Memuks | Ben Hjertmann

PVC Memuks

Want a fun weekend project that won't use your whole allowance? Build a Memuk!

Below you will find descriptions and tunings of my first few memuks, and scroll down for instructions on how to build your own!

The Memuk (as I call it, from membrane-duduk) is a membrane reed instrument. The body can be made or wood or bamboo, or PVC pipe and is similar to the body of a flute. The key difference is the mouthpiece and reed.

Aerophones (wind instruments, pipe organs, voices) work by cutting or interrupting an air stream. On a flute or organ pipe the air stream is cut by the relatively sharp edge of the instrument. Flutists aim the air over the edge of the mouthpiece.

Reed instruments are a subset of aerophones including clarinets, oboes, bassoons, saxophones, and reed organs. Take the clarinet as an example. As the clarinet player blows over the reed it vibrates and alternates between opening and closing the air path. That interruption occurs hundreds/thousands times per second and creates a waveform which is very similar to a square (a.k.a. pulse) wave (which alternates on...off...on...off, like digital clock). For this reason the timbre of a clarinet is very similar to square wave in having only (or mostly) odd harmonics present in its spectrum.

Membranes are normally heard in percussion instruments as drum heads, or as buzzy mirlitons on kazoos and balafons. But in this rare case, I am using a membrane as a reed. The air in blown in a smaller tube that is forced under a tight membrane of plastic shopping bag before exiting the instrument through it's body. The membrane vibrates, interrupting the air stream like a reed, but with a different timbre caused by it's shape, weight, material, etc.

The result is a buzzy, blaring wind instrument, possibly sounding similar to a duck call.

I was inspired by someone who made bagpipes in a similar fashion, later finding the incredible work of Bart Hopkin who himself has made many membrane reed instruments and who pointed to the practice separately arising by street artisans in Indonesia (who made them from old film canisters and balloons, I believe). His classic Musical Instrument Design book is worth every page of paper it was ever printed on. Highly recommended.

Memuk #1

Memuk I, shown above has equally-spaced finger holes. Ignore my DIY inaccuracies. There are 8 holes, enough for all the fingers on both hands and no thumb holes on the back. (If you want a challenge, try to guess the scale it produces before checking the answer below. The pitch of the full pipe length, with all holes covered, is the F below middle C.)

Kathleen Schlessinger's The Greek Aulos, published almost 100 years ago, which was referenced in Harry Partch's Genesis of a Music, has been the subject of much debate then and now. Simply put, she contended that the ancient greek aulos (double-reed wind instrument) did not use the scales other historians and theorists contended but instead used equally-spaced finger holes. It seems to me that what she described (equally--spaced holes) on a wind instrument certainly did happen in Greece and elsewhere, but that doesn't mean it negates all the other well-documented Ancient Greek tunings and scales.

She mentions the intuitive, Occam's Razor element, which resonates with me. Don't you think some folks would have made equally-spaced holes on wind instruments? Yes. It's visually symmetrical, easy to measure and produce, it is easy on the hands/fingers, and to the eye it just makes sense. In fact, when I was 14 or so I bought a wooden flute from a street vendor in New Orleans, and played and recorded it years wondering what the heck the tuning was. It sounded both intuitive in many ways and just a little "wrong" in others. It wasn't until I started making these memuks and revisiting Schlessinger that I realized. It was six equally spaced holes!

When we have equal divisions of a scale length, like the equally-spaced holes in this example, we get a Utonal scale as Harry Parth would call it, meaning under-tonal rather than over-tonal. At first blush this might not seem right, but the visual symmetry is scale length, i.e. wavelength of vibration, and therefore inversely proportional to vibrating frequency. What looks equal sounds like exponentially higher intervals as we move up the scale. See my Rogue 48-Equal-Divisions-of-the-Scale-Length guitar for another example. Especially if you play guitar, you will be struck by how odd it looks to see equally spaced frets. We are used to frets shrinking as we move up in pitch, giving an "equal" sound to each interval (equal divisions of the octave, EDO).

And now for the tuning reveal...

The scale for Memuk #1 is given above, showing the proportion of the pipe (wavelength) above the staff and the frequency ratio below. The lowest pitch at the left is for the full pipe length and the highest pitch at the right is with all the holes uncovered, open. Each notated pitch shows the pitch created by *opening* a hole. The air column vibrates from approximately the reed to the nearest 'escape route' out the first open hole it finds. Even though we think about the action required to *cover* a hole with our finger, the air escapes where we have a hole uncovered or out the end of the pipe if they are all covered.

When have Utonal scales whose numerator (Numerary Nexus as Partch would call it) is an even number we can divide them at the octave (half the scale length). This is what I recommend for Memuk building, as per the instructions below. Thus, the highest note played on the instrument is an octave higher than the lowest.

When the numerator is also highly divisible (18 is divisible by 2, 3, 6, and 9) we get pitches whose ratios are accordingly simple, and familiar. In other words 18/9 = 2/1 = octave, 18/12 = 3/2 = perfect 5th, 18/15 = 6/5 = 5-Limit minor third, 18/16 = 9/8 = whole step, etc.

These highly-divisible-numerator Utonal sets thus give us a magical hybrid of Otonal and Utonal intervals, if you will. The familiar ones mentioned above plus some slightly rare ones: 9/7, 9/5; some more rare ones: 18/11, 18/13, and rarer still 18/17. Notice how the 18/17 pitch is skipped, both for a lack of fingers to cover the holes, and because it keeps the scale in 13-Limit and with only 8 pitches to the octave.

Compare this to my 48-Utonal Guitar, if you're interested.

Memuk #2

Here is Memuk #2, seen in the picture above and the scale below. For this instrument, I wanted to try a longer total length and therefore a lower pitch range. I wanted to see how comfortably I could fit an Otonal scale under the fingers and include a thumb hole.

The scale for Memuk #2 is given above, in the same format as Memuk #1.

I placed a left hand thumb hole as the second-to-highest hole. This fit comfortably since the holes get closer together in this Otonal scale. They would be too close to fit next to each other but I was able to squeeze it in with the thumb. The right hand thumb is not in use. See image below.

This scale is rather simple in that it is a 13-Limit scale including Harmonics 8-16 plus 7/6. The conceptual purity of 8-16 appealed to me for this design. Like the Utonal, it also contains some of the most familiar intervals and (9/8, 5/4, 3/2, 7/4, 15/8) and gateway microtones 11/8 and 13/8.

But then, why did I add 7/6? Not only is it one of my favorite intervals, heard in much of my work (see Spiral Garden's Septangle, Shovel, Aurora, Paramonde), but it also provides a minor third and a intervallic set which repeats in the octave: 1/1–7/6–5/4 and 3/2–7/4–15/8. An inverted [014] trichord from set/cell theory, if you like. Even more importantly...When I marked out the holes for Harmonics 8-16 and laid my fingers on the marks, I noticed the fingers laid out well, but that the right hand ring finger was unused and sitting right where the 7/6 hole would be.

Finger-Hole Spacing

In the image above, you can see the finger (and left hand thumb) hole placement on the instrument.

Memuk #1 and Memuk #2 not only have different scales, but therefore different finger-hole placement and hand positions. Memuk #1's scale includes both familiar and unusual intervals, the evenly-spaced holes on Memuk #1 not only look visually organized, they are also easy to fit under the fingers (at least generally). The way the fingers might lay in their most comfortable position wouldn't be exactly evenly-spaced. In Memuk #2, you can see that the holes do lay approximately where the fingers naturally fall, but do have to stretch a bit.

All told, I am happy with Memuk #2's scale and design except for how far the right hand index finger has to stretch to reach its hole. This could be amended in two ways. I could simply remake with at a smaller total length, thus needing to stretch less far.

Or, I could adjust the scale to move that pitch into a more comfortable position for that finger. In fact, this may be a useful way to approach instrument design. Try a prototype and then compromise overall length (and thus, key/fundamental) and if needed, the scale itself.

In this case, that hole when uncovered is 11/8. This is one of my favorite JI pitches, but is admittedly uncomfortable at this scale length. So, we might ask ourselves, what pitch would be located at the comfortable position for my hand? In this case, moving the index finger down the body toward my other fingers would lower the pitch. As it happens, the pitch a quartertone lower, in a very comfortable finger position would 4/3 (Fa).

Following this logic, I designed Memuk #3, seen below.

Memuk #3

Memuk #3, not yet been built, will have the above scale. This scale is identical to Memuk #2 except for the 4/3, included for the reasons discussed above and also 5/3. I could have left 13/8 in the scale, but the lack of 11/8 made the 13/8 less appealing since the Harmonics 8-16 were not all present and there was a gap in the primes used. Furthermore, 5/3 includes another 5-Limit pitch, giving a perfect 4th (4:3) above 5/4 and a whole step (9:8) below 15/8. Note that the scale is almost but not fully repeating its intervals in its two halves (tetrachords). The lower half from 1/1 to 4/3 and the upper half from 3/2 to 2/1 are almost identical intervallically except that the 9/8 would need to be 10/9 or the 5/3 would need to be 27/16 for that to be true. Still the other four pitches in each tetrachord are symmetrical, and there are other reasons why this scale makes sense. It includes the so-called Ptolemaic 5-Limit Major scale (1/1–9/8–5/4–4/3–3/2–5/3–15/8) as well as the beautiful 7-Limit minor pentatonic (1/1–7/6–4/3–3/2–7/4).

Build Your Own Memuk

I encourage you to build your own memuk. I started with PVC for it's availability and tight fittings, but I intend to move to wood and bamboo soon. I won't go into every detail here, but I want to provide you some basic advice if you embark on this activity. I do teach private lessons in music composition and instrument building, if you are interested. Here are the basics:

Materials & Tools Needed

PVC pipe 3/4-inch Pipe, at least 3ft in length
PVC 1/2-inch Pipe, at least 1ft in length
1/2-inch to 3/4-inch Adapter
T-Joint with 3/4-inch on two sides and 1/2-inch coming out perpendicular
3/4-inch Coupling for "Cap"
Painter’s or masking tape
Drill (ideally drill press), 1/4-Inch drill bit (you can try other sizes too), sandpaper, mask/goggles

Parts and Exploded View

In the above image you can see the parts of the memuk in an exploded view. Note that the Reed Coupling and Barrel Coupling can be identical and the barrel and blow tube are identical except for the painter's tape on the barrel. Also note that the Cap at the far right is technically a PVC coupling, but it is being used as an end cap, so there's nothing it's coupling to on the unused side.

Now let's dive into the instructions! Each step below has written instructions and a video segment explaining it.

Part 1. Mouthpiece Assembly

The mouthpiece assembly contains the five middle pieces of the memuk: Barrel Coupling, Barrel, T-Joint, Blow Tube, and Reed Coupling. When this is complete, you can blow into the blow tube into the barrel as an output for the air. In this step you are prepping the assembly for the reed and body.

Directions

1. Cut two 4-inch pieces from 1/2-inch pipe with a hacksaw for Blow Tube & Barrel. If you are using PVC, you do not want to breath any of the dust. Do it with a vacuum running and a respirator or mask. After cutting, sand the ends with sand paper (keep the vacuum going and mask on), inside and outside to remove any hanging pieces. Make sure to do this so you don't breathe or swallow any PVC bits once the instrument is done.

2. Insert one of these 1/2-inch pipe pieces into the inlet of the T-Joint. This is now the Blow Tube.

3. Cut two 1-inch pieces of 3/4-inch pipe. Insert these into the sides of the T-Joint. These are now the Barrel Coupling and Reed Coupling.

4. Wrap a few winds of painters tape around around one of the pipes about a 1/2-inch from one end. This is now the Barrel. The tape is to fit the barrel snugly (airtight) into a 3/4-inch piece. Wrap just as much tape as you need to get it to fit airtight into a 3/4-inch piece. You may need to add or remove tape to make it fit properly. This tape will stop the air from flowing out over the Barrel on one side.

5. Insert the Barrel's un-taped end into and through the Couplings/T-Joint assembly so that the Barrel's end comes through to be flush with the end of the Reed Coupling and sticks out the end of the Barrel Coupling by a 1/2-inch or more. Make sure that the tape is on the Barrel Coupling side and that it holds firm and air tight.

When you blow into the Blow Tube, the air will flow out of the Reed Coupling and not out of the Barrel Coupling side where it is blocked by the tape.

Part 2. Membrane Reed

The membrane reed (in this case, a plastic shopping bag) will create an interruption in the air's pathway out the instrument. Your air is blown into the Blow Tube and Couplings, over the outside of the Barrel, and is forced under the reed and out the inside of the Barrel toward the Body. It has nowhere else to go.

Directions

1. Cut a square from a plastic shopping bag to be your Membrane Reed. As long as it's not ripped or stretched, it doesn't need to be perfectly shaped.

2. Place the Membrane Reed on the Reed Coupling. Make sure your Barrel is sticking through and is flush so that the Membrane Reed is laying flat on both the Reed Coupling and the Barrel.

3. Gently push/screw the the Cap over the Membrane Reed and Reed Coupling. The cap will hold the membrane in place (pretty tight but not so tight that it rips) over a larger pipe. If you push too hard you may rip the bag. If so, just replace the Membrane Reed. You should be able to harvest at least a dozen out of a normal bag.

4. Adjust the Cap as needed so that the Membrane Reed is relatively-tight and not wrinkled. Also adjust the Barrel as needed by screwing it toward or away from the Reed a tiny bit at a time to get it to touch the reed but not push it.

5. Blow through the blow tube and see what happens! If you hear a honk, you're in business. If you hear nothing or a very high whistling, the Barrel is likely pushing too much on the Reed. Lightly unscrew the Barrel a tiny bit and see if sound appears. If you hear an unstable squeal or pitches moving around, you may have a multiphonic or wrinkled Reed. Try gently adjusting the Cap and Barrel until you get a nice, steady honk.

This honk is your base-pitch. Next you will add pipe length and divide it up to make lower pitches.

Part 3. Full Pipe Length & Tuning the Octave

Next, we'll assemble the whole instrument and find the lowest pitch, followed by drilling an octave hole.

Directions

1. Gently screw the Adapter onto the Barrel. Be careful not to also screw the Barrel further into the Reed. But if you do and the Reed is undamaged, you can just readjust the Barrel/Reed contact again.

2. Cut a piece of 3/4-Inch pipe to any length between approximately 1 and 2 feet to be the Body. The longer it is, the lower the overall pitch of your Memuk will be.

3. Optional: You can experiment with lengths and cut off pipe gradually to get a pitch you like, or you can just go with whatever comes out. This pitch will be the lowest note of your scale, the same note you'll hear when all your fingers are pressed over the holes. Note that sometimes the Reed may produce a slightly higher or lower base pitch and thus the whole key of your memuk could shift a bit. This does happen but not as much as I would have guessed. If you are playing solo it shouldn't matter much. If you need to be in tune with other instruments, you'll need to dial in the overall tuning when setting up and use trial and error with the Reed tightness under the Cap.

Furthermore, when you adjust the octave in the steps below, you may need to change the overall pitch to accommodate a mistuned octave. This doesn't mean you can't plan the pitch of your instrument, but you may want to keep it open-ended for your first prototype and then dial it in exactly for a second build.

4. Next you will drill the octave hole. On the simplest level what you want is to drill a hole halfway between the Reed and the end of the Body when assembled (not halfway on the Body itself). In theory, this should create an octave hole that when uncovered makes a pitch an octave higher than the pitch produced by the full pipe length (when the hole is covered).

In Part 3b below, I will dive into the "Funny Business" that complicates this "halfway" point. But if you want to keep it simple, just mark the hole approximately halfway from the Reed to the end of the Body and drill. Make sure to use that mask and goggles and sand thoroughly to remove PVC chunks. Drilling PVC is tricky. The bit can get stuck. Ideally you should start with a small bit and gradually step it larger.

5. Now you can play the low pitch (hole covered) and octave pitch (hole uncovered) and compare by ear or with a tuner if the octave is in-tune enough for your purposes. If it's not, you'll need to remove pipe from one side or the other, which will get you an in-tune octave in a slightly different overall key.

If the octave pitch is too low, that means the segment of pipe between the Reed and octave hole is too long in comparison to the overall length. In that case, you can take off the body and cut off little segments of the body pipe on the side where it attaches to the adapter. This will raise both the lower note and the octave note, but it will raise the octave note more than the lower note, thus gradually giving you an in-tune octave once you've removed enough.

If the octave note is too high, then the segment of pipe between the Reed and octave hole is too short in comparison to the overall length. The same process is followed but by removing material from the far end of the Body. This will raise the lower pitch while keeping the higher pitch the same, thus approaching an in-tune octave in a slightly higher key.

Obviously, one could experiment with replacing the Barrel with a longer one or slightly loosening the adapter, but I've chosen the above method for solidness and simplicity.

This process can take some time, but it is the main tinkering of this instrument build. It's worth it.

Part 3b. Tuning the Octave: Funny Business

In this segment, I will explain some of the "funny business", the quirks of wind instrument tuning and length. You are welcome to skip this section if you are not too worried about exact tuning and want to keep it simple.

Wind instruments are physically different than strings and other vibrating bodies. The harmonic series, and thus Just Intonation, is the same for air as it is for strings, but there are idiosyncrasies that should be mentioned.

The size of the hole, the inner diameter of the bore of the pipe, and the shape and sharpness of the hole do affect frequency and to some extent timbre. The pipe material (bamboo, PVC, wood) matter as well, especially for timbre, but not as much as you might guess. The reed itself and basic size are the main factors.

The following complications arise...

1) Hole-versus-End Size Discrepancy: The drilled finger holes are not as wide as the end opening.So an open hole does not equal a pipe of that length. The hole lets less air through and thus is lower in pitch than a cut pipe at that spot. *For this reason, the octave pitch is lower than expected.

2. Effective Pipe Length: This applies to all wind instruments, exhaust pipes, etc. When the air exits a pipe it can not simply stop right at the end of the pipe. Imagine a colored gas flowing out of a pipe. What happens at the end where it ejects? It exits the pipe and moves out a bit from the pipe's end before dispersing into the space. Therefore the "effective pipe length", the vibrating length of the instrument, is slightly longer than the pipe.

*For this reason, the octave pitch is very slightly higher than expected.

3. Inner Diameter: One complication which effects predictable pitch and pipe length center is the fact that the vibrating air column from the reed to the end, in this design, has an inner diameter of 1/2" for the first 4 inches near the reed, then is adapted to 3/4" for the remaining length. Since the inner diameter is a major factor in pitch-to-length ratio, it's not as predictable as we would wish. Essentially, this means the pitch will be a bit higher since the restricted smaller pipe has a higher resonance than the longer/larger pipe.

*For this reason, the octave pitch is very slightly higher than expected.

These three elements counteract each other somewhat but #1 (the holes being smaller than the end) is the biggest factor. In the end the octave hole (and all the holes) will likely need to be closer to the reed than their pure fractions of pipe length.

Part 4. Scale and Tuning

Now the most fun part: making your scale!

Directions

1. Choose a scale that fits under the fingers, involving 8 or less fingers and 0-2 thumb holes. You are welcome to use one my designs at the top of this page. You can also try offsetting the wholes from a straight line into more where the fingers naturally fall on the pipe.

Just Intonation is fun, easy, ancient, Sci-Fi, and uses lengths that make sense, like 2/3. You are welcome to do an Equal Tempereament, but you'll need to get your calculator out. And prepare yourself to measure a lenght that is 0.02 % away from 2/3's, etc.

2. Mark and drill your holes. Keep in mind that the top of the hole (nearest the Reed) is the point where the air will escape, so you may want to measure from there versus the center of the hole.

3. If the holes are out of tune, you may be able to raise the pitch by widening the hole, but only a small bit.

4. Use embouchure (mouth control) to tune them while playing.

5. Have fun!