Without that boundary you would have one enormous ringing dome, not nine separate notes.

The dimple or small dome at the centre of the field plays into this too. It stiffens the middle of the plate, which changes the shapes the field can vibrate in and helps suppress some high, harsh modes. Makers differ on exactly how they use it.

Finally, the field is not radiating in free air. It is the skin of a closed cavity with a port, and that cavity pushes back. See PHY-09.

See also: PHY-02

PHY-02What are the three tuned partials?#

beginner

This is the defining trick of the instrument and it comes straight from the Trinidadian steelpan tradition that PANArt came out of. Wikipedia’s description of the Hang puts it plainly: each tone field contains a fundamental tone, an overtone tuned to an octave above that fundamental, and an additional overtone a perfect fifth above that octave. PANArt’s own writing uses the same three: the fundamental note, its octave, and its fifth above that octave.

In interval terms the three partials sit at frequency ratios of roughly 1 : 2 : 3. That matters, because 1 : 2 : 3 is the beginning of the natural harmonic series, the same series a vibrating string produces. A plate does not naturally do this. Left alone, a flat plate’s modes fall at ratios that are not simple whole numbers at all, which is why an unshaped sheet of steel sounds like a crash rather than a note. The tuner’s job is to force three of those inharmonic plate modes into a harmonic relationship by shaping and stressing the metal.

Because the three partials line up with the harmonic series, your ear fuses them into a single pitch with a rich timbre rather than hearing three separate tones. That fusion is what makes a handpan note read as a note.

Higher modes exist and are not tuned to anything in particular. PANArt described up to a dozen further natural harmonics distributed across the higher frequency regions, and these contribute the shimmer and complexity above the tuned three. A tuner will suppress the ugliest of them but will not try to place them precisely.

Variations exist. Some makers and some instruments use a fourth rather than a fifth as the third partial, or aim at fundamental plus two octaves. These are deliberate design choices, not errors, but the octave plus compound fifth arrangement is overwhelmingly the standard.

See also: PHY-03, PHY-19

PHY-03What happens when the partials drift?#

intermediate

Alignment is what makes three modes read as one sound. When the octave partial sits, say, fifteen cents sharp of a true octave, it no longer coincides with the second harmonic your ear expects from the fundamental. The two beat against each other, producing a slow pulsing that you hear as instability rather than as two pitches. Drift the fifth as well and the fusion breaks down further and the note takes on a clangy, gong like quality.

Sustain suffers too. When modes are harmonically related they share energy coherently; when they are not, the energy exchange becomes messy and the note dies faster and less smoothly.

Drift has several causes, and they behave differently:

• Playing too hard, especially with mallets or sticks, gradually deforms the tone field and moves the partials. This is the most common cause and it is permanent until retuned.
• Impact damage from a drop or a knock can move a note dramatically in one event.
• Repeated temperature extremes stress the steel and the seam over time. Ordinary daily temperature variation is not a concern.
• Poor original tuning. An instrument rushed through its final tuning has stresses that have not been properly relieved, and it will settle and drift much sooner than a patiently built one.

Note that not all wobble is drift. Crossover, the wave interference in the air cavity, produces a wobble on specific notes that is a property of the shell geometry and cannot be tuned out. Saraz measured typically 20 to 50 cents of wobble on B flat 4 in the sustain of their 21 inch instruments, and stated plainly that this happens no matter how well the note is tuned. Before concluding an instrument is drifting, check whether the affected note sits in that band for its shell size.

Handpans can be retuned, by the original maker or by a specialist. It is skilled work and not every instrument is worth it.

See also: PHY-13, TRB section

PHY-04Why does a handpan note sound harp-like or bell-like?#

beginner

Break the spectrum into two layers and it becomes clear.

The bottom layer is the three tuned partials. Fundamental, octave, compound fifth. That is the opening of the harmonic series, and it is what a string does naturally. Your auditory system is superbly good at recognising that pattern and collapsing it into a single fused pitch with a warm, singing character. This is the harp, or the plucked string, in the sound.

The top layer is everything above those three. Plate modes that have not been forced into any particular relationship, spread across the higher frequencies. That is what bells, gongs and cymbals produce, and it gives the shimmer, the metallic sparkle, and the slight sense of a cloud of sound hovering above the pitch.

Two more ingredients thicken it further. The Helmholtz resonance of the cavity, typically somewhere around C2 to G2 and measured at about 85 Hz on the Hang, sits underneath everything and adds a low breath. And every strike also excites the neighbouring tone fields, which answer at their own pitches. PANArt catalogued seven distinct contributors to the Hang’s sound: contact noise from the hand, the cluster response of the whole resonator, hammered vibration modes, coupling between harmonically related fields, the overtones of each field, the indirect stimulation of neighbouring fields, and the Helmholtz resonance of the cavity.

The proportions between these layers are what you are actually judging when you compare instruments. A very bright instrument has a strong inharmonic upper layer, which reads as metallic or, unkindly, tinny. A very dark one has it suppressed, which reads as warm but can sound dull. Good makers place it deliberately.

The attack transient matters too. The first few milliseconds, before the modes settle, contain a burst of broadband noise from the hand meeting the steel. That is a large part of why fingers, fingertips and thumbs all sound different on the same note.

See also: PHY-07

PHY-05Why do neighbouring notes ring when I strike only one?#

intermediate

This is sympathetic resonance, the same phenomenon that makes an undamped piano ring when you sing into it. A tone field is a tuned oscillator, and any oscillator will pick up energy from a driving force close to one of its own frequencies.

The mechanical path is the shell itself. The interstitial steel is a good boundary but not a perfect one, so a small fraction of the struck field’s energy travels outward as bending waves and arrives at other fields. PANArt named this explicitly as one of their seven sound sources, distinguishing coupling, meaning energy transfer between harmonically related fields, from neighbours, meaning the indirect mechanical stimulation of adjacent fields.

The acoustic path runs through the enclosed air. The struck field radiates inward as well as outward, the cavity air carries that energy across the instrument, and it arrives at the underside of every other field. This path is why the effect is stronger with the port unobstructed and why it changes when you sit the instrument on your lap.

The zigzag note layout is designed partly around this. By putting scale neighbours on opposite sides of the circle, makers ensure that the notes which are physically adjacent, and therefore couple most strongly through the steel, tend to be a third, fourth or fifth apart. Those relationships are consonant, so the sympathetic ringing reinforces the harmony rather than clouding it. See ANA-03.

There is a limit to how much you want. Too much coupling and individual notes lose definition, sustain shortens because energy is escaping the struck field faster, and fast playing turns into a wash. This is one of the practical costs of squeezing extra notes onto a shell, and one of the things experienced players listen for when evaluating an instrument: strike one note firmly, and ask whether the answer from the rest of the instrument is a halo or a mess.

See also: PHY-06

PHY-06What is sustain and what governs it?#

intermediate

A struck tone field holds a fixed budget of energy and spends it. Sustain is simply how slowly it spends.

Internal damping. Every flex cycle turns a little of the energy into heat inside the metal. This is a material property and it is why steel choice matters. PANArt listed low energy absorption and high restoring force among their explicit design targets for the nitrided sheet. Stainless instruments are widely reported to sustain longer than nitrided ones, and long controlled sustain is the main selling point of proprietary stainless such as Ember.

Radiation. Energy that becomes sound has left the field, and that is the useful loss. A field coupled efficiently to the air is loud and short; one coupled inefficiently is quiet and long. There is a real trade off here, and it is not one makers can escape.

Leakage. Energy travelling out of the field into the surrounding steel and into neighbouring fields is gone from the note you played. Well isolated fields with generous interstitial steel around them ring longer than crowded ones, which is one of the hidden costs of high note count layouts.

Two more factors:

• Thickness and stiffness. Thicker, stiffer fields store more energy relative to what they lose per cycle, so they generally ring longer.
• Tuning quality. Well aligned partials sustain more smoothly. Misaligned ones beat against each other, and the note both dies faster and dies unevenly. See PHY-03.

Sustain is not straightforwardly a virtue. Very long sustain means notes overlap, which is glorious for slow ambient playing and problematic for fast rhythmic playing. It also gives you more time to hear crossover wobble on affected notes. Plenty of experienced players deliberately choose shorter sustaining nitrided instruments for exactly this reason.

Typical figures vary far too much between instruments, notes and materials for a single number to mean anything. Judge it by ear, on the instrument, playing what you actually play.

See also: ANA-14, PHY-08

PHY-07Why does hitting harder change the timbre and not just the volume?#

advanced

A linear oscillator scales cleanly: twice the input gives twice the output at the same frequencies. Real tone fields are not linear. Two things break the linearity.

Geometric nonlinearity. A shallow dished shell resists small deflections one way and large deflections differently, because deflecting it far enough starts to stretch the material in the plane of the sheet rather than merely bending it. Stretching is much stiffer than bending. The result is that effective stiffness rises with amplitude, so a very hard strike momentarily sharpens the note before it settles back as the amplitude decays. That downward pitch glide during the first moments of a loud note is audible on most instruments if you listen for it.

Mode coupling. Once nonlinearity is in play, modes stop being independent. Energy pumped into the fundamental can transfer into higher modes, including the untuned inharmonic ones. That is why a hard strike sounds not just louder but brighter, edgier, more metallic and more bell like, while a soft strike sounds pure and flute like.

There is a third, more mundane contributor: the attack transient. The contact between hand and steel is broadband noise, and its spectrum depends on how fast and how rigidly the hand arrives. A relaxed fingertip and a stiff knuckle at the same volume produce measurably different transients.

Practically, this is the whole basis of expressive handpan playing. Dynamics on a handpan are timbral, not merely loud and quiet. Ghost notes played at very low amplitude sound warm and rounded because the upper modes are barely excited; accents sound bright and cutting because they are. Most of what distinguishes an experienced player from a beginner is control over this dimension.

It is also why hitting hard damages instruments. Deform a field far enough, often enough, and the deformation stops being elastic and starts being permanent, which moves the partials. See PHY-03.

PHY-08Why does a handpan note decay so slowly compared with a drum?#

advanced

Compare the two systems directly.

Mass and stiffness. A drum head is a thin membrane with no bending stiffness of its own, held up entirely by tension. Its restoring force comes from that tension, and it is light enough to be strongly loaded by the air it pushes. A steel tone field a millimetre thick has real bending stiffness and real mass. It is far less affected by the air it is driving.

Radiation efficiency. This is the biggest factor. A drum head is a large, light piston that couples extremely well to the air, which is exactly why drums are loud and why they stop quickly. Good coupling means fast energy transfer, and fast energy transfer means short decay. A handpan tone field is smaller, heavier and stiffer, and it radiates far less efficiently. That inefficiency is why it is quieter than a drum and why it rings for seconds rather than a fraction of a second.

Internal damping. Skin, plastic and the rope or lug hardware of a drum all convert vibration to heat readily. Nitrided or stainless steel is an unusually low loss material, and makers select and treat it specifically to keep those losses low.

Harmonic alignment. Because the three tuned partials sit at ratios near 1 : 2 : 3, they do not beat destructively against each other. Inharmonic partials, which dominate most drums, interfere and smear the sound into a short, noisy burst.

Termination. A drum head is clamped at its rim to a shell that absorbs energy. A tone field is bounded by a stiffness mismatch that reflects energy back into it rather than absorbing it.

There is one more contribution unique to this instrument: the cavity. Energy that leaves the field is not immediately lost to the room. Some of it circulates in the enclosed air and in the other tone fields, and comes back. That recirculation extends the audible tail even after the struck field itself has quietened.

See also: PHY-12, REL section

3 - Tuning theory and measurement

PHY-15What does “in tune” mean for a handpan, and why is it harder than for a guitar?#

intermediate

A guitar string has one dominant fundamental and a naturally harmonic overtone series that follows it automatically. Tighten the string and everything moves together. The tuner has one degree of freedom per string and immediate feedback.

A handpan tone field has to satisfy three conditions at once. The fundamental must be at the right absolute pitch. The second partial must be a true octave above it. The third must be a fifth above that octave. And the tuner’s only tools are the shape, thickness and internal stress of the steel, all of which affect all three partials simultaneously and in different proportions. Hammering to flatten the fundamental will move the octave and the compound fifth too, usually by different amounts and sometimes in different directions. Tuning is therefore an iterative search: adjust, measure, adjust again, converge.

Then multiply that by nine or more notes on one continuous piece of metal. Working on one field disturbs its neighbours, so the tuner is not solving nine independent problems but one coupled problem with about thirty simultaneous targets. This is why building a handpan takes days rather than minutes, why makers have waiting lists, and why price correlates so strongly with tuning quality.

The permanence is the other half of it. A guitar goes out of tune constantly and you retune it constantly. A handpan holds its tuning for years and then, when it drifts, requires a skilled person with a hammer to bring it back. There is no user serviceable adjustment. Nothing about the instrument can be corrected by the owner.

One consequence that surprises new owners: a handpan cannot be tuned to another instrument. If you want to play with a piano at A=440, you buy an instrument built at A=440. If you buy one at A=432, you have bought a different instrument, permanently.

See also: PHY-16, PHY-03

PHY-16Cents, A=440 and A=432: what is actually true?#

intermediate

Cents. An octave is 1200 cents and a semitone is 100. The scale is logarithmic, so a cent is the same perceptual size at every pitch even though it corresponds to a different number of hertz. Roughly, most listeners can detect a difference of about 5 to 10 cents on sustained tones; 20 cents is clearly audible; 50 cents is a quarter tone and unmistakable. Makers commonly quote tolerances in single figures of cents.

Where 440 came from. Before the twentieth century, concert pitch varied enormously, from around A=376 Hz on a Lille organ of 1700 to about A=506.9 Hz at Halberstadt in 1361. France legislated the diapason normal at A=435 in 1859, partly in response to complaints from singers about pitch inflation. A=440 was recommended at an international conference in London in 1939 and confirmed by the International Organization for Standardization as ISO 16 in 1955. It is a convention that won, not a discovery.

Where 432 came from. Two strands. Joseph Sauveur’s scientific pitch, around 1700, fixed middle C at exactly 256 Hz for mathematical tidiness, which puts A at about 430.54 Hz, not 432. Separately, Verdi campaigned for standardisation in Italy: he actually advocated matching France at 435, and when the Italian government’s commission proposed 432 for mathematical convenience he accepted it, calling the difference almost imperceptible. Italy decreed 432 in 1884. So “Verdi tuning” is a real historical episode, but Verdi’s own preference was 435 and he treated the difference as trivial.

The modern claims. The frequently repeated link to the Schumann resonance does not survive checking: that resonance is about 7.83 Hz and has no clean arithmetic relationship to 432. There is no peer reviewed evidence that 432 Hz has therapeutic properties that other tunings lack.

What this means for buyers. Both are widely offered. Some makers charge a small premium for 432 because it is less common; many charge the same. The one real consideration is practical: an A=432 instrument will not play with anything tuned to A=440 without retuning the other instrument. Choose on that basis, and on whether you prefer the sound, rather than on physics claims in either direction.

See also: PHY-15

PHY-17How do temperature and humidity shift a handpan’s pitch?#

intermediate

Take the two mechanisms separately.

The steel. Heating steel expands it slightly and reduces its elastic modulus slightly. Both effects lower the natural frequencies of a tone field, but for the temperature swings you encounter in normal life the movement is small compared with the 5 to 10 cents a listener can detect. Makers are consistent that ordinary everyday temperature change is not something to worry about. What does matter is repeated exposure to extremes, which stresses the metal and, importantly, the adhesive seam over time. A hot car is the standard cautionary example, and the seam is usually the least heat tolerant part of the instrument.

The air. This is where the audible change lives. The speed of sound in air rises with temperature by roughly 0.6 m/s per degree Celsius, so a cold instrument has a lower Helmholtz frequency and lower cavity standing wave frequencies than a warm one. Since the crossover bands are set by those standing waves, they move with temperature. Saraz give a specific example: A4 on their 21 inch chamber sounds good at around 27 degrees Celsius but becomes problematic below about 16. The note itself has not gone out of tune. The interference pattern has moved onto it.

Humidity changes the speed of sound too, because water vapour is lighter than dry air, but the effect is small compared with temperature at ordinary conditions. Humidity’s real significance for a handpan is corrosion, not tuning: moisture on nitrided or raw steel is what causes rust. See ANA-15.

The practical upshot for players is to let a cold instrument come up to room temperature before judging it, and never to evaluate an instrument you have just carried in from the cold. A quarter of an hour is usually enough. Avoid forcing it with heaters or hot water, which stresses the seam for no benefit.

See also: PHY-14, CAR section

PHY-18Equal temperament or just intonation: which does a handpan use?#

advanced

This sounds contradictory until you separate the two things being tuned.

Between notes, makers use equal temperament because that is what everything else uses. It lets the instrument play with pianos, guitars and recordings, and it makes scale names meaningful. In equal temperament every semitone is exactly 100 cents, which means most intervals are slightly impure: an equal tempered perfect fifth is about 2 cents narrow of a pure 3 : 2, and an equal tempered major third is about 14 cents wide of a pure 5 : 4. Those compromises are the price of being able to play in any key.

Within a note, the tuner aims at pure ratios. The octave partial should be exactly twice the fundamental and the compound fifth exactly three times it. There is no reason to compromise here, because these are partials of a single sound rather than separate notes, and any deviation produces beating within the note itself. See PHY-03.

The interesting consequence is that a handpan is subtly more consonant than the same notes on a piano. Because a handpan scale is usually a single mode with seven to nine notes and no chromatic obligations, and because each note carries a strong pure twelfth, the intervals you actually play tend to reinforce each other. Play a fifth: the compound fifth partial of the lower note lands very close to a partial of the upper note, and they lock.

Genuinely just intoned handpans, where the notes themselves are placed at pure ratios from the tonic rather than at equal tempered frequencies, do exist. They are rare, almost always commissioned, and they trade away compatibility with other instruments. A few makers experiment with other tunings entirely, including microtonal and non Western systems, and PANArt eventually abandoned an external reference altogether: from 2010 the Free Integral Hang was freed from the 440 Hz standard and each instrument was attuned to itself.

Ask before assuming. If it matters to you, the maker will tell you what reference they use.

PHY-19How do makers and players measure tuning?#

advanced

Why an ordinary tuner is not enough. A guitar tuner takes an input, picks out what it thinks the fundamental is, and shows one number. Feed it a handpan note and two problems appear. First, it tells you nothing about the two partials that determine whether the note actually sounds right. Second, it can lock onto the wrong partial, especially on notes where the octave is strong, and report a pitch an octave up. It is fine for confirming that a note is roughly where the maker said, and useless for diagnosing why a note sounds wrong.

What is actually used. Tuners work with real time FFT spectrum analysis. The signal from a microphone is decomposed into its frequency components and displayed as a spectrum, so all three partials are visible simultaneously along with everything above them. Software commonly mentioned in the community includes general purpose analysers on laptops and phone apps built for the job; the specific tool matters much less than having enough frequency resolution and a display that updates fast enough to watch a note decay. Strobe tuners are also used, since they resolve individual partials precisely.

Practicalities that catch people out.

• Microphone placement. Close to the field for isolation, further back for a representative overall sound. They give different answers, and both are legitimate.
• Strike consistency. Nonlinearity means a hard strike momentarily sharpens the note. Measure at a moderate, repeatable dynamic and read the pitch after the initial transient has passed, not during it.
• Which part of the decay. Partials do not decay at the same rate. A note measured immediately after the strike and the same note measured two seconds later can read differently, particularly if crossover is affecting it.
• Temperature. Let the instrument settle at room temperature first. See PHY-17.
• Neighbours. Other fields ring sympathetically and put their own peaks in your spectrum. Learn to recognise which peaks belong to the note you struck.

For an owner, the honest advice is that measurement is diagnostic, not prescriptive. Knowing a note is 8 cents flat does not help you fix it, and small readings are easy to over interpret. Measure when something sounds wrong, to find out what.

See also: PHY-20

PHY-20How do I read a tuning report or a spectrum?#

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Not every maker supplies a report and there is no standard format. A typical one gives per note: the note name, the intended fundamental in hertz, the measured fundamental, and then the same for the two tuned partials, with deviations in cents.

How to read it.

• Deviation on the fundamental tells you whether the instrument is at the pitch standard it claims. A consistent offset across all notes usually means the whole instrument is a little sharp or flat rather than mistuned, which is not a fault.
• Deviation on the octave and compound fifth is the interesting column. This is where fusion lives. A note whose fundamental is spot on but whose octave is 20 cents out will sound worse than one whose fundamental is 8 cents off but whose partials are perfectly aligned.
• Consistency across notes matters more than any single figure. An instrument where every note sits within a few cents is the work of someone who converged properly. One with two immaculate notes and one wild one usually means the tuner ran out of patience or out of metal.
• Do not expect zeros. Steel is not a spreadsheet. Small deviations are normal on excellent instruments.

Reading a live spectrum. Strike a note and look for the pattern. The fundamental is normally, though not always, the tallest peak. Multiply its frequency by 2 and by 3 and check that peaks sit at those points. If the peak near 2f is visibly offset from exactly 2f, that is the drift you can hear. Above the third peak you will see a scatter of unaligned peaks, which is normal and is the bell-like layer of the sound. Down at the bottom, often below 100 Hz, there is usually a broad low peak that appears on every note: that is the Helmholtz resonance of the cavity, and PANArt noted it is detectable in every spectrum the instrument produces.

A caution. A report describes the instrument on the day it was measured, in the conditions it was measured in, by the person who built it. It is evidence of care, and it is a useful baseline for spotting drift years later. It is not a guarantee, and it is not a substitute for playing the instrument.

See also: PHY-02, BUY section