What makes a note?

The words ‘tone’ and ‘note’ refiect the subjective/objective nature of sound: a tone is a sound wave with a particular frequency, a note is its subjective impact, with a particular pitch.

In addition to pitch, a note also has duration, loudness, and timbre. Timbre is by far the most important in identifying instruments by their sound, and is also the main carrier of emotional content. It is actually an uneasy bedfellow with the others, being far more complicated. It is a bit like deffning a person by gender, height, weight, and ffngerprint: the ffrst three parameters can each be speciffed in terms of one value of a single unit, but the full description of an individual’s ffngerprint would be highly complicated and multidimensional. But, like a ffngerprint, timbre is the only thing unique to a particular instrument or person, so it’s the only thing that the brain can use as an identiffer.

A problem for the brain which the ffngerprint detective need not worry about is that timbre is a dynamic quality; it changes over time. The timbres of a cymbal, piano note, or drum all change radically from start to ffnish (this change is known as fiux). The timbre of a particular instrument or speaker also changes with pitch and loudness: a cello’s high notes have a diflerent quality to its low ones, a shouted word is not simply louder than a spoken one, and a man’s voice at the top of his range sounds much thinner than when he is singing low notes. Fortunately, we can rely on our highly evolved ability to focus on the very ffrst sounds made by a source to untangle all this.

Prehistoric agendas

Our modern appreciation of music and our dislike of noise probably stem from the evolutionary pressures that moulded the hearing systems of our distant ancestors. Their ffrst priority on hearing a sound would have been to identify it, and there was no time to ponder. The twang of a bowstring, the rumble of an avalanche, the thunder of approaching hooves or the warning hiss of a snake are only of benefft to the hearer if (s)he can react fast, and so the hearing system concentrates its analytical prowess on the earliest moments of a sound. This has the surprising consequence that the ‘attack’ sounds that an instrument makes in the ffrst fraction of a second, though generally discordant and nothing like the instrument’s ‘steady state’ sounds, are the ones that enable us to identify what that instrument is. A recorded piece of music edited to remove all the attacks sounds very strange, and the instruments could be anything. This fact stymied for many years attempts to synthesize instruments convincingly.Often not just the instrument but the composition too can be identiffed within the ffrst second. There was once a fairly popular radio (and then TV) quiz show called Name that Tune, in which contestants frequently succeeded in identifying tunes from just four or even three notes. It is very easy to outdo this if one is presented with a familiar recording: even a preliminary fumble or intake of breath is enough to identify it. Conversely, some musical sounds immediately inform the listener of the fiavour of the whole piece: a single chord may have a ‘Mexican’ sound, a few violin strokes might sound ‘folksy’, a bagpipe skirl ‘Scots’, or a couple of notes ‘fferce shark approaching’.

The responses to such brief cues are primarily emotional, as beffts their original role as hazard warnings: the roar of a lion or the click of a safety catch being released deliver an immediate visceral response, releasing adrenalin in preparation for fiight—or ffght. In fact, our refiex response to any sudden loud sound close at hand is to put distance between us and it: a feedback shriek from a loudspeaker will literally make us jump away. Even continuous sounds are intrinsically repellent if they are loud enough: hence the almost physical reluctance one feels to pass close by a pneumatic drill.

The fiipside to our focus on the very ffrst parts of a sound is disinterest concerning sounds that last for a while, leading to the seeming paradox that a continuous sound at constant volume will sound quieter after a few dozen seconds: in nature, such sounds are likely to be as harmless as the breeze. But if that long-duration sound should suddenly stop, the silence is just as attention-getting as was its onset.

The act of listening to music has received considerable attention from a sound studies perspective. The musicologist and philosopher Peter Szendy, for example, argues that an essential part of listening to a piece of music is comparison with other works, performers, instruments—and other listeners too. His view is that, since the act of listening constantly ‘appropriates’ other things in this way, the essence of a piece of music can never be fully grasped.

Learning to sing

Musical sounds are far more important to many of us than those of other types—so much so that many of us can hardly restrain ourselves from bursting into song at the slightest provocation. Perhaps you have entertained yourself and, to a rather lesser extent, everyone within earshot, by singing ‘Somewhere Over the Rainbow’. It’s a fair bet that Judy Garland did it better: but how? Although your listeners may not enjoy the tune, they will surely recognize it because, even if a lot of the notes are wrong, they will at least go up and down in pitch in the right order, and vary in length in a familiar way.

Durations of notes (and of rests; gaps between notes) are indicated by their shapes, and deffned as fractions of a ‘whole note’, which is a semibreve, as shown in Table 2.

There is no standard duration for a note, though in some cases a composer will provide one on an individual score: ‘fi = 66’, for example, means ‘a crotchet lasts 1/66 of a minute’. Usually however, the only indication of the speed (technically, tempo) at which a piece should be played is a phrase (often in Italian) of variable helpfulness, such as andante (‘at a walking pace’) or allegro non ma troppo (‘fast but not too fast’). Perhaps because the concept of tempo is not very applicable to natural sounds, we are poor at judging it—amateur or professional alike, spotting a 4 per cent diflerence in tempo is about the best we can do.

Unless you are a trained singer, or a naturally good one, you are probably singing some notes slightly ‘fiat’ (that is, a bit lower than they should be) or ‘sharp’ (a bit higher). But what does ‘should’ mean here? It doesn’t mean ‘hitting the right notes’—it doesn’t matter whether the frequency of the sound you make while singing ‘Some . . .’ is 300 Hz or 333 Hz. But you do need to get the ratios of the frequencies correct. So, if you sing ‘Some . . .’ at 300 Hz then you must sing ‘. . . where’ at600 Hz—that is, one octave higher—to avoid people wincing.

Table 2. Notes and rests

It follows from this that if you accompanied yourself on a piano without altering the pitches of your singing, you would almost certainly be out of tune with the instrument. As far as a pianist is concerned, ‘Some’ is an F. There are eight F keys on an eighty-eight-key piano, and any of them may be used here—if the fourth F is chosen, the piano will play a note of 349 Hz.

If you do ffnd yourself to be ‘automatically’ in tune with a piano, you probably have that rare thing: absolute (or ‘perfect’) pitch. Generating the same notes as your piano is all there is to having absolute pitch. If you were transported back two centuries, when pianos were not tuned to the same frequencies as they are now, you would of course not be in tune with them. And if you attempted to sing an unaccompanied duet with a singer of the period who had perfect pitch, the result would not sound pleasant.

Your pitch is nevertheless better than your 19th-century friend’s in a certain sense: if you travelled two centuries into the future, your perfect pitch would match everyone else’s, but your friend’s would not. That is because, in 1939, at a London meeting of the International Standards Organization, many countries agreed on particular frequencies for particular notes. Like many other international agreements, this one only happened because the situation had become intolerable some considerable time before.

Since instrument makers, musicians, and composers had developed largely independently in diflerent countries, each had adopted their pitches arbitrarily. In countries with several musical centres, pitches even varied from city to city. In 1780, a Berliner with perfect pitch would fall sadly fiat in Vienna; a trumpet made in one city would be out of tune in the other—and trumpets cannot be retuned. Hence, as national and international travel among musicians became common,

and successful instrument makers expanded their customer bases further affeld, the need for an international standard became rapidly more apparent—hence the meeting, even on the eve of war.

It follows that absolute pitch cannot be an inborn talent; it must be learned. And learned before the age of six, usually by memorizing all the notes on a musical instrument. This is, on the face of it, an almost incredible feat of memory, and such memorization skills are alien to the adult mind. It seems that some children are predisposed to learn absolute pitch—but on the other hand there is a higher fraction of pitch-perfect persons in China and Vietnam than in Europe or the US, which may be due to the greater dependence in Eastern languages on the pitch at which words are pronounced.

For those of us who lack absolute pitch, it is the diflerences (intervals) between notes, not the notes themselves, that we memorize; hence a familiar tune is instantly recognized whether it is played on the double bass or the violin.

Why do we like what we do?

By far the most important interval in music is the octave, the interval in which one note has twice the frequency of the other. The primacy of the octave is demonstrated by the fact that, in the A to G notation system most of us use today, notes an octave apart are given the same letter. To distinguish diflerent versions of each note, numerical subscripts are used as required (so the fourth F on the piano is F4).Notes one octave apart are in harmony, and the impression we receive of a harmonious interval is that of auditory pleasantness: consonance. Other than a pair of identical notes, the octave is the most harmonious and consonant interval of all.

Exactly why harmonious intervals sound consonant is not quite clear, though we do know that the brain responds to harmonic sounds with synchronous neural ffrings. That is, the neurons which respond to each component of such sounds tend to synchronize their ffring rates with each other. So, harmonious intervals are clearly important to us—but why do we ffnd them pleasant, and inharmonious (dissonant) intervals to be less so? Actually, though we don’t usually enjoy discords in isolation, the appetites of composers and their audiences for dissonance have grown steadily since the ancient Greeks—in fact, one could look at the history of Western music as the increasing adoption of dissonance (which is why listening to Stravinsky’s Rite of Spring or Mozart’s Dissonance quartet is not as disturbing as it once was). Nevertheless, if one ranks intervals by their perceived consonance, the result is pretty independent of geography or history. So there is there is something objective about consonance. In fact, two things:

1. A lack of ‘roughness’. When the ear receives two tones close together in frequency (about 5 per cent diflerent, or two or three semitones), they are perceived as a single rough-sounding note.

2. Similarity to a harmonic series, which is a set of tones with frequencies such as 1 kHz, 2 kHz, 3 kHz, 4 kHz, etc.

More notes

Music making cannot rely on octaves alone. For one thing, we can’t hear more than about ten of them. Also, producing such a range is a challenge: violins and guitars cover about four octaves, exceptional humans can manage ffve or six, pianos seven or eight. Furthermore, every tune would be nothing but the purest harmonies—which very soon become boring.

Once the octave had been deffned, Pythagoras and others set about adding notes to it, embarking on a long research project that was to last for well over a thousand years. Although Pythagoras actually used a monochord, it’s simplest to the job with several strings of variable lengths, all with the same tension and width and all made of the same material.

The next most harmonious/consonant pair of notes after the octave is that given by a pair of strings in which one string is 2/3 the length of the other. Three other simple ratios of string lengths yield other fairly nice-sounding note combinations, and the results are shown in Table 3.

Table 3. Harmonious intervals

If we were to build a harp with strings of lengths deffned in Table 3, but all of the same thickness, tension, and material, we would very easily be able to make simple, reasonably pleasant-sounding chords with it—in fact, any pair or larger group of such strings played together wouldn’t sound too bad.

This system is called the pentatonic (ffve-tone) scale. It was discovered independently by numerous ancient musicians in many parts of the world and is still very popular today (‘Amazing Grace’, ‘My Girl’, and ‘I Shot the Sherifl’ are written in it). The black keys on the piano are a series of pentatonic scales, so if you press them randomly it won’t sound as horrible as if you do the same with the white ones.

Even more notes

Although people like musical harmony, they also like a bit of discord, and the pentatonic scale was just too tuneful and safe for composers who wanted to challenge their audiences and push the boundaries. Also, ffve notes per octave is still not that many: but how to add more? Answering this question initiated centuries of careful experiment and academic debate, leading ffnally to a system called equal temperament. In this system, an octave is divided up into twelve notes, each a semitone, or one hundred cents, apart.

In keeping with the idea that what matters in music are ratios of notes, not notes themselves, semitones and cents are deffned in terms of ratios. Each successive semitone is about 6 per cent higher than the one before. This means that the higher the number of hertz corresponding to a semitone, the higher the note is.

A few composers have experimented with more than twelve notes per octave, and extra notes may appear briefiy, in moving gradually from one note to another to another (this is called a glissando, or slide). However, in all cultures, the number of ‘proper’ notes per octave is almost always twelve.

Having deffned twelve notes, people proceeded to use just eight of them per octave (hence the name). There are only seven difierent notes in an octave—the eighth is the same as the ffrst, just one octave higher (even professional musicians who can immediately identify a note struggle to say which octave it is).

The reason why we use only eight of the twelve notes in an octave was resolved in 1956 by George Miller, a psychologist, who found experimentally that our short-term memory can store no more than about seven items—hence seven diflerent notes—at a time.

There is a semitone jump between adjacent notes in the full group of twelve, so any group of seven notes that we choose to make our scale will include some which are two semitones (one tone) apart. So, we might have this scale: A gap B C gap D gap E F gap G. (A scale is any sequence of notes in which each is higher than the preceding one.)

The fact that we have chosen a set of seven diflerent notes to deffne our scale does not mean that we may not use other notes in a piece of music. If we want to use those ‘gap’ notes, we mark them with symbols which mean ‘a semitone higher than the next lowest note in the scale’ or ‘a semitone lower than the next highest note’.

The optional extra note that fflls the ffrst gap in our scale above is cfuarlltehde re istuhbedr iAvi dsheadr ipf　(rweqruititreend ;fi) s ourc hB　sfimata (lwlerri ftrteanct ffi)o. nNs oatrees　rmefaeyr rbeed to as microtones.

In writing a piece of music there is usually a note that matters more than the others—the key note, or tonic. Usually, this note is the one on which a song begins and ends. In ‘Somewhere Over the Rainbow’, the key note is the one sung on ‘Some’ and ‘I’. The way Jvuerdsyio Gna irsl asnaidd　stion gbse　iitn i nth teh ke effyl mof,　Eth fiisa tis. E fiat (Eff). Hence, her

How is a scale chosen? The main consideration is the mood of the piece: if the composer is writing a conffdent, celebratory, up-beat piece, (s)he is likely to choose a major scale. To write a piece which is less emotionally clear a minor key is usually chosen. The primary objective diflerence between major and minor scales is that a (natural) major scale consists of a tonic (which can be any note), plus the six notes which ‘fft best’ with it, in the sense that their wavelengths bear the maximum number of the simplest possible whole-number ratios with each other. The sound waves hence combine to give the most regular/even patterns possible. In practice, one takes the pentatonic and adds two more notes. One of these two notes, the leading note, has a frequency one and seven-eighths that of the lowest note.

In a natural minor scale, two of the notes of the pentatonic, plus the leading note, have been lost (they are down-shifted by a semitone). The result is that there is no longer a big set of simple whole-number ratios, and the impact is vaguer, more complex, and less complete-sounding.

Additionally, when we hear any sung or played note, it is invariably (except in the case of some electronic instruments) accompanied by its full set of harmonies. Major scales contain all such harmonies too, but minor scales do not. Hence, there is a genuine ‘naturalness’ or ‘completeness’ in major scales which is lacking in minor ones. ‘Amazing Grace’ and ‘My Girl’ are both in major scales, ‘I Shot the Sherifl’　is minor.

It used to be (and occasionally still is) claimed that individual keys have their own emotional qualities (in addition to the distinction between major and minor). Numerous experiments have demonstrated that this is not so. It is likely that this idea arose through the reputations of famous or infiuential pieces of music—imitations tended to be in the same key, which hence became associated with the emotional quality of the original piece. That is not to say that the choice of key is arbitrary: some instruments are designed so that the notes of a particular key are physically easier to play.

Sound sequences

While the raw materials of musical composition are similar the world over, there has been a great diflerence in its development: in Western music, relatively few notes are used, but they are often played together (chords) or in relation to each other (harmonies). If we had to juggle more than seven distinct notes, musical composition would be more difflcult. in particular, polyphony—the simultaneous playing or singing of diflerent melodies—would become well-nigh impossible. In Eastern music, many more notes tend to be used, but combinations are rarer. This diflerence in approach fed through to instrument design: Western instruments like the guitar and organ are naturally polyphonic, while Eastern ones, like the sitar, can often only produce one note at a time, but can easily vary that note rapidly and subtly.

The diflerences between Western and other music may have their origins in the 10th century, when polyphony began in Europe (though there are some who claim that polyphony has far earlier roots). From polyphony sprang both the characteristically multi-tune approach of the West and the studies of harmony required to develop it. It has been suggested that the reason for the ffrst experiments with polyphony was a desire to have men, women, and children singing together.

Melodies

Play some notes in sequence, and you have a tune—technically a melody. If we forget about the diflerent pitches, then what is loosely called the rhythm is all that remains—the relative lengths of the notes and rests, the speed (tempo) with which the whole thing is played, and the pattern of beats (metre, or sometimes measure). This is not quite the technical meaning of the word rhythm, which refers only to the length pattern. In ‘Somewhere Over the Rainbow’, the rhythm (technical version) is: ‘long, long, medium, short, short, medium, medium’.

The metre is indicated by the time signature. The time signature of the commonest metre (‘common time’) is written 44. The lower number gives the units used to specify the beat: 1/4 notes (crotchets). The upper speciffes the number of these beats per group. In a score, the end of each group being shown by a vertical line called a bar (so common time is ‘four crotchet beats to the bar’).

These are not the only kinds of beats that matter in music—the other kind occurs when two tones of similar wavelength play together. Every so often the peaks or troughs of the two sound waves will coincide, adding together to make regions of extra-high or -low pressure. The eflect is heard as a low-frequency ‘beat’, the frequency of which is the diflerence between the frequencies that make it up (Figure 13).

Watch any black and white thriller featuring London policemen, and you’ll hear an example of beats when one of them blows his whistle: such whistles used two pipes of slightly diflerent lengths to produce their arresting sound. But beats aren’t always unpleasant: some organs include a stop called the voix céleste, which controls a set of slightly out-of-tune pipes. When played along with normal pipes, the beats produced make a pleasantly wavering sound.

13. Beats.

Instrumental break

The conventional way to classify musical instruments is partly by what they were originally made of, hence strings, brass, woodwind, and miscellaneous (percussion). Another way is by whether an instrument is pitched (like a piano) or unpitched (like maracas). Any piece of music needs rhythm, and using a non-pitched source avoids dissonances with the ‘melody’ instruments. It is not essential that the rhythm source be a musical instrument: Jean-Baptiste Lully (1632–87) used to thump a big stick on the ground. This is no longer fashionable, perhaps partly because Lully died from it, having hit himself on the toe and contracted terminal gangrene as a result. Drums soon became a more popular source, though they are also used as a source of the ‘actual’ music. For this reason, while drums such as bass drums and snare drums are unpitched, kettle drums are pitched.

Most pitched instruments make their notes either by striking, plucking, or bowing a string, wire, plate, or other solid object, or making a column of air vibrate by providing it with energy from lungs or bellows. In every case, it is resonance plus overtones (and, in the case of bells, undertones, also called subharmonics) that provide the required sound.

This makes it seem simple to construct a musical instrument, but there are three complicating factors. The ffrst is that an object such as a metal plate will not only resonate at a wavelength twice its length, but also at wavelengths twice its width and thickness—and it will produce other sounds as it twists, too.

The second point—a very useful one for string players—is that when an object such as a 120 cm string is struck (or plucked or bowed) it will move in a pattern determined not only by its length but also by the position of the striking point, since that point has no option but to be an antinode. The ends of the string have no choice but to be nodes, so if the string is struck at a point 40 cm from an end, it will make a fundamental with a node-antinode distance of 40 cm, and hence a wavelength of 160 cm. There will be another sound with a node-antinode distance of 80 cm. These components will fade rapidly as the string’s vibration shifts towards its natural mode of vibration, which is to have an antinode at the centre and hence make a 240 cm wavelength tone. The subjective eflect is that near-centre plucking produces a mellower sound, near-end plucking a harsher one.

Pipes and tubes behave in a somewhat similar way. In an open pipe, the simplest motion is one in which there is free movement at the open end and none (since there can be none) at the closed end: so a 12 cm pipe will have a fundamental with a node at 0 cm and the ffrst antinode at 12 cm (plus a bit due to the end correction), hence a wavelength of about 48 cm. But, just as in a string, this is not the end of the story: though the fundamental is deffned by the pipe’s length, other resonances will be produced according to its width. The mixing of these with the fundamental and its overtones produce diflerent timbres: in wider tubes, there is more energy in lower harmonics and the timbre is more rounded, while thinner pipes are brighter (or shriller, depending on your taste).The ffnal consideration for instrument makers is that a string held between two points makes a very quiet sound indeed, because its very thin cross section only aflects a tiny surrounding volume of air. In order to turn the string into a musical instrument, a much greater volume of air must be put in motion. In an electric guitar, this is accomplished by using the vibration of the metal string to induce a small electric current in pickups (magnets wound with ffne wire). In acoustic guitars and other stringed instruments, the wooden soundboard (top) is vibrated by the string and its large area moves much more air than the string alone. Also, at low frequencies the hollow bodies of such instruments act as Helmholtz resonators.

Non-electric instruments do not add energy. Rather, they convert the energy provided by bow, plectrum, or air blast to an acoustic form. In cases where the body of the instrument shifts the frequency towards the 4 kHz region, this will sound louder, despite the fact that the sound power is actually reduced a little by frictional losses. This loudness increase stems from the construction of our hearing systems, as we shall see in Chapter 4.