Before Bach

Pythagoras settled in Croton, in southern Italy, around 530 BC. Later writers told how he passed a blacksmith’s shop where the hammers sounded in consonant intervals, weighed the hammers and found the numerical ratios behind them. The legend is attached to the idea that the octave, the fifth and the fourth can be expressed as ratios of small whole numbers.

The string also vibrates in several ways at once. As well as vibrating along its whole length, it vibrates in halves, thirds and smaller divisions. These produce its partials. For an ideal flexible string, their frequencies are one, two, three and more times the lowest. Over a low C, the first six are C, C, G, C, E and G, rising through the octaves. The fifth partial gives an E, a pure major third above the C of the fourth partial.

Around the beginning of the sixth century AD, Boethius gathered Greek musical learning into his Latin De institutione musica. His book carried the ratios into medieval classrooms, where music belonged to the quadrivium with arithmetic, geometry and astronomy.

Greek theorists also divided scales into tetrachords, groups of four notes spanning a fourth. Medieval musicians later gave the names Dorian, Phrygian and Lydian to the church modes. A white-note scale from D to D models medieval Dorian; ancient Greek Dorian used a different arrangement.

Pepin and his son Charlemagne made Roman worship a concern of the Frankish kings. From the middle of the eighth century the chant of Rome spread through their churches and monasteries, and Frankish singers changed it as they sang it. This became the repertory now called Gregorian chant. Its name honours Pope Gregory the Great, who had died in 604.

The singers had a great deal to remember. At Mass, the Kyrie, Gloria and Sanctus returned with the same words each time, and other texts changed with the feast. Around the Mass lay the Divine Office, the daily round of psalms, readings and prayers. All of these could be sung on a single melodic line, by one singer or by a whole choir. A setting with one note to a syllable carried the words quickly. A melisma set one vowel to a succession of notes.

A psalm tone made a long text manageable. A few opening notes brought the singers to a reciting pitch, where they could stay for as many syllables as the verse required. A small turn marked the middle of the verse and another marked its end. The antiphon sung around the psalm determined which formula would fit. A choir could sing a new verse to a tune it already knew.

The later medieval sequence Dies irae begins F–E–F–D–E–C–D–D. The melody circles D with a C♮ below it, where a modern minor key would have a sharpened leading note. Its opening stanza calls David and the Sibyl as witnesses to the day of judgement. Those eight notes appear in Berlioz’s Symphonie fantastique and recur in Rachmaninoff’s music.

At Rupertsberg in the twelfth century, Hildegard of Bingen wrote chants for her nuns with leaps and long melismas that took the voice beyond the range of many older melodies. Near the end of her life, a dispute over a burial brought an interdict on the community, and the women had to recite their services instead of singing them. Writing to the prelates of Mainz in 1178–⁠79, Hildegard told them that those who unjustly silenced a church would “lose their share in the angels’ praises in heaven”.

Around 1028, Guido of Arezzo brought his chant book to Pope John XIX in Rome. The pope turned its pages and studied the rules. Guido later told his fellow monk Michael of Pomposa that John would not leave his seat until he had learnt a verse he had never heard, because he wanted to try for himself what he found scarcely believable in the schoolboys.

Guido was concerned with the slow business of teaching an enormous repertory by ear. His Micrologus, written around 1025–⁠28, combined practical instruction with interval theory. Pitch letters and reference lines already existed. In the staff system he promoted, both lines and spaces gave each note a fixed position. A C or F at the beginning of the staff fixed the surrounding tones and semitones, and coloured lines marked them for the reader.

Later teachers developed overlapping six-note scales, or hexachords. The natural hexachord began on C. The hard hexachord began on G and included B♮; the soft hexachord began on F and included B♭. Every hexachord kept its semitone between mi and fa. When a tune went beyond six notes, the singer changed hexachord, and the change was called a mutation. G could become ut where it had been sol a moment before, without changing pitch.

A staff could carry a melody far beyond Guido’s classroom, with its intervals intact. Singers still learnt pronunciation and phrasing from one another. The notes on the page fixed the pitch. Once composers began to set several voices moving together, scribes also had to show how long each note should last.

An English theorist writing after 1280 remembered two Parisian masters. Léonin had made a great book of organum for worship at Notre-⁠Dame; Pérotin had revised it and written music in three and four parts. The theorist, whose name is lost, called him “Pérotin the Great”. He named Viderunt and Sederunt among his excellent four-part pieces. This witness is known as Anonymous IV.

The extra voice had a much older history. The ninth-century Musica enchiriadis describes singers joining a chant at the fourth or fifth, sometimes doubling the parts at the octave. In a parallel passage the two voices rise and fall together. Elsewhere one voice holds a note while the other moves, and they end on the same note.

In the Notre-⁠Dame repertory the added voice could become much more elaborate. The chant moved into a tenor part, from the Latin tenere, to hold. One tenor note might last through a whole phrase of the upper voice. When both parts moved in measured rhythm, the passage was in discant. A service could pass from plainchant into these elaborate sections and back again.

A measured section could be lifted out and replaced with another setting of the same chant fragment. Such a section was called a clausula. When singers added words to an upper part, they helped create the motet. Soon different voices could sing different texts at once, while the tenor kept to its fragment of chant.

Guillaume de Machaut spent years in the service of John, King of Bohemia, before settling in Reims, where he was a canon of the cathedral. He wrote love songs, long narrative poems and sacred music, and saw them collected in carefully arranged manuscript books. In the illustrations to these books, Nature comes to him and gives him Sense, Rhetoric and Music.

He inherited a new precision in musical notation. Around 1320 the ars nova (‘new art’), associated with Philippe de Vitry, extended the ways scribes could divide a note. A breve could hold two semibreves or three; each semibreve could in turn hold two minims or three. The two choices were independent of each other. A singer could sustain a note across an expected division while another part marked it.

Above a slowly repeating tenor, Machaut’s upper voices can trade quick notes and rests. In hocket, one voice sounds exactly where another stops, breaking a phrase into short fragments. A cadence brings the parts together again. The tenor’s recurring rhythm can shape a whole span of music while the upper voices move on to the next syllable.

Machaut also used repetition in his secular songs. In a rondeau the refrain returns with its words; a virelai alternates between refrain and verse; a ballade repeats its stanza form. The same manuscript could contain a lover’s complaint and a Mass, both by Machaut as poet and composer.

On 25 March 1436, Pope Eugene IV consecrated Florence Cathedral. Guillaume Dufay supplied Nuper rosarum flores, a motet whose two lower parts draw on the chant for the dedication of a church. Above their long notes, two quicker voices sing of the pope’s gift of roses and ask the Virgin to hear the people of Florence.

A borrowed melody could also run through the movements of a Mass. This cantus firmus, or ‘fixed song’, might come from worship or from a secular song. Dufay and many successors built Masses on L’homme armé, a song about an armed man. The tune could move to a different voice or stretch into longer notes. At the same time, thirds and sixths were becoming familiar consonances between the open fifths and octaves of cadences. In fauxbourdon, voices move together through a chain of sixth chords.

In Josquin’s Ave Maria … virgo serena, the greeting descends through four voices, each entering with the same melody. Later, pairs of singers answer each other; at the final plea, ‘O mother of God, remember me’, all four sing together.

Palestrina’s Missa Papae Marcelli, published in Rome in 1567, is written for six voices and keeps the words audible. In the long Gloria and Credo, groups of singers often pronounce their syllables together. Elsewhere, one voice holds a note while the voices around it move, so that a consonance becomes a dissonance and then resolves down by a step. This figure is called a suspension.

Dieterich Buxtehude became organist of St Mary’s in Lübeck in 1668. In 1705 the young Bach walked there to hear him. An organist could keep a bass going with the feet while both hands played above it, and changing keyboards or drawing a stop brought another set of pipes into the music. Bach stayed far longer than his employers in Arnstadt had allowed.

Bellows feed air to the organ’s pipes. A held key admits wind, and the note continues for as long as the supply lasts. An 8-foot stop sounds at ordinary keyboard pitch; a 4-foot stop sounds an octave higher, a 16-foot stop an octave lower. Several stops can sound together from one key. The organist chooses which pipes will sound before choosing the notes.

The bow lets a string sound for longer than a plucked note. A player can increase the pressure on a note or let it fade before changing pitch. Viols usually have frets and six strings, tuned mostly in fourths with a third in the middle; even the smaller sizes are held against the legs. Violins have no frets and normally carry four strings tuned in fifths. Their curved bridges let the bow reach one string without touching the strings beside it.

In sixteenth-century Cremona, Andrea Amati made violins with the familiar narrow waist and arched wooden body. His family’s workshops passed the craft through four generations. One surviving Amati violin from the 1560s, now in the Musical Instrument Museum in Phoenix, combines spruce and maple with ebony and rosewood.

On 23 February 1607 Carlo Magno wrote from Mantua to his brother in Rome about the entertainment planned for the following evening. He called it unusual, because “all the characters will speak musically”. The work was Monteverdi’s L’Orfeo, with words by Alessandro Striggio, performed at the Gonzaga court on 24 February.

The experiment had a Florentine past. In the 1570s and 1580s, musicians and scholars met at Giovanni de’ Bardi’s house to discuss ancient Greek drama. Among them were Vincenzo Galilei, Galileo’s father, and the singer Giulio Caccini. They wanted a solo voice that carried every word, with instrumental support that left the text audible. Caccini’s Le nuove musiche, published in 1602, contained solo songs and advice on how to sing them. Jacopo Peri had already brought Dafne to the stage in 1598 and Euridice in 1600.

Cruda Amarilli, one of the madrigals under attack, opened Monteverdi’s Fifth Book in 1605. The lover in the poem praises Amarilli’s beauty, then calls her deafer and more elusive than a snake. In 1607 Monteverdi’s brother Giulio Cesare explained the seconda pratica as a practice in which the words govern the harmony.

Charon sings in a low register, accompanied by a small reed organ. Orpheus sings Possente spirto, a song with elaborate flourishes addressed to Charon. Two violins answer, then two cornetts, then a double harp. In the 1609 printed score, a plain vocal line is printed beside an elaborately ornamented one. Charon refuses Orpheus passage. Orpheus crosses only after his later lament has put Charon to sleep.

The Mantuan audience came by invitation. From 1637, Venice offered opera to people who bought a ticket. Monteverdi had been in the city since 1613 as music director at San Marco; in his last years he also wrote for its commercial theatres.

Agostino Agazzari objected to busy lute players. In his 1607 book on accompanying an ensemble, published in Siena, he complained of players who ran through divisions from beginning to end, especially when others were doing the same. The result, he wrote, was “soup and confusion”. In his view a good accompanist needed to hear the singer and leave space.

The basso continuo gave that accompanist a written bass line and, where needed, figures specifying the notes above it. An organ, harpsichord or plucked-string instrument could fill in the chords; a bowed bass could share the lower line. Agazzari advised fuller chords for many voices and fewer notes for a soloist. He also noted the convenience of the system, since an organist expected to keep every vocal part in full score would need a library larger than a lawyer’s.

The cadence G–C in the bass, with B rising to C above it, became one of the familiar ways to close a phrase in C major. Composers could establish another key with another such cadence and then return to the home key. In his Traité de l’harmonie of 1722, Rameau explained chords through their roots and inversions, so that the lowest sounding note and the root of the chord can differ. His ‘fundamental bass’ follows those roots beneath the notes the players actually sound.

Unequal circulating temperaments make every key available while giving their thirds and fifths different sizes. Bach dated the first book of The Well-⁠Tempered Clavier 1722. It contains a prelude and fugue in each of the twelve major keys and twelve minor keys. A player begins in C major, moves to C minor and works through the keyboard to B minor.