The Science of Music - PowerPoint Presentation

Slide1

The Science of Music

Dr. David Hamrick

Zale Library at Paul Quinn College

16 November 2012Slide2

What is Sound?

Sound is a mechanical wave

It moves through a medium

Like waves in waterOr earthquakes through the groundWe usually think of air as the mediumCan travel through other gasesCan travel through liquidsCan travel through solids (varies depending on material)Why does helium make your voice sound higher?Helium is a lower-density mediumMore on this later! Slide3

What is Sound?

Sound is a compression wave

Vibrating body transfers energy to medium

Medium is compressed, then releasedThe “wave” is really a series of high and low pressure areasIt’s easier to represent this as a 2-D wave

The Speed of Sound

Density of the medium determines how fast it can compress/decompress

The average density of air allows a wave to travel about 768 mph

Helium’s lower density allows sound to travel 3x faster!Slide4

Measuring the Wave

Wave =

Complete cycle of compression/decompression

In a 2D representation, 2 points at same place in the cycleUsually measured from midpoint to midpointSlide5

Measuring the Wave

Frequency = Number of waves per second

Measured in “

Herz” (Hz), “kiloHertz” (kHz), megaHertz (mHz)In musical terms this is called “pitch”We call shorter waves (high frequency) “high” pitchesWe call longer waves (low frequency) “low” pitchesSlide6

Measuring the Wave

Amplitude = Intensity of each wave (power exerted)

In the image below, the frequency (pitch) remains the same while the amplitude (volume) increases and decreases

Measured in “decibels”Zero decibels (0 dB) is just below range of human hearingThe decibel scale is logarithmic, not linearEvery 10 decibels describes 10x power increase20 dB is not twice as loud as 10 dB, it is 10x as loud!In musicals terms this is called volume or dynamicsSlide7

Measuring the Wave

Radio works by modulating

either frequency or amplitude

Radio waves are electromagnetic, not mechanical, but described the same

Amplitude Modulation (AM) =

Constant frequency

Changing amplitude

Frequency Modulation (FM) =

Constant amplitude

Changing frequency

Also much higher frequency than AM

Shorter waves make FM signal easier

to bounce around corners, inside buildings

AM limited by amount of amplitude change you can force

FM carries more complex signals (stereo & quadrophonic)Slide8

What We Can Hear

Human hearing can detect an amazing range of amplitude

Normal conversation (about 50 dB) has an amplitude 1,000x the hearing threshold (0-1 dB)

Jet engine (about 100 dB) has an amplitude 100,000x the thresholdHuman hearing can also detect a wide range of frequenciesAbout 20 Hz to 20 kHz is the typical rangeLowest note on piano (A0) is 27.5 Hz; highest (C8) is 4.2 kHzAnimal hearing can go far beyond ours!

Most dogs hear about 40 Hz to 60 kHz (about 3x human range)

Bats use echolocation calls at frequencies up to 150 kHz

Baleen whales vocalize at about 10-30 Hz, at up to 80 decibels!Slide9

Music or Noise? The Role of Harmonics

Almost all sounds are a mix of a large number of frequencies

A sound made of a single-frequency wave sounds artificial

So what is the difference between a musical tone and noise?The musical tone has a regular frequencyThe musical tone is composed of waves that fit together easilySlide10

Music or Noise? The Role of Harmonics

How frequencies fit together in a musical pitch

Which wave is the loudest? Which has the highest pitch?

What is the ratio or proportion between the two frequencies?Why doesn’t it make two different notes?The wave with greatest amplitude will sound like the “real” noteThe shorter wave fits within the longer wave and reinforces itSee examples at UNSW Physclips: adding harmonics

,

composite toneSlide11

The Harmonic Series

Harmonics: frequencies that naturally combine as a musical pitch

Discovered by Pythagoras in the 6

th century B.C.(?)The lowest tone (longest frequency) is called the “fundamental”Each harmonic is a multiple of that fundamental’s frequency

First Five Harmonics of the Pitch A

0

Pitch name

Frequency

Interval above previous pitch

E3 (two octaves & 5

th

)

165

Hz

Minor 3

rd

C#

3

(two octaves & major 3

rd

)

137.5

Hz

Major 3

rd

A

2

(two octaves)

110 HzPerfect 4thE1 (octave & 5th)

82.5 Hz

Perfect 5

th

A

1

(one octave higher)

55 Hz

Octave

A

0

(lowest A on grand piano)

27.5 Hz

(Fundamental)Slide12

The Harmonic Series

This video shows a real-world demonstration using an oscilloscopeSlide13

The Role of Harmonics in Timbre

“Timbre” is the quality of a musical pitch

What is the difference between a middle “C” played on a piano, or sung by a woman, or sung by a man?

Same fundamental pitch, different combination of harmonicsWhy does your own voice sound funny in a recording?You are used to hearing your voice through two media:Through the surrounding air, into your earsThrough your own head (conductive hearing)A recording device is only recording the sound in the airThe recording device is limited to the frequencies it can detectThe playback device is limited to the frequencies it can reproduceExample: telephone audio is only 300 Hz to 3.4 kHz (saves bandwidth!)Slide14

What is Harmony?

Combination of two or more different notes at once

Distance between two notes is the “interval”

Combination of intervals (3 or more notes) is a chordWhich ones sound good? Why?We tend to prefer the intervals at the beginning of the harmonic seriesSimpler ratios; harmonics of each note clash lessSlide15

What is Harmony?

The first interval is called the octave (8

va

)Frequency ratio is 2:1 (top note 2x frequency of lower note)Harmonics of each note are the same—sound like same noteMost universal interval in all music (men, women sing together at 8va)Scales repeat at the octave (start the series of notes over again)In letter notation, each note of an octave is same letter (low C, high C)Slide16

What is Harmony?

The next two intervals are the 5

th

and 4th (2-3, 3-4 in chart)After the octave, these are the most universal intervalsMost scales split the octave with a step at this point (3 in chart)5 steps from bottom to top notes of 5th (2-3 in chart)4 steps from bottom to top notes of 4th (3-4 in chart)Many kinds of folk music use the octave, 5th

, and 4

th

as harmony

5

th

is a 3:2 ratio (frequency of top note is 1½x that of lower note)

4

th

is a 4:3 ratio (frequency of top note is 1

1

/

3

x that of lower note)Slide17

The Octave, Fifth, and Fourth

Instruments using this combination go back to ancient times!Slide18

The Octave, Fifth, and Fourth

The drone pipes on bagpipes are tuned to make this combination:Slide19

The Octave, Fifth, and Fourth

In Indian

raga

music the tambura plays this combination as accompaniment to the sitar soloistSlide20

The Octave, Fifth, and Fourth

The Western tradition of harmony began during the Middle Ages with the use of these intervals:Slide21

The Major and Minor Thirds

The next intervals up the harmonic series are the 3rds

These come in two sizes: major (4-5 on chart) and minor (5-6 on chart)

Both called 3rds because take up three notes in scale (C-D-E, E-F-G)The major 3rd has a 5:4 ratio (frequency of top note is 1¼x that of lower)The minor 3rd has a 6:5 ratio (frequency of top note is 11/5x that of lower)Slide22

The Major and Minor Thirds

The major chord

Major 3

rd joined with minor 3rd (4-5-6 in chart)Why do we like this sound?It occurs naturally in the harmonic seriesThe middle note splits the difference in frequencies of the outer two…Just like the 5th splits the difference in frequencies in an octaveSlide23

Where to next?

At this point in the harmonic series, cultures took different paths

Some notes in the harmonic series weren’t used in Western music

Notes marked in blue in the chart are too flat (low) to fit into our scalesThe note marked in red is too sharp (high)Obviously the intervals involving these notes won’t fit eitherThis is a cultural preference (and matter of conditioning!)Music of Middle East, Southeast Asia has used these notes & intervalsSeveral different sizes of 3

rd

and 2

nd

, not just major and minor

Most music cultures have preferred a simpler system!Slide24

The Major and Minor Seconds

L

ast two intervals we need are the seconds (two adjacent notes)

Western music uses sizes most common in upper end of the harmonic seriesMajor 2nd (8-9 on chart)Commonly called a “whole step”Interval 9-10 is almost a major 2nd but is a little flatMinor 2nd (15-16, 16-17, 17-18, 18-19)

Commonly

called a “half

step”

Intervals on high end of the series are actually successively smaller, but the differences are within the threshold of our ability to detectSlide25

Building Scales

What is a scale?

“Scale” is from the Italian “

scala,” and means “ladder”A way of climbing up and down in pitch during a melodyThe “rungs” of the ladder are the individual notesCan be fixed in many different positions!Modern Western music uses major and minorKarnatic (South Indian) music has 72 different melas

(scales)

In many musical cultures, certain scales are associated with certain moods

Common ground across cultures

Every theory of scales uses divisions of the octave (Impossible to avoid!)

Every(?) theory of scales splits the octave at the 5

th

Almost every scale is either 5 or 7 different notesSlide26

Building Scales

The Pentatonic (5-note) Scale

Found in folk music and children’s songs around the world

Also fundamental to blues, jazz, rock, pop musicMajor PentatonicMade of only 2 different intervals: major 2nd, minor 3rd Called “major” because of emphasis on major 3rd (DO-re-MI)Black keys on piano are arranged (by coincidence) in major pentatonicCommon arrangement is: maj. 2nd,

maj.

2

nd

, min. 3rd,

maj.

2

nd

, min. 3

rdSlide27

Major Pentatonic

These men are celebrating their safe return from fighting the 2009 La Brea forest fire in California.

The Irish

hymn

“

Rop

Tú

mo

Baile

”

(“

Be Thou my Vision

”) is

mostly

pentatonic.

Many (Most?) children’s songs use pentatonic scales. Note that the child is most in tune on the octave & 5

th

(bottom, middle, and top notes of the tune).Slide28

Another Form of Major Pentatonic

The same intervals can be ordered:

maj.

2nd, min. 3rd, maj. 2nd, maj. 2nd, min. 3rd

“

Arirang

” is a famous folk song in KoreaSlide29

Minor Pentatonic

Arranges intervals: min. 3

rd

, maj. 2nd, maj. 2nd, min. 3rd, maj. 2ndCalled “minor” because of emphasis on min. 3rd (LA-DO)Slide30

Blues Scale and the Minor Pentatonic

One of the earliest forms of the blues scale probably came from adding minor 2nds to the minor pentatonic.

Big Mama Thornton, “Hound Dog”

(the

original

version)Slide31

Minor Pentatonic using Minor 2

nd

Some minor pentatonic scales use minor 3rds, major 2nds, and minor 2nds

Particularly common to folk music of Southeast AsiaA common arrangement is: maj. 2nd, min. 2nd, min. 3rd, min. 2, min. 3rd

One form of the Japanese

hirajoshi

scale

This tune is “Sakura” or “Cherry blossom.”

The cherry tree is a national symbol of Japan.Slide32

Western Seven-Note Scales

European music based on 7-note combinations of major, minor 2nds

From ancient Greece through the Western Renaissance, there were several different 7-note scales or “modes”

In the modern period, most Western music uses just 2: major and minorSome folk and popular music still uses the older modes

C major scale

C minor scale

Maj.2

nd

Min.2

nd

Maj.2

nd

Maj.2

nd

Min.2

nd

Maj.2

nd

Maj.2

nd

Maj.2

nd

Maj.2

nd

Maj.2

nd

Min.2

nd

Maj.2

nd

Maj.2

nd

Min.2

ndSlide33

Western Seven-Note Scales

One of the other modes that turns up often is called “Dorian”

Like minor, except minor 2

nd moved from 5th-6th notes to 6th-7th notesCommon in folk music, rock, jazz

Appalachian hymn “Wondrous love”Slide34

Western Seven-Note Scales

Phrygian mode was common in the Renaissance, and was revived in modern jazz

Sounds neither major nor minor

(but leans toward minor)Unusual for having a minor 2nd above the key-note

Psalm tune by Thomas

Tallis

, 1567 Slide35

Middle Eastern & Indian Scales

Scales of the classical music of Middle East, India & Pakistan are based on smaller intervals than used in Western scales

Theoretically divides the octave into

quarter-steps, not half-stepsIn addition to min. 2nd (half-step) and maj. 2nd (whole-step) …¼-step¾-step1¼-stepThese intervals are also in the harmonic series, just not used in West

Concept of “scale” is more complicated

Still

7-note

scales,

but

many

different forms (not just major & minor)

Scale includes not just series of notes, but mood, style,

melody

ideasSlide36

Scales in the Middle East

Arabic

maq

ām (Turkish makam)Made by stacking two tetrachords (four-note groups)Lowest, highest notes are octave, really just 7 different notesUpper tetrachord usually starts a perfect 5th above octave

Many

maq

ā

m

, but some little

used

Best-known in the West is the “

Hijaz

”

Lower

tetrachord

is the “

Hijaz

” tuningSlide37

Scales in the Middle East

The “

Bayati

” maqāmLike a Western minor scale except…Uses two ¾-steps at the bottom instead of whole-step, half-stepThat is, the second note from lowest sounds ¼-step flat to WesternersIf this is not learned from childhood, difficult to hear, much less to sing!

Maj.2

nd

Maj.2

nd

¾

step

Maj.2

nd

Maj.2

nd

Min.2

nd

¾

stepSlide38

Scales in Indian Music

South Indian

Karnatic

tradition (other is Hindustani)Octave divided into 22 shruti (smallest perceptible difference in pitch?)Scale (mela) made of combining two tetrachords (as in Middle East)

“SA” and “PA” stay the same (octave and 5

th

!)

“MA” has a low position and a high position

“RI,” “GA,” “

DA

,” and “NI” each have a low, middle, and high position

Unlike Western music, a “RI sharp” is

not the same

as a “GA flat”Slide39

Scales in Indian Music

Mela

or

thaat (Hindustani) is the foundation for a ragaRaga is not only scale, but melodic ideas, style, mood, rhythmic patternsEach raga is associated with a time of day, sometimes also with a seasonConsidered inappropriate (even unlucky!) to play a raga at thewrong time

Improvisation is essential to

raga

, will never be played same way twice

Tansen

, the great 16

th

-century musician, was said to have made it rain by playing a

raga

for monsoon season!Slide40

Scales in Indian Music

Raag

KhamajBuilt on one of the scales common to the ancient Hindustani thaat and more modern Karnatic melasTo be played in the mid-eveningScale equivalent to:Major scale when ascending, but…7th note flatted when descending

Performance by Ravi Shankar (

sitar

) and his daughter

Anoushka

Shankar (

sitar

); player of

tabla

unidentified

This flat-7 scale is called “

Mixolydian

” in Western music.Slide41

Scales in Indian Music

This chart shows all 72

Karnatic

melas (all possible combinations of note positions)Slide42

From the simplest drone harmony to the most complex jazz chords, from the pentatonic scale to the 72

Karnatic

melas, everything comes back to the harmonic series. As different as our music is, it all has elements in common.THE ENDSlide43

Works Consulted

Sound waves and music

. The Physics Classroom.

http://www.physicsclassroom.com/class/sound/ Music acoustics. University of New South Wales. http://www.phys.unsw.edu.au/jw/basics.html “Hearing range.” Wikipedia. http://

en.wikipedia.org/wiki/Hearing_range

Physics of music notes: Frequencies for equal-tempered scale.

http

://www.phy.mtu.edu/~

suits/notefreqs.html

“What is the frequency response of the NAPSTN?”

Hubtechinsider

.

http

://hubtechinsider.wordpress.com/2009/06/03/what-is-the-frequency-response-of-the-north-american-public-switched-telephone-network

/

Courtney, David. “Rag

Khammaj

(

Khamaj

).”

Indian Classical Music

.

http://

chandrakantha.com/raga_raag/khammaj/khammaaj.html

Slide44

Image Credits

http://

commons.wikimedia.org/wiki/File:Ripple_effect_on_water.jpg

http://commons.wikimedia.org/w/index.php?title=File:CPT-sound-physical-manifestation.svg&page=1http://commons.wikimedia.org/wiki/File:Wave_frequency.gifhttp://commons.wikimedia.org/wiki/File:Modulation_d%27amplitude_figure_2.2.1.3.pnghttp

://

commons.wikimedia.org/wiki/File:Amfm3-en-de.gif

http://

images.tutorvista.com/content/waves/noise-music.gif

http://

commons.wikimedia.org/wiki/File:Aulos_player_MAR_Palermo_NI22711.jpg

http://

en.wikipedia.org/wiki/File:C_major_pentatonic_scale.PNG

http://

upload.wikimedia.org/wikipedia/commons/0/08/Green_harp_flag_of_Ireland.svg

http://

commons.wikimedia.org/wiki/File:C_major_scale.PNG

http://

commons.wikimedia.org/wiki/File:C_minor_pentatonic_scale.png

http://

commons.wikimedia.org/wiki/File:Aeolian_mode_C.png

http://

commons.wikimedia.org/wiki/File:Dorian_mode_C.png

http://

upload.wikimedia.org/wikipedia/commons/c/ca/Hijaz_scale.png

http://

en.wikipedia.org/wiki/File:Bayati.png

http://

commons.wikimedia.org/wiki/File:Akbar_and_Tansen_visit_Haridas.jpg

http://commons.wikimedia.org/wiki/File:Melakarta.katapayadi.sankhya.72.png“Rop Tú mo Baile

”

sung by Gareth Hughes.

http

://

en.wikipedia.org/wiki/File:Rop_tu_mo_baile.ogg