Transcript: Stuart Isacoff on the History of Harmonies | Oct 15, 2006

[Theme music plays]

The opening sequence rolls. The logo of "Big Ideas" featuring a lit lamp bulb appears against an animated yellow slate.
Then, Andrew Moodie appears in the studio, playing a simple tune on an electric piano. The walls are decorated with screens featuring lit lamp bulbs, and two signs read "Big Ideas."
Andrew is in his early forties, clean-shaven, with short curly black hair. He's wearing a red shirt.

Andrew says HELLO, I'M
ANDREW MOODIE, AND WELCOME TO
BIG IDEAS.
IT'S GOOD TO BE BACK IN
TORONTO.
I LOVE THIS TOWN.
OKAY, ENOUGH OF THAT.
WELL, LOOK AT THIS BABY.
I'VE BEEN RENTING HER FROM A
STORE FOR THE PAST COUPLE OF MONTHS.
I'M THINKING ABOUT BUYING ONE,
BUT MAN, YOU KNOW, I REMEMBER
THE DAYS OF MOOGS, AND CORGS,
THE EARLY DAYS OF SAMPLING THAT
HAVE COME TO DEFINE WHAT YOU'VE
KNOWN AS MY FAVOURITE DECADE,
THE '80s.
YOU'RE TOO SHY-SHY,
HUSH, HUSH, EYE TO EYE
GOD, YOU KNOW, I REMEMBER SOME
OF THE MUSIC STORE CLERKS
TRYING TO CONVINCE ME THAT YOU
KNOW, ONE DAY COMPUTERS WILL BE
ABLE TO MATCH THE SOUND OF A
GRAND PIANO THROUGH SAMPLING,
AND YOU WON'T BE ABLE TO TELL
THE DIFFERENCE.
YEAH, WELL, NO, YOU KNOW.
I'M ALSO WAITING FOR MY OWN
PERSONAL JET PACK AND MY DICK
TRACY VIDEO WATCH.
NO, THIS BABY DEFINITELY SOUNDS
LIKE AN ELECTRIC PIANO.

[Playing Piano]

He continues BUT YOU KNOW WHAT, THAT'S OKAY.
BECAUSE IN MY HOUSE, I DON'T
REALLY HAVE THE ROOM FOR A FULL
SIZED PIANO, AND THE KEYS ARE
NICELY WEIGHTED.
THE PROBLEM IS WITH THE TUNING.
ELECTRIC PIANOS ARE JUST TUNED
SO COLD AND PRECISE, AND WELL,
ELECTRIC.
REAL PIANOS ARE A PAIN IN THE
BUTT TO TUNE, BUT THE SOUND IS
RICHER, IT'S DENSER, IT'S MORE
HUMAN.
AND TUNING IS SO ESSENTIAL TO
THE WAY THAT MUSIC ENTERS OUR
CONSCIOUSNESS, AN IMPROPERLY
TUNED INSTRUMENT, IT'S LIKE AN
IRON WALL BETWEEN THE MUSIC AND
OUR EMOTIONS.
IT-- IT'S JUST SO PAINFUL.
IF YOU'RE A SONGWRITER, OR IF
YOU'RE JUST SOMEBODY WHO'S
CURIOUS ABOUT THE HISTORY OF
THE INSTRUMENT, THEN YOU ARE IN
FOR A REAL TREAT.
WE HAVE STUART ISACOFF ON THE
PROGRAM.
HE IS A PIANIST AND A COMPOSER.
HE IS A FOUNDING EDITOR OF THE
MAGAZINE PIANO TODAY, AND HE IS
TRULY ONE OF OUR MOST ENGAGING
SPEAKERS THAT WE'VE EVER HAD ON
THIS PROGRAM.
LADIES AND GENTLEMEN...

[Playing Piano]

He continues STUART ISACOFF DOING HIS THING
AT THE PERIMETER INSTITUTE.

A clip plays in which Stuart Isacoff stands behind a wooden lectern and addresses an unseen audience.
He's in his late fifties, bald, with a moustache. He's wearing glasses, a gray suit, pink shirt, and beige tie.

He says TO BEGIN,
I'D LIKE TO INTRODUCE YOU TO
TWO FRIENDS.
ONE, MAESTRO LES DIATH.

[Applause]

Maestro Les Diath is in his sixties, clean-shaven and bald. He's wearing glasses and a beige suit.
He walks past Stuart smiling and bows. Then, he sits at a grand piano.

Stuart says AND THE OTHER IS THE MODERN PIANO.

[Applause]

Maestro Les Diath prepares a few scores and plays the grand piano.

As he plays, Stuart says IT'S RANGE
IS AS LARGE AS AN ORCHESTRA'S.
IT ALLOWS TEN TONES, SOMETIMES
MORE, TO BE STRUCK
SIMULTANEOUSLY, AND HOLDS THEM
IN THE AIR AT THE PIANIST'S
WILL.
THE PIANO CAN GROWL AND SING
AND BEAT TIME.
IT CAN RENDER ARID FUGUES AND
IMPRESSIONIST WATERFALLS WITH
EQUAL NATURALNESS.

Piano continues playing.

Stuart continues NOW THERE'S A REASON THAT THE
PIANO CAN DO ALL THESE WONDROUS
THINGS, AND IT HAS TO DO WITH
THE FACT THAT THEY KEYBOARD
ITSELF IS A WORK OF SYMMETRY.
I WOULD SAY PERFECT SYMMETRY,
BUT I WOULD BE LYING.
BUT IT IS A WORK OF SYMMETRY SO
THAT ANY STEP ANY OF THE
SMALLEST STEPS ON THIS PIANO
KEYBOARD--
WHAT MUSICIANS CALL HALF STEPS,
SAY, FROM THIS NOTE TO THIS NOTE...

He plays a note and continues
IS THE SAME AS FROM THIS NOTE...

He plays another note and continues TO THE ONE RIGHT NEXT TO IT, IS
THE SAME AS THE STEP FROM THIS
ONE...
[Playing Piano]
TO THE ONE RIGHT NEXT TO IT.
EVERYTHING IS SYMMETRICAL.
BECAUSE OF THIS, I CAN PLAY A
SONG BEGINNING ON ANY KEY.
SEE IF THIS IS FAMILIAR TO YOU.

He plays the happy birthday song.

He says DOES ANYONE RECOGNISE THAT?

[Audience laughter]

Stuart continues OKAY.
NOW IF I WERE TO GO DOWN ONE
HALF STEP AND PLAY IT IN A
DIFFERENT KEY...

He plays it in a different key.

He continues IT WORKS EQUALLY WELL, BECAUSE
EVERYTHING IS CONSTRUCTED IN
SUCH A WAY THAT I CAN BE SURE
THAN MY DISTANCES WILL STAY THE
SAME, NO MATTER WHERE I'M
STARTING.
NOW IF WE TAKE A PIANO IN AN
EARLIER TUNING -- NOW WE'LL
TALK ABOUT THESE DIFFERENT
TUNINGS, BUT THIS TUNING IS
CALLED MEAN TONE, ONE QUARTER
COMMA MEAN TONE.
THAT'S NOT NECESSARILY THE
CASE.
I CAN PLAY IT...

He plays it in a different key.

He continues AND IT SOUNDS PRETTY MUCH THE
WAY IT DID ON THERE.
BUT IF I WERE TO MOVE IT DOWN A
HALF STEP, I MIGHT GET A RESULT
THAT I'M NOT COMPLETELY
THRILLED WITH.

He plays it differently.

He continues DID YOU HEAR A DIFFERENCE THERE?
OKAY, SO THIS IS NOT COMPLETELY
SATISFACTORY.
IT HAS WHAT MUSICIANS WOULD
CALL A CERTAIN MINEFIELD OF
WOLF SOUNDS.
THAT IS SOUNDS THAT REMINDED
PEOPLE OF THE HOWLING OF
WOLVES, BECAUSE OF THE
DISSONANCE.
AND YET, FOR CENTURIES AND
CENTURIES, THIS PIANO, TUNING
WAS CONSIDERED A CRIME AGAINST
NATURE AND AGAINST GOD.
SO WHAT I WANT TO TALK ABOUT
PARTLY TODAY IS WHY THAT WAS
THE CASE.
THIS ALL BEGAN MANY, MANY YEARS
AGO IN THE 6th CENTURY BC.
AND IT STARTS WITH A MAN NAMED
PYTHAGORAS.
HOW MANY PEOPLE HAVE HEARD OF
PYTHAGORAS.
HOW MANY PEOPLE HAVE HEARD OF
PYTHAGORAS BECAUSE OF A LITTLE
FORMULA CALLED A SQUARED PLUS B
SQUARED EQUALS C SQUARED?

[Audience laughter]

Stuart continues PYTHAGORAS WAS MUCH MORE THAN
THIS FORMULA I MUST TELL YOU.
HE WAS PART MYSTIC, PART
HUCKSTER, PART MATHEMATICAL
GENIUS.
HE USED TO WALK AROUND IN WHITE
ROBES A GOLD CROWN, AND PROMISE
SPIRITUAL SERENITY TO HIS
FOLLOWERS.
HE LED A CULT, HE WAS WHAT WE
WOULD CALL TODAY A GURU.
IMPEDICLES RECOUNTED TALES OF
HOW PYTHAGORAS HAD MAGICALLY
STAYED THE WINDS, RESTORED LIFE
TO A DEAD WOMAN, VANISHED
BODILY FROM THE EARTH...
IT'S ACTUALLY NO WONDER HE WAS
RUN OUT OF TOWN, IS IT?
SO PYTHAGORAS, LIKE MANY PEOPLE
IN HIS TIME, WAS INTERESTED IN
FINDING WHAT THE NATURE OF THE
UNIVERSE WAS.
WHAT IS IT MADE OF?
PERICLIDES HAD SAID THE
FUNDAMENTAL NATURE OF THE
UNIVERSE WAS FIRE.
THALEUS HAD SAID IT WAS WATER.
AND PYTHAGORAS CAME UP WITH A
DIFFERENT ANSWER.

A caption appears on screen. It reads "Stuart Isacoff. Pianist, composer, and writer. 'The science of music, the music of science.' Perimeter Institute. April 5, 2006."

Stuart says HE SAID IT
WASN'T ANY OF THOSE THINGS.
IT'S SOMETHING THAT CAN'T BE
SEEN, AND YET EXISTS AND
DESCRIBES EVERYTHING AROUND US,
AND THAT THING WAS NUMBER.
AND SO HE BEGAN PURSUING.
NOW A LOT OF
INTERESTING THINGS WERE GOING
ON IN THE WORLD OF MATHEMATICS
IN HIS TIME.
THERE WERE THINGS--
PYTHAGORAS HAD BEGUN BY
LEARNING HOW TO MEASURE THE
HEIGHTS OF PYRAMIDS IN THE
DESERT IN EGYPT BY THE SHADOW
THEY CAST ON THE GROUND FOR
EXAMPLE, BUT HE BECAME VERY
INTERESTED IN THIS PLAY OF
NUMBER.
THERE WERE THINGS LIKE PERFECT
NUMBERS, FOR EXAMPLE, NUMBERS
THAT ARE EQUAL TO THE SUM OF
THEIR DEVISORS, LIKE THE NUMBER 6.
IF YOU ADD 1+2+3, YOU GET 6,
BUT ALSO 1x2x3 IS 6.
SO THERE WAS SOME MAGICAL
QUALITY TO NUMBERS LIKE THIS.
NOW PLATO WAS VERY INTERESTED
IN NUMBER AND CAME UP WITH THE
IDEAL NUMBER OF CITIZENS IN A
STATE, AS 5,040.

[Audience laughter]

Stuart continues WHICH HE GOT BY MULTIPLYING
1x2x3x4x5x6x7.
SO...
THERE WAS SOMETHING VERY
POWERFUL IN THIS.
AND OF COURSE SOMEONE IN
PYTHAGORAS' TIME, WHO REALLY
COULD WORK WITH NUMBERS, HAD
CERTAIN ABILITIES THAT WERE
KIND OF AMAZING.
SUPPOSE YOU HAD NINE PEOPLE AND
SEVEN LOAVES OF BREAD.
IT'S A PRETTY NEAT TRICK TO BE
ABLE TO COME UP WITH THE RIGHT
WAY TO DIVIDE THE GOODS.
SO THERE WAS SOMETHING
PRACTICAL ABOUT THIS, TOO.
IN ANY EVENT, PYTHAGORAS DID
COME UP WITH A SQUARED PLUS B
SQUARED EQUALS C SQUARED, AND
HE ALSO CAME UP WITH THE
MATHEMATICS OF MUSICAL BEAUTY.
THE STORY GOES THAT PYTHAGORAS
WAS WALKING BY A BLACKSMITH'S
SHOP ONE DAY, AND HE HEARD
HAMMERS HITTING ANVILS, AND
SOMETIMES THESE HAMMERS CREATED
YOU KNOW, A RAUCOUS MESS,
ABSOLUTE NOISE, AND AT OTHER
TIMES HE HEARD BEAUTIFUL
HARMONIES, AND HE DECIDED TO
INVESTIGATE.
WHY IS IT THAT THERE IS SUCH A
THING AS MUSICAL CONSONANTS,
BEAUTIFUL SOUNDS, AND THERE ARE
ALSO UGLY SOUNDS, AND SOMETIMES
YOU GET ONE SENTENCE, SOMETIMES
YOU GET THE OTHER.
SO THE STORY IS APOCRYPHAL,
BECAUSE FROM THE STANDPOINT OF
PHYSICS IT DOESN'T WORK.
BUT THE STORY IS THAT HE WENT
IN AND HE MEASURED THE WEIGHTS
OF THE HAMMER HEADS, AND HE
FOUND THAT WHEN THESE HAMMER
HEADS WERE IN A CERTAIN
PROPORTION TO EACH OTHER THAT
YOU GOT BEAUTIFUL SOUNDS, AND
WHEN THEY WEREN'T YOU GOT UGLY
SOUNDS.
THE NEXT PART OF THE STORY
ACTUALLY WORKS, WHICH IS THAT
HE WENT HOME, AND HE TRIED THE
SAME THING WITH LENGTHS OF
STRING.
AND HE FOUND THAT VIBRATING
STRINGS, AND HE USED AN
INSTRUMENT CALLED THE
MONOCHORD, WHICH WAS A SINGLE
STRING INSTRUMENT.
YOU COULD VARY THE LENGTH OF
THE STRING, AND IF YOU VARY THE
LENGTHS OF STRINGS, JUST AS IF
YOU VARY THE SHAFT OF THE
PENDULUM -- YOU SHORTEN THE
SHAFT OF THE PENDULUM, THE
PENDULUM WILL GO MORE QUICKLY.
THE SAME THING HAPPENS WITH A
STRING.
THAT IS, IF YOU SHORTEN A
STRING IT GOES MORE QUICKLY, IF
YOU LENGTHEN A STRING, IT
VIBRATES MORE SLOWLY.
AND PYTHAGORAS FOUND THAT IF HE
USED THOSE HAMMER HEAD
EQUATIONS, AND HE USED THEM FOR
STRING LENGTH, FOR VIBRATING
STRINGS, THAT HE COULD ACTUALLY
FIND THE MATHEMATICS BEHIND
THIS BEAUTY.
SO I'M WONDERING, HOW MANY
PEOPLE HERE CAN SING?
[Murmuring]
UH...
HOW ABOUT, DO YOU HAVE A LITTLE
MORE FORTITUDE IN A GROUP?
BECAUSE I'M-- I'D LIKE TO SHOW
YOU WHAT THESE PROPORTIONS
PRODUCE.
BUT IT'S SO MUCH MORE EFFECTIVE
WITH HUMAN VOICE THAN WITH AN
INSTRUMENT.
SO I'M GOING TO DEMONSTRATE ON
THE INSTRUMENT, BUT I'M
THINKING, MAYBE IF WE COULD
DIVIDE THE ROOM BETWEEN LOW
VOICES AND HIGH VOICES, MAYBE I
COULD GET YOU TO SING THESE
THINGS WITH ME.
ALL RIGHT, WE'LL SEE, WE'LL SEE.

[Audience laughter]

Stuart continues PYTHAGORAS' FIRST PROPORTION
WAS TWO TO ONE.
IF YOU HAVE ONE SOUND VIBRATING
TWICE AS FAST AS ANOTHER SOUND,
YOU HAVE WHAT MUSICIANS CALL AN
OCTAVE.
THAT IS, IF I WERE TO USE DO
RE MI FAH SO LA TI DO, FROM
DO TO DO...

He plays a key and continues
IS AN OCTAVE.
LET'S SEE IF I CAN GET LOW
VOICES TO SING THIS.

He plays a key.

The audience signs the note.

Stuart continues AND HIGH VOICES TO SING THIS.

He plays another key and the audience sings it.

Stuart continues SEE, THAT WAS GREAT.

[Audience laughter]

Stuart continues THAT WAS GREAT.
THAT IS AN OCTAVE.
NOW AN OCTAVE, THOSE TWO TONES
SOUND SO MUCH ALIKE THAT WE
ACTUALLY CALL THEM BY THE SAME
NAME.
THE BOTTOM ONE IS DO, THE TOP
ONE IS DO.
AND THE TOP ONE IS VIBRATING
TWICE AS FAST AS THE LOWER ONE.
I'LL TELL YOU WHAT PIETRO
AARON, THE 16th CENTURY
MUSICIAN SAID ABOUT THE OCTAVE.
HE SAID, "IT IS SO PURE, SO
FULL, SO PERFECT BEFORE ALL
INTERVALS, THAT NOT ONLY ALL
VOICES, BUT ALSO ALL OTHER
CONSONANCES FLOW TOGETHER INTO
THIS ONE AS THEIR LEADER.
THEY SUBJECT THEMSELVES TO IT
AS TO THEIR PRINCE, THEY REVERE
AND RECEIVE IT AS MODERATOR OF
EACH CONCORD AND ITS QUEEN.
IT RELEASES ALL POSSIBLE
CONSONANCES LIKE A FERTILE
MOTHER."
THAT'S THE OCTAVE.
GALILEO, ON THE OTHER HAND,
FOUND IT BORING.

[Audience laughter]

Stuart continues NOW PYTHAGORAS' SECOND PROPORTION.
FIRST PROPORTION, TWO TO ONE.
SECOND PROPORTION, THREE TO TWO.
THAT PRODUCES WHAT MUSICIANS
CALL A FIFTH.

He plays two keys and says CAN WE TRY THAT ONE?
LET'S SEE.

He repeats and the audience sings the notes.

He continues OKAY...
SO THE FIFTH--

[Audience laughter]

Stuart says THERE WERE
SOME OTHER THINGS IN THERE BESIDES...

[Audience laughter]

Stuart continues WELL, IT WAS A GOOD TRY.
THE FIFTH PRODUCES QUITE A
DIFFERENT EFFECT THAN THE OCTAVE.

He plays the piano and then says
IT HAS KIND
OF A HOLLOW SOUND TO IT.
IF YOU THINK OF MEDIEVAL CHANT,
THE FIRST KIND OF HARMONY THAT
APPEARED IN MEDIEVAL CHANT,
CALLED ORGANUM, WAS HARMONISED
USING FIFTHS.

[Playing Piano]

Stuart continues DOES THAT HAVE A FAMILIAR SOUND TO IT?
IT'S KIND OF HOLLOW AND
HAUNTING AND BEAUTIFUL.
GALILEO CALLED THIS -- IF YOU
NOTICE THERE'S A LITTLE BIT OF
A BITE TO IT.
WHEREAS, AN OCTAVE IS JUST SORT
OF, THEY'RE LIKE BROTHER AND
SISTER.
GALILEO CALLED THE FIFTH, "A
TICKLING OF THE EARDRUM, SUCH
THAT ITS SOFTNESS IS MODIFIED
WITH SPRIGHTLINESS, GIVING AT
THE SAME MOMENT, THE IMPRESSION
OF A GENTLE KISS, AND OF A BITE.

[Audience laughter]

Stuart continues I THINK THAT'S REALLY RATHER
BEAUTIFUL.
HIS THIRD WONDERFUL MUSICAL
RATIO WAS FOUR TO THREE, AND
THAT PRODUCES A FOURTH...

He plays the piano and then continues WHICH IS REALLY A FIFTH UPSIDE DOWN.
IF I TAKE THIS BOTTOM NOTE, AND
I PUT IT ON TOP...

He plays the piano and then continues
I HAVE MY FIFTH.
SO THAT DEFINED PYTHAGORAS'
MATHEMATICS OF BEAUTY.
SO ALL IS WELL, BUT REALLY ALL
IS NOT WELL.
THERE WAS A FLAW IN HIS
MATHEMATICS OF BEAUTY, JUST AS
THERE WAS A FLAW IN A SQUARED
PLUS B SQUARED EQUALS C
SQUARED.
I DON'T KNOW IF ANYBODY TELLS
YOU THIS IN SCHOOL, BUT IF YOU
WERE TO USE, A SQUARED PLUS B
SQUARED EQUALS C SQUARED, TO
DEFINE THE DIAGONAL OF A
SQUARE, YOU END UP WITH AN
IRRATIONAL NUMBER.
IT'S A NUMBER LIKE PI THAT GOES
ON FOREVER.
AND WE SHRUG OUR SHOULDERS.
I MEAN WE LIVE IN AN AGE OF
BLACK HOLES, AND MULTIPLE
DIMENSIONS.
SO WHAT, AN IRRATIONAL NUMBER,
THAT'S OKAY.
MOST OF THE PEOPLE WE KNOW ARE
IRRATIONAL.

[Audience laughter]

Stuart continues BUT THERE WAS SOMETHING
TERRIBLE AND THREATENING ABOUT
AN IRRATIONAL NUMBER IN THE
TIME OF PYTHAGORAS.
HE HAD DEFINED THE UNIVERSE IN
A WAY THAT WAS BOUNDED, THAT
FIT TOGETHER.
THERE WAS NO IDEA OF A
CONTINUOUS LINE THAT WAS MADE
UP OF DISCREET POINTS.
IF YOU HAVE AN IRRATIONAL
NUMBER, SOMETHING THAT JUST
SIMPLY GOES ON FOREVER, IT
REALLY DESTROYS THE WHOLE PLAN.
I MEAN YOU DON'T WANT THAT TO
HAPPEN.
IN FACT, SUPPOSEDLY THIS WAS A
DEEP DARK SECRET OF THE
PYTHAGOREANS, AND PEOPLE WHO
REVEALED IT, PROCLOS TELLS US,
WERE SHIPWRECKED TO A MAN, MADE
THE GODS ANGRY.
SO THE VERY FORMULA, A SQUARED
PLUS B SQUARED EQUALS C
SQUARED, THAT PYTHAGORAS USED
AS A WAY TO CREATE AN ORDERLY
WORLD, OPENED A WAA-- A WINDOW.
I WAS GOING TO SAY DOOR, AND I
WANTED TO CHANGE TO WINDOW, SO
I SAID WAA.
BUT HE OPENED THE WINDOW TO THE
DESTRUCTION OF THAT
ORDERLINESS.
THE SAME THING HAPPENS IN
MUSIC.
AND PYTHAGORAS SUPPOSEDLY
DISCOVERED THIS AT HOME WHEN HE
WAS WORKING WITH THESE STRINGS
OF DIFFERENT LENGTHS.
AND HE FOUND THAT IF HE PUT--
IF HE...
CREATED OCTAVES...

He plays the piano and then continues
AND THEN HE PUT THOSE NEXT TO A
SERIES OF FIFTHS, IF HE JUST
BUILT FIFTHS, WHICH YOU CAN DO...

He plays and continues
IF YOU BUILD ENOUGH FIFTHS, IF
YOU'VE GONE THROUGH 12 OF THEM,
IN FACT, YOU END UP AT THE VERY
TOP, WITH THE SAME NOTE, THE
SAME NAME NOTE WITH WHICH YOU
BEGAN.
SO HE BUILT ALL OF THESE
FIFTHS, AND ENDED UP WITH THE
SAME NAME NOTE WITH WHICH HE
HAD BEGUN, AND HE DID THE SAME
THING WITH OCTAVES.
AND HE DISCOVERED THAT THEY
WERE NOT THE SAME NOTE.
THAT IS, THAT FIFTHS AND
OCTAVES, WHEN YOU MULTIPLY THEM
UP THE KEYBOARD AS WE DID HERE,
BUT THEY DON'T LAND IN THE SAME
PLACE.
IT'S AS IF MUSICAL SPACE WAS
WARPED IN SOME WAY.
THERE IS AN EXPLANATION FOR
THIS, AND THE EXPLANATION IS
THAT OCTAVES ARE BASED ON TWO,
TWO TO ONE, AND FIFTHS ARE
BASED ON THREE, THREE TO TWO,
AND TWO AND THREE ARE BOTH
PRIME NUMBERS.
PEOPLE KNOW WHAT PRIME NUMBERS
ARE, THEY'RE NUMBERS THAT HAVE
AS THEIR FACTOR ONLY THEMSELVES
AND THE NUMBER ONE.
POWERS OF PRIME NUMBERS CAN
NEVER MEET.
THEY CAN NEVER END UP IN THE
SAME PLACE.
SO IF YOU HAVE CARPENTERS
BUILDING A LADDER AND ONE SIDE
OF THE LADDER IS USING A
MEASUREMENT, A RULER THAT
MEASURES OCTAVES, AND THE OTHER
SIDE, A RULER THAT ONLY
MEASURES FIFTHS, YOU COULD
NEVER GET THEM SO THAT THE STEP
OF THE LADDER WOULD GO STRAIGHT
ACROSS.
JUST WON'T HAPPEN.
SO WHAT DID PYTHAGORAS DO ABOUT THIS?
REALLY HE DID NOTHING ABOUT IT.
BUT IT WAS A SECRET THAT WOULD
COME BACK TO HAUNT PEOPLE IN LATER AGES.
AT THE TIME,
IT WAS OKAY, BECAUSE GREEK
MUSIC, AS FAR AS WE KNOW,
ANCIENT GREEK MUSIC WAS NOT
BASED AS LATER MUSIC WAS, ON
THIS IDEA OF HARMONY, WHERE AN
INSTRUMENT WITH FIXED PITCHES,
LIKE THE PIANO, WHERE YOU HAVE
TO MAKE EVERYTHING GET ALONG SO
WELL AS THEY DID NOT GET ALONG
WHEN I PLAYED "HAPPY BIRTHDAY."
IN THE WRONG KEY OVER HERE.
THAT DIDN'T HAPPEN IN ANCIENT GREEK MUSIC,
AND PYTHAGORAS WAS OKAY WITH IT.
SO NOW WE JUMP TO THE MIDDLE AGES.
WE HAVE BOETHIUS, WHO WAS A
GREAT THEORIST, VERY IMPORTANT,
AND HERE AGAIN, WE HAVE, IT'S A
SLIGHTLY BETTER PICTURE OF
PYTHAGORAS OVER HERE, RINGING
HIS BELLS, BOETHIUS USING A
MONOCHORD, AND SUDDENLY, WE
FIND OURSELVES INVOLVED IN
SLIGHTLY MORE ADVANCED MUSIC
THEORY, AND STILL THESE
PROPORTIONS ARE THE MAGICAL
PROPORTIONS, TWO TO ONE, THREE
TO TWO, FOUR TO THREE.
BY THE 2nd CENTURY, CLEMENT OF
ALEXANDRIA IS ANNOUNCING THAT
IT WAS THE SON OF GOD WHO TUNED
THE WORLD IN THIS WAY, AND SO
IT BECOMES A RELIGIOUS ISSUE,
AND THE CHURCH, IN FACT, ADOPTS
THESE PROPORTIONS AS BEING A
SORT OF INVIOLABLE.
HOWEVER, MUSICIANS BEING
CURIOUS TYPES AND ALSO SOMEWHAT
PROFANE, USUALLY, WOULDN'T YOU
SAY, LES?

[Audience laughter]

Stuart continues WERE NOT CONTENT TO JUST LET
THINGS GO IN THAT WAY.
SO YOU HAVE COMPLICATION UPON
COMPLICATION, STRETCHING THE
BOUNDARIES IN THE 14th CENTURY,
YOU HAD POPE JOHN XXII, ISSUING
THE FIRST PAPAL ORDER AGAINST
ALL THE NEW DEVELOPMENTS
HAPPENING IN MUSIC.
FOR EXAMPLE, THERE WAS A DEVICE
KNOWN AS HOCKETT, THAT SOUNDED
TO PEOPLE LIKE HICCOUGHS, THESE
LITTLE RHYTHMIC THINGS GOING
ON, AND POPE JOHN XXII, SAID,
CAN WE PLEASE JUST GO BACK TO
CHANT AND ORGANUM, AND KEEP
THINGS PROPER THE WAY THEY
SHOULD BE.
MEANWHILE, THERE IS ANOTHER
PROPORTION THAT IS ENTERING
MUSIC, AND IS FAVOURED
ESPECIALLY BY THE ENGLISH.
AND THE PROPORTION IS FIVE TO
FOUR.
THIS IS SOMETHING THAT
PYTHAGORAS DIDN'T ENCOUNTER,
BUT WE KNOW IT TODAY AS A
THIRD.
THIS IS FROM THE 13th CENTURY
ONWARD IN ENGLAND, THIS
PROPORTION CREEPS IN, AND HERE
IT IS.

He plays the piano and then continues
WHEN WE ADD THIS, AND WE ADD A
FIFTH INTO IT...

He plays the piano and then continues
WE GET A MAJOR CHORD.

He plays the piano and then continues
SO LET'S TRY THIS ONE.
LOW VOICES...

The audience sings the note.

Stuart continues AH, ISN'T THAT BEAUTIFUL?
THAT, TO ME IS THE SOUND--
WHEREAS A FIFTH IS SOMETHING
SOMEWHAT ABSTRACT AND HOLLOW,
WHEN YOU BRING THAT THIRD IN,
TO ME IT'S THE SOUND OF THE
HUMAN HEART.
AND THIS ENTERED MUSIC AND
CREATED EVEN MORE PROBLEMS,
BECAUSE...
WE ALREADY LEARNED THAT THE
OCTAVES AND THE FIFTHS DON'T
REALLY GET ALONG.
THE THIRDS MAKE IT MUCH WORSE.
MUSICIANS WERE NOW READY TO
START TOYING WITH THESE DIVINE
PROPORTIONS, TOO, SO THAT TONES
COULD PRODUCE DESIRABLE EFFECTS
AS THEY COALESCED ON THE CANVAS
OF TIME.
THEY NEEDED A MUSICAL
PERSPECTIVE, AND THE ANSWER FOR
MUSICIANS WAS TEMPERAMENT.
TEMPERAMENT COMES FROM VARIOUS
WORDS MEANING TO ALTER, TO MIX
INGREDIENTS PROPORTIONATELY,
FROM THE OLD ENGLISH TEMPRIANT,
TO REGULATE, FROM TEMPUS, TO DO
THINGS AT THE RIGHT TIME IN THE
RIGHT SEASON, FROM TEMPLUM, A
SPACE CUT OFF AND CONSECRATED
TO THE GODS, WHICH IS THE
ORIGIN OF TEMPO.
EACH TERM CONNOTES A WORLD
PARTITIONED INTO DISSIMILAR
FRAGMENTS, THEN MADE WHOLE
THROUGH A PROCESS OF JUDICIOUS
BLENDING.
HOW DID THEY DO THIS?
WELL THE VERY FIRST ATTEMPT WAS
SOMETHING LIKE THIS.
THIS IS A TUNING IN WHICH EACH
OF THESE FIFTHS THAT, AS WE SAW
BEFORE, CREATE A THIRD THAT'S
NOT A VERY GOOD THIRD.
WE UH...

He plays the piano and then continues
THAT'S THE THIRD, BUT IF I'M
BUILDING IT THROUGH FIFTHS,
IT'S NOT THE RIGHT PROPORTION.
THIRDS SHOULD BE FIVE TO FOUR.
AND IF I BUILD A THIRD...

He plays the piano and then continues
IF I BUILD A THIRD THROUGH THE
PROPORTION OF FIFTHS, THREE TO
TWO, I'M GOING TO END UP WITH A
VERY UGLY THIRD, IT'S JUST NOT
GOING TO BE RIGHT.
SO, GENIUS IDEA, TAKE A LITTLE
PIECE OUT OF EACH OF THESE...

He plays the piano and then continues
JUST SHORTEN THEM A LITTLE BIT.

He plays the piano and then continues SO THAT BY THE TIME YOU GET HERE...

He plays the piano and then continues
YOU END UP WITH THE RIGHT
SOUNDING THIRD.
IF YOU SHORTEN EACH OF THE
FIFTHS, THAT THIRD WILL COME
OUT SOUNDING RIGHT.
AND HENCE, WHAT YOU HAVE IS
QUARTER COMMA MEAN TONE,
BECAUSE EACH OF THESE FIFTHS
HAS A QUARTER THAT COMMA OF THE
THIRD, BETWEEN THE WAY IT'S
CONSTRUCTED, USING FIFTHS, AND
THE WAY IT'S SUPPOSED TO BE IN
ITS PURE STATE.
THAT COMMA IS DIVIDED UP INTO
FOUR PARTS, AND ONE FOURTH OF
IT IS TAKEN OUT OF EACH OF
THESE FIFTHS.
SO WE HAVE ON THIS PIANO,
THIRDS THAT ARE MUCH MORE PURE
THAN IN THE MODERN TUNING.
HERE, IF I PLAY THIS, AND I
HOPE THIS WORKS.
IT'S VERY HARD TO HEAR.
I HOPE IT WORKS OUT WELL.
BUT...

He plays the piano and then continues
DO YOU HEAR HOW THERE'S A KIND
OF A BEATING, A ROUGHNESS HERE?

He plays the piano and then continues
A WAVERING, MUSICIANS CALL THIS BEATING.
ON THIS PIANO, THE THIRDS
SHOULD BE VERY PURE AND SO...

He plays the piano and then continues
IT'S HARD TO HEAR, BUT IT
SHOULD BE MORE SERENE, WHEN YOU
HAVE REAL THIRDS, THE SOUND IS VERY PLACID.

He plays the piano and then continues
IT'S A LITTLE BETTER, RIGHT?
IT'S A LITTLE BETTER.
SO I'LL PLAY
A LITTLE MUSIC FOR YOU ON THIS
PIANO, THAT WAS INTENDED FOR
THIS KIND OF A TUNING, IN WHICH
THE FIFTHS ARE SHORTENED, BUT
WE DON'T SEEM TO MIND THE
FIFTHS BEING SHORTENED A LITTLE
BIT, IT DOESN'T BOTHER US MUCH.
SO THAT THE
THIRDS CAN SHINE AND BE THEIR
PURE SERENE SELVES.

He plays a complete, soft tune.

Then, he says
I DON'T KNOW IF THAT SOUNDED A
LITTLE PURER TO YOU THAN THE
WAY YOU USUALLY HEAR A PIANO,
BUT IT'S DIFFICULT, BECAUSE IT
DEPENDS ON THE INSTRUMENT AND
IT DEPENDS ON THE CONDITIONS IN
THE HALL AND SO ON.
THAT'S WHAT THIS WAS INTENDED FOR.
BUT AS YOU SAW WITH "HAPPY
BIRTHDAY," THERE ARE SOME
LIMITATIONS TO HAVING THIS
TUNING.
SO ACTUALLY, WE'RE GOING TO DO
A LITTLE DEMONSTRATION FOR YOU
ABOUT THAT.
AND WE'RE GOING TO TAKE A
BEETHOVEN SONATA, OPUS 31,
NUMBER 1.
NOW WHAT HAPPENED AS MUSIC
PROGRESSED WAS THAT COMPOSERS
BEGAN CREATING PIECES LIKE
SONATAS, WHICH DEPICT A KIND OF
MUSICAL JOURNEY.
THEY START IN ONE PLACE, THEY
TRAVEL.
IN A WAY IT'S SIMILAR TO
BAROQUE ARCHITECTURE, WHERE, AS
YOU MOVE FROM ROOM TO ROOM, YOU
HAVE DIFFERENCES IN LIGHT AND
SHADING AND COLOUR AND THERE'S
A CLIMAX.
IN THE MUSICAL SONATA FORM, YOU
HAVE A KIND OF JOURNEY TAKING
PLACE, WHERE THE MUSIC BEGINS
IN ONE PLACE, TRAVELS, COLLECTS
SOUVENIRS, AND THEN EVENTUALLY
COMES BACK.
SO WE'RE GOING TO JUST PLAY A
LITTLE BIT OF THIS BEETHOVEN
SONATA, BECAUSE BEETHOVEN
BEGINS IN ONE KEY, AND VERY
QUICKLY BEGINS TO TRAVEL.

Both Stuart and Maestro Les Diath play simultaneously on two pianos.

Stuart says SO WHAT HAPPENS...

[Applause]

Stuart continues THANKS.

Both men continue playing.

Stuart says THAT'S NOT TOO GOOD.
NOT TOO GOOD.
SO...
THIS TUNING IS NOW FAILING US
IF WE WANT TO TAKE ADVANCES
INTO MUSIC ALONG BEETHOVEN'S
LINES.
WHEN WE GET TO THE ROMANTIC
ERA, WE'RE IN REALLY DEEP
TROUBLE.
HERE IS A LITTLE BIT OF THE
FAMOUS CHOPIN PRELUDE IN E MINOR.

Maestro Les Diath plays the piano.

Then, Stuart joins in.

He says THAT'S ENOUGH.

[Audience laughter]

Stuart continues SO THERE THE LIMITATIONS ARE
REALLY CLEAR.
WHAT DO MUSICIANS DO ABOUT IT?
WELL THEY'VE ALREADY TAMPERED
IN THIS TUNING WITH THE FIFTHS.
BUT THAT WASN'T SO HORRIBLE,
THAT WAS FAIRLY ACCEPTABLE.
TAMPERING WITH OTHER
PROPORTIONS, YOU'RE TREADING ON
DANGEROUS GROUND.
SO THEY CREATED KEYBOARDS WITH
MORE KEYS.
NOW PERSONALLY I HAVE ENOUGH
TROUBLE DEALING WITH 12 IN AN
OCTAVE, BUT HERE YOU HAVE THEM,
THIS ONE HAS 19.
AND THERE WERE ALL KINDS OF
PEOPLE CREATING WILD
INSTRUMENTS AT THE TIME.
BUT EVENTUALLY A PROPOSAL CAME
ALONG FOR A DIFFERENT KIND OF
TUNING CALLED EQUAL
TEMPERAMENT, THE ONE THAT WE
HAVE TODAY.
IN THIS TEMPERAMENT, WE DIVIDE
THE OCTAVE UP INTO 12 EQUAL
PARTS, SO ALMOST EVERY
PROPORTION THAT WAS CONSIDERED
IMPORTANT AND SACRED, WAS DESTROYED.

[Audience laughter]

Stuart continues FIFTHS, THE
OCTAVES, WE KEEP THE OCTAVES.
WE NEED THE OCTAVE, BUT FIFTHS,
FORGET IT.
ALTHOUGH THE FIFTHS ON THAT ONE
ARE A LITTLE BETTER THAN THE
FIFTHS ON THIS ONE.
THIRDS... NO.
DON'T NEED 'EM.
EVERYTHING IS COMPROMISED, AND
TWO THINGS HAPPEN.
ONE WAS THAT THIS WAS
THEOLOGICALLY REPREHENSIBLE.
THE OTHER IS THAT IN TRUTH,
ALTHOUGH IT'S HARD TO HEAR, AND
THE INSTRUMENT YOU PLAY THIS ON
MAKES A VERY BIG DIFFERENCE,
TOO, BECAUSE, FOR EXAMPLE,
EQUAL TEMPERAMENT ON AN ORGAN
SOUNDS HORRIBLE.
PIANOS, BECAUSE OF THE PHYSICAL
STRUCTURE OF THE PIANO, IT
WORKS WELL ON PIANOS.
BUT THE MUSIC DOES BECOME
ROBBED OF CERTAIN BEAUTIFUL
QUALITIES.
WHEN YOU SANG THAT THIRD, THAT
MAJOR THIRD HERE, IT WAS
HEAVENLY, BECAUSE THERE'S
SOMETHING GORGEOUS ABOUT THAT
FIVE TO FOUR PROPORTION.
AND PEOPLE REALLY WANTED TO
HOLD ONTO THAT AND NOT LET IT
ESCAPE.
BUT THINGS MOVE ON.
EQUAL TEMPERAMENT CREATES MANY
PERSPECTIVES, SO THAT A NOTE
THAT WE THOUGHT WAS AN E FLAT,
AND COULD ONLY WORK WITH A
FIFTH...

He plays the piano and then continues
ALSO BECOMES A D SHARP, SO IT
CAN WORK WITH A THIRD.

He plays the piano and then continues
NOT ON THIS ONE, BUT ON THIS ONE, YES.
SO THEREFORE ALL THE TONES CAN
PLAY MULTIPLE ROLES AND YOU
DON'T RUN INTO ANY OF THOSE
CONFLICTS.
HOWEVER, IT'S NOT SO EASY,
BECAUSE MEDIEVAL AND
RENAISSANCE THEORISTS DENY THAT
EQUAL TEMPERAMENT WAS POSSIBLE.
BOETHIUS EXPLAINED THAT SINCE A
WHOLE STEP IS PRODUCED BY TWO
STRINGS VIBRATING IN THE RATIO
NINE TO EIGHT, IT'S IMPOSSIBLE
TO DIVIDE IT.
WHAT HAPPENS IF YOU TRY TO
DIVIDE NINE TO EIGHT DOWN THE
MIDDLE, YOU GET AN IRRATIONAL
NUMBER.
THAT'S NOT GOOD.
SO HE SAID THAT IN THESE LITTLE
HALF STEPS ON THE KEYBOARD,
THAT ONE SIDE HAS TO BE IN A
PROPORTION 18, 17, THE OTHER
SIDE HAS TO BE IN A PROPORTION
71, 16.
IT WASN'T UNTIL EUCLID'S
ELEMENTS WERE TRANSLATED IN
1482, THAT A GEOMETRIC SOLUTION
WAS FOUND, WHERE YOU COULD FIND
THE MEAN TO ANYTHING THROUGH
GEOMETRY.
MEANTIME, GALILEO'S FATHER,
VINCENZO GALILEI, CREATED EQUAL
TEMPERAMENT ON THE LUTE BY
USING 18, 17 AS A PROPORTION
AND IT SEEMED TO WORK PERFECTLY
WELL.
AND IT WAS ACCEPTABLE, BECAUSE
NOBODY COULD FIGURE OUT WHAT
ELSE TO DO ON IT.

[Audience laughter]

Stuart continues YOU HAVE, YOU KNOW, YOU HAVE
FRETS AND STRINGS, AND YOU HAVE
TO BE ABLE TO MAKE ALL THE
DIFFERENT STRINGS ALL WORK WITH
EACH OTHER.
SO IF YOU DON'T HAVE EQUAL
TEMPERAMENT ON THE LUTE, YOU'RE
IN A LOT OF TROUBLE.
BUT EVEN GREAT THINKERS LIKE
NEWTON FOUND THIS SOLUTION OF
THIS EQUAL TEMPERAMENT TO BE
REALLY UNSATISFACTORY.
NEWTON SAID THAT THE MUSICAL
TONES THAT YOU GET IN THIS CASE
ARE LIKE SOILED AND FADED
COLOURS.
BESIDES WHICH, IN THE
RENAISSANCE, YOU HAD PEOPLE
LOOKING FOR A WAY TO RECAPTURE
THE POWER OF MUSIC THAT THEY
FELT THAT THE ANCIENTS HAD.
RAMOS, FOR EXAMPLE, TALKED
ABOUT HOW ONCE UPON A TIME IN
ANCIENT GREECE, THAT MUSIC
COULD MOVE WILD BEASTS THROUGH
THE SWEETNESS OF THEIR SONG,
COULD CAPTURE THE HEARTS OF
MEN, COULD REVIVE THE DEAD,
COULD BEND TO MERCY THE SPIRITS
OF THE UNDERWORLD, COULD DRAW
TREES FROM THE MOUNTAINS.
PEOPLE WANTED TO RECAPTURE THIS
POWER OF MUSIC, AND THEY FELT
THAT BY PERVERTING THE TUNING,
WE WERE MOVING FURTHER AND
FURTHER AWAY FROM THAT POWER.
SO THERE WERE HUGE FIGHTS GOING ON.
BUT PROBABLY, IN THE MIDST OF
ALL OF THIS FIGHTING AND
CARRYING ON, PROBABLY MOST
PEOPLE AT THE TIME AGREED THE
BAROQUE COMPOSER AND THEORIST
JOHAN GEORG NEIDHARDT WHO SAID,
"EQUAL TEMPERAMENT BRINGS WITH
IT ITS COMFORT AND DISCOMFORT
LIKE BLESSED MATRIMONY."

[Audience laughter]

Stuart continues MEANWHILE, DURING THE
RENAISSANCE, THE GREAT THEORIST
ZARLINO, TRIED TO FIND A WAY TO
GET PYTHAGORAS' NUMBERS...
REMEMBER PYTHAGORAS HAD TWO TO
ONE, THREE TO TWO, FOUR TO
THREE, SO THERE WERE ONLY--
ONLY GOES UP TO NUMBER FOUR.
THAT WILL NOT INCLUDE OUR FIFTH
THAT WE LOVE, OUR FIVE TO FOUR,
OR SOME OTHER INTERVALS, LIKE
THE MINOR THIRD, WHICH IS SIX
TO FIVE, AND THE MAJOR SIXTH,
WHICH IS FIVE TO THREE.
SO HE HAD TO COME UP WITH SOME
SOLUTION, AND HE JUST SAID,
WELL, FOR PYTHAGORAS, FOUR WAS
A GOOD NUMBER, BUT ACTUALLY WE
SHOULD BRING IT UP TO SIX.
IF WE INCLUDE 1, 2, 3, 4, 5, 6, WE
CAN CREATE ALL THE RATIOS WE
NEED.
AND HE HAD SOME GOOD
JUSTIFICATIONS FOR IT.
SIX IS THE FIRST PERFECT
NUMBER, BEING THE SUM OF ALL
THE NUMBERS OF WHICH IT IS A
MULTIPLE.
THERE ARE SIX PLANETS IN THE SKY...

[Murmuring]

Stuart continues PLATO IN HIS SYLLABUS INDICATED
THAT HYMNS SHOULD NOT CELEBRATE
MORE THAN SIX GENERATIONS, THE
WORLD WAS CREATED IN SIX DAYS.
WHO COULD ARGUE WITH THIS?

[Audience laughter]

Stuart continues ONE PROBLEM REMAINED, WHICH WAS
THE MINOR SIXTH, WHICH WAS IN
THE PROPORTION EIGHT TO FIVE,
BUT ZARLINO COULDN'T START
BRINGING SEVEN AND EIGHT IN,
BECAUSE THERE WERE ALL KINDS OF
UGLY PROPORTIONS THAT YOU GET
WHEN YOU USE THOSE NUMBERS.
SO HE JUST CONSIDERED EIGHT AS
THERE POTENTIALLY IN THE SIX.
YOU CAN CALL IT TWICE FOUR, OR
COME UP WITH ALL KINDS OF OTHER
CALCULATIONS TO MAKE IT ALL
WORK.
BUT STILL, HE WAS ADAMANT THAT
THIS EQUAL TEMPERAMENT
BUSINESS, THIS WAS JUST A
HORRIBLE THING, AND NOT
SOMETHING WE SHOULD LIVE WITH.
SO HE BECAME VERY EMBROILED IN
A FIGHT WITH VINCENZO GALILEI,
HIS FORMER STUDENT.
GALILEI HAD WORKED OUT THIS
SOLUTION ON THE LUTE, OF
COURSE, AND ALSO MADE THIS
REALLY, REALLY RADICAL CLAIM.
HE CLAIMED THAT ALL SCALES ARE
MANMADE.
HE SAID, I
DON'T WANT TO HEAR ABOUT YOUR
NUMBERS.
EVERYTHING IS MANMADE, IT'S ALL
SUBJECTIVE ANYWAY, CASE CLOSED.
WELL THERE THE ARGUMENT STOOD UNTIL 1581,
WHEN NEW EXPERIMENTS GAVE
GALILEI FURTHER AMMUNITION.
HE DISCOVERED THAT WHEN THE
STRINGS ARE CHANGED, NOT BY
LENGTH, BUT BY THE AMOUNT OF
TENSION ON THEM, AND THIS IS
HOW WE TUNE INSTRUMENTS TODAY,
BOTH A COMBINATION OF STRING
LENGTH, AND ALSO HOW MUCH
TENSION WE PUT ON THEM, THAT
WHEN TENSION IS USED THE
FORMULAS HAVE TO BE SQUARED.
SO OCTAVES ARE NOT PRODUCED BY
CHANGED TENSION IN THE RATIO OF
TWO TO ONE, BUT FOUR TO ONE,
FIFTHS BY NINE TO FOUR, FIFTHS
BY 16 TO 9, SO ZARLINO'S
NUMBERS ARE ACTUALLY MEANINGLESS.
EVEN WORSE, ALL THE PROPORTIONS
ARE COMPLETELY UNRELIABLE
UNLESS THE STRINGS USED ARE
MADE OF THE SAME MATERIAL,
LENGTH, THICKNESS AND GOODNESS.
SO PHYSICAL REALITY INTERFERES
WITH THIS GRAND THEORY.
AND OTHER SCIENTIFIC MINDS ALSO
JOINED IN THE PARADE HERE.
WE HAVE, FOR EXAMPLE, THE DUTCH
SCIENTIST SIMON STEVEN, WHO
SAID, LOOK, IT'S OBVIOUS,
PYTHAGORAS MEASURED WRONG.
THE NATURAL TUNING IS EQUAL
TEMPERAMENT, BECAUSE WE DON'T
RUN INTO ALL THESE COMMAS AND
ALL THESE CRAZY, YOU KNOW,
DISSONANCES.
SO ACTUALLY, IT'S JUST A
MEASUREMENT PROBLEM, AND WHY
DID PYTHAGORAS MEASURE
INCORRECTLY?
SIMPLE, HE SPOKE GREEK INSTEAD
OF DUTCH.

[Audience laughter]

Stuart continues MEANWHILE, KEPLER LOOKED AT THE
ELLIPTICAL ORBITS OF THE
PLANETS, AND BECAUSE THE ORBITS
ARE ELLIPTICAL, THEY VARY IN
SPEED, SO SATURN, FOR EXAMPLE,
WOULD BE PERCEIVED, FROM THE
SUN -- HE DID THIS FROM THE
STANDPOINT OF THE SUN -- WOULD
BE PERCEIVED TO MOVE THROUGH AN
ARC OF 135 SECONDS PER DAY WHEN
CLOSEST, BUT ONLY 106 SECONDS
WHEN FURTHEST AWAY.
PLACE THESE TWO IN PROPORTION,
135 TO 106...
NO ANSWERS?

[Audience laughter]

Stuart continues THE RESULT WILL BE ROUGHLY FIVE
TO FOUR, THEREFORE SATURN IS A THIRD.

[Audience laughter]

Stuart continues JUPITER GENERATES A MINOR
THIRD, MARS PRODUCES A PERFECT FIFTH.
SO THEREFORE THE UNIVERSE IS
TUNED ACCORDING TO THE PURE
HARMONIC RATIOS.
THEN IN 1673, TWO OXFORD MEN,
WILLIAM NOBLE AND THOMAS
PIGOTT, DISCOVERED THAT A
SINGLE STRING SUBDIVIDES AND
PRODUCES A WHOLE SERIES OF
USEABLE TONES.
THAT IS, THAT ANY VIBRATING
STRING SUBDIVIDES ITSELF AND
PRODUCES TONES AS IF IT WAS CUT
IN TWO AND THREE AND FOUR AND
SO ON.
THERE ARE ENDLESS--
ENDLESS OVERTONES EMANATING
FROM A VIBRATING STRING.
IT'S JUST THAT THE HIGHER TONES
ARE FAINTER AND FAINTER AND
FAINTER, SO WE DON'T HEAR THEM.
THEREFORE...
UM, ANY DISSONANCE, ALL
VIBRATING BODIES VIBRATE IN AN
OCEAN OF DISSONANCE.
ANY DISSONANCE CAN BE JUSTIFIED
IN NATURE BY THESE OVERTONES
EMANATING.
IT DIDN'T STOP NEWTON FROM
CLAIMING THAT THE COLOURS OF
LIGHT THROUGH A PRISM
CORRESPOND TO THE DISTANCES
CREATED BY THE PURE MUSICAL
PROPORTIONS.
MEANWHILE, THERE WAS ANOTHER
KIND OF TUNING CREATED, AROUND
BACH'S TIME.
ACTUALLY, IT WAS IN 1681, THIS
TUNING WAS CREATED BY A MAN
NAMED BRUCKMEISTER.
IT'S CALLED WELL TEMPERAMENT.
AND IN WELL TEMPERAMENT, ALL OF
THE KEYS ARE USEABLE, BUT THERE
ARE DIFFERENCES.
SOME ARE MORE IN TUNE, SOME ARE
LESS IN TUNE.
IN SOME KEYS, THE THIRDS ARE
MORE PURE, IN SOME KEYS, THE
FIFTHS ARE MORE PURE.
AND THIS GAVE RISE TO THE IDEA
THAT A KEY HAD A KIND OF
CHARACTER.
SO SOME KEYS WILL BE JOYOUS,
SOME KEYS WILL BE ANGUISHED.
AND I'M GOING TO DEMONSTRATE
THAT FOR YOU NOW.
I HOPE THIS IS EASY ENOUGH TO
HEAR.
LES IS GOING TO PLAY A LITTLE
BIT OF THIS BACH PRELUDE IN E
FLAT MINOR, FROM THE WELL
TEMPERED CLAVIER, BOOK ONE, IN
THE MODERN TUNING, AND THEN I'M
GOING TO TRY IT IN THE WELL
TEMPERAMENT AND SEE IF YOU
DETECT A DIFFERENCE IN THE
QUALITY AND THE CHARACTER OF
THE PIECE.
BY THE WAY, THIS PIECE WAS
WRITTEN, ACCORDING TO RALPH
KIRKPATRICK, THE LATE
HARPSICHORDIST AND SCHOLAR,
THIS PIECE WAS WRITTEN BY BACH
AFTER THE DEATH OF HIS FIRST
WIFE.
AND E FLAT MINOR IS A KEY OF
ANGUISH IN THE LIST OF KEY
CHARACTERISTICS.

Maestro Les Diath plays the piano.

Stuart continues OKAY, AND NOW WE COULD TRY IT
IN THE WELL TEMPERAMENT.
BEFORE I PLAY IT IN E FLAT
MINOR ON THIS, I'M JUST GOING
TO PLAY A LITTLE BIT OF IT IN
THE KEY OF D MINOR INSTEAD, AND
SEE IF YOU CAN DETECT A
DIFFERENCE IN THE CHARACTER OF
THE KEYS.

He plays.

He says OKAY, NOW THE E FLAT MINOR.

He plays the same tune in a different key.

Then, he says
SO I DON'T KNOW IF THAT QUALITY
IS CLEARLY DIFFERENT TO YOU,
BUT IN E FLAT MINOR, THAT'S AN
ANGUISHED KEY, AND THIS IS A
WELL TEMPERAMENT THAT'S
SUPPOSED TO HEIGHTEN THAT.
JUST TO GIVE
YOU A QUICK OTHER EXAMPLE,
WHICH IS REALLY FAST, WHERE AN
INSTRUMENT LIKE THIS IN A WELL
TEMPERAMENT IS NOT SUITABLE FOR
ALL KINDS OF MUSIC, EVEN THOUGH
YOU COULD PLAY-- ALL THE
DIFFERENT KEYS IN THIS TUNING
ARE USEABLE.
BUT BECAUSE OF THE QUALITIES
THAT THE DIFFERENT KEYS IMPART,
IT'S NOT APPROPRIATE FOR ALL MUSIC.
SO LES IS
GOING TO PLAY A LITTLE
SCHUBERT, THEN I'M GOING TO DO
IT JUST TO SHOW YOU.

Maestro Les Diath plays a fast-paced tune.

Stuart continues AND NOW IN THE WELL
TEMPERAMENT.

He plays.

Then, he says TO ME, IT'S--
I DON'T KNOW, HOW DO YOU FEEL?
TO ME IT WORKS BETTER IN EQUAL
TEMPERAMENT.
THERE'S A SLIGHT, OUT OF
TUNENESS...

He plays the piano and then continues
HERE THAT DAMPENS THE
BEAUTY OF WHAT SCHUBERT IS DOING.
OF COURSE THERE ARE PEOPLE WHO
WILL DEBATE THIS NON-STOP, AND
FIGHT OVER IT, AND MANY OF THEM
CONTACT ME PERSONALLY.

[Audience laughter]

Stuart continues IN ANY EVENT, THE STORY
ACTUALLY ENDS, OR THE WAY I
HAVE IT ENDING -- IT NEVER
REALLY ENDS, BUT THE WAY I HAVE
IT ENDING IS A HUGE FIGHT
BETWEEN JEAN-JACQUES ROUSSEAU
AND THE COMPOSER RAMEAU.
THIS IS DURING THE AGE OF
ENLIGHTENMENT.
ROUSSEAU, AS YOU KNOW, WAS THE
AUTHOR OF,
ON THE ORIGIN OF
INEQUALITY,
AND HE SAID
THAT SOCIETY CORRUPTS US, THAT
WE'RE BORN IN THIS WONDERFUL
STATE, AND THEN WE'RE DESTROYED
BY SOCIETY.
IF ONLY WE WERE LEFT ALONE IN
NATURE, EVERYTHING WOULD BE
WONDERFUL.
AND HE APPLIED HIS THEORIES TO
MUSIC.
HE SAID THAT MELODY, LIKE
LANGUAGE, WAS BORN OF AN EROTIC
FERVOUR, UNTAMED IMPULSES
CREATING RELEASE.
HE REALLY LIKED UNTAMED
IMPULSES.
UH... AND SO HE WAS AGAINST
EQUAL TEMPERAMENT, BECAUSE HE
FELT THAT IT'S REALLY
CORRUPTING THIS PURE NATURAL
STATE OF THINGS.
RAMEAU LOVED PLAYING WITH
HARMONY, AND HE WANTED EQUAL
TEMPERAMENT, BECAUSE IN FACT,
IT BECAME KNOWN AS RAMEAU'S
TEMPERAMENT IN HIS TIME,
BECAUSE HE FELT THAT IT WAS
NECESSARY FOR THE PROGRESS OF
MUSIC.
AND HE TALKED ABOUT THE
TENDENCY OF A VIBRATING OBJECT
TO RADIATE THE OCTAVE, FIFTH
AND THIRD, AS THE STRONGEST
OVERTONES.
BUT HE SAID THAT OUR EARS
LISTEN TO THE FUNDAMENTAL BASS,
THE FUNDAMENTAL FREQUENCY IN A
PIECE OF MUSIC, AND WE PERCEIVE
THE INTENTIONS.
IN OTHER WORDS, EVEN IF A FIFTH
IS CORRUPTED OR A THIRD IS
CORRUPTED, OUR MINDS CAN
PERCEIVE THAT WE REALLY MEAN A
FIFTH OR A THIRD, AND THAT
FUNDAMENTAL BASS GUIDES US.
AND SO EQUAL TEMPERAMENT WORKS,
BECAUSE WE UNDERSTAND THAT THE
MUSIC IS SYMBOLISED.
THE PURE FIFTH IS SYMBOLISED,
THE PURE THIRD IS SYMBOLISED IN
THESE TEMPERED INTERVALS.
AND THE TWO OF THEM REALLY WENT
AT IT.
OF COURSE THERE WAS AN INCIDENT
WHERE ROUSSEAU, WHO WAS AN
INCOMPETENT COMPOSER, WROTE A
PIECE, RAMEAU HUMILIATED HIM,
AND THE THING WENT ON FOR YEARS
AND YEARS AND YEARS.
BOTH MEN, BY THE WAY, KIND OF
WENT OFF THE DEEP END AT THE
END OF THEIR LIVES, AND IT WAS
NEVER RESOLVED.
INSTRUMENTS IN THEIR TIME, EVEN
THE EARLY PIANO, WERE NOT WHAT
WE HAVE TODAY.
WE HAVE AN INSTRUMENT TODAY
WITH-- IN A GRAND PIANO,
ESPECIALLY, WITH AN IRON FRAME,
WITH TREMENDOUS AMOUNTS OF
TENSION ON THE STRINGS, AND
THERE IS SOMETHING IN THE PIANO
CALLED INHARMONICITY, NATURAL
INHARMONICITY IN THE STRINGS.
THAT IS THE TENDENCY OF THE
STRINGS TO BEHAVE IN A WAY NOT
IN KEEPING WITH, THEORETICALLY
WHAT WE THINK THEY SHOULD BE
DOING.
SO IF A STRING IS VIBRATING A
CERTAIN WAY, WE THINK IT'S
GOING TO SUBDIVIDE INTO TWO AND
THREE AND FOUR AND SO ON, BUT
IT DOESN'T.
THERE ARE FLAWS IN THE STRING,
PHYSICAL REALITY INTERVENES,
THE MORE TENSION YOU PUT ON IT,
THE LESS INHARMONICITY WE GET,
AND YET, THE PROBLEM WORKS
ALWAYS.
SO WE NEVER GET A PURE EQUAL
TEMPERAMENT, WE NEVER GET A
PURE ANYTHING.
BUT THE PROBLEMS OF THE
CORRUPTED INTERVALS ARE MORE
APPARENT ON CERTAIN
INSTRUMENTS.
ON CERTAIN EARLY HARPSICHORDS,
ON MONOCHORDS, ON ORGANS.
TODAY, THE PIANO, IF WE DIDN'T
HAVE EQUAL TEMPERAMENT ON THE
PIANO, WE'D BE RUNNING INTO A
LOT OF TROUBLE, BECAUSE IT
ACTUALLY, THE TUNING ACTUALLY
BRINGS THE INSTRUMENT ALIVE.
AND THERE'S SOME MUSIC THAT I
BELIEVE SHOULD BE PLAYED ONLY
IN EQUAL TEMPERAMENT.
AND YET THERE ARE OTHERS WHO
DISAGREE.
TODAY THE LATEST TRENDS IN
MUSIC AND COMPOSITION HAVE TO
DO WITH GOING BACK TO THE
ORIGINAL TUNINGS, TO THE PURE
TUNINGS, AND CREATING A KIND OF
MUSIC-- I HAVE A FRIEND NAMED
MICHAEL HARRISON, A COMPOSER,
AND YOU CAN LOOK HIM UP ON THE
INTERNET, michaelharrison.com,
I THINK IS HIS WEBSITE.
HE CREATES WORKS WHERE HE TUNES
THE PIANO SO THAT THOSE PURE
HARMONIES EMERGE FROM THE PIANO.
AND WHAT HAPPENS SOMETIMES IS
THAT THE OVERTONES OF THOSE
HARMONIES COALESCE AND CREATE
AMAZING EFFECTS THAT YOU CANNOT
GET ON A PIANO LIKE THIS,
BECAUSE THE OVERTONES CLASH
WITH EACH OTHER, WHEN THE
RATIOS ARE PERVERTED OR
DISTORTED.
SO I'M HAPPY WE HAVE IT.
THERE'S A LOT OF MUSIC I
COULDN'T PLAY IF WE DIDN'T HAVE IT.
BUT IT'S NOT, AS I'M OFTEN
ACCUSED OF SAYING, THIS IS THE
END OF THE LINE, AND IT'S THE
GREAT FINAL SOLUTION -- IT'S
NOT.
BUT IT'S STILL A WONDROUS
THING, I THINK, AND THAT'S-- IN
A NUTSHELL, THAT'S THE STORY.

[Applause]

The clip ends, and Andrew reappears in the studio with a caption reading his name.

He says AMAZING, WASN'T IT?
AND I KNOW THAT FOR SOME OF
YOU, THE DIFFERENCES IN TUNING
WENT RIGHT OVER YOUR HEADS, AND
DON'T FEEL BAD, DON'T FEEL STUPID.
WHAT YOU
REALLY NEED IS TO HAVE A
RECORDING OF THE ENTIRE CHOPIN
PRELUDE IN E MINOR, IN BOTH
TUNINGS AND IN DIFFERENT KEYS,
AND LISTEN TO THEM OVER AND
OVER AGAIN.
AND THEN, TRUST ME, THE MORE
YOU LISTENED, THE MORE IT WOULD
BECOME CLEAR AS DAY, THE
MONUMENTAL SHIFT THAT VINCENZO
GALILEI WAS PROPOSING.
AND IT TRULY WAS A MONUMENTAL
WORLD ALTERING REVOLUTION OF
THE SOUL.
ISACOFF IS ABSOLUTELY JUSTIFIED
IN HIS CONDESCENSION TOWARD THE
PYTHAGOREANS AND THEIR
INTRACTABLE DESIRE TO MAINTAIN
THE OLD TUNING, HOWEVER, THESE
CRITICS OF EVEN TEMPERAMENT
WERE NOT TRYING TO UPHOLD SOME
OBSCURE MYSTICISM.
NOW THEY SAID THAT THEY WERE,
BUT TRUST ME, THEY WEREN'T.
WHAT THEY WERE TRYING TO HOLD
ONTO WAS THAT LUSCIOUS PURE
THIRD.
OH, CAN YOU BLAME THEM?
IT'S JUST SO BEAUTIFULLY SO
SUMPTUOUS.
IT WOULD BE AMAZING, YOU KNOW,
IF YOU COULD JUST FLIP A SWITCH
OR PLUG IN SOME FILTER INTO Q-
BASE, AND YOUR ELECTRIC PIANO
COULD BE SET TO THE OLD TUNING,
AND THEN YOU COULD HAVE THE
CHOICE TO EXPERIMENT WITH WHAT
THAT TUNING GAVE TO THE WORLD.
EQUAL TEMPERAMENT IS GREAT, I
LOVE IT, BUT IT'S A COMPROMISE.
AND BY DEFINITION, COMPROMISES
ARE UGLY, AND IF NOT UGLY,
THEY'RE JUST BORING.
THEY'RE BORN OF NECESSITY, AND
YET, WITHOUT THIS COMPROMISE,
YOU WOULD NOT BE ABLE TO DO THIS...

He plays a dissonant tune on the electric piano.

Then, he says
OR YOU WOULD NOT BE ABLE TO DO THIS...

He plays a classic jazz ending tune and says
FOR
BIG IDEAS,
I'M
ANDREW MOODIE.
THANK YOU, TORONTO, GOOD NIGHT.

[Theme music plays]

The end credits roll.

bigideas@tvo.org

416-484-2746

Big Ideas. Producer, Wodek Szemberg.

Producers, Lara Hindle, Mike Miner, Gregg Thurlbeck.

Logos: Unifor, Canadian Media Guild.

A production of TVOntario. Copyright 2006, The Ontario Educational Communications Authority.

Watch: Stuart Isacoff on the History of Harmonies