Jens Johler - Bach and The Tuning of the World

‘Yes indeed,’ said Bach.

‘What’s that?’ the Rector asked, raising his arm as if to threaten them with blows. But he only put his hand behind his ear.

‘We have seen the limestone cliff,’ said Bach in a clear voice. ‘It was certainly very impressive.’

Cantor August Braun was a gaunt man of around fifty. His wig was on the table next to him when they entered; he didn’t bother putting it on. A crown of thin grey hair adorned his pointed head. He had Erdmann sing something, then Bach, and he was pleased, nodding after listening to Bach’s boy soprano. He asked them a couple of questions about their instruments and gave them the music score for the choir practice next day. He said they might do a little practising beforehand. Regrettably, they had missed Annunciation Day, he said reproachfully, but next Sunday was Judica, and they would be singing in the matins choir. And he had scheduled them for the Saturday before Palm Sunday to sing in the large choir, as well as for the Passion on Good Friday. Did they have any questions?

Bach and Erdmann shook their heads.

‘Well then, let’s get going. Our Waldemar here, whom you seem to have already made friends with, will show you the rest. By the way, he’s also a good singer, despite the fact he’s not from Thuringia.’

Waldemar winked at them conspiratorially in a way that seemed to say he couldn’t really sing and was just pretending. Before showing them the dormitories, he warned them in a hushed voice about the young gentlemen from the Collegium Illustre, who also had their dormitories in the inner courtyard. A bagarre with them would occur every once in a while.

‘What’s that?’ asked Bach.

‘A brawl.’

‘No, I mean the Collegium Illustre.’

‘Oh that,’ said Waldemar with a dismissive gesture.

‘Well?’

‘The Knights’ School. Some also call it the Knights’ Academy, but it’s a Latin school just like ours, only for the nobility, so the great lords can mingle among themselves. They learn all sorts of things there, things us mere mortals don’t need. Heraldry, courtly dances, carving, making compliments, bowing and scraping and such-like. The young gentlemen pride themselves hugely over the whole thing.’

‘How many of them are there?’ Bach asked.

‘Fifteen.’

‘And how many are on scholarships?’

‘The same number.’

‘Then, one of these days, we should organize a contest,’ said Bach. ‘Not in bowing and scraping, of course, but perhaps …’

‘In philosophizing,’ Erdmann suggested.

‘Or in singing,’ said Bach. ‘We can certainly do that much better than they do.

A singing contest never came about, though, and would anyway have been meaningless. They often sang together with the knightly students, and there was nobody who could deny that the choir students were more musical. The aristocratic gentlemen didn’t much care. They looked down on the scholarship students like they would on poor chirping birds who were born to warble, who had to do so out of necessity. The only one among them to whom they looked with something approaching respect after a while was Erdmann, because he spoke so well and got a kick out of styling his language to courtly etiquette.

‘I’ve thought it all over,’ he said after some time had passed. ‘I don’t want to become a philosopher after all, but a diplomat.’

This surprised Bach. Not so much because Erdmann all of a sudden wanted something different than what he’d wanted only a couple weeks ago but, rather because he had actually made such a decision. For him, Bach, the question didn’t exist. It had been clear from the onset he would be a musician. He came from a family of musicians, so what was there to think about? At most, the question was: What kind of musician? Town musician like his father? Organist like his uncle and his brother? Cantor like Elias Herda? Or kapellmeister at one court or another? And there was another question he asked himself sometimes before he fell asleep: With whom would he vie in the future? With the greatest musicians of his craft, with Reincken and Buxtehude, Corelli and Lully?

The discipline at the school was very strict. Every little thing was planned, and any deviation from the rules was strictly punished – when you were a scholarship student anyway.

But while Erdmann clandestinely rebelled against the unnaturalness of the unyielding rules, Bach acquiesced to the strictly disciplined system.

Along with the others, he got up at five in the morning, washed, combed his hair, dressed and, right where he was, got down on his knees for their first prayer, whether on a stone floor or scrubbed floorboards, as soon as the first quarter struck. During meals, he heard the chapter of the Bible that was read to them, refraining from speaking or any mischief, exactly as prescribed by the school’s set of rules. He kept his clothes, shoes, stockings and underwear clean; he swept the rooms when his turn came. During classes, he was attentive, made notes and memorized as much as he could, which required little effort since his memory had always been excellent.

The curriculum consisted of Latin and Greek, Religion and Logic, History and Geography, Mathematics, Physics and German Literature.

Bach had already found a special knack for mathematics when he went to school in Eisenach and Ohrdruf and so in this subject he could shine. During the first week, he had the chance to prove the theorem of Pythagoras and, when the teacher asked him what else he knew about Pythagoras, he answered that Pythagoras was one of the great sages of antiquity. Not least, he explained, Pythagoras was famous for finding the mathematical proportions of the harmony. The teacher asked whether he also knew how Pythagoras came to his discovery.

‘Certainly,’ Bach replied, stealing a quick look at Erdmann. ‘Lost in thought, Pythagoras was walking by a smithy, where several journeymen were hammering the iron on an anvil and suddenly he noticed how they created harmonic sounds; to wit, the fourth, the fifth and the octave. Astonished, he walked into the smithy to look for the cause of this array of sounds and ultimately discovered that the harmonic proportions of the notes have whole number ratios. He then demonstrated it on the monochord, which the Greeks called the kanón .’

‘How would you describe a monochord?’ the teacher asked, doing so because some of the students looked puzzled.

‘Well,’ said Bach, ‘it’s a board or, rather, a sound box over which a single string is stretched, let’s say with a length of four cubits. When strumming this string, you hear a note you could call the tonic. If the string is divided up into two equal halves by positioning it over a wooden bridge and the half-string is hit, the octave will sound. Hence the proportion: whole string to half string, or 2:1. If you now divide off two-thirds of the string and strum the longer part, you get the fifth. So the fifth has the ratio: three-thirds to two-thirds, i.e. 3:2. The fourth, in turn, is ruled by the ratio of 4:3, the major third by the ratio 5:4, and so forth. And, as mentioned before: all harmonic intervals are governed by whole number ratios.’

‘Excellent,’ said the teacher. ‘Then you also probably know what the Pythagorean Comma is?’

‘Oh, yes,’ Bach said eagerly, without noticing how the others’ eyes by now were turned on him with envy.

‘Well?’ asked the teacher.

‘A comma,’ said Bach, ‘if you translate it literally from Greek, is nothing but a section , and in this case – well, it’s not so easy to explain. Do I have permission to go to the blackboard and draw a sketch?’

‘Please do so,’ said the teacher.

Bach got up from his desk and walked to the blackboard. ‘Here is how it is,’ he said, turning to the class. ‘If you tune perfect fifths on an instrument, namely exactly in a ratio of 3:2, and go up higher from fifth to fifth, from C to G, from G to D, from D to A and so forth, you’ll return to the C after exactly twelve steps, only seven octaves higher. It’s called the circle of fifths.’