The World's Longest Piano
The World's Longest Piano
And the Musical Physics Behind Its 19-ft Design
Starting at age 15, Adrian Alexander Mann created the world’s longest piano. The project took him 5 years to complete. He named it the ‘Alexander Piano’ after his great-great-grandfather. The design of this amazing, 18-ft, 9-inch piano was a battle against practicality, in pursuit of brilliance. In the article linked below, Thomas Davenport provides an interesting account of Mann designing and building the Alexander Piano.
Although there is nothing glaringly wrong with Davenport’s article, and I encourage you to read it, it does have some slightly inaccurate aspects, which seem to sacrifice clarity in the interest of brevity.
I’ve written the following for those who would like a more in-depth take on why one would build such a long piano (and why they wouldn’t), why the sound is superior, etc. Along with comparisons to other stringed instruments, I’ve included very basic physics in my analysis, which musicians and scientists will appreciate. Secondarily, this article makes points that highlight the applicability of a broad scientific understanding.
Davenport writes: “Inside a piano, the bass strings are wrapped with copper wire to deepen the sound without needing more length. In 2004, Adrian Alexander Mann wondered how long the bass strings would have to be without the copper wire to hit the right notes.”
This explanation could be misleading, because hitting the right notes has nothing to do with copper, per se. Note that the bass strings of an acoustic guitar are sometimes wrapped in copper, sometimes in bronze (an alloy of copper and tin), and sometimes in nickel, while the treble strings are single, unwrapped wires. The different metals provide slightly different characteristic sounds, but the reason for wrapping the strings is to increase their thicknesses, and in this regard, the use of copper is somewhat arbitrary.
This is true for piano strings as well. The different metals, used for achieving the correct thickness, will vary what people describe as ‘brightness,’ ‘depth,’ ‘crispness,’ ‘brilliance,’ ‘warmth,’ etc., as well as loudness and sustain (how long a note rings). The aforementioned concepts in semi-quotes are subjective/abstract, whereas the actual notes being played are not. When we talk about a ‘note’ or ‘tone,’ we are talking about the actual frequency of the sound waves, which can objectively be measured with a tuning device.
To achieve a bass note (or any note for that matter) there are two factors at play: the mass of the string, and the tension. Wrapping the bass strings of stringed instruments gives them enough mass to create deep notes without being overly long. Length and thickness both effect the mass. This is because the mass is determined by the amount of metal in the string (which I write at risk of stating the obvious). Length x thickness = amount of metal.
Mass is the amount of matter in an object. Mass differs from weight, in that weight changes according to the force of gravity, whereas mass does not. For example, an astronaut’s mass would be the same inside the International Space Station as it is on Earth, although they would be essentially (but not completely!) weightless when in the space station. Perhaps the biggest conundrum in all of science is that—since relativity is irreparably falsified, utter nonsense***—we don’t know what produces gravity, and therefore we don’t understand what gives matter its weight.
***See my article here for my beatdown on relativity
The problem with having too short of bass strings would be that to achieve the desired notes, they would have to be too floppy (too little tension) to be struck with the little piano hammers—that is, unless you made them very thick. And at some point, if they were too thick, they wouldn’t be loud enough when struck, because as the radius or diameter—i.e. the thickness—of the string increases, the internal volume increases at a greater rate than the size of the surface producing the sound.
Picture a cross section of the string being a circle. Now recall the formula for area of a circle:
That is, Area = pi x the radius squared. Calculating the volume of a cylinder (like the string) requires only a simple three-dimensional extension of this concept:
The formula for the volume of a cylinder is just the area of a cross-section of the string, times the length of the string (volume = pi x the radius squared x length). What I want you to note here, is that the radius is squared. You will see why momentarily.
Recall the formula for the circumference of a circle (the circumference is the distance around the circle’s perimeter):
That is, circumference = 2 x pi x the radius.
As I mentioned before, the surface of the string emits the sound as it interacts with the air. Calculating the surface area of the string—the amount of surface present for emitting sound—is simply a matter of two-dimensionally extending the concept of this circumference formula :
The surface area of the string is calculated by multiplying the circumference of the string by the length of the string. Surface area = (2 x pi x the radius) x the length.
Now, here’s the reason I wanted the reader to take note of the radius being squared in the volume formula: raising the radius by ‘the power of 2’ (in other words, squaring it), is called exponential, 2 being the exponent. It’s exponential because as the radius gets bigger, the amount you multiply it by gets equally bigger. Consequently, increasing the string thickness results in exponential volume growth; meanwhile, the surface area does NOT increase exponentially, but instead increases steadily.
Let’s look at an example, to see what happens to the volume of the string relative to the surface area of the string, if the radius is increased: If the radius is 2 mm, and the length is 100 mm, then the volume of the string is V = pi x (2 mm^2) x 100 mm, which is the same as saying,
V = pi x (2 mm x 2 mm) x 100 mm = 1,257 cubic mm of volume
and,
Surface area = 2 x pi x 2 mm x 100 mm = 1,257 square mm of surface area
Bear with me. Now, let’s see what happens if the thickness of the string is increased, so that the radius is 3 mm, but the length remains the same: V = pi x (3 mm^2 ) x 100 mm, which is the same as saying
V = pi x (3 mm x 3) x 100 mm = 2,827 cubic mm of volume
Surface area = 2 x pi x 3 mm x 100 mm = 1,885 square mm of surface area
So, as you can see, by increasing the radius from 2 mm to 3 mm, the volume increased by 225%, whereas the surface area only increased 150%.
Now, to really drive this point home, let’s see what happens when we increase the radius to 4 mm.
V = pi x (4 mm x 4) x 100 mm = 5,027 cubic mm of volume
Surface area = 2 x pi x 4 mm x 100 mm = 2,513 square mm of surface area
Here we see that by increasing the radius of the string from 2 mm to 4 mm, the volume of the string increased by 400%, while the surface area increased by 200%. When we added 1 mm to the original radius, the volume increased at 1.5 times the rate that the surface area increased: 225% ÷ 150% = 1.5. When we added 2 mm to the original radius, the volume increased at 2 times the rate that the surface area increased: 400% ÷ 200% = 2. If we were to keep extrapolating this concept, we would find a bigger and bigger—hence exponential—difference in the rates of change.
This relatively greater change in volume compared to surface area is a primary reason why too thick of a string will not emit enough sound. The string’s ability to vibrate will decrease due to the increase in volume (and thickness), and this decreased vibration will not be compensated for with increased surface area, since the surface area will not increase to the same degree as the volume.
As an interesting aside, this is also the reason why animals are larger in cold climates. The bigger they are, the greater their volume, relative to their surface area from which they lose heat, so it’s easier for them to stay warm. Thus, deer, bears, etc., are larger up north. But I digress.
Imagine stretching a rubber band and plucking it, and getting higher notes the tighter you stretch it. The mass of the rubber band can’t change, so you can only get so low of a note before it is too floppy to play. But if you have a thicker rubber band, and you bring it to a reasonable tension, you’ll get a deeper note than you would from the thinner rubber band at that same tension.
So, as I mentioned, the wrapping/winding of piano strings would not have to be copper, and its purpose is to make the strings thicker to achieve a deeper note, just as the thicker strings on a guitar or bass guitar, or on an instrument in the violin family, have a deeper tone than the thinner strings, though they are the same length. The length of the instrument can only be so short, and the strings can only be so thick, or they will not function properly.
Some musicians prefer shorter-‘scale-length’ guitars (i.e. the playable portion of the string, between the nut at the end of the neck and bridge on the body, is shorter) over longer-scale-length guitars, because shorter-scale-length guitars have slightly floppier strings to achieve the standard notes of a guitar. The lower tension of these floppier strings makes bending notes to a higher pitch require less strength (bends are a cool-sounding technique, often used, for instance, to hit the high root note at the climax of a solo).
A Gibson Les Paul electric guitar has 24.75-inch-long strings, whereas a Fender Stratocaster electric guitar has 25.5-inch-long strings. Darrell Abbott of Pantera preferred the 24.75” length, whereas Jimi Hendrix preferred the 25.5” length. Of course another factor in this preference is hand/finger size, because the longer scale is more comfortable for larger hands, and vice versa. The string length also effects the guitar’s sound, which I’ll explain more later.
A related, new concept is ‘multi-scale’ guitars and bass guitars, which have longer bass strings and shorter treble strings, with ‘fanned’ frets that slant across the neck, and a steeply angled bridge. But I’ve strayed from my theme again.
Black Gibson Les Paul guitar (left) and goofy-colored Fender Stratocaster (right), hanging on the same wall rack. We cannot see their nuts (the nut is the piece where the playable portion of the strings ends at the end of the neck), and, the Les Paul has 22 frets compared to the Strat’s 21 frets. Nonetheless, you can see that the bridges (pointed to with horizontal arrows) hang with a 3/4” difference in their heights, due to the 24.75” scale vs 25.5” scale. The bridge is the metal piece where the playable portion (‘scale length’) of the strings terminates at the body end of the guitar.
To be redundant for emphasis: note once more that the thicker/ bass strings on a guitar are wrapped, and the treble strings are not.
Now, if you don’t wrap the strings of a piano, you’re going to have thinner strings. Therefore, to increase a string’s mass to achieve the same bass note normally produced by its corresponding piano key, the string will need to be longer. If it were not longer, it would need to be too floppy to be struck by the piano hammer. The thin string being longer will give it enough mass, and therefore enough bass.
Now, if you take the length of the strings to the extreme, which apparently this builder has done, the strings can only be so thin, or they will be too weak to achieve HIGH ENOUGH notes, even if we are talking about relatively very low notes, on the low-end of the piano. If you make a string very long, it will have a lot of mass, so it will have to be relatively very tight, or its piano key will produce a note lower than the standard note of a piano. Likewise, as I mentioned, the 3/4”-longer strings of a Stratocaster are tighter than the strings of a Les Paul, when both are tuned to standard tuning.
You can only make the piano string so thin, because if it’s too thin, you won’t be able to make it tight enough to be within the range (not too low) of the piano, without it breaking from tension or when hit with the piano hammer. On the other hand, if a string is very long, it has to be thin, otherwise it will have to be too tight (so as not to produce too low of a note) for the wooden structure of the piano to resist the tension without warping. In other words, a balance must be struck between tension and string thickness (and structural integrity).
So, on a long piano like the Alexander Piano, you’ll have to have reasonably thick—albeit thinner than normal—strings, AND they’ll still have to be tighter than the strings on a normal-length piano. This high-tension and thinner string combination, when tuned to produce the standard notes (i.e. standard frequencies/tones) of a piano, will produce, along with the tones, a ‘brighter’ set of overtones.
The overtones are whole-number multiples and fractions of the frequency of the tone (i.e. of the note, AKA the ‘fundamental’ tone). Overtones ring at the same time as the fundamental tone, albeit quieter and less prominently. If the fundamental tone is middle C (261.63 Hz; i.e. 261.63 sound waves per second), the overtones are at 2 x 261.63 Hz (=523.26 Hz), 3 x 261.63 Hz (=784.89 Hz), 4x, 5x, and so on and so on, and at 1/2 of 261.63 Hz (=130.815 Hz), 1/3 of 261.63 Hz (=87.21 Hz), 1/4x, 1/5x and so on and so on.
I think what is happening with longer, tighter, thinner strings, when producing the same tones as shorter, looser, thicker strings, is that you hear overtones at higher-multiples of the fundamental tone. For example, say upon playing a looser string you hear all the overtones up to the one that is 8 times the frequency of the fundamental tone. Perhaps with a tighter string tuned to the same fundamental tone, you might hear the overtones all the way up to the one that is say, 10 times the frequency of the fundamental tone, therefore achieving a ‘brighter’ sound, by audibly producing two extra, higher-pitched overtones. Indeed the Alexander Piano does achieve a brighter, fantastic sound.
For this same reason, I prefer a 35”-scale bass guitar to a 34”-scale bass guitar: the strings are tighter on a 35”-scale bass, and therefore, in my opinion, have a better, brighter overall sound. The lowest notes on a 35” bass are less ‘muddy,’ and more distinctive. Not only does this sound better, it makes the bass easier to play by ear. My primary instrument is a 35”, six-string bass.
One more ‘note’ (duh-dun tssss): The biggest engineering challenge to building the Alexander Piano was likely the fact that the long strings need to have more tension, which requires the piano to have formidable structural strength to withstand. That is probably why it weighs so much—more than a metric ton. Its structure contains lots of thick wood for reinforcement/bracing.
What a great build. Beautiful instrument, Adrian Mann!
Thanks for reading! God bless you all.
Thomas Davenport’s article: