Meditation (Zen) Chime

Chime bars that produce a high pitched ringing tone when struck with a mallet are helpful for focusing attention, whether it’s to denote the start of a yoga class or meditation session or for something more prosaic, like announcing that dinner is ready. They’re easily produced with basic metalworking and woodworking skills. You can make a simple, one-bar chime or a twin one that either produces harmonising notes or beats (rhythmic pulses of loudness).

The main material you need for this project is cylindrical metal bar. Stainless steel, aluminium, bronze, copper and brass are the most suitable metals, so look out for cheap sources of these rods. Mild steel will work too, although it will need to be kept highly polished to prevent rusting. And it’s worth choosing a nice piece of hardwood for the base so that the chime will look as beautiful as it sounds.

I’m no musician so I’ve kept the theory in this ‘Ible fairly light, and you don’t even need to read it to make a chime. But if you are interested then Step 7 explains what’s happening in the bars waveform-wise and how to tune a chime to a particular pitch, should you wish to.

Circular metal bar/rod, ideally polished, 6-12mm (¼-½”) diameter and 15-30cm (6-12”) long

Block of hardwood slightly longer than the metal bar and about 40mmx40mm (1⅝” x 1⅝”) in cross section

Fine, strong, inextensible cord

20-25mm (¾-1”) diameter wooden ball or near-spherical cupboard knob

20cm (8”) length of wooden dowel, 6-8mm (¼-⅜”) diameter

2 ring-pull tin lids (eg from tuna cans)

Sharpie or other permanent marker

Hacksaw

Metal file

Carpenter’s square

Wood saw

Router and bullnose/cove router bit - not essential

Wood glue - may not be needed

Sandpaper

Wood finish such as oil or wax

Black paint - optional

Superglue (CA glue) - optional

The first thing to do is to assess the bar you have and decide how best to use it. You could even make a two-bar chime if it’s long or if you have bars of different diameters – see Steps 4 and 7 for more details. All you need to know at this stage is the bigger the diameter of a bar of any given material the higher its pitch will be, and the longer it is the lower the pitch. A sensible length for a chime bar is somewhere between 15 and 30 cm (6-12”). Given the relationship with diameter, you might want to be nearer the 30cm end of the scale for a fat bar and closer to 15cm for a skinny one.

We’ll get the loudest, longest note if the bar is simply supported at the points corresponding to the nodes of the standing wave within it. Start by measuring the length of each bar and working out what 22.4% of that length is. Make a mark at that distance from each end with an indelible pen. Why 22.4% you ask? Surely at the fundamental frequency the antinodes will be in the centre of the rod and at each end, meaning that the length of the rod will be one wavelength and the nodes will be 25% of the distance from each end? Alas no, rods are not strings – although I had no idea they behaved differently until I researched this. For a detailed explanation refer to:

http://coccweb.cocc.edu/bemerson/public_html/physics/PH213/213Topics/Documents/ChimePaper.pdf, The Physics Teacher, Vol 36, April 1998, A Student Project on Wind Chimes

This explains that a 4^th order equation (yikes!) is needed to describe the oscillation of a wave in a free rod. For those who want to know more, the derivation of the node points can be found in that paper and its appendix, but your maths had better be good if you want to work through it.

To create temporary supports for the bar, take a pair of steel ring-pull tin lids and bend the ring pulls upright as shown in the photo above so that they will hold the bar. Having made the supports, place the bar on them such that it rests on each ring at a 22.4% mark.

Strike the centre of the bar (downwards) with the edge of a piece of wood, lifting your hand up quickly to prevent the improvised mallet from damping the vibrations by remaining in contact. You should hear a clear, ringing note that persists for several seconds. Don’t worry if it isn’t very loud, at present the sound is radiating out from the bar in all directions and one purpose of the stand we’ll make in Step 3 is to reflect more sound in an upwards direction.

So, do you like that note? If it’s too high there’s nothing you can do about it except find a longer bar or one with a smaller diameter. But if it’s too low, you can raise the pitch by shortening it. How much? Well, the frequency F is inversely proportional to the square of the length L, and doubling the frequency will take the note up an octave, which means halving the length will raise the pitch by 2 octaves. Expressing this mathematically, where k is a constant:

F=k/L²

If the length halved to L/2, the new frequency f is 4k/L² and f/F = 4. Which means f = 4F, ie two doublings of frequency, which is 2 octaves.

It makes for a more interesting chime to have two bars that will create beats when sounding together, or which will harmonise (see Step 7). But if you only have a modest length of fairly thick bar to work with then think carefully before cutting it into two equal lengths because you might end up with a pitch that’s too high for anyone other than a child to hear.

Now you’ve decided how long to make your chime, and which bar to use if you are lucky enough to have a choice of diameters, cut it to length with a hacksaw. Unless you have perfect pitch and are striving to hit a particular frequency (see Step 7 for how to achieve this) it isn’t necessary to be super-accurate.

Having made the cuts, use a file to remove any unevenness or burrs from the ends, because they will be visible. Also apply a very slight bevel/chamfer to the circular edge at each end, just enough to dull the sharp edges.

Now remove any ink marks that remain from when you were testing the bars in the previous step – even Sharpie ink will rub off polished metal with a little effort. Then re-measure the length and mark the 22.4% suspension points again with a single dot for each one, on the same side of the bar. This side will be mounted downwards so that any part of the mark not covered by the suspension cords will not be seen.

To make a stand to support the chime, cut your block of hardwood a little longer than the bar, say 12-25mm (½-1”) longer. (But for a short bar you might want to leave the block long for now so it's easier to handle, and cut it to length later - that's what I did.)

You need to cut a central channel down the length of the stand to help reflect the sound out into the room. The easiest and quickest way to do that, if you have a router or router table, is to use a cove bit (aka a round nose or core box bit) which will cut a nicely curved slot. Ideally, use the type of bit that doesn’t have a guide bearing on the tip. Unfortunately, I only have the bearing type (see 1st photo above), which meant I had to cut my piece of wood in half lengthwise and router each side individually before sticking them back together (again, see photos). That worked fine.

Without a router, you could create a flat-bottomed slot by making a series of parallel cuts with a table saw or hand saw and then removing the remaining wood with a chisel in the case of hand saw cuts. A slot with a flat base is better than no slot at all.

Alternatively if all you have is a hand saw you’ll need to cut the wooden block down the middle lengthways then saw down from the top of each piece to the desired depth, before sawing perpendicular to those cuts to create the flat base of the slot. Finally, glue the block back together to make a U-shaped slot.

The slot’s width at the top should be about 50-75% wider than the bar.

I haven’t tried making a beating or harmonising pair, but I’m guessing that for a beating pair (see next step) you could just make a double-width stand with a single slot because the 22.4% points will be so similar that both bars can be suspended using the same cord placement. But a harmonising pair (Step 7) of the same diameter will be quite different lengths, with correspondingly different suspension points, which could be difficult to achieve unless each bar has its own slot “walls” to support its suspension cords. In any case, two bars will need to be separated by enough distance to make it easy to strike each one individually, so allow for that when deciding on the width of the stand.

A beating pair needs to be close in pitch but not identical. The number of beats per second is the difference in frequencies. The frequency of beats is up to you, but somewhere around 1-2 per second is a good place to start.

You’ll need two rods of (nominally) the same length, cut from the same bar. Support your pair of rods next to each other in the same way as you did in Step 1, ie with ring pulls at the 22.4% marks. Strike each one in turn first, to check it makes a pleasing sound. The notes should sound identical unless you have an extraordinarily good musical sense.

Now strike one rod followed immediately by the other one and you should hear the rhythmic beats. If they are too fast for your liking then the difference between the frequencies is too great and you will need to file a bit off the end of the longer rod to make it closer in length to the shorter one. If they’re too slow, then widen the frequency gap by filing metal off the end of the shorter bar. (And if you can’t tell which is which, just designate one as longer and mark it accordingly. If you’ve guessed wrong it just means a bit of extra filing.) Keep testing until you are happy. It shouldn’t be necessary to move the suspension points for the bar you are adjusting, a millimetre or two isn’t going to make any significant difference. But once you’ve finished, re-measure and re-apply the marks at the 22.4% points.

The bar will be suspended with cord at the marked points, in such a way that it sits just above the wooden stand.

Start by marking the middle of the stand (lengthwise) with a pencil, and also making a mark in the middle of the chime bar. Place the bar in the slot with these marks aligned, so that the bar is centrally positioned. Then make pencil marks on the top face of the stand to correspond with the marks on each bar at the 22.4% points.

Use a carpenter’s square to draw lines across the top face at these marks, parallel to the ends of the stand, and also lines down the side faces of the stand and across the base. You’re going to cut a continuous narrow slot along these lines to carry the cord from which the bar will be suspended.

The suspension cord should be a fine, strong, inelastic cord that can be tightly knotted. I used a braided backing line, as used for fly fishing. Strong sewing thread, such as the linen or bonded nylon that’s used for stitching leather, would be suitable too. Avoid anything that’s difficult to knot, like monofilament.

With a saw, cut shallow slots along the pencil lines across the top face of the stand. Ideally these two slots will be just wide enough and deep enough to take the cord, so that it sits flush with the top surface. The slots down the side faces of the stand and underneath it need to be the same width but a little deeper, to hide the cord. I used a Japanese pull saw with a very fine kerf which made a slot the same width as the cord. That was great except there was no room to hide the knots within it. If you have the same issue, I suggest drilling a small hole over each of the two slots on the underside of the stand, then the knots can be tucked into these holes and the stand will sit perfectly flat on a table.

Sand the stand smooth, remove any remaining pencil marks and then give it two coats of oil or any other wood finish of your choice. I used teak oil. Leave it to dry before proceeding.

The bar needs to be suspended so that it’s held with its base at more or less the same height as the top face of the stand, which is only possible if the suspension cords are tied very tightly. I started out by using a couple of tiny wooden wedges in the slot to support the bar temporarily at the correct height while I tied the cords, but then I realised that laying the bar on a bench or table with the top face of the stand butted up to it would work too (see 7th image of this step). The bar is resting against one of the twin top faces in this position rather than being over the central slot, but that’s fine, it can be moved across after the cords are tied.

Cut a generous length of cord – 3 times the circumference of the stand will be ample - and take the centre of it in a 360° loop around the bar at or near one of the marked node points before crossing the ends and taking them in opposite directions around the stand to meet on what will be the underside (see diagram). Slide the cord into all the slots and then pull it as tight as you can before knotting the ends together securely, preferably on the underside of the stand – but that’s not vital. I used a simple reef knot, aka a square knot. Having tied the cord at one end of the bar, do the same for the other end.

Now turn the stand upright and move the bar into the central, above-slot position while also ensuring that the knots end up on the underside if they aren’t there already. You’ll find that lifting the bar slightly slackens the cords enough to be able to slide them over the bar and through the slots. The best way to do the sliding is to rest the stand with one end sticking over the edge of the table, then you can move the cord at that end to where you want it by pulling on its two ends. Once you have the bar central and the knots where they should be (ie in the underside slots or in the holes, if you drilled holes), check that the bar is held high enough above the slot. When you view it from one end, the sag in the suspension cords as they pass over the top of the slot should be barely noticeable.

That done, if necessary slide the bar through the loops of cord until they are at the marked points, again by lifting the bar slightly to reduce the tension. If the cord isn’t thick enough to cover the 22.4% marks on it, just rotate the bar to bring them to the underside where they won’t be seen.

Now you can carefully turn the whole thing upside down and add a drop of CA glue over each knot if you wish, to stop them coming undone or moving. Just make sure the glue is dry before you turn the stand the right way up again, you don’t want to end up with a chime that’s stuck to the table.

The chime needs to be struck at its centre with something that’s reasonably hard – being a bit off centre won’t make a huge difference so don’t feel you need to mark the centre point. You can test it at this point by hitting it in a downwards direction with the edge of a piece of wood. Be sure to lift the test mallet smartly away after the strike, because if it remains in contact it will damp the vibrations and the chime won’t sound as loud or for as long as it could.

A ball-shaped mallet head is good because the point of contact between head and chime bar will then be small and precise. But if you can’t find a wooden ball or large bead of a suitable size then look for other things that will work, like a rounded cabinet knob or a cord pull. A small child’s ball made from hard rubber might be suitable too – just try it if you have one. The diameter of the ball needs to be in proportion to both the chime bar and the dowel that will become the handle of the mallet, or it will look odd.

Measure the diameter of the dowel and then drill a hole part way into the ball to take it. Doing that is easier if you first create a circular flat on the ball by rubbing it on coarse sandpaper on a table. Then you will be drilling into a flat surface that you can first mark the centre of.

Stuff the dowel temporarily into the mallet head and then decide where to cut off the excess length. Again, the mallet will look odd if the handle is out of proportion, but it does need to be long enough to fit in a hand.

As a guide, the head of my mallet is a 22mm (⅞”) ball and the dowel handle is 19.5cm (7¾”) long and 6mm (¼”) in diameter. This is for a stand that’s 32cm (12½”) long.

Saw the handle to length then smooth the cut end with sandpaper before sticking the other end into the head. Either apply a wood finish or paint the whole thing one colour.

Your meditation chime is finished, but read on if you’re interested in how to achieve a particular note, or two (or more) chimes that harmonise.

The basics – what’s happening in the chime

When a bar is struck in its centre, a wave will propagate through it and bounce off its ends, causing it to continue to vibrate for a while, producing sound as it does so. The point where it is struck will deflect the most, and this is the antinode of the waveform. The nodes of the fundamental frequency are, as mentioned in Step 1, 22.4% of the total length from each end, and the amplitude of vibration here is (theoretically) zero. There will also be harmonic frequencies that are higher in pitch, with shorter wavelengths and more nodes.

As explained in Step 1, the relationship between the fundamental frequency and bar length is

F=k/L²

where F is frequency, L is the length and k is a constant.

The frequency is also proportional to the diameter of the bar, ie F=aD/L²

where D is the diameter and a is a (different) constant which depends on the material the bar is made of.

Getting the note you want

What all of this means is that the pitch of a chime can be predicted if you know the dimensions of the bar and what metal it is. And if you want the chime to produce a certain note, you can work out what length you need of a bar of a particular diameter. Fear not, tedious looking-up of constants and calculations can be avoided by using online calculators produced by others – try googling “musical note chime calculator”. I recommend the one at Lee Hite’s site: https://leehite.org/Chimes.htm Many such calculators are intended for use by those making wind chimes from tubes, just set the internal diameter to zero if necessary.

Harmonic pairs

Two chimes will sound good together when they harmonise, which just means that their frequencies have a mathematical relationship, the usual ones being 4:5 (a major third) or 2:3 (a perfect fifth). Given the F=aD/L² relationship, you can see that you could cut lengths from a bar of a particular diameter D to give a harmonic pair.

For example, if the lower note of frequency F₁ is produced by a bar of length l, then for a bar that will give a note F₂ which is a major third higher, its length L is found as follows:

a = L²F₂/D = l²F₁/D which means that L² = l²F₁/F₂

But F₁/F₂ = 4/5 therefore L = √(4/5)l = 0.894l

In other words, the higher note requires a bar that’s about 11% shorter than the bar that produces the base note of the major third.

Personally, I think chime bar pairs look better when they are the same length, then the stand length suits them both and they can be suspended with a single cord at each end because the nodes will be the same distance from the ends for both. That can be achieved by making the ratio of their diameters the same as the desired frequency relationship, eg 4:5 for a major third. So if you can find bars made from the same material that are, say, 8mm and 10mm in diameter, or 8mm and 12mm for a perfect fifth, that will work.

Just make a single stand for the pair, wide enough for them both and with a single slot down the centre.