Beethoven – Bean Thinking

From Beethoven to Pythagoras via Kin Cafe, Fitzrovia

I had been waiting for an opportunity to try Kin Cafe in Fitzrovia for a while. Having followed them on Twitter, I had been tempted by the large selection of great-looking vegetarian and vegan food choices tweeted almost daily. Although I’m no longer a vegetarian, appetising meat-free meals are always appealing. So it had been on my “to try” list for a long time (preferably for lunch). However, sometimes things don’t work out quite the way you had initially hoped and so it was late afternoon by the time we ended up at Kin, sadly no lunch then. So we settled on an Americano, soya hot chocolate and a slice of Butternut and ginger cake. The coffee (from Clifton Coffee) was very fruity and full of character, highly enjoyable while sitting in the window overlooking the street outside. The cake meanwhile deserves a special mention. Not only was the cake very good, the helpful staff at Kin were very confident in their knowledge that this cake was nut-free and they also ensured that the new member of staff (being trained) used a new cake slice to serve it. Extra ‘points’ for a nut-allergy aware café and definitely a tick in the “cafes with good nut knowledge box”.

As we sat with our drinks, one of Beethoven’s quartets was playing through the loudspeakers. For me, Beethoven being played in the background is a bonus for any café but it did, perhaps, mean that I was less sociable than normal with my frequent companion in these reviews; the quartets are too absorbing. I do hope the hot chocolate made up for it.

Interior of Kin cafe — Tables are supported by struts forming triangles. But this is not the Pythagorean link.

Inside the café, tables along the wall were each stabilised by a diagonal support. A practical arrangement that had the visual effect of forming a triangle with the wall. While this did make me think about force-balancing and Pythagoras, this is not the link to Pythagoras alluded to in the title. No, instead the connection goes back to the Beethoven and the links between music and mathematics. Perhaps we no longer immediately think of music and mathematics as being particularly connected, after all one is an ‘art’ and the other a ‘science’. But music and mathematics have, traditionally, been so inextricably linked that, as Susan Wollenberg wrote in ‘Music and Mathematics’* “… it is their separation that elicits surprise”.

Some of the links between music and mathematics are explored in this TED-Ed talk about the maths to be found in Beethoven’s Moonlight Sonata. This part of the link between music and mathematics comes in the relation between what is known as consonant and dissonant notes. The first part of the Moonlight Sonata is made up of triplets of notes that sound good to our ears when they are played together. As Pythagoras is said to have discovered (see link here, opens as pdf), there is an interestingly simple relation between notes that are consonant with each other. Whether you look at the frequency of the notes or the length of a string required to play them, the ratio of two consonant notes seems to be a simple number ratio.

For example, the A of an oboe has a frequency of 440 Hz*. The A one octave higher is at 880 Hz, a factor of 2. If we took instead a series of notes of frequency f, then we could find a series of consonant notes at f:2f:3f. But now, remembering that octaves are separated by a factor of 2 and that they ‘sound good’ together, this will mean that the ratio of frequencies f:1.5f:2f will also sound good. This set of frequencies just happens to coincide with the C-G-C’ chord that forms the basis of many guitar based pieces of music. As you continue looking at these simple number ratios you can start to build a set of notes that eventually forms a scale.

Blue plaque Foley St — The artist Fuseli once lived diagonally opposite Kin Cafe. J. James notes that Fuseli was part of the artistic revolution that was paralleled by Beethoven and the Romantics in the musical sphere**.

But the links go deeper than this. In the same book “Music and Mathematics”, JV Field wrote “..in Ancient, medieval and Renaissance times, to claim that the order of the universe was ‘musical’ was to claim that it was expressible in terms of mathematics.” Indeed, Kepler looked for these musical harmonies in the maths of the planetary system. Although he found no ‘harmonies’ in the ratio of the periods of the planets then known, he did find musical scales in the ratios of the speeds of the planets (measured when they were closest to the Sun, at the perihelion, and furthest from the Sun, at the aphelion). Other simple number ratios can be found when we look to different regions of the Solar System. The periods of three of the Galilean moons of Jupiter for example have the ratio 1:2:4 (Io:Europa:Ganymede). While we would no longer describe these patterns as reflecting the harmony of the Universe (see here instead for current understanding), perhaps we ought to ponder the next sentence that Field wrote in the chapter on Musical Cosmology:

“We still believe [that the universe is expressible in terms of mathematics] now. Indeed, mathematical cosmology has proved so powerful that it is perhaps difficult to take a sufficiently cold hard look at the metaphysical basis on which it rests. On the other hand, the explicitly musical cosmologies derived more directly from the Ancient tradition seem sufficiently fantastic to invite instant questioning of their underlying metaphysics…”

One to consider next time you happen to wander into Kin Cafe, or another café playing such mathematical composers as Beethoven.

Kin Cafe can be found at 22 Foley St, W1W 6DT

*Music and Mathematics, Edited by J. Fauvel, R. Flood, R. Wilson, Oxford University Press (2003)

** The Music of the Spheres, J. James, Copernicus (Springer-Verlag), (1993)

Lastly, a video of Wilhelm Kempff playing Beethoven’s Moonlight Sonata. I would really recommend playing it twice, the first time to listen only, the second to watch while Kempff plays. His performance is fascinating.

Time to enjoy a Beethoven coffee

Portrait bust of Beethoven, Anna EG Hoffman, in the British Museum collection © Trustees of the British Museum

It is said that Beethoven prepared his coffee by counting, precisely, 60 beans per cup. Biographies of Beethoven certainly suggest that he had a significant coffee habit. Banned by his doctor from drinking coffee towards the end of his life, there are many references to him frequenting coffee houses in earlier years. Sadly, I have not found the source for the 60 beans story and so would not like to comment on its veracity. Nonetheless, it is a good story and it does link with coffee so, as today (17th December) is the 244th anniversary of his baptism (it is assumed that he was born the day before on 16th December 1770), it is “Beethoven day” on the Daily Grind.

To me, what lends some credibility to the 60 beans story is the fact that, as coffee lovers, we can be very particular about the way we prepare our brew. Some people, for example, weigh the amount of the coffee and the quantity of water and brew their coffee according to instructions from one of the various online brewing tutorials (see here for a good one from Hasbean). Personally, in the morning, I am far too bleary eyed to consider getting the kitchen scales out, nor would I count a certain number of beans. I do however count the number of seconds that I take to grind my coffee with my trusty burr grinder (always set to the same level of grind of course). Can counting the number of seconds for a quantity of grind possibly be a good way of measuring a specific quantity of coffee?

Did Galileo drop balls from the top of the tower?

Galileo Galilei (1564-1642) died before coffee was properly introduced to Europe. He is relevant to this story though owing to his work on clocks and timing devices. One way that Galileo measured time was to collect water in a jug over the measurement period. It seems that this is almost the reverse of my morning coffee ritual. To check that he was measuring time correctly however, he needed a second, independent method. Of course, Galileo couldn’t use a watch or pendulum because watches hadn’t been developed at the time and Galileo himself was doing the work needed to understand pendulums and make them useful for clocks. So what else could he use to measure time? There is a clue to another method that Galileo used in his experiments on falling balls. Although there are questions as to whether Galileo really did drop balls from the top of the Tower of Pisa, we do know that he did experiments which involved rolling bronze balls down a groove. Along the groove were marks where strings made from gut had been pulled across the groove such that they made a sound as the ball passed, perhaps like the sound of a harp being plucked. By adjusting the position of these strings, the interval between the sounds from different gut strings could be made to match a known rhythm. The time it took for a ball to fall down the groove was being measured by matching its descent to a known tune. This suggests that Galileo sang while he was making his key measurements and that it was this that allowed him to start to understand how bodies fell under gravity. Singing was Galileo’s (surprisingly accurate) method of measuring time.

Which brings me full circle back to Beethoven. Beethoven certainly knew the “mechanician” Mälzel who invented the metronome as we now know it. There are also indications that Beethoven was aware of early versions of Mälzel’s invention. In 1813, the Wiener Vaterländische Blätter wrote “…Herr Beethoven looks upon this invention as a welcome means with which to secure the performance of his brilliant compositions in all places in the tempos conceived by him, which to his regret have so often been misunderstood“. It seems that in the two hundred years between Galileo and Beethoven, there had been so many improvements to clocks and timing devices that singing, which had started off as a way to measure time, was now itself being regulated by the clocks that singing may have helped to develop.

How many beans go to make your morning coffee?

So how is a Beethoven coffee, assuming that there is any veracity to the legend? Sixty beans works out as 8-10g which, depending on the amount of water in the cup could be weaker (or stronger) than modern brews. In my cup, it was slightly weaker than I am used to. I enjoyed my “Beethoven coffee” while listening to his String Quartet Op 74, “Harp”. As I sipped the coffee while listening to the first movement, I could almost hear the gut strings of Galileo’s experiment being plucked as the balls rolled by. The coffee itself (Costa Rica, Finca Arbar El Manatial, Yellow Honey, Caturra/Catual) was very smooth and rich, as you would expect from a coffee from Has Bean. Described in the tasting notes as “….An amazing caramel and milk chocolate sweetness partnered with delicate peach and apricot acidity…” It was the perfect coffee to enjoy with the Harp quartet piece. Sometimes it is important to take time to go slow and enjoy the coffee.

So why not raise a mug today to Beethoven and savour a Beethoven coffee? Please leave any comments using the form below, especially if you know a reliable reference to Beethoven’s coffee habit or have suggestions as to how to improve my morning brew.