Howard Goodall Big Bangs 2 Equal Temperament

Muzyczny pejzarz Europy zachodniej został nieodwracalnie zmieniony kilka wieków temu w efekcie wyjątkowego rozwoju ewolucyjnego.

Duża część pięknej muzyki światowej nie mogłaby bez tego istnieć, couldn't exist without it, and the others claim that it was sterylized the very routs that our music grew from.

I'm talking about something called equal temperament.

You may never heard of it, but equal temperament is one of mans most ordatious attempts to taim the elementar form of nature.

Mans relationship with music is routed in nature and goes back over 40 000 years to the time when our cave duelling ancestors first began making musical sound.

Gradually man started to create a musical scale by arranging notes into some kind of natural pattern.

This man is plying the bamboo flute. A traditional chineese instrument, that is remained unchanged for thousands of years.

All the notes he is using are derived in nature.

The sound is undoubtedly excuisid.

But it's very different from this.

Using natures simpliest pattern of notes is impossible to create a big orchestral sound like this.

So western musicians of tempered the natural structure of music to create our own made tuning system.

For the last three hundred years at least big named composers have been able to make big scale music, thanks to the big bang of equal temperament.

The implications of this particular big bang effect every single piece of music we listen to.

As western man tried to restructure time through the callendar an the clock so through equeal temperament we have taken the music, that nature gave us and manipuleted it artificially.

Every note of our music called repetuar is a monterous compromise.

The road of the raw sound of nature to the artificial smoothness of equal temperament is long and torturous and structues right back to the acient Greece, where musicians first became inrigued by the idea of a ladder or scale of notes.

And believe it or not the cleverdic who came up with this configuration of notes was a certain mr Pitagoras.

The same man who brought us the mathematics of triangles.

Music was extremely popular in acient Greece.

As it had been in the Egipt of the pharaous.

But as far as we know its shapened structure was somewhat hap hazard.

Pythagorases goal was to give order to the musical freforaul he hears at every all night toga party in a backenelienoreve.

What Pythagoras discovered was that rather way of architecture are lies on perfect proportions to make a pleasing structure, musical notes also worked harmoniusly together when they had a simple mathematical relationship.

His discovery according to the ;egend happened quite by an accident. So the story goes, he was walking passed a blacksmiths, when he heard a harmonious cord of chains coming from the sound of hammer on envile.

The harmony of the chains sounded do perfect to Pythagoras, that he rushed it in to find out more.

Whenn he weight the hammers that were making the sounds he dscovered that they were simple ratious of each other.

One was half the size of the first and other was two thirds the size, and so on.

What Pythagoras was actually hearing were the demonstration of natural harminics.

Now, if you take a piece of metal and strike it,

it makes a note.

It's a simple note, but with many other notes and its overtones or harmonics rather in the way that light is made up of a spectrum of different colors.

Just because you can't see them with a naked eye, doesn't mean to say that they're not there. If you listen to the metal bars note, in the resonance of suound you might be able to hear a various higher versions of the same note.

If notes were colors you could call this note red, and it's higher version light red.

These higher versions of what we now call octaves and they all contain within the original note wheter you like it or not.

That's nature for you.

Now, if you take a piece of metal exactly half the size of the original it'll produce as it's main note that light red.

And if you play the two together they make a sound almost like a one note

An octave though is a natural dictance inbetween notes.

This is the same sound, only a higher version of that.

But if you strike a piece of metal exactly two thirds the size of the original, you actually create a new note.

Call it yellow.

And believe it or not, this new note is also containing the overtones or harmonics of the original.

And that's because two thirds is a naturally harmonious ratio in maths.

It was this creation of the new notes of the relationship of the two thirds that called Pytagorases imagination.

In his time Pythagoras as famous for a being mystic as a mathematician.

He believed that the universe has it's own music.

A harmony created by the movement of the planets in relation to each other.

The cosmos was to him one vast harmonic ratio made out of lots of smaller ratious which together formed a harmonious musical universe.

Just as the seas tight were affected by the moons relationship to earth so everything on earth was affected by the movement of the spheres.

To Pythagoras mousic was the link between the man and cosmos.

He even went so far to claim that he could hear the music of the spheres and used to sing the tunes to his disciples.

Since music came, he believed, from the heavens, it would be a power and mystical when obyeing the natural laws of physics.

So he set to work creating a scale of notes by dividing metal into simple ratioes in what we can only imagine to being some sort of musical laboratory.

Pythagorases teaching on the natural science of notes had a profound influence on early western music.

If you've ever wondered why we have a particular set of notes to play with, were ever chosen first by Pythagoras.

And he found them by dividing a piece of metal by two thirds.

If you carry on dividing by two thirds again and again you create an infinite sequence or spiral of notes.

Now it's quite hard to visualize Pythagorases endless cycle of notes, so we're going to build a piral to show how it works.

With these colored tiles representing the notes.

The first note, red, is easy, because of that was the note we made from our riginal metal bare.

And that's the foundation of the base of our spiral.

By dividing that first piece of metal by two thirds we were able to create a perfectly tuned new note. Call it yellow.

And thet goes in a bit higher up.

The pith of the sound dictates it's exact position on the spiral.

By dividing yellow by two thirds we can create a third note higher still on further round.

And so on an so fourth into and infant spiral of new notes.

The mathematical dictance inbetween them makes us rather satisfied in shape.

With the tvelveth note in position you can se from a packing emerging with a notes roughtly spaced around the circle of the octave.

But when you'll get to the thirteenth note all goes horribly wrong which I can show you if I collapse the model.

because the thirteenth note wants to shave the first note out of the way.

This battles are occupied the same space creates a terrible and upsetting justements and it's the result of something known as the Pythagorian come.

Pythagorases solution was simple and routhless to due away with the notes of thirteen that pulls all toghether.

But the problem of the dreaded coma was even greathet than Pythagoras had imagined

It didn't just affect the thirteenth note but the distance inbetween every note in the octave.

The distance between two notes is determined by tuning.

To tune a note is to adjust that distance.

For all the notes to work perfectly together they'd need to be tuned say there were exactly equally spaced like the dials on a clock face.

As it was the coma shifted each note a little off center producing a slightly uneven pattern which got progressively worse with each step of the apiral.

To begin with musicians played extra safe by using only the first seven notes of the spiral, which together with the original made up the basic eight notes scale from which the word octave derives.

From the acient greeks right to the middle ages european music made due with the eights step version of this pythagorean scale.

One way of keeping a troublesome coma at bay was keep music as simple as possible.

which is more or less what they did.

Even as lat as the 13th century musicians were sticking the notes derived from the first few steps of the spiral, which rearangend into basic tunes playing just one note at a time.

In any case match of it it was popular music made by bands of boardy bascqes thrushing out simple but joyous tunes to the rhythm of the many drum.

More ambivious composers were working for the church felt the music could be more than just catchy rifs of repetitive dance beat.

Golds hause music had a serious subtext and with there for required a sufficticated approach.

Church scholars started to look for way to make it sound as glorious as possible. To raise it above the ravel of the secular world and worthy of the exultation of God.

One way was to give music texture by adding new musical lines to an axisting melody

The idea was, that the combination of notes might create sweet sounding harminies, the sound of angels.

By combining notes though these musical monks were asking for trouble

Sooner or later Pythagorases naughty coma would raise itæs ugly head again.

The problem was that unfortunately many of the notes created from the Pythagorean system sounded rather strange when layed together.

These two notes. The first and the fifth sounded fine, thatæs because they were a perfect harmony the ones we created from our two thirds metal ratio

Likewise the fourth five that was the perfect ratio

But the third was derived from much further on the spiral of notes. Whether effect of the dreaded coma had shifted it out of kilto with the foundation note.

And so to medieval ages it sounded rather unpalatable when combining with it.

The same was true of the sixth note.

So musicians tended to avoid thirds and sixths all together and just stick to basic tunes with fifts and fourths for harmoy.

The reason why medieval music sounds to us rather osteran or embarand is because of the lack of the warm harmonies of that thirds and sixts gave to the later music.

But the point of sacred music was to be more than just a pleasing sound.

It was supposed to mirror the perfection of Gods creation.

And so it could have been tempered with lightly.

To medieval ears the note combinations that derive from impure ratioes felt unnatural and unwholesome, so the church ulbet prohibited their use.

To brake the rules by experimenting with chords including thirds or sixths was tend to mount teheracy.

To show you what they ware missing out on. Here is a simple example.

Listen to this tune whichcould have been written in medieval times.

Bud add modern harmonies and it transform to something medieval composers couldæn even hear in their dreams.

(opera )misic

To make the journey from medieval simplicity to rich chocolate harmony would mean playing around with Pythagorean tuning and interfering with the laws of nature.

Happily for us temptation prooved just too much for some religious composers.

In the 15th century they taseted harmonies forbiddenfruit and never looked back.

European music was still being made from the scale of notes created by Pythagoras as latest 2000 years after his death.

But then along came a dreamer with other ideas.

Amazingly was an english man in the early fifteenth century who first started to rock the boat.

And whose note combinations first dared challenge the Pythagorean norm.

This english man was a composer with a particular fascination for all things astrological.

Surprisingly as little as none about John Dunstaplewe don't even know how what he looked lik.

But his only surviving manuscript contains drawings of the constelations.

Hint that he was a man like Pythagoras with the keen interest in the link between music and the stars.

Althoug John Dunstaples live is rather than mistery there's no confusion about impact of his work.

In fact it's noe exageration to say that he was the most influential english composer in Europe before the beetles. Imagine!

`(monk usic)

Like most medieval composers Dunstiple wrote mostlychurch music, but unlike all other composers he started to break the rules.

Not content with the simple fourths and fifths that other composers used Dunstiple started to experiment with those sourcefully and impure thirds and sixths . But adhere to be in so frown by musical theorists.

To make these new harmonies work he kept well away from keyboards whose tuning was alrealdy fixed and flexible.

He experimented instead with the wonderfully flexiable tones of the human voice.

What singers are able to do is to reach tune their voices every time they hit a third.

or a sixth.

linila de gitarisattwiddling the peg on the neck of their instrument hundreds of times dusring the single persormance.

Duncetable used the supple tool of the voice to reach tunes thirda and the sixths.

And found that they brought new light and colour to the basic melody.

Before larm has compositions were riddled with this radicle new sound.

Duncetable showed off his strange and sweet new harmonies in the serious of the sacred choral works.

One of these weinee sanctus spiritus was first performed with a special service held here in Cuntenbury cathedral in 1416

The occasion was thanksgiving mass for the english military victory at asincore in the presence of Henry the fifth himself.

(music)]

In his time Duncetable music must have sound incredibly avangard and modern.

He was taking braze and libiraties with the rhythm as well as the harmony of the periode.

He didn't think of himself as a revolutionary, but with the benefit of highnesside we can see what ineffect what he heard.

HIs music is the first sing of the seachainge on composers attitude to harmony.

Nature has been left behind and replaced with something much more marmaid and saductive.

None of this radical rulebraking would have add so much if Duncetable have stayed in backwater england.

As it was military matters had a hand in changing the course of musical history.

After the success of aginchord mDuncetable traveled to northern France as chord composer to the victorious english

They were to remain France til the conclusion of the hundred years more.

With Duncetable went all his fantasy new harmonies.

Which were to capture the imagination of his continental counterpots.

The occupying english forces were garnisoned here on the louire under controll of the duke of bedford the kings brother.

Bertford made two rather contrasting contributions to the history.

One was to have the good sense and taste to hide john's Duncetables as chord pomposer.

The other less intellingent idea was to have Joan d'Arc burned at the stake.

What Duncetable made with his bosses gringle campaign against the made or orleans in unclear

What we do know is tha Duncetables music was thought continental composers to be exeptional.

Indeed the great french composers of the day were quick to imitate his dearing style on harmonic tecnique

The thirds and sixths he'd pioneered became common place.

The course of musical history weiled off into unchanted waters.

Thanks to risk takers like Duncetable and his continental counterparts music moved out of the stagnant dark ages

into the color and watmth or the reinescance

The hub of Reinessance was northern Italy

Where for the first time since Pythagoras society started to look again with renewed interest of the valuable relationship between mathematics and the arts.

While artists were still grapling of the new perspective in art composers were increasingly intrigued by the notion of debth could be given to music by the combining of notes in all sorts of weird and wonderful waves'

(music)

Three part harmonies grew to four andbeond

voices of chords could bend to the tuning of the notes to make them new harmonies work

but the use of an ucompannied keyboard ment that the tuning of instruments had to be specially adjusted to cope with the plathorou of the new chords and harmonies

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Science and the arts were transformed during Reinessance by acraise of invention and experimantation

while scientists like Galileo were busy throwing canon balls of the leaning tour of Piza, composers were throwing all sorts of sounds together in evermore ambicious composisions

All this experimental aboundance had a down side

Pythagorases original twelve notes scale was beggining to fall apart

o the scens of the destrainable new sounds

`The problem the old greek philosopoher ahd chosen to ignore that dreaded coma would come back to live with avengence

to clarify just a serious a problem this so called comma was

we need to understand the mistery of keys

and to do that I think I'll need a drink

So for example I wanted to create a scale from a single note

The Pythagorean way

Now this wine glas for example

is mor or less a G

Now like different lenghts of metal different levels of wine in a glass would change the notes

So if I sip a little

it should go higher as indeed went I

ah and I see now it's an A flat

And if I poar more in it should go lower again

ahh, and I see another G

now from this mother G

I can create a whole family of notes

Which is called a key

so this is my key

or family of G

Now if I wanted to take one of the notes belonging to the family of G

say

c

I could create from it a whole new family of notes

the key of C

Completely different from the key of G

Indeed all notes give birht to their own particular family or key

The problem thanks to the disruptive influence of the coma is that very few keys or families work succesfully together

in the same piece of music

Now up to the late Reinessance practically all music was written in one key or anotherr

You didn't move between them

So all instruments were carefully tuned like these glasses to play a particular piece in a particular key

so far so good

But then composers started to get greedy

and asked why can't we have more than one key in a piece, or two

or three or four

an then it will result was to make tuning absolutly a nightmare

The process was called tempering

The tuning system created by tempering was called a temperament

Every tom de can heinrich across Europe has dis own temperament

chaos riegned

notes were being pulled this way and that took accomodate to different needs of different keys

The trouble was a tuning worked for one piece of music sounded wrong in another

putting instruments in a different tuning together in the same piece of music was increasingly problematical

But trying manfully to cope with all the extra notes composers wanted keyboard tuners ended up with some hidiously deformed and multated relationships

these were knows as wolf tones on account of grenlalnd savory howling of the dissonance'

lerking behind of this tempering tuning and the wolf thing about lay a simpple terifying trough waiting to be onearth

this was the concept of an equal temperament

That is a tuning system that divided up the octave artificially into twelve exacly equal parts

instead of having twelve different keys with their own indvidual patterns lof notes like coans belonging to different weels that count into mock

The idea of an equal temperament was to create a single mathematical pattern of notes

this would become the blue print for all the keys so they could fit together in the same piece of music

The question was how could musicians who tuned their instruments by ear create a mathematically perfect scale

for a while it seemed an impossible dream

But then out of the blue

a genious burst abruptly unto the scene and changed musical history once and for all with the compositon

The big bang actually occured in this castle in eastern Germany and the man behind it was no other than Johann Sebastian Bach

By the beggining of the 18th century keyboard tuners all over europe were struggling through trial an era to find the temperament that would allow the musicians to play in a variety of different keys on a single keyboard

But Bach layed down an even bigger challenge to find the tuning system that could handle all no ifs no buts

in his day, bach was one of the celebrated and revealed keyboard players of europe

His influences a teacher with his considerable to its probably out of the quater and a half courtan he worked fo ra while his now a music school

whilst in the services of account leopold here in1722 bach produced what must be the single most important collectionof keyboard pieces ever written

the 48 preliudes and fugueas known collectively as the well tempered keyboard

Every piece of history rellies

on good timing and a little luck

the chanses area that hend bach landed on these relatively coushie pauseded of curtain that 48 preludes and fugues would never hav ebeen written

as it was bach found himself in the employ of the wealthy 23 year old count it hapened to be a great lover of secular music

dispite being capelmyster bach had no actual chapel duties so thare's plenty of times he concentrated on challenging excercises for all his harpsichord pupils of which his 48 preludes and fugues was the most spectacular

The crucial thing about this collection of tunes is that it contains pieces in all the keys of the keyboard

yes, indeed

the moment it became circulated in every one knew that Bach had somehow found

the lost city of eldorado

But he alone seem to have cracked the mistery of temperaments

because what this book means is that the keyboard had a loss been tuned that COULD LET YOU PLAYN ALL THE KEys at one sitting

this modest book turned out to be a mightly big bang

no one knows exactly whether it was Bach himself or a colleague who initially cracked the code and found the way of tuning keyboard play all these pieces for the first time

and out of it was a lenghty process of triumph inera which resulted in this near perfect compromise

What we do know is that the system was perfect written up in few years later for all the world to see by Bachs star pupil Johann philip kimberger

once the 48 preludes and fugues became known all composers and tuners knew the game was up, it could after all be done

you could have a keyboard that accomodated all the keys and scales together

harmoniuesly

A single tuning system that could play all the keys did for music what the supermarked did for shopping

for better or worse

instead of shopping around in all the small stores you could find everything under one roof

instead of specially tuning our instrument for each individual key you could find them all on one keyboard

love it or load it the well tempered keyboard was here to stay

Bach himself moved to a more prestigious job as music director of the st thomas church in leipzig not long after he wrote his ground braking preludes and fugues in all 12 keys

Leipzig then as it's now was a major trding and cultur center then 500 years bachs keyboard works have been published eaurope wide the well tempered keyboard had become a universal effect of life

The arrival of the well tempered keyboard was a critical turning point in the history of european music

Without it the complex works of greated composers like mozart and bethoven brahms and thaikovsky could nevere hav ebeen written

It gave all composers the ability to move easily from key to key to andulged themselfes with previously remote and ineccessible families of sounds

It's no exaggeration to say that the well tempered system revolutionized classical music all over the western europe

but it would taken another revolution all together to ensure that it spread to every corner of the globe

If Bachs preludes and fugues launged the idea of a succesfully tempered keyboard it was something else alltogether that it technically possible and universally available

Victorian engineering

Thanks to new technology, machines could be manufactured with absolute accuracy

Wholes could be bored in exact places tension fine tune the fraction of a turn

This was the era of precission engineering which radically effected all aspects of live

The tuning system at Bachs time which should been devines in triumph era could it last be implemented using mathematics

The formula for equal temperament produced a findustely percise figure

The tvelth route of two which could now be applied with accuracy and ease

keyboards and other instruments could be mass produced with the help of machines

pianoes were given huge iron frames allowing metals strings with incredible tension to be held tought and stable

the wholes in oboes, clarinets and basoons could be bored with minute exactness

the age of the truly equal temperament had arrived

from about the 1840s onwords all factory made instruments confirmed to this new mathematicall standard

once the instruments were mass produced they could be exported all over the world

the global invasion of the equal temperament had begun

this innoques seemingly harmless instrument was one of most devastatingly weapons in the triumph of equal temperament

The accordion invented in 1840 and mass produced towards the end of the 19th century was extremely portable

and it had two other importand characteristics

first- it was fixed stubbornly to the equal temperaments system

the name accordion actually means tuned

and secondly- it was loud

accordion spread through europe like wild fire with its promiss of a fuller sound than it's ability to play a melody and accompaniament simultaniously

it took with it the regimented norm of equal temperament forcing all other instruments to conform to its rigit dictates

In countries where ethnic and folk music were more privilant than classical music the arrival of the accordion was to have a particularly insidious effect

As the 20th century dormed accordions were brought into moron more remote cultures on the fringe of europe

like here in Romania

They came ready tuned of course to equal temperament

because it was loud than everything around that forced the other older and quieter instruments to addapt themselfes to its tuning by so doing the more ancient ethnic tuning systems wer unwittingly singning their own death warrants

Before the age of ampifiers and PAs the accordion was perfect for a company in dancing

because of its strong rhythnic sound

it was fankly irresistible to folk bands like gypsy wedding ansable

As the accordion was introduced in the early 20th century the olld harmonies and chords of remeny music were replaced with the equalized compatible key system that Bach had so succesfully exploited

This gypsy music doesn't need to change key all the time yet it's now restricted by the same tuning system that was essential to the composer like Bethoven

A common criticism of the equal temperament is that it has drowned out its rivals with all loud wonderfull exotic idiosyncrecies

Actuallly though what were witnessing in this Romanian music is a marriage of acient eastern flavours with the newer western harmonies

The strings are hangigng on to the ornaments and phrazes of the old and wild

whilst the chords and the accopaniament are the newer regulated western style

And maybe a shotgun marriage brought about by accident of the history but the tention between the tune produces and an exciting mish mash of hearly bearly of sound

If this music sounds out of tune to you it's because the norm of equal temperament is so all pervasive and powerfull that you too are listening to the filter of the western tuning in your head

Whe world used to be choco-block with other alternative temperaments now it's overwhelmingly dominated by just one

folk culture is residing everywhere

even tradicional weddings like this amoungs romanian gypsies are becoming a thing of the past

But while equal temperament has steam role of its way across the most of the globe flatening all other tuning systems in its path

there's still one culture that stubbornly continues to offer an alternative to it

Tehis culture has made eliberate decission to reject the seductive promisses of the man made system in favour of natural simplicity

The chineese had also figured out that sience of equal temperament

the magic formula of the 12th route of two

but unlikely the west they weren't interested in a mathematical fudge

they still concidered the relationship between music and nature to be sacro-saint

like pythagoras the chineese still believe in the strong likn between music and the cosmos

drawing from the same scale pythagoras used back in acient greece

they work mainly with the first five notes of the series which is known as the pentatonic scale

Tradicional chineese misic has none of the nervous tension of a highly strong western tuning system

instead it has a tranqiulity and natural stillnes to it that makes is much more suitable to meditation in the pulsating, vibrating music so privilent in the west

But even here the the wrote has begin to set in

young people in china are becoming more and more exposed to western tuning

and gradually their own acient musical style is starting to soound out of tune

in the next twenty all so years this last strong hold of the known western sound will it seems inevetibly begin the process of re tuning itself to the louder more insistant voice of equally tempered music

there's no doubt that in a long struggle for an equal temperament we in the west have lost the connection of the natural world

form pythagoras to duncetable, from jazz bach to stevie wonder we have deliberated the eternal back of nature and forged a man made compromise

We're now living in a musical environment utterly dominated by the artificial tuning of equal temperament

so much european music is so exqusitedly beautiful and it's impossible to imagine the world without it

most music written since bachs time actually needs equal temperament for to function properly

ifo one believe the rewards of equal temperament fall out way it's flaws and could even think individual pieces thah justiies invention on their own

this is one of them

(music)