Having never played a xylophone (or even seen one up close) I decided my first step was to check some out – first on the web, and the up close and personal.

Typical Characteristics of Commercial Instruments

I found a lot of pictures on the web of commercial instruments made by Musser, Malletech, Deagan, Yamaha, etc. that I used to sort of check out the least common denominators. Most concert instruments were 3.5 octaves, which means they had 44 bars that typically spanned the range F4-C8. This range seemed to be most common, so I decided to use it to baseline my design. I also discovered that that there are basically two tunings: The A4 bar can either be tuned to a frequency of 440 Hz or 442 Hz. The literature suggested that 442 tended to sound brighter with an orchestra and is more common, so I decided to tune mine to that frequency.

Bar Materials

I also saw that there were at least three bar materials that were common. The first is a synthetic called Kelon. I’m not sure exactly what Kelon is, but it kind of feels like fiberglass. The advantage of Kelon is that it is cost effective and doesn’t change tune with humidity and temperature. Here’s a link to a pretty nice Musser xylo made of Kelon.  Through my research, it appeared that Kelon is primarily used for instruments that see a lot of travel and abuse (e.g. schools).

I also saw a lot of instruments made of an exotic hardwood called Padauk. Here is a link to a Yamaha xylophone made of Padauk. It appeared that instruments made of Padauk were more expensive than those with Kelon, yet less expensive than those built with Honduras Rosewood, which is the traditional wood used to build xylophones and marimbas.

Ah Honduras Rosewood…the holy grail of xylophone woods (cue angel chorus and sunbeams). As you move up the xylophone food chain, pretty much all of the high-quality instruments are made of Honduras Rosewood. It turns out that this wood is unique in its properties relative to making idiophones (Remember? Instruments that you whack.) If you check out the paper by Aramaki cited below, you can see that they build bars from 59 species of wood. Which one came out on top? You guessed it, Honduras Rosewood.

Dimensions

OK, so after a little research, I had settled on a note range, a tuning pitch, and a  bar material. The only basic characteristic left to decide  was size. If you troll around the web, you can see that bar sizes vary quite a bit. For example, from the LaFavre site, I found the dimensions of the F4 bar (the longest bar) on a Deagan was 12.81 x 1.93 x 0.95 inches. However, the F4 from a the Kori instrument I measured was almost 17 inches long. These tended to be the extremes I found, and most other instruments had bar lengths within this range. As we will see later, a wide range of bar lengths can be shaped to yield the desired frequencies. From a physics standpoint, the larger bars will produce more more volume, as they have more surface area that is creating sound. However, this greater amplitude comes at the expense of compactness and portability.

In the end, I modeled the dimensions of my instrument off of a rosewood Yamaha instrument that seemed to be popular. The specific instrument is a Yamaha YX-500R and can be found at this site.  I liked the overall dimensions of the Yamaha, as my instrument has to fit in my house. Best of all, I was able to find a exploded diagram with parts list on the Yamaha site! Here is one of the diagrams.

and here is a section of the parts list.

The bar description has the length and width of the bars. Sweet! The longest bar on this instrument is 380 x 38 mm which is about 15 x 1.5 inches, which is right in the middle of the range of most of the xylos I found. Also, by following the dimensions of the Yamaha instrument, I was able to ensure that I would build a xylophone that was 1) about the size expected by a musician and 2) had bar lengths that were guaranteed to be tunable.

Next Up

In this discussion, I focused mostly on the physical attributes of the commercial instruments that I found. In my next post I will dig in to the sound characteristics, including more than you probably want to hear about the spectral analysis software I wrote, and the results from a few instruments I analyzed.

References

Aramaki et al. 2007: Aramaki, M., Baille`res, H.,Brancheriau, L., Kronland-Martinet, R., and Ystad, S.(2007). “Sound quality assessment of wood for xylophone bars”, J. Acoust. Soc. Am. 121, 2407–2421.

OK, we’re getting smarter. We now know that it is necessary to shape the underside of the bars to tune them; this is a good start!

“But what is the right shape?” An even more fundamental question is, “What are the desired frequency characteristics for each xylophone bar?”

Before anything else, I want you to know that I am not a musician; I have dabbled in guitar and ukulele, but my instruments mostly just collect dust in my closet nowadays. My point is that while I’ve got a decent handle on the engineering and science, I am less than an expert on the musical implications of xylophone tuning. So for the musical purists out there, please cut me some slack.

One very important fact about xylophone bar tuning is that it is necessary to control the fundamental and overtone frequencies in order to make a harmonious bar. Tones produced by the bar should produce a chord, rather than a series of unrelated sounds. Note that the term “partials” is used to describe the various tones produced by the bar. The first partial (the lowest, and most dominant tone) is called the fundamental, and the higher partials are often called the overtones. To clarify:

fundamental = first partial

second partial = first overtone

third partial = second overtone

And so on…

A Semantic Warning!

There seems to be some overloading of the term “partial” in the literature. It appears that the engineers use the term differently than the musicians. For example, the Bork paper defines the term “partial” to be any of the dominant tones produced by the bar (consistent with my use above). These might be frequencies that are integral multiples of the fundamental, or they might not be. However, in the musical literature, it appears that the term is often used to describe the integral harmonic. For an example, check out this informative site from the Vienna Symphonic Library. In that post they state, “Xylophone bars are often tuned in such a way that the 3rd partial (= octave + a fifth above the pitch of the fundamental) is more prominent, …” An octave plus a fifth corresponds to the frequency ratio of 3, relative to the fundamental. So when they say the “3rd partial” they are referring to the tone that has a frequency of 3*fundamental. However, this is the second dominant tone, so Bork and I would call that the 2nd partial. I am not sure what the “correct” use is, but be aware of this confusion and note that I will use the Bork definition consistently.

More Semantics…

Sometimes the term harmonic is also used. Harmonics are partials that are integral multiples of the fundamental frequency. That is, they are frequencies that are like 2*f, 3*f, etc., where ‘f’ is the fundamental frequency. Values like 2.153*f or 5.416*f are not harmonics because they are not integral multiples (i.e., they are not whole numbers times the fundamental). Lots of folks incorrectly use the terms harmonic to mean any frequency higher than the fundamental.  I am guilty of this semantic misuse too, but will try to use the proper term partial to avoid confusion. See Wikipedia for a much more careful description of these terms.

Semantics aside, here is the important part: for a xylophone bar to sound good, the ratios between the first two overtones, relative to the fundamental, must be specific values. Namely, in the United States, the bars are tuned so that the ratios are 3 and 6. That is, the second partial has a frequency of 3 times the fundamental (i.e., first partial), and third partial has a ratio of 6 times the fundamental.  In shorthand, the ratios are 1:3:6. This is sometimes called “quint” tuning because the second partial is a major fifth above an octave. You can learn a little more about quint tuning at the Deagan ebsite.

Without getting too far ahead of myself, here is a chart that provides the tuning of the first 3 partials for the Kori xylophone at UNM.

On the graph, the notes are plotted along the bottom, and the frequency ratios for the measured partials are plotted on the y axis. Clearly, the first and second partials are right on the money (at least for the lower notes). Third partial, however, sort of wanders around the desired ratio of 6. You will hear lots more about my spectral analyses of various instruments later.

Why 1:3:6?

It is reasonable inquire about the origin of the 1:3:6 tuning ratio. To be honest, I didn’t find any great explanations of this, but there is some good literature on the web that describes why certain tones sound good together. For example, check out “The Physics of Music and Musical Instruments,” which has all kinds of good info. Alsocheck out “The Art and Science of Mallet Instrument Tuning,” which has an excellent discussion of some history of tuning and some discussion of the rationale for quint tuning.

In the next post, I will start to get into the approach to determining the correct bar shape.

REFERENCES

[1] I. Bork, “Practical Tuning of Xylophone Bars and Resonators”, Applied Acoustics 46, 103-127 (1995).

It didn’t take a ton of research to figure out that the xylophone bars had to be shaped, not just cut to length. In this case, tuning means carving the bottom of the bar to yield the desired tonal characteristics.

Here is a picture of the underside of the bars for a Kori xylophone that I checked out at the University of New Mexico. Thanks to Scott Ney, I was able to dissect this instrument!

While I don’t have the skill (or patience) to provide a full-on description of the physics related to vibrating objects (like a xylophone bar,) I will describe a few basics to get you started. Nerds: you probably already know this stuff and can safely skip to the next section.

Vibrating Bodies

We all know that when something, like a bar of wood, is whacked, it vibrates for a while and then the sound eventually dies out. The duration of the sound is referred to as the “decay” of the signal, and there is a precise definition that quantifies the decay duration in seconds. What many people don’t know is that pretty much every object has a preferred frequency at which it generally vibrates. Think of whacking a frying pan versus big pot; you can hear the difference in the tones between these two objects. The frying pan “wants” to vibrate at a higher frequency than the big pot. Further, each object will typically vibrate at a series of discrete frequencies called modes.

For those without science knowledge, what you may not know is  that what you are really hearing is one “fundamental” tone, and then a series of different, higher tones that are related to the fundamental tone in complex ways. It is the relationship of this fundamental tone and the “overtones” (and how quickly each tone dies off) that creates the overall tonal characteristics (i.e., the timbre) of the object.

It turns out that it is possible, by choosing the shape of the object, to control the fundamental and overtones.

WARNING: You’re entering a zone of extreme nerdiness. If you don’t care about physics and math, you may want to skip the next few sections. Although, be warned – nerd-speak is sprinkled throughout  the rest of this blog.