Music & Maths: Baroque & Beyond with Marcus du Sautoy

[Music] welcome to our concert exploring maths music baroque and beyond i must admit that i've always found the baroque period of art quite a challenging one when i mentioned this to a colleague he offered an interesting explanation he compared it to watching cricket unless you understand the rules of the game the match is hard to follow as i began to explore the rules of the baroque to find out how to play this game i discovered that the rules artists were coming up with very much mirrored the obsessions of the science emerging at the same time 17th century science was full of apples falling planets orbiting fluids flowing gases swirling scientists wanted a way to take a snapshot of all this dynamic scenarios it was newton and leibniz invention of the calculus that provided a way to freeze frame all this motion what's striking to me is that this mirrored what was happening in the art at the time the baroque was interested in painting soldiers falling from horses creating buildings with sweeping dynamic curves capturing in stone the moment daphne transforms into a tree in apollo's arms this is dynamic art in contrast to the static art of the renaissance one of the fascinating things we see emerging during this period is the use of mathematics to realize the effects artists were after in creating the dynamism and illusion of the baroque take this wonderful space we're performing in the sheldonian theatre in oxford is the building where our university students receive their degrees and it was designed by one of the great architects of the baroque christopher wren before becoming one of england's leading architects ren had cut his teeth learning mathematics my old undergraduate college here in oxford wadham college the beauty of this building is that it has a huge roof with no supporting columns the roof floats as if by magic this wasn't so parents could see their loved ones getting their degrees but because the space was to be used principally for dancing the way ren achieved this extraordinary expanse of roof with no visible supports was with a lattice structure of beams that moved the load-bearing to the beams at the edge that were sitting on the perimeter wall but in order to find the arrangement that would work wren was faced with solving 25 simultaneous linear equations despite having trained as a mathematician he was somewhat defeated by the problem and ended up having to get help from the civilian professor of geometry john wallace who was a fellow in my current college new college the architecture of the day was certainly exploiting the mathematics available when it comes to the music of the baroque we also see a real synthesis of art and science mathematicians and musicians are wrestling over the best way to tune a keyboard instrument so it can play in different keys we also find the first attempts to understand whether there are rules that underpin the choices that a composer is making if a planet follows the inverse square law of gravity in its motion are there laws that govern the movement of notes through a piece of music for me the composer that really tried to decode what it was he was doing the newton of music is the composer of the first piece in our concert jean philip ramo please welcome marius papadopoulos and the oxford philharmonic orchestra to play the arts and the hours from ramos le boriard [Music] me [Music] me [Music] [Applause] [Music] um [Music] hmm [Music] thank you to marius and the orchestra the arts and the hours from ramos li bodiard it's a sublime piece of music the instruments almost sound like planets gracefully orbiting the sun as ramo famously declared in 1722 notwithstanding all the experience i may have acquired and music from being associated with it for so long i must confess that only with the aid of mathematics did my ideas become clear the comparison of ramo with newton i think is an apt one in many ways newton's great breakthrough on gravity was to understand that it's the same fundamental law that explains both the falling of an apple and the orbiting of a planet ramo wanted to know if there were similar universal laws that could explain the huge range of ways the composers had come up with to resolve dissonance what he discovered is that using a new perspective he called the fundamental base he could show that what at first sight looked like lots of different ways of analyzing dissonance that they were all actually examples of one underlying principle for me ramo's approach has such a fundamental mathematical feel to it it's what mathematics is all about understanding the simple underlying structure that explains many different examples galileo understanding that however you throw a ball the trajectory is always defined by a quadratic equation it's the movement from arithmetic to the language of algebra where one equation explains many numerical examples one of the challenges for musicians during the brock was learning how to improvise an accompaniment of chords above a bass line it's a bit like solving a musical sudoku ramo claimed that instead of having to learn 1584 patterns of chords that was required in the old system an accompanist could now use his new system to reduce all of this to two basic building blocks the consonant triad and the dissonant seventh chord a skill that had previously taken years of practice to perfect could now be accomplished in just a few months time it's this synthesis and scientific approach to music that led to the publication of his most famous theoretical work the insights he gleaned turned the chaos of musical composition into some sort of order it was no wonder that the scientists of the day celebrated ramo as one of their own he was invited to present his work at the royal society in london and the academy decions in paris in some ways one can credit ramo with understanding the importance of the chord to music viewing music not just horizontally but also stressing the importance of the vertical direction ramuel believed that by understanding the vertical chord structure one could make sense of where the music was heading in the horizontal direction rammer wasn't creating a new musical sound through his theoretical analysis the music had already been written it's just that ramo brought to composer's consciousness what it is they were often doing to explain his ideas ramo would often use scientific analogies ramo believed that just as there are two states that mata can be in moving or stationary the music two had two clear states dissonance and consonants consonance was like mechanical equilibrium dissonance disrupts this stability and causes movement ramo believe that just as a body in motion striking a still body will cause the still body to move that dissonance colliding with consonants can set the consonants in motion almost like a newton's cradle where the incoming ball remains still while causing the still ball to fly through the air here's ramo's example where each time the first violin moves it turns the consonants of the second violin into dissonance causing it to move as the second violin moves it leaves the first violin in a state of consonance or equilibrium let's hear newton's cradle in music [Music] for me what's fascinating is not whether ramo has successfully reeled some revealed some fundamental musical truth but more that he's applying the language of science to understand the art of music but not all scientists approve of using mathematics to explain art the french mathematician jean lauren dallombe who originally was a supporter of ramo eventually turned against him as he once wrote how much ought one disapprove of certain musicians who employ in their writings calculation on top of calculation and believe that all this apparatus is necessary to their art the urge to give their productions a false scientific air which could only fool the ignorant has led them into this era which renders their treatises much less useful and much more obscure but ramo was not a composer that would allow the numbers to dominate the music as he articulated in his treatise we may judge music only through our hearing and reason has no authority unless it is in agreement with the ear it's this ability to fuse the intellectual with the emotional the mathematical with the musical that makes this such an exciting period of both scientific and artistic development of course the master composer of the baroque who was able to fuse the intellectual and the emotional is the composer of our next piece johann sebastian bach a man whose music was described by his contemporary mitzler as the process of sounding mathematics so please welcome thomas andras and charlotte scott to bring the mathematics alive and perform bach's double violin concerto in d minor bwv 1043 not a prime number i'm afraid [Music] um [Music] [Music] hmm [Music] me [Music] foreign [Music] hmm [Music] so [Music] um [Music] [Music] what a wonderful performance and what a stunning sound those two violins made the violins are actually two stradivari violins tamasha's violin has been linked to the orchestra for this performance by the beers international violin society we also have another stradivari lent by the society that alicia who's leading the second violins is playing and will play as a solo in the last piece and charlotte is playing her own strat and in the second half of the concert i wanted to talk about another important meeting point of science and art during the baroque which is the making of the instruments that play the music but i'm interested to ask our soloists what it is that they find so special about these instruments sean up for you what makes a stradivarius sound well first of all to play these instruments is a total privilege for any of us and i always believe that the wood that was used has such a great history and purity because back in this is from 1540 the wood um and you can imagine how the lack of pollution back in those in that year you know what what comes to be used for the violin interesting yeah which is different today yeah exactly so tommash for you is there a sound that a stradivarius makes that a modern instrument just can't can't compete with it's a total mystery how these create these incredible colors and and sounds um i i absolutely love the the range of colors and in this particular instrument from 1701 um it it's got a wonderfully bright and powerful sound which was a great sort of liberating feeling well it did found sound like the two violins almost had a relationship uh you know not just the music but i think they they've met each other before i think maybe so can science tell us why the instruments made by antonio stradivari are so special and why can't we reproduce the instruments today an interesting hypothesis relates to a unique climate that existed between 1645 and 1715 it's known as the maunder minimum this was a period with reduced solar activity that led to lower temperatures and this in turn caused the trees around cremona where stradivari lived to grow slower producing wood with the superior sound quality that we heard just now this climactic environment was unique to this period and has not occurred again since stradivari's so-called golden period however recent chemical analysis of the wood used by stradivari has thrown up an alternative suggestion which might actually be reproducible scientists from taiwan have discovered that stradivari's maples were treated with complex mineral preservatives containing aluminium copper zinc among other minerals this type of chemical seasoning was an unusual practice and was unknown to later generations of violin makers in their current state maples and stradivari violins have very different chemical properties compared with their modern counterparts this scientific analysis opens up the possibility of resurrecting the seasoning stradivari employed for the instruments we're making in the 21st century one of the other striking questions about the violin is why the box should make so much difference after all isn't it the strings that are vibrating and why did violins end up with this strange shape that we see today rather than say a simple rectangular box actually this shape again goes back to experimentation that was happening in the baroque period and stradivari is credited with having been influential in promoting the shape we see today as the one that creates the best sound indeed one of our stradivari violins is rather special because it has more of a guitar-like shape than usual but it wasn't really until the end of the 18th century that we really understood why shape was so important it was the amazing experiments and performances of scientist ann schladny that revealed that there is an amazing symmetry hiding in the sound of things vibrating cladney discovered that if he sprinkled sand on top of a square metal plate and then vibrated the plate with a violin bow that he could set up the most extraordinary and unexpected symmetrical patterns in the sand on the plates his performances of these symmetries in sound was so popular that audiences across europe flocked to witness the strange shifting shapes that he could produce and napoleon even gave him a gift of 6 000 francs to reward the spectacle so we thought that we would recreate this wonderful experiment of cladney so you too could see the amazing symmetry in sound what matthias is going to do is to vibrate the plates that we've got here not with a violin bow but an oscillator attach the bottom of the plate and as we increase the frequency of the oscillator you're going to start to see at certain frequencies the pattern on the plates suddenly shift and change now the sound is quite loud so i'm just going to let the plate do the talking for a little bit as the symmetries emerge in the plates [Music] [Music] [Music] [Music] [Music] hey [Music] [Music] this experiment is part of a new project that matthias and i are making in collaboration with the center that i've helped to set up at the royal northern college of music in manchester called prism which stands for practice and research in science and music i like to think of it a bit like the 21st century version of the great baroque group that bach was part of called the corresponding society of the musical sciences as part of our work at prism we're currently exploring the possibility of creating a new musical instrument made up of these different ranges of plates that tessellate together to make a kind of sonic alhambra the cladney plates are a two-dimensional version of the one-dimensional harmonics that you can generate with a vibrating string when you vibrate a two-dimensional plate instead of the fixed points you get in the vibrating string we find instead curves appearing where the plate is still called the nodes this is where the sand is collecting and each different shaped plate has its own patterns and its own frequencies called modes at which these patterns appear one of the challenges is to understand given a shape whether you can predict the frequencies of the moods and the patterns that will appear so this is one reason why the shape of the violin matters because it has resonant frequencies like the moment the sand shifts on the plates to create a new shape that give each vibrating box its own resonant sound and it seems that stradivari had hit on a shape that helps the vibrating strings to sound as wonderful as we heard in that performance of the bach double violin concerto what's interesting is the challenge of understanding the resonant frequencies of vibrating systems isn't limited to musical instruments the mathematic behind these frequencies has a vast range of applications the part of the research we're doing here today in oxford from understanding energy levels in quantum mechanics to the modelling of hulls and ships and submarines from analyzing earthquake patterns to even a possible inspiration for tracking down how to find the next prime numbers but to end our concert we're going to head back to the baroque to perform one of my favorite pieces barks brandenburg concerto number two bwv 2047 still not a prime number unfortunately but the reason i've chosen this brandenburg rather than number four whose bwb number is a prime number is that being a trumpeter this piece is the everest of our repertoire in the baroque period they still hadn't invented trumpets with valves that could change the length of the tubing and hence the notes the trumpet produced were quite limited bach had to rely on the harmonics or resonant frequencies of a single length of tubing now just as we heard with our chladni plate as the frequency gets higher the resonant notes get closer this means on the trumpet if you want to play a tune then you're going to have to play really high which makes this a hugely challenging piece for a trumpeter i've played this piece once in my life at an evening soiree here in oxford organized by a string playing colleague we played through the piece and i just about survived the ascent but as i started to put away my instrument my friend on violin said that was wonderful why don't we play through it again just to reassure tonight's trumpeter we won't be climbing everest twice in a night so let us welcome back the oxford philharmonic orchestra to play box brand american chair to number two bwv 2047. 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Channel: Oxford Philharmonic Orchestra

Views: 1,929

Rating: 5 out of 5

Keywords: baroque, classical music, violins, chladni

Id: cuDBrKJVEc8

Length: 55min 16sec (3316 seconds)

Published: Sun Apr 18 2021