“What attracts the eye may not attract the ear” Evan Davis 
After that interlude looking at hearing and psychoacoustics, we can return to unfinished business with stringed instruments. We aren’t ready to look at bowed-string instruments yet: we still want to learn as much as we can using linear methods, and the bowed string is very definitely nonlinear. But we have only scratched the surface of the extraordinary variety of musical instruments from around the world that use plucked or struck strings. We have looked at the guitar and the banjo, but what about the harp or the lute, the piano or the harpsichord, let alone the Indian sitar, the Chinese pipa, or the west African kora?
We will not, of course, deal with every instrument on an individual basis. But there are some common themes that will be explored in this chapter. A useful starting point is to ask “How do you recognise what instrument is being played?” As we have already heard with the comparison of the guitar and banjo, it is sometimes possible to distinguish which is which of two instruments from the sounds of just a few notes. But is that always true? Probably the sound of a sitar would be recognised straight away, at least in comparison to something like a guitar or a piano. But what about comparing a guitar to a harp, or a lute, or a mandolin?
If you ask a musician a question like “Why does a lute sound different from a guitar or a harp?”, they will usually assume that the main reason is something to do with the obvious difference in body shape between the instruments. But we should take note of the dictum quoted at the head of this page. Out of the many factors that contribute, body shape is in fact surprisingly unimportant for this question of telling instruments apart. It would be different if we were asking about the difference of sound between similar instruments; two guitars, two harps, two violins. In that case, the other factors that we will discuss in a moment are all fixed, so that relatively subtle variations in body size, shape, thickness distribution and material become the dominant influence.
When it comes to recognising what instrument is being played in a real musical context, by far the most important factors are to do with what the performer does. Each instrument offers particular possibilities to the player, and also imposes particular constraints. On top of that, there are questions of culture, training and repertoire. I suggest that you recognise that a guitar is being played when you hear “guitarish” things, as opposed to “harpish” things or, in the extreme, “violinish” things.
That all seems a bit vague, so let’s look at some specific examples. A fretted instrument like the guitar has only a limited number of strings, and the player will often play successive notes on the same string. That obviously means that the previous note is cut off when the next one is played. But on a harp you have a separate string for each note. Unless the player chooses to stop the vibration, each string will continue to ring on, and the sound will overlap with succeeding notes. This gives the listener an immediate clue to what instrument is being played.
But performers like to play games to confound the listener. In some fretted instruments, a performance technique called “campanella” may be used. It is especially common in instruments with re-entrant tuning like the baroque guitar or the ukulele. The tuned frequencies of the strings are not all in a descending sequence as you strum from the “top string” to the “bottom string”; instead, the pitch jumps up at some stage. The player can take advantage of a string that is tuned high like this: something like a scale can be played by interleaving notes on different strings, so that notes ring on in a harp-like manner. Or, of course, a bell-like manner, explaining the name “campanella”.
There are plenty of other examples of performance details that give an immediate clue about what instrument is being played. The characteristic harp glissando is an example. Somewhat more subtle, there are characteristic features of keyboard playing, tending to produce mannerisms different from those of a finger-plucked instrument or, indeed, a plectrum-strummed instrument.
As usual, you should not believe any claims like these without evidence. Computer-synthesised sounds give a clean way to make comparisons (accepting that no such sounds are really a perfect representation of real instruments). Listen to the four sounds below, and give an immediate vote for what instrument is being played. Perhaps your first impression is that the first two are played on harps of some kind, while the second pair are played on guitars, or possibly on some kind of keyboard instrument?
In fact, the first pair use harp string data and “harpish” music, but the first uses the measured bridge admittance of the small harp in Fig. 1, while the second uses the admittance of a guitar. The second pair uses guitar string data and “guitarish” or “lutish” music, but this time the first uses the guitar admittance, while the second uses the harp admittance. So Sound 2 has “harp strings on a guitar body”, while Sound 4 has “guitar strings on a harp body”. To my ears, the first pair both sound like harps, and if anything the second one sounds like a better harp. In the second pair of sounds, I am aware of the lack of bass response in Sound 4, but it doesn’t immediately strike me as “sounding like a harp”.
Now for a more difficult task. If clues from musical style are removed by playing a single note on a variety of stringed instruments, can you reliably decide what you are listening to? Try the experiment yourself. Figure 1 shows a collection of 7 stringed instruments. Below it are 7 sound examples: the note E$_4$ has been played on each of these instruments, using a typical performance technique in each case (finger pluck, fingernail pluck, plectrum pluck etc.) The recordings are not of studio quality, but they are all made in the same room under very similar conditions. The notes have been trimmed to 1 second length, scaled so that they all have the same peak signal level, and then saved as the set of sound files. Can you identify which of the 7 instruments in the picture is playing each sound? I will reveal the answers at the end of the section, to allow you to try the test “blind”.
Even if you could not immediately name all the instruments, you probably found that the 7 sounds were all quite distinctly different. So what are the factors that allow you to distinguish them? I have already suggested that the difference of body shapes visible in the picture will only be part of the story. There are several things to do with strings that can be important. Most obviously, the strings may be driven in different ways in different instruments. A harpsichord sounds immediately different from a piano, partly because of a very different choice of string gauges, but also because a harpsichord string is plucked by a narrow plectrum, while a piano string is struck by a felt-covered hammer.
We have already seen in the banjo study that the impedance of the strings relative to the soundboard can have a strong influence on the decay rates of played notes, and that decay rates can be very important for recognising an instrument. But there are other important aspects of string choice. Metal strings sound different from polymer strings, and at a more subtle level polymer strings don’t all sound the same: gut, nylon and fluorocarbon strings are all different, as will be explored in section 7.2. Some instruments have strings in pairs, or even (in the case of the piano) triples. The strings of a pair or triple may be tuned to nominal unison, or in some cases they are tuned an octave apart. In section 7.3 the significance of multiple stringing will be explored, drawing inspiration from a classic study by Gabriel Weinreich .
Finally, instruments like the piano and the lute can exhibit subtle but audible effects of nonlinearity, modifying the sound from what would be predicted using linear theory. In section 7.4 we will have a preliminary look at these effects, preparing the ground for Chapter 8 in which we take a deep breath and start to look properly at nonlinear phenomena. That will prepare the way for later chapters, in which we look at bowed strings and also at the extensive family of wind instruments, all of which are intrinsically nonlinear.
So what were the 7 sounds?
Sound 5 was a classical/flamenco guitar. The note was the open top string, played with a fingernail using an apoyando stroke. The string is plain nylon.
Sound 6 was probably the easiest to recognise: it was the piano. This note is in the range where the piano is strung with plain steel wire, three strings per note. The recording reveals that my piano is tuned slightly flat!
Sound 7 was the harp, plucked with a fingertip. The string is made of nylon. We will find out in section 7.4 that this particular sound is influenced by nonlinear effects, so that it doesn’t entirely sound the same as the linearly synthesised “harp” in Sound 1.
Sound 8 was the banjo: the second fret on the top string was plucked with a fingertip. The string is plain steel, far thinner than the strings of the piano.
Sound 9 was a Neapolitan mandolin. This instrument is tuned in the same way as a violin, and the note here was played at the second fret on the 3rd course of strings, plucked with a plectrum. This pair of nominal unison strings have steel cores, over-wound with wire.
Sound 10 was a lute, played with a fingertip at the 2nd fret on the second course, a unison pair of plain nylon strings.
Sound 11 was a pizzicato note on a violin. The note was fingered in first position on the 3rd (D) string, and plucked with a fingertip. The string has a stranded polymer core, over-wrapped with flat metal tape to give a smooth outer surface.
 Evan Davis: a comment made during a talk on cello acoustics to the Oberlin Violin Acoustics Workshop, 2021.
 Gabriel Weinreich “Coupled piano strings”; Journal of the Acoustical Society of America 62, 1474–1484 (1977).