Greek Power Point1.4 Segment 3

HARMONYHARMONY & &

PROPORTIONPROPORTION

ANCIENT ANCIENT GREEKGREEK

AESTHETICSAESTHETICS

"Man is the Measure of all Things." Protagoras

Click for Vitruvian Man interview

Influenced by the Greeks, the Ancient Roman Influenced by the Greeks, the Ancient Roman architect VITRUVIUSarchitect VITRUVIUS

wrote that in the human body:wrote that in the human body:

Influenced by the Greeks, the Ancient Roman Influenced by the Greeks, the Ancient Roman architect VITRUVIUSarchitect VITRUVIUS

wrote that in the human body:wrote that in the human body:

a palm is the width of four fingers a foot is the width of four palms a cubit is the width of six palms

a man's height is four cubits (and thus 24 palms) a pace is four cubits

the length of a man's outspread arms is equal to his height the distance from the hairline to the bottom of the chin is one-tenth of a man's height

the distance from the top of the head to the bottom of the chin is one-eighth of a man's height the distance from the hairline to the top of the breast is one-seventh of a man's height

the distance from the top of the head to the nipples is one-fourth of a man's height the maximum width of the shoulders is one-fourth of a man's height

the distance from the elbow to the tip of the hand is one-fifth of a man's height the distance from the elbow to the armpit is one-eight of a man's height

the length of the hand is one-tenth of a man's height the distance from the bottom of the chin to the nose is one-third of the length of the face

the distance from the hairline to the eyebrows is one-third of the length of the face the length of the ear is one-third of the length of the face

6:16:1

ProportionProportion

One Foot

Six

Feet

Six Feet

Twelve

Feet

Two Feet

Doric OrderDoric Order

8:18:1

ProportionProportion

Corinthian Corinthian OrderOrder

Corinthian Style:

Temple Temple to the to the

goddessgoddess

NikeNike

Temple to the Corporate god, NikeTemple to the Corporate god, Nike

Post-Modern Consumer StylePost-Modern Consumer Style

Earliest SurvivingEarliest Surviving

Doric StructureDoric Structure

Temple of Apollo at CorinthTemple of Apollo at Corinth

The Oracle at DelphiThe Oracle at Delphi

Northeast of CorinthNortheast of Corinth

What did Bodhi Tree say upon What did Bodhi Tree say upon attaining enlightenment and attaining enlightenment and realizing he was merely a green, realizing he was merely a green, fruit-bearing sphere atop a fruit-bearing sphere atop a brown, bark-covered cylinder?brown, bark-covered cylinder?

Ge-om-e-try

What did Bodhi Tree say upon What did Bodhi Tree say upon attaining enlightenment and attaining enlightenment and realizing he was merely a green, realizing he was merely a green, fruit-bearing sphere atop a fruit-bearing sphere atop a brown, bark-covered cylinder?brown, bark-covered cylinder?

Ge-om-e-tryGe-om-e-try

GEE, GEE, I’m a tree!I’m a tree!

The Greeks perfected The Greeks perfected the use of Geometrythe use of Geometry

““Beauty is Truth and Truth Beauty, That is All Ye Beauty is Truth and Truth Beauty, That is All Ye Know on Earth and All Ye Need to Know.” KeatsKnow on Earth and All Ye Need to Know.” Keats

The Greeks wished to maintainThe Greeks wished to maintain

idealideal proportionsproportions when building when building any room or like structure from the any room or like structure from the

ground up.ground up.

The Golden RectangleThe Golden Rectangle


Q:Q: Given a flat rectangle, Given a flat rectangle,


what is its most aesthetically what is its most aesthetically pleasing height?pleasing height?


What Does that What Does that

““MEAN” ?MEAN” ?


The arithmetic mean occurs when the

length of the sides of a square whose

PERIMETER is the same as the rectangle.

( L + W ) / 2

( 12 + 6 ) / 2 = 9

9 exceeds 6 by 3, which is the same amount by which 12 exceeds 9.

LOGIC

LOGIC

The geometric mean is the nth root of the product of the variables (sides). Here n = 2.

The arithmetic mean occurs when the

length of the sides of a square* whose

AREA is the same as the rectangle.

9 X 4 = 36

The square root of 36 is 6

* 6 x 6

The harmonic mean is the number of variables (sides) divided by the sum of each side’s reciprocal. Here n=2 and the sides are 12 and 6.

1/12 + 1/6 = 3/12, or ¼. 2 divided by ¼ equals 8

LOGIC

LOGIC

PhysicalPhysicalHarmonyHarmony

Leon Battista Alberti,Leon Battista Alberti,

Florentine Architect (1407-1472)Florentine Architect (1407-1472)

"We shall therefore borrow all our Rules for the Finishing our

Proportions, from the MUSICIANS,

who are the greatest Masters

of this Sort of Numbers, and

from those Things wherein Nature shows herself

most excellent and complete."

Music, Numbers Music, Numbers and the and the UniverseUniverse ? ?

"Seek truth and beauty together; "Seek truth and beauty together; you will never find them apart."you will never find them apart."

Pythagoras of Samos Pythagoras of Samos


Big Idea: M

athematics is

the

Big Idea: M

athematics is

the

language of nature.

language of nature.

LOGIC

LOGIC

Music’s Music’s RhythmRhythm

is based onis based on

Mathematical FractionsMathematical Fractions

SUBDIVISIONSSUBDIVISIONS

SUBDIVISIONS OF THE WHOLESUBDIVISIONS OF THE WHOLE

FRACTIONS of FRACTIONSFRACTIONS of FRACTIONS

J.S. Bach’s Little Fugue in G minor

Bach1685-1750

Baroque Period

SUPERIMPOSED, RECURSIVE RHYTHMS

Bach1685-1750

Baroque Period

RECURSIVE RECURSIVE RhythmRhythm

SUPERIMPOSED MIRRORED MOTIFS IN ART

Bach1685-1750

Baroque Period

M.C. Escher(1898 - 1972)

Modern Period

Recursion in ArtRecursion in Art

Recursion in Recursion in ArtArt

THEMETHEME &&

VARIATIONVARIATIONIN MUSICIN MUSIC

LOGIC

LOGIC

AESTHETICS

AESTHETICS

Fifth Symphony

Ludwig van Beethoven

1770-1827

Classical Period

Fifth Symphony

Ludwig Van Beethoven

1770-1827

Classical Period

Fifth Symphony

Ludwig van Beethoven

1770-1827

Classical Period

Mathematics is ALSO the language of

Mathematics is ALSO the language of

HARMONY &

HARMONY &

PITCHPITCH

Diatonic ScaleDiatonic Scale

(Ionian Mode)(Ionian Mode)

Q: What is the scientific symbol for

Wavelength?

Hint:

It’s the 11th letter of the

Greek alphabet …

Daaah.

lamb-dalamb-da

Concert A=440 means that the

universally agreed upon standard for the tone of “A” is 440 Hertz, or 440

cycles (vibrations) per second.

Each tone can be subdivided into

100ths to ensure an almost perfect

match.

Q:

Why is it so easy to

understand how a Chromatic

tuner works?

Hint

BECAUSE IT MAKES CENTS !

Q:

Why might a chromatic tuner

also be useful in diagnosing

pain?

BECAUSE IT KNOWS ALL

YOUR HERTZ !

SemitoneSemitone

(Half-step or (Half-step or MinorMinor Second) Second)

Wholetone Wholetone

(Whole-step or (Whole-step or MajorMajor Second) Second)

DiapasoDiapasonn

(Octave(Octave

))

Diatonic Diatonic ScaleScaleTonic 1:1 9:8 81:64 4:3 3:2 27:16 243:128 2:1

Intra-Ratio

9:8 9:8 256:243 9:8 9:8 9:8 256:243

Step W W H W W W H

Tone C to D

D to E

E to F F to G

G to A

A to B B to C

1:2 RATIO1:2 RATIO

OctaveOctave

2:3 RATIO2:3 RATIO

Perfect FifthPerfect Fifth

2:3 RATIO2:3 RATIO

Perfect Fifth

3:4 RATIO3:4 RATIO

Perfect FourthPerfect Fourth

3:4 RATIO3:4 RATIO Perfect FourthPerfect Fourth

SACRED CONSONANCESACRED CONSONANCE

But what about all But what about all of those black of those black

notes in between?notes in between?

Filling in the Gaps

Filling in the Gaps

The harmonic mean is the number of variables (notes) divided by the sum of each side’s reciprocal. Here n=2 and the sides are 12 and 6.

TASK: Calculate the harmonic mean for the numbers 1 and 2…

Filling in the Gaps

The harmonic mean is the number of variables (notes) divided by the sum of each side’s reciprocal. Here n=2 and the sides are 12 and 6.

ANSWER: For 1 and 2…1/1 + 1/2 = 3/2 . 2 divided by 3/2 equals 4/3

Filling in the Gaps

HARMONY

Is

PERFECTION…

Pythagoras of SamosPythagoras of Samos

And since harmony is reducible to number, perfection is likewise reducible to number.

The universe is harmonious, so it follows that the universe as a whole can be explained in

terms of number.


LOGIC

LOGIC

I perfected the logical

syllogism as a method for discovering

TRUTH.

Aristotle says,Aristotle says,

AGAIN… AGAIN…

AAPPOOLLLLOO

God ofGod of TruthTruth andand MusicMusic

Goddess of Goddess of Harmony Harmony

and and ConcordConcord

www.aris-titanium.com/.../ hirez/harmonia.jpg

The Role of Greek MusicThe Role of Greek Music

Department of Department of Classics, Classics, University of University of CincinnatiCincinnati

Sacred Sacred FragmentsFragments

Q: Which ancient Greek philosopher

took Pythagoras’ theory of the universe

and “shaped” it further?

Q: Which ancient Greek philosopher

took Pythagoras’ theory of the universe

and “shaped” it further?

HINTHINT: He expanded the scale of the musical scale AND the scale

of the universe. PLAY

PLATO’S CONTRIBUTION

PYTHAGORAS’ CONTRIBUTION

Plato, through Timaeus, reasoned in reverse stating that the creator made the world soul out of various ingredients, and formed it into a long strip…

The strip was then marked out into intervals…

Plato

“First [the creator] took one portion from the strip (1st unit)

and next a portion double the first (2nd unit)

a third portion half again as much as the second (3rd unit)

the fourth portion double the second (4th unit)

the fifth three times the third (9th unit)

the sixth eight times the first (8th unit)

and the seventh 27 times the first (27th unit) ”

They give the seven integers; 1, 2, 3, 4, 8, 9, 27. These contain the monad, source of all numbers, the first even and first odd, and their squares and cubes.

Plato

LAMBDALAMBDA

Plato

METAPHYSICS

METAPHYSICS

The Universe is One The Universe is One BigBig……

BeautyBeauty Truth Truth

Truth Truth BeautyBeauty

LETTERLETTER ? ?

BeautyBeauty Truth Truth

Truth Truth BeautyBeauty

CHIASMUSCHIASMUS

Armillary Sphere

CelestialCircles

Plato

BeautyBeauty TruthTruth

TruthTruth BeautyBeauty

Tangible Beauty (in the circle of the different) is a

Representation of Intangible Truth (in the circle of the

Same).

If you know BEAUTY, you know

TRUTH.

If you know TRUTH, you can begin to understand life’s

profound mysteries.

And THAT’S Why I’m

So Darned Important

in the Grand

Scheme of Things!

Art Says…

MusicMusic

of theof the

SpheresSpheres

LAMBDALAMBDA

They give the They give the seven integers; seven integers;

1, 2, 3, 4, 8, 9, 1, 2, 3, 4, 8, 9, 27. These 27. These

contain the contain the monad, source monad, source of all numbers, of all numbers,

the first even the first even and first odd, and first odd,

and their and their squares and squares and

cubes.cubes.

But my system wasn’t exactly

perfect…


But first, let’s C who

knows what the word ENHARMONIC means.

HINT: If you answer correctly, you

must really B#.

BB SShhaarrppss

And the award

goes to…

THE

WITH

AllusionTrivia

Following their final live performance atop a rooftop in 1969, which band’s musician

quipped,

“I'd like to say thank you very much on behalf of the group and myself and I hope we passed

the audition” ?

It wasTHE

BBEEAATTLLEESS

JOHN LENNON

ENHARMONIC TONES

Minute shift

Superimposed shift

OrderOrder inin Chaos ChaosOrOr

Chaos Chaos inin OrderOrder??

STYL

E AL

ERT!

STYL

E AL

ERT!

OrderOrder Chaos Chaos

Chaos Chaos OrderOrder

CHIASMUSCHIASMUS

OrderOrder Chaos Chaos

Chaos Chaos OrderOrder

Not to be confused Not to be confused with…with…

A more primal A more primal equation…equation…

Pie.Ilikeapeachblueberryorbananacreamandlemonmeringueraspberryrhubarbmincemeatpie

insky

apple a lamodecherry

orhumbleshoo

flypie

mulberrymudor

pumpkinchocolate

pecan

ohruin yourappetite

by Lorreen Pelletier

Poe, E. Near a Raven

Midnights so dreary, tired and weary. Silently pondering volumes extolling all by-now obsolete lore.

During my rather long nap - the weirdest tap! An ominous vibrating sound disturbing my chamber's antedoor.

"This", I whispered quietly, "I ignore". Perfectly, the intellect remembers: the ghostly fires, a glittering ember.

Inflamed by lightning's outbursts, windows cast penumbras upon this floor. Sorrowful, as one mistreated, unhappy thoughts I heeded:

That inimitable lesson in elegance - Lenore -

Is delighting, exciting...nevermore. Ominously, curtains parted (my serenity outsmarted), And fear overcame my being - the fear of "forevermore".

Fearful foreboding abided, selfish sentiment confided, As I said, "Methinks mysterious traveler knocks afore.

A man is visiting, of age threescore."

Simpler Pi Poems

Did I tell a witty wisecrack? (3.14159)

Yes, I love a green grassland. (3.14159)

Boy, I want a glass half-full of Sprite. (3.1415926)

Poetry of Poetry of Your OwnYour Own

Okay, Now Try Some Okay, Now Try Some Pi…Pi…

3. 141592653589793238462643383279502884197169399375105820974944 592307816406286208998628034825342117067982148086513282306647 093844609550582231725359408128481117450284102701938521105559 644622948954930381964428810975665933446128475648233786783165 271201909145648566923460348610454326648213393607260249141273 724587006606315588174881520920962829254091715364367892590360 011330530548820466521384146951941511609433057270365759591953 092186117381932611793105118548074462379962749567351885752724 891227938183011949129833673362440656643086021394946395224737 190702179860943702770539217176293176752384674818467669405132 000568127145263560827785771342757789609173637178721468440901 224953430146549585371050792279689258923542019956112129021960 864034418159813629774771309960518707211349999998372978049951 059731732816096318595024459455346908302642522308253344685035 261931188171010003137838752886587533208381420617177669147303 598253490428755468731159562863882353787593751957781857780532 171226806613001927876611195909216420198938095257201065485863 278865936153381827968230301952035301852968995773622599413891 249721775283479131515574857242454150695950829533116861727855 889075098381754637464939319255060400927701671139009848824012 858361603563707660104710181942955596198946767837449448255379

Robert Fludd: Utriusque Robert Fludd: Utriusque Cosmi Maioris scilicet et Cosmi Maioris scilicet et Minoris MetaphysicaMinoris MetaphysicaPhysica Atque Technica Physica Atque Technica Historia, pub.1617.Historia, pub.1617.

LAMBDALAMBDA

AAPPOOLLLLOO

God ofGod of TruthTruth andand MusicMusic

A THOUSAND YEARS of A THOUSAND YEARS of

Greek AreteGreek Arete

David’s Death of Socrates: Neoclassical Period (1787)David’s Death of Socrates: Neoclassical Period (1787)

The only true wisdom consists The only true wisdom consists in knowing that you know in knowing that you know

nothing.nothing.

SOCRATESSOCRATES

SocratesSocrates

So-crates, dude

The only true wisdom consists The only true wisdom consists in knowing that you know in knowing that you know

nothing.nothing.

Bill & TedBill & Ted

SocratesSocrates

PlatoPlato

SocratesSocrates

AristotleAristotlePlatoPlato

SocratesSocrates

AristotleAristotlePlatoPlato

PlatoPlato

PlatoPlato

““Let No Man Let No Man

Destitute of Destitute of GeometryGeometry

Enter My Doors.”Enter My Doors.”

POINT

LINE

PLANE

SOLID

SQUARES

CUBES

1st even & odd

Celestial CirclesCelestial Circles

Armillary Sphere Turner, Gerard. Antique Scientific Instruments. Dorset: Blandford

PlatoPlato

All sense experience is faulty & transient.

PlatoPlato

Thus, the truth can be found by looking beyond

nature.EPISTEMOLOGY

EPISTEMOLOGY

PlatoPlato

HorseHorsevs.vs.Horseness:Horseness:

Theory of Theory of FormsForms

PlatoPlato

Diagram of Plato’sDiagram of Plato’sThe Allegory of the CaveThe Allegory of the Cave

AristotleAristotle

No matter No matter without form; without form;

no form no form without without matter.matter.

Aristotle’s Aristotle’s PoeticsPoetics

AristotleAristotle

The truth can be found by analyzing

nature (breaking

in to parts).

……so the hotdog guy makes the so the hotdog guy makes the hotdog with everything on it. The hotdog with everything on it. The monk exchanges a $20 for the monk exchanges a $20 for the hotdog and waits for his change. hotdog and waits for his change. When no change is forthcoming, When no change is forthcoming, the monk asks,the monk asks, "Hey, where's my change?" The hotdog guy replies, "Change must come from within."

"Hey, "Hey, where's my where's my change?"change?"

…and the hotdog guy replies…Hey, where's my change?" The hotdog guy replies, "Change must come from within."

““Sorry, but you should already Sorry, but you should already know… know…

Change comes from Change comes from within."within."

AristotleAristotle

BIG IDEABIG IDEA: “Moral virtue is a state of : “Moral virtue is a state of character lying in acharacter lying in a

mean between two extremesmean between two extremes..””

ETHICS

ETHICS

Aristotle’s Aristotle’s

GOLDEN MEANGOLDEN MEAN ACTION Deficiency Goodness/Mean Excess

Fear cowardice courage rashness/foolhardy

Drinking/Eating insensible temperate self-indulgentTruth telling modesty/ truthful self-deprecation

Lending $$ stingy liberality prodigality Amusement boring ready wit buffoonery

““Moral virtue is a state of Moral virtue is a state of character lying in acharacter lying in a

mean between two extremesmean between two extremes..””

the the

GOLDEN MEAN GOLDEN MEAN &&

PHIPHI

the the

GOLDEN GOLDEN RECTANGLERECTANGLE

GOLDEN SECTIONGOLDEN SECTION

Standard sized credit cards are 54mm x 86mm, creating a ratio of 0.628, less than a millimeter from a perfect golden section of 0.618.

http://goldennumber.net/classic/fibonser.htm

the the

Fibonacci SeriesFibonacci Series

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . .


GOLDEN GOLDEN SECTION:SECTION:

PHIPHI Starting with 0 and 1, each new number in the series is simply the sum of the two before it.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .The ratio of each successive pair of numbers in the series approximates phi (1.618. . .) , as 5 divided by 3 is 1.666..., and 8 divided by 5 is 1.60.

The ratios of the successive numbers in the Fibonacci series quickly converge on Phi or Φ. After the 40th number in the series, the ratio is accurate to 15 decimal places.1.618033988749895 . . .


the the

GOLDEN MEANGOLDEN MEAN Musical scales are based on Fibonacci numbers

The Fibonacci series appears in the foundation of aspects of art, beauty and life. Even music has a foundation in the series, as:

There are 13 notes in the span of any note through its octave.A scale is comprised of 8 notes, of which the

5th and 3rd notes create the basic foundation of all chords, and are based on whole tone which is2 steps from the root tone, that is the

1st note of the scale. Note too how the piano keyboard scale of C to C above of 13 keys has 8 white keys and 5 black keys, split into groups of 3

and 2.


http://www.amazon.com/exec/obidos/ASIN/0866513434/theevolutioftrut

the the

GOLDEN MEANGOLDEN MEAN

the the

GOLDEN MEANGOLDEN MEAN The Fibonacci series appears in the foundation of aspects of art, beauty and life. Even music has a

foundation in the series, as: There are 13 notes in the span of any note

through its octave.A scale is comprised of 8 notes, of which the

5th and 3rd notes create the basic foundation of all chords, and are based on whole tone which is

2 steps from the root tone, that is the1st note of the scale.

the the


AESTHETICS

AESTHETICS

the the


Later applications ofLater applications of


TheThe

the the


Later applications ofLater applications of

the the



““Moral virtue is a state of character lying in a Moral virtue is a state of character lying in a mean between two extremesmean between two extremes..””

Inherent in Perfection is Inherent in Perfection is the the UNATTAINABLEUNATTAINABLE

““Moral virtue is a state of character lying in a Moral virtue is a state of character lying in a mean between two extremesmean between two extremes..””

The Spiral of FifthsThe Spiral of Fifths

"My new Hypothesis: If we're "My new Hypothesis: If we're built from Spirals while living built from Spirals while living in a giant Spiral, then is it in a giant Spiral, then is it possible that everything we possible that everything we put our hands to is infused put our hands to is infused with the Spiral?"with the Spiral?"

-- Max Cohen in the motion picture PI -- Max Cohen in the motion picture PI

Now here’s Now here’s real real a a ““PARADOXPARADOX”…”…

But first, a But first, a realreal “ “Pair Pair o’ Docks”…o’ Docks”…

What is the difference What is the difference between…between…




the truth the truth andand



the truth the truth

andand TTruthruth ? ?

The eternal The eternal paradoxparadox of literature: of literature:

Art Art always tells always tells the the TruthTruth


John Malkovich as himself in John Malkovich as himself in Being John MalkovichBeing John Malkovich19991999

Art Art always tells always tells the the TruthTruth

even when even when it’s lying.it’s lying.


What’s What’s TTruerue

need not need not be true.be true.


Although a story Although a story is fictional…is fictional…

Its THEME is Its THEME is always True.always True.

THEMETHEME

equalsequals

TruthTruth

EPISTEMOLOGY

EPISTEMOLOGY

When reading

literature…

Art Says…

Truth doesn’t come easily.

Art Says…

Using your

powers of inference

…

Art Says…

…you have to “urn”

it.

Art Says…

What we What we obtain obtain

too too cheap, cheap,

we we esteem esteem

too too lightly.lightly.

ThomasPaine Says…

(1737-1809)(1737-1809)Writer and Revolutionary Writer and Revolutionary

Authors rarely come

right out and TELL you the story’s

THEME.

Art Says…By imagining, struggling, sympathizin

g, as we read, we make the life lesson

more personally

meaningful .

AND more memorable.

Art Says…

Greek Power Point1.4 Segment 3

Entertainment & Humor

Transcript of Greek Power Point1.4 Segment 3