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Lecture 4. Acoustics Musical Instruments The Elements of Music. Lecture 4. Acoustics. … from the Greek akoustikos … which means … “hearing”. Acoustics. Pythagorean proportions (review). Pythagoras observed relationships between:

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lecture 4

Lecture 4

Acoustics

Musical Instruments

The Elements of Music

acoustics

Lecture 4

Acoustics

… from the Greek akoustikos

… which means …

“hearing”

pythagorean proportions review

Acoustics

Pythagorean proportions (review)

Pythagoras observed relationships between:

musical intervals that are naturally “contained” within vibrating objects and

simple mathematical proportions

pythagorean proportions review1

Acoustics

Pythagorean proportions (review)

Pythagoras observed relationships between:

musical intervals that are naturally “contained” within vibrating objects and

simple mathematical proportions

observations

Acoustics

Pythagorean proportions (review)

Observations:

A simple flute “overblows” at the:

octave

the fifth above that

the fourth above that

the major third above that

the minor third above that

observations1

Acoustics

Pythagorean proportions (review)

Observations:

A simple flute “overblows” at the:

octave

the fifth above that

the fourth above that

the major third above that

the minor third above that

observations2

Acoustics

Pythagorean proportions (review)

Observations:

A simple flute “overblows” at the:

octave

the fifth above that

the major third above that

the fourth above that

the minor third above that

do re mi fa sol la ti do

observations3

Acoustics

Pythagorean proportions (review)

Observations:

A simple flute “overblows” at the:

octave

the fifth above that

the fourth above that

the major third above that

the minor third above that

octave

do re mi fa sol la ti do

observations4

Acoustics

Pythagorean proportions (review)

Observations:

A simple flute “overblows” at the:

octave

the fifth above that

the fourth above that

the major third above that

the minor third above that

fifth

octave

do re mi fa sol la ti do

observations5

Acoustics

Pythagorean proportions (review)

Observations:

A simple flute “overblows” at the:

octave

the fifth above that

the fourth above that

the major third above that

the minor third above that

fourth

fifth

octave

do re mi fa sol la ti do

observations6

Acoustics

Pythagorean proportions (review)

Observations:

major third

A simple flute “overblows” at the:

octave

the fifth above that

the fourth above that

the major third above that

the minor third above that

fourth

fifth

octave

do re mi fa sol la ti do

observations7

Acoustics

Pythagorean proportions (review)

Observations:

minor third

major third

A simple flute “overblows” at the:

octave

the fifth above that

the fourth above that

the major third above that

the minor third above that

fourth

fifth

octave

do re mi fa sol la ti do

another observation

Acoustics

Pythagorean proportions (review)

Another observation:

minor third

major third

Trumpet-like instruments sound at:

octave

the fifth above that

the fourth above that

the major third above that

the minor third above that

fourth

fifth

octave

do re mi fa sol la ti do

yet another observation

Acoustics

Pythagorean proportions (review)

Yet another observation:

minor third

major third

String “harmonics” sound at:

octave

the fifth above that

the fourth above that

the major third above that

the minor third above that

fourth

fifth

octave

do re mi fa sol la ti do

still another observation

Acoustics

Pythagorean proportions (review)

Still another observation:

minor third

major third

Cavity “harmonics” sound at:

octave

the fifth above that

the fourth above that

the major third above that

the minor third above that

fourth

fifth

octave

do re mi fa sol la ti do

pythagorean proportions review2

Acoustics

Pythagorean proportions (review)

Pythagoras used his monochord to produce musical intervals based on the proportions:

1:1 = unison

2:1 = octave

3:2 = fifth

4:3 = fourth

followers of pythagoras extended the process to include musical intervals based on the proportions

Acoustics

Pythagorean proportions (review)

Followers of Pythagoras extended the process to include musical intervals based on the proportions:

  • 1:1 = unison
  • 2:1 = octave
  • 3:2 = fifth
  • 4:3 = fourth

5:4 = major third

6:5 = minor third

9:8 = major second

10:9 = major second

16:15 = minor second

why should this be so why should natural vibrations match up so neatly with simple proportions

Acoustics

Pythagorean proportions (review)

Why should this be so?Why should “natural” vibrations match up so neatly with simple proportions?

monochord

why should this be so why should natural vibrations match up so neatly with simple proportions1

Acoustics

Pythagorean proportions (review)

Why should this be so?Why should “natural” vibrations match up so neatly with simple proportions?

monochord

monochord

Acoustics

Pythagorean proportions (review)

monochord

2

divided by 2 creates:

the octave (2:1)

1

monochord1

Acoustics

Pythagorean proportions (review)

monochord

3

divided by 3 creates:

the fifth (3:2)

2

monochord2

Acoustics

Pythagorean proportions (review)

monochord

3

3

divided by 3 creates:

the fifth (3:2) – above the “fundamental”

2

2

monochord3

Acoustics

Pythagorean proportions (review)

monochord

3

3

divided by 3 creates:

the fifth (3:2) – above the “fundamental”

the fifth (3:2) above the octave

2

2

monochord4

Acoustics

Pythagorean proportions (review)

monochord

2

divided by 4 creates:

the octave (2:1) above the octave (the “double octave”)

1

monochord5

Acoustics

Pythagorean proportions (review)

monochord

5

divided by 5 creates:

the fourth (5:4) ???????

4

monochord6

Acoustics

Pythagorean proportions (review)

monochord

5

5

divided by 10 creates:

the fourth (5:4) above the “double octave”

4

4

the vibrating object

Acoustics

Pythagorean proportions (review)

The vibrating object …

… vibrates simultaneously at all these “divisions.”

the vibrating object1

Acoustics

Pythagorean proportions (review)

The vibrating object …

… vibrates simultaneously at all these “divisions.”

the small vibrations contained within the single large vibration are called

Acoustics

Pythagorean proportions (review)

The “small” vibrations contained within the single “large” vibration are called …

partials

overtones

harmonics

slide30

Acoustics

Pythagorean proportions (review)

The “partial” vibrations, or “overtones,” occur in all vibrating objects.But they will be heard as “tones” only if:

the “object” is consistent in material, density, and tension

the energy that triggers the vibration is steady

slide31

Acoustics

Pythagorean proportions (review)

The “partial” vibrations, or “overtones,” occur in all vibrating objects.But they will be heard as “tones” only if:

the “object” is consistent in material, density, and tension

the energy that triggers the vibration is steady

slide32

Acoustics

Pythagorean proportions (review)

The “partial” vibrations, or “overtones,” occur in all vibrating objects.But they will be heard as “tones” only if:

Otherwise, the mix of vibrations will be heard as “noise.”

  • the “object” is consistent in material, density, and tension
  • the energy that triggers the vibration is steady
among the vibrating objects that might produce audible overtones are

Acoustics

Pythagorean proportions (review)

Among the “vibrating objects” that might produce audible overtones are:

automobile, motorcycle and airplane engines

the body of an automobile as it moves on a highway

the “squeaky” brakes of a car or truck

the air contained within a room

electrical power lines

water moving through pipes

musical instruments

musical instruments

Musical Instruments

“instrument”

… from the Latin instrumentum, meaning “tool”

n. 1. A means by which something is done; agency. 2a. One used to accomplish some purpose. b. a person used and controlled by another; dupe. 3. A mechanical implement. 4. A device for recording or measuring … . 5. A device for producing music. 6. A legal document.

American Heritage Dictionary

musical instruments1

Musical Instruments

“instrument”

… from the Latin instrumentum, meaning “tool”

n. 1. A means by which something is done; agency. 2a. One used to accomplish some purpose. b. a person used and controlled by another; dupe. 3. A mechanical implement. 4. A device for recording or measuring … . 5. A device for producing music. 6. A legal document.

American Heritage Dictionary

three basic types

Musical Instruments

three basic types:

wind instruments

string instruments

percussion instruments

wind instruments

Musical Instruments

wind instruments

three basic types:

  • string instruments
  • percussion instruments

air column activated by:

buzzing lips

vibrating reeds

movement of wind across a sharp edge

string instruments

Musical Instruments

string instruments

three basic types:

  • wind instruments
  • string instruments
  • percussion instruments

string set in motion by:

bowing

plucking or strumming

striking

wind

percussion instruments

Musical Instruments

percussion instruments

three basic types:

  • wind instruments
  • string instruments
  • percussion instruments

materials set in vibrational motion by:

striking

rubbing

plucking

shaking

buzzing lips vibrating reeds movement of wind across a sharp edge

Musical Instruments

•buzzing lips• vibrating reeds• movement of wind across a sharp edge

Wind instruments activated by:

trumpet

trombone

French horn

tuba

bugle

buzzing lips vibrating reeds movement of wind across a sharp edge1

Musical Instruments

•buzzing lips• vibrating reeds• movement of wind across a sharp edge

Wind instruments activated by:

commonly known as “brass” instruments

  • trumpet
  • trombone
  • French horn
  • tuba
  • bugle
buzzing lips vibrating reeds movement of wind across a sharp edge2

Musical Instruments

•buzzing lips• vibrating reeds• movement of wind across a sharp edge

Wind instruments activated by:

conch shell

shofar

didjeridoo

garden hose

  • trumpet
  • trombone
  • French horn
  • tuba
  • bugle
the basic sound of these instruments is determined by

Musical Instruments

The basic sound of these instruments is determined by:

Wind instruments activated by:

  • buzzing lips• vibrating reeds• movement of wind across a sharp edge

shape of the air column

the amount of “noise” that is part of the blowing process

the pitch of these instruments is determined by

Musical Instruments

The pitch of these instruments is determined by:

Wind instruments activated by:

  • buzzing lips• vibrating reeds• movement of wind across a sharp edge

the tension of the vibrating lips

the length of the air column

buzzing lips vibrating reeds movement of wind across a sharp edge3

Musical Instruments

• buzzing lips•vibrating reeds• movement of wind across a sharp edge

Wind instruments activated by:

clarinet

saxophone

oboe

bassoon

buzzing lips vibrating reeds movement of wind across a sharp edge4

Musical Instruments

• buzzing lips•vibrating reeds• movement of wind across a sharp edge

Wind instruments activated by:

single reed

  • clarinet
  • saxophone
  • oboe
  • bassoon
buzzing lips vibrating reeds movement of wind across a sharp edge5

Musical Instruments

• buzzing lips•vibrating reeds• movement of wind across a sharp edge

Wind instruments activated by:

double reed

  • clarinet
  • saxophone
  • oboe
  • bassoon
buzzing lips vibrating reeds movement of wind across a sharp edge6

Musical Instruments

• buzzing lips•vibrating reeds• movement of wind across a sharp edge

Wind instruments activated by:

some organ pipes

harmonica

a blade of grass

  • clarinet
  • saxophone
  • oboe
  • bassoon
the basic sound of these instruments is determined by1

Musical Instruments

The basic sound of these instruments is determined by:

Wind instruments activated by:

  • buzzing lips•vibrating reeds• movement of wind across a sharp edge

the nature of the reed (“closed” or “open”)

the amount of “noise” featured in the blowing process

the shape of the air column (conical or cylindrical)

the “overtones” contained in the vibrating air column

the pitch of these instruments is determined by1

Musical Instruments

The pitch of these instruments is determined by:

Wind instruments activated by:

  • buzzing lips•vibrating reeds• movement of wind across a sharp edge

the length of the air column

the activation of “overtones”

NOTE: a “closed” cone produces all the overtones, but a “closed” cylinder producesonly the odd-numbered overtones.

buzzing lips vibrating reeds movement of wind across a sharp edge7

Musical Instruments

buzzing lips• vibrating reeds•movement of wind across a sharp edge

Wind instruments activated by:

flute

piccolo

shakuhachi

recorder

penny whistle

buzzing lips vibrating reeds movement of wind across a sharp edge8

Musical Instruments

buzzing lips• vibrating reeds•movement of wind across a sharp edge

Wind instruments activated by:

transverse flutes

  • flute
  • piccolo
  • shakuhachi
  • recorder
  • penny whistle
buzzing lips vibrating reeds movement of wind across a sharp edge9

Musical Instruments

buzzing lips• vibrating reeds•movement of wind across a sharp edge

Wind instruments activated by:

end-blown flutes

  • flute
  • piccolo
  • shakuhachi
  • recorder
  • penny whistle
buzzing lips vibrating reeds movement of wind across a sharp edge10

Musical Instruments

buzzing lips• vibrating reeds•movement of wind across a sharp edge

Wind instruments activated by:

fipple flutes

  • flute
  • piccolo
  • shakuhachi
  • recorder
  • penny whistle
buzzing lips vibrating reeds movement of wind across a sharp edge11

Musical Instruments

buzzing lips• vibrating reeds•movement of wind across a sharp edge

Wind instruments activated by:

some organ pipes

the “coke bottle”

“swinging tubes”

ocarinas

nose flutes

  • flute
  • piccolo
  • shakuhachi
  • recorder
  • penny whistle
the basic sound of these instruments is determined by2

Musical Instruments

The basic sound of these instruments is determined by:

Wind instruments activated by:

  • buzzing lips• vibrating reeds•movement of wind across a sharp edge

the amount of “noise” featured in the blowing process

the “overtones” contained in the vibrating air column

the pitch of these instruments is determined by2

Musical Instruments

The pitch of these instruments is determined by:

Wind instruments activated by:

  • buzzing lips• vibrating reeds•movement of wind across a sharp edge

the length of the air column

the activation of “overtones”

NOTE: an “open” cylinder produces all the overtones.

string instruments activated by

Musical Instruments

String instruments activated by:

bowing• plucking or strumming• striking• wind

bowing plucking or strumming striking wind

Musical Instruments

bowing• plucking or strumming• striking• wind

String instruments activated by:

violin

viola

cello

double bass

bowing plucking or strumming striking wind1

Musical Instruments

bowing• plucking or strumming• striking• wind

String instruments activated by:

guitar

banjo

ukulele

lute

harpsichord

bowing plucking or strumming striking wind2

Musical Instruments

bowing• plucking or strumming•striking• wind

String instruments activated by:

hammer dulcimer

piano

bowing plucking or strumming striking wind3

Musical Instruments

bowing• plucking or strumming• striking•wind

String instruments activated by:

the “aeolian harp”

the basic sound of these instruments is determined by3

Musical Instruments

The basic sound of these instruments is determined by:

String instruments activated by:

  • bowing• plucking or strumming• striking• wind

the nature of the vibrating string

the nature (shape, material) of the “resonator”

the amount of “noise” featured in the activation process

the pitch of these instruments is determined by3

Musical Instruments

The pitch of these instruments is determined by:

String instruments activated by:

  • bowing• plucking or strumming• striking• wind

the density of the vibrating string

the tension of the vibrating string

the length of the vibrating string

striking rubbing plucking shaking

Musical Instruments

• striking• rubbing • plucking• shaking

Percussion instruments activated by:

instruments with vibrating “membranes”

(“membranophones”)

instruments whose entire structure vibrates

(“idiophones” – from the Gr. idio, meaning “self”)

Two basic types:

membranophones idiophones

Musical Instruments

• membranophones• idiophones

Percussion instruments activated by:

• striking• rubbing • plucking• shaking

membranophones idiophones1

Musical Instruments

•membranophones• idiophones

Percussion instruments activated by:

• striking• rubbing • plucking• shaking

drums

membranophones idiophones2

Musical Instruments

•membranophones• idiophones

Percussion instruments activated by:

• striking• rubbing • plucking• shaking

single-headed drums

“open”

“closed

double-headed drums

  • drums
the basic sound of these instruments is determined by4

Musical Instruments

The basic sound of these instruments is determined by:

Percussion instruments activated by:

• striking• rubbing • plucking• shaking

•membranophones•idiophones

the nature of the vibrating membrane

“noise” factors

the nature of the “attack”

the nature of the resonating cavity

a “closed” drum produces a distinct pitch

a “double-headed” drum produces a great deal of “noise”

the pitch of these instruments is determined by4

Musical Instruments

The pitch of these instruments is determined by:

Percussion instruments activated by:

• striking• rubbing • plucking• shaking

•membranophones•idiophones

the nature of the vibrating membrane

the size and density of the vibrating membrane

the size and shape of the resonating cavity

membranophones idiophones3

Musical Instruments

• membranophones•idiophones

Percussion instruments activated by:

• striking• rubbing • plucking• shaking

bells

cymbals

xylophones

from Gr. xylon, meaning “wood”

kalimbas (“thumb piano”)

membranophones idiophones4

Musical Instruments

• membranophones•idiophones

Percussion instruments activated by:

• striking• rubbing • plucking• shaking

rattles

shakers

rain stick

  • bells
  • cymbals
  • xylophones
    • from Gr. xylon, meaning “wood”
  • kalimbas (“thumb piano”)
the basic sound of these instruments is determined by5

Musical Instruments

The basic sound of these instruments is determined by:

Percussion instruments activated by:

• striking• rubbing • plucking• shaking

• membranophones•idiophones

the nature of the vibrating material

density, consistency

the nature of the “attack”

intensity, nature of the “attacking” material

the pitch of these instruments is determined by5

Musical Instruments

The pitch of these instruments is determined by:

Percussion instruments activated by:

• striking• rubbing • plucking• shaking

• membranophones•idiophones

the nature of the vibrating material

the size and density of the vibrating object