Paris in the twelfth century was expanding fast, as was its university, which was beginning to shrug off its ecclesiastical roots and embrace a more secular approach to learning. This was the era of the troubadours and trouvères: skilled, far-travelled poet-singer-songwriters whose fame was built on songs of ‘refined’ love. For them, Paris was the jewel in any tour programme. At the peak of the troubadour-trouvère craze, several hundred of them plied their trade, with troubadours from Occitania, the southern half of France, then virtually a separate country with its own language and culture, and trouvères from the northern half. It sparked a lively exchange of ideas and tunes between countries, but also between contemporary church music and its secular counterpart. And it was a two-way street: folk songs were made from well-liked passages of sacred music and popular tunes found themselves layered on to existing religious plainchant, an exchange so beloved that it continued for the next three hundred years.
The troubadour phenomenon had been inspired by the example of professional singers in the courts of al-Ándalus, Muslim Spain, which had its resplendent capital at Córdoba. As Christian armies of the reconquista began to sweep south in the eleventh and twelfth centuries, seizing province after province from the collapsing Caliphate, they plundered the libraries of Muslim cities, ransacked the palaces and villas of the fleeing Moors and pillaged the treasures of their culture. As a result, European musicians inherited from the Arab world at least three instruments that became central to secular music in the centuries to follow: the al’Ud (literally ‘strip of wood’), of Persian provenance, which developed into the lute, thence the guitar; the rebab, a primitive form of violin; and the qanun, a variant of the Ancient Greek psalterion, which had spawned the psaltery elsewhere in Europe.
The poetic songs of the Caliph’s court, sometimes called ghinā’mutqan (the perfect singing), came from a long tradition nurtured by both qaynas, professional women performers, many of them slaves, and male composer-scholars such as Ibn Bājja (also known as Avenpace). The mingling of musicians with Arabic training with those of a European background in the final, chaotic stages of the al-Ándalus Caliphate gave rise to a form of rhymed song, the zajal, which became a key ingredient of the growing troubadour repertoire. These songs were shaped by the poetic metre of their lyrics, and consequently most of the troubadour songs, even the sad ones, have a gentle, foot-tapping pulse.
Which brings us back to our Parisian composer, Pérotin, and his great legacy to Western music. The revolutionary element he introduced into the sacred music he wrote at Notre-Dame was something he’d clearly learnt from the troubadours, who had in turn picked it up from Spain: rhythm.
Before Pérotin the subject of rhythm in sacred music is a thorny one. No one knows for sure if medieval plainchant singing had a pulse or beat of any kind, because there was no way of writing it down. No surviving medieval plainchant reveals to us that a pulse was intended, and books of theory and instruction are ambiguous on the subject. The first we really know about rhythm is that Pérotin found a way of notating it.
These days, guitarists who want to play a well-known pop or folk song can do so simply by reading a chart with the names of the chords. Guitarists familiar with the tune of ‘Morning Has Broken’, for example, would be able to play the song just by seeing the lyrics alongside the chords:
But if, in eight hundred years, musicians come across a piece of paper with just the chord names on it and a few lyrics, with no further information as to the speed, rhythm, mood or groove of the song, they will be in trouble. This is what it’s like for us looking at twelfth-century notation.
Pérotin, though, began using an upgraded method of notation that did for the first time indicate the rhythmic value of notes. The system he used, while not as flexible or sophisticated as the one used today, relied on the grouping together of notes with horizontal bars called ligatures. Every time he grouped notes together with a ligature, he meant that those notes should be shorter than the others. And once you start specifying long and short notes in a chain, you generate a rhythmic pattern.
Pérotin was particularly fond of one rhythmic pattern, one you can easily remember because it is the rhythm of the theme tune to The Archers: dum ti dum ti dum ti dum. It is generated by alternating notes long-short-long-short-long-short, and so on. Pérotin made this pattern his own, using it throughout the hymn he composed for Christmas Day 1198, ‘Viderunt Omnes’. It is the same rhythmic pattern that drives the only popular non-religious song of the early thirteenth century still known today: ‘Sumer is icumen in’. It is not known who wrote this catchy English song – it may have been a man from Herefordshire known mysteriously just as ‘W de Wycombe’ – but as a piece for six simultaneous voices that ingeniously interlock, it sounds as if the composer took Pérotin’s style, made it more accessible, gave it bawdy rustic words and expected folk to dance to it. A delightfully clear original manuscript of ‘Sumer is icumen in’, possibly in W’s own hand, survives at the British Library. It features a simpler version of rhythmic (sometimes called ‘mensural’) notation than Pérotin’s ligatures, but nonetheless it does the trick.
Without question, the ability to write down rhythms fired the imaginations of composers. In fact, for the whole of the thirteenth and fourteenth centuries, composers thought of little else than how to construct ever more complex layers of sound with their four voices, singing simultaneously but at different speeds and with different rhythms. Now they had the building blocks with which to construct long pieces of music that you didn’t have to memorise, they set about creating the equivalent of musical labyrinths – mathematical and geometrical structures embedded in the texture of the music. Which isn’t really surprising, I suppose; this was also the age of ecclesiastical mazes – which may have served as metaphors for pilgrimages to Jerusalem – such as those at Chartres and Lucca Cathedrals.
Examples of musical labyrinths can be found in abundance in the choral music of Guillaume de Machaut, a composer-poet working in northern France in the mid-fourteenth century. One is a Mass he wrote for Reims Cathedral, newly rebuilt but subsequently destroyed in the French Revolution, and which, as it happens, had a complex maze set into its nave. The score of this Notre-Dame Mass has four lines of music, each of them representing one of the voices singing. This is more or less how all choral music is laid out to this day: one line of music for each singing part, running alongside each other on the page. So what was so special about Machaut’s mass setting?
This is the thing. Machaut and his fellow fourteenth-century composers thought of the notes to be sung as units in a vast mathematical game, so the duration values of the notes (that is, how many beats) were treated as a long string of numbers. The top voice, for example, begins the first part of the mass, the Kyrie Eleison, with duration values that make up the following number sequence: 6, 2, 2, 2, 4, 1, 1, 2, 2, 2, 4. The sequence runs along for a while and then repeats itself. Each of the four singing parts had its own duration-value sequence that started and ended at a different point, creating an overlapping lattice of notes of different lengths. And alongside each singing part’s duration-value sequence, Machaut added a repeating pitch-value sequence: A, A, B, G, A, F, E, D, E, F, G.
Making things even more complex, the pitch-value sequence would normally be of a different length to the duration-value sequence, so the two sequences would repeat at different rates. Sometimes Machaut would double or halve the sequences in his compositions, or run them in reverse order, or invert the pitch pattern, or use a mathematical formula like the Golden Section – much exploited in architecture and painting in the late Middle Ages and Renaissance – to configure the sequence of numbers.
But all of this intricate structuring was hidden. It is not possible, by listening to the music, to perceive the underlying design, although a skilled score reader may be able to plot its workings by studying the music on the page. The musical term for the secret guiding sequences in fourteenth-century composition is isorhythm, and the pieces that employ
ed it are among the most complex musical structures ever attempted. Indeed polyphony, the interweaving of separate vocal lines, had become so complicated by the time of Pope John XXII that he actually issued a decree in 1325 ordering church music to be made more simple. No one took any notice.
What makes the achievements of Machaut and his contemporaries even more incredible was that they were composing at a time when a third of the population of Europe was being wiped out by the Black Death. How on earth did they find the inspiration to create such bafflingly intricate music? The answer, surely, is that they had recently acquired these extraordinary new gifts – the notation of music and the multiple layering of voices – and they were flexing their intellectual muscles. Alongside death and despair, this was also the period of astounding Gothic architecture, with the most extraordinary cathedrals, abbeys and churches being built all over Europe. To sing a note in one of these cavernous spaces is to hear its sound echo and reverberate, returning to its source modified by the building itself. Composers of Machaut’s time were undoubtedly playing with the acoustics of the cathedrals they worked in, creating vocal manifestations of them, building layer upon layer of sound on a mathematically plotted foundation of isorhythm – and all of it to glorify (or impress) God.
Much like the Gothic architecture that shaped the buildings for which it was written, isorhythm did not last as a tool in the organisation of music. Guillaume de Machaut was its champion and its paragon.
Before leaving isorhythm, there is a footnote to be added about the way it is organised as strings of note values. There is a strikingly comparable procedure in the practice of tala in Hindustani and Carnatic classical music, whereby cycles of note values in the rhythm pattern may operate independently of a sequential melodic cycle, known as raga. That the Indian technique pre-dates European isorhythm by a considerable period is incontrovertible: tala (literally ‘clap’) is described in the text version of the eleventh-century Ramayana, a Sanskrit epic whose oral version is thought to have existed as early as the fifth century BC. It may be mere coincidence, but the fourteenth-century term for the rhythmic cycles in isorhythmic compositions by Machaut and others was talea (from the Latin for ‘stick’ or ‘cutting’).
By the end of the fourteenth century, nearly all of music’s vital components had been discovered: notation, both melodic and rhythmic; structural organisation; and polyphony, the layering of voices on top of one another. But one final piece of the jigsaw still needed to click into position. When it did, in England in around 1400, it took musical harmony on to a radical new plane, and altered the way music sounded for ever.
From Pérotin in 1200 to Machaut in 1350, composers had enjoyed the resonant, sonorous effect of simultaneous notes in clusters, or chords. Although Pérotin’s use of chords would have to be described as eccentric bordering on haphazard, by the time of Machaut the general menu of approved-of chords was in fact extremely limited. This was partly due to ecclesiastical interference – priests, bishops and cardinals knowing better than composers which sounds were godly, pure and appropriate – and partly due, I suppose, to fear of the unknown.
To understand the musical revolution that occurred in around 1400, at the hands of a composer and astrologer named John Dunstaple, we need to play with some notes. In the century leading up to Dunstaple’s time, composers layered notes on top of each other but chose only from a very limited number of possible combinations. These revolved around the basic ‘octave’ – Big A and Little A, Big C and Little C – and what they called diatessaron and diapente (from Greek: ‘through four’ and ‘through five’). Nowadays known as the ‘perfect fourth’ and ‘perfect fifth’, these are the pleasing-sounding combination of a note and the one four or five rungs above it, which we encountered earlier in the chapter. What makes them ‘perfect’ is that both have a mathematically pure ‘pitch ratio’; dividing a taut plucked string by exactly two-thirds, for instance, will produce a perfect fifth. Where the ‘pitch ratio’ of two identical pitches is 1:1 and that of an octave 2:1, the ratio of a perfect fifth is 3:2 and a perfect fourth is 4:3.
Perfect fourths on a keyboard
Perfect fifths on a keyboard
You will notice that I have not included F to B in the possible menu of perfect fourths. This is because F to B is not perfect: to achieve the desired pitch ratio of 4:3 we would need to pair F with B-flat (B♭), or F-sharp (F#) with B – the flats and sharps are the black notes on a keyboard. F to B was considered so unpleasant that it was given the names ‘the devil in music’ and the ‘wolf tone’, and disallowed from the list of perfect fourths. The ‘diabolical’ sound produced by F and B, a distance known as a tritone, is likewise produced by pairing B♭ and E, E and A#, C and G♭, and all the other possible tritones. (This has more to do with traditional keyboard layout than the logic of the ‘four steps’ idea. In the sound world of the period AD 300-1600, more or less, the allowable perfect fourth ran, in fact, from F to B♭ – that is, the black note just to the left of B. It is only a black note on a keyboard: a voice, or any other instrument, does not discriminate between ‘black’ and ‘white’ notes – and nor, aurally, does a keyboard – but the look of the arrangement of notes makes one think of the two types differently. It is a psychological rather than a musical problem.)
Where we are in history at this moment, 1400, you can safely ignore the black notes, even though in theory and occasionally in practice they were fully operational.
So in fourteenth-century polyphony, the perfect fifth, the perfect fourth and the octave comprised the vast majority of note combinations, or chords, on offer. Two features of this sound immediately spring to mind when you listen to it. One is that it sounds quite bare compared to later harmony. The other is that no piece ever really sounds as though it has ended properly. There’s a reason for this. To our ears, accustomed to the subsequent six hundred years of harmony, there’s something missing that accounts for the bareness of sound. What’s missing is any sense of logic in the use of these chords. When we listen to the music of Bach, or Gershwin, or Sting, or Alicia Keys, we are being taken on a journey of chords, a ‘progression’. We are guided towards the all-important end of the phrase, called the ‘cadence’.
Imagine, if you will, the spiritual song, ‘Amazing Grace’. In the first phrase of the song, the words ‘Amazing grace’ share one chord, our ‘home’ chord. Let’s call it Chord I. Then, as the tune moves towards the word ‘sweet’, the chord shifts to what we will call Chord IV – because, as it happens, we have moved up a perfect fourth in the bass. At the end of the first line, as we land on the word ‘sound’, the harmony moves back to where we started, Chord I:
Everything feels ‘right’ about that little journey of chords. We felt good falling back to where we had started. This was our first little cadence – a term that has its origin in the Italian cadere, to fall.
In the second phrase we go on another short chord journey:
This time, we travel to a new chord on the word ‘me.’ This is Chord V because, yes, it is a perfect fifth. Again, this progression feels logical and satisfying. We are being led from one place to another and then back again.
The verse completes itself by making two further mini-moves, from I to IV and back, and then from I to V and back:
You can quite clearly hear that there’s nothing haphazard about the choice of chords accompanying this tune. What is at work here is a logic in the progression of the chords. They are obeying strict laws, rather like the laws of gravity or of planets in orbit, whereby some chords exert more power than others.
The laws that chords obey, like the chain in ‘Amazing Grace’, were first teased out in the music of our English composer-astrologer John Dunstaple in the early 1400s, by the unveiling of a powerful new chord combination. It was neither a perfect fourth nor a perfect fifth. It was the mighty, but imperfect, third.
Back at the keyboard, if you count three white notes up from your starting point, C, you arrive at E. It sounds quite pleasant, so wh
y isn’t this third a perfect distance? The reason is that the third, unlike perfect fourths and fifths, has both a major and a minor version. It is Mr Ambiguous. If I count three white notes from D, for example, I come to F, creating a minor third.
Ditto E to G:
But F to A, like C to E, is a major third:
We can turn major thirds into minor thirds, and vice versa, by using the black notes to shorten or lengthen the distance between our two notes. To hear the minor third starting on C, for instance, we would land on E♭ instead of E, and to hear the minor third starting on F we would land on A♭ instead of A. Similarly, to hear the major third starting on D we just carry on past F to F#, and to hear the major third starting on E we continue past G to G#.
All the way up the ladder of notes, the third can either be major or minor, and the pivot between the major third and the minor third is the pivot upon which all Western music balances. In very crude terms one sounds happy and one sounds sad, but it’s much more intriguing than that; allowing the third into note clusters had one other big by-product: the triad.
The Story of Music: From Babylon to the Beatles: How Music Has Shaped Civilization Page 4