This is PHYS 1240 - Sound and Music

Lecture 17

Tricia and Tyler!

Cell Phones silent

Clickers on

Physics 1240 Lecture 17

Today: Scales, Intensity,Decibels

Next time: Intensity, Loudness,Hearing

physicscourses.colorado.edu/phys1240

Canvas Site: assignments, administration, grades

Homework – HW7 due Wed March 11th 5pm

Homelabs – Hlab4 due March 16th

• (Pick up at the end of class)

Midterm

Review

Octave

(2/1)

12

Perfect

Fifth

(3/2)

7

Perfect

Fourth

(4/3)

5

Major

Third

(5/4)

4

minor

Third

(6/5)

3

Major

Second

(9/8)

2

minor

Second

(16/15)

1

…………

(frequency ratio):

# half steps:

Review

Questions:

1) Why does a piano have 12 notes in each octave?

2) How do we tune those 12 notes (how do we decide what frequencies to

assign to each note)?

• Just Tuning: uses only pure, harmonic intervals

• Pros: all pure intervals from C

• Cons: can only play in one key

• Pythagorean Tuning: makes all fifths pure (3/2)

• Pros: all fifths are pure

• Cons: Pythagorean comma

• Equal Temperament: same interval for all half steps

• Pros: can play in any key

• Cons: all intervals are very slightly dissonant

Note

name:C D E F G A B C

Just

Frequency

ratio to C:

1

1

9

8

5

4

4

3

3

2

5

3

15

8

2

1

Pythagorean1

1

9

8

81

64

4

3

3

2

27

16

243

128

2.03?

1

Equal-

Tempered

1

1 2112

2

2112

4

2112

5

2112

7

2112

9

2112

11 2

1

• Any musical system has to balance two competing ideas:

1) Minimizing dissonance

(the more notes, the closer the intervals and the more beats there are)

2) Giving enough complexity to make it interesting

(the fewer notes there are, the less ways you can combine them to form

harmonies)

But why 12 notes?

György Ligeti –

Musica Ricercata

mvmt. I (1969)

Ivan Wyschnegradsky –

24 Preludes in quarter-

tone system, Op. 40,

mvmt. XXI (1934/70)

Systems with <12 notes

• Pentatonic scale

• Major pentatonic: black keys on piano

(e.g. Camptown Races, Mary Had a Little Lamb)

• Minor pentatonic: simple blues scale

• Equal-tempered pentatonic:

• Other:

• Javanese Gamelan - slendro tuning

12 notes is special!

• Twelve-note equal temperament: 122

7−

3

2is small

Systems with > 12 notes

• 43 unequal tones:

https://www.youtube.com/watch?v=tv

6V4m_kV2A

• 106 equal tones:

https://www.youtube.com/watch?v=a

Rw9fCQIn6Q

• 24 tones:

https://www.youtube.com/watch?v=0

akGtDPVRxk

Indian Classical Music

• About 150 different microtonal scales (called “ragas”)

• Sa Re Ga Ma Pa Dha Ni

• No fixed base frequency

Indian Classical Music

https://www.youtube.com/watch?v=99i5rb2Je_8

Student performance

• Ethan Wang, piano

Intensity

Intensity is the amount of energy hitting a certain area in a certain time

Intensity is proportional to the square of the pressure amplitude

• If we double the amplitude, then we quadruple the intensity

I = 0.01 W/m2

I = 0.04 W/m2

Sound Intensity

O when the Saints!

Go marching in!

Remember – air molecules do not move along with wave but

oscillate – What is transferred is energy - Sound carries energy.

Intensity is

Intensity =energy

time∙area=

𝑃𝑜𝑤𝑒𝑟

area(Energy = power * time)

joules

seconds ∙ meters2=

watts

meters2=

𝑊

m2

Clicker 17.1

We measure the intensity of the sound coming from two sources.

Source 1 is at 1 W/m2 and Source 2 is at 4 W/m2

The amplitude of the sound wave from Source 2 is:

a) 2 times larger than that from Source 1

b) 4 times larger than that from Source 1

c) 8 times larger than that from Source 1

Clicker 17.1 A

We measure the intensity of the sound coming from two sources.

Source 1 is at 1 W/m2 and Source 2 is at 4 W/m2

The amplitude of the sound wave from Source 2 is:

a) 2 times larger than that from Source 1

b) 4 times larger than that from Source 1

c) 8 times larger than that from Source 1

Inverse square law

Doubling distance from the source changes intensity by factor of 1/4

Tripling distance changes intensity by factor of 1/9

Remember – looking at power/area (same effect – double distance from a light bulb)

Will come back to this when cover decibels

I ∝1

𝑟2

Clicker 17.2

A light bulb is not strong enough for reading when you are 32 meters away. If you need the intensity to be 16 times higher how close do you need to be to the bulb?

a) 1 m

b) 2 m

c) 4 m

d) 8 m

e) 16 m

Clicker 17.2 D

A light bulb is not strong enough for reading when you are 32 meters away. If you need the intensity to be 16 times higher how close do you need to be to the bulb?

a) 1 m

b) 2 m

c) 4 m

d) 8 m (intensity 4 times higher than at 16m)

e) 16 m (intensity 4 times higher if halve)

I ∝1

𝑟2

so I22 = 16 I1 ;

16 = I2/I1 = r211/r

22

so r2 = r1/ (sqrt (16))

Formula for

Sound Intensity Level

SIL (dB)

If the SIL of a sound is 0 dB (at the threshold of hearing) we call this 0 dB SIL sound intensity I0

I0 = 1x10-12 W/m2

SIL (dB) = 10 x log( I / I0)

Sound Levels