Final ReviewFinal Review

1.1. Same interval means the same ratio of Same interval means the same ratio of frequenciesfrequencies

2.2. Doubling the frequency gives the same Doubling the frequency gives the same pitch sensationpitch sensation

In Western music the pitch range from f to 2f is In Western music the pitch range from f to 2f is split in 12 stepssplit in 12 steps

(entirely cultural)(entirely cultural)

ff

ff00 2 f2 f00

C, C#/Db, D, D#/Eb, E, E#, Fb, F, F#/Gb, G, G#/Ab, A, C, C#/Db, D, D#/Eb, E, E#, Fb, F, F#/Gb, G, G#/Ab, A, A#/Bb, BA#/Bb, B

semitone

CC

C# D D# E F F# G G# A A# B CC# D D# E F F# G G# A A# B Cminor minor

22ndnd major major

22ndnd minor minor

33rdrd major major

33rdrd 44thth tritonetritone 55thth minor minor

66thth major major

66thth minor minor

77thth major major

77thth

Consonances: sensation of calm and reposeConsonances: sensation of calm and repose

Frequency ratios nameFrequency ratios name

2/1 octave (7 tones)2/1 octave (7 tones) 3/2 fifth (3 ½ tones)3/2 fifth (3 ½ tones) 4/3 forth (2 ½ tones)4/3 forth (2 ½ tones) 5/4 major third (2 tones)5/4 major third (2 tones)

Dissonances: sensation of tensionDissonances: sensation of tension

Frequency ratios nameFrequency ratios name

729/512 tritone729/512 tritone

243/128 minor second243/128 minor second

Equal temperamentEqual temperament

C C# D D# E F F# G G# A A# B CC C# D D# E F F# G G# A A# B C

rr

12 122 2 1.05946...r r

rr22

rr1212=2=2

ReverberationReverberation

direct direct soundsound

reflected reflected soundssounds

Room AcousticsRoom Acoustics

Acoustics characteristics of auditoriumsAcoustics characteristics of auditoriums

““liveness” : liveness” : reverberation timereverberation time

““intimacy”: intimacy”: time to the first reflected sound to arrivetime to the first reflected sound to arrive

““fullness/clarity”: fullness/clarity”: direct sound versus reflected sound direct sound versus reflected sound volumevolume

““warmth/brilliance”:warmth/brilliance”: reverberation time for low reverberation time for low frequencies larger/smaller than for high frequenciesfrequencies larger/smaller than for high frequencies

We want lots of resonances, evenly spread in the We want lots of resonances, evenly spread in the frequency (no favored frequencies)frequency (no favored frequencies)

Dimension

Design #1

Design #2

Design #3

Width

1.14 x Height

1.28 x Height

1.60 x Height

Length

1.39 x Height

1.54 x Height

2.33 x Height

Dimension

Design #1

Design #2

Design #3

Width

1.14 x Height

1.28 x Height

1.60 x Height

Length

1.39 x Height

1.54 x Height

2.33 x Height

8-ft high, 16-ft wide, 8-ft high, 16-ft wide, and 16 ft long and 16 ft long

10.89-ft high, 12.4-ft 10.89-ft high, 12.4-ft wide, and 15.14 ft long wide, and 15.14 ft long

Calculation of reverberation time (engineer style)Calculation of reverberation time (engineer style)

55.2 0.050Rs

V VT

v A A

volume (ftvolume (ft33))

absorption (ftabsorption (ft22))

A is the sum over all absorbing surfacesA is the sum over all absorbing surfaces

reverberation time (s)reverberation time (s)

Example:Example:

13ft by 20ft by 8ft room13ft by 20ft by 8ft room

4 walls of plaster (absorption coefficient 0.1)4 walls of plaster (absorption coefficient 0.1)

carpet floor (absorption coefficient 0.3)carpet floor (absorption coefficient 0.3)

absorptive tile ceiling (absorption coefficient 0.6)absorptive tile ceiling (absorption coefficient 0.6)

2 (20 8) 2 (13 8) 0.1 (13 20) 0.3 (13 20) 0.6

286 sabins

A

wallswalls floorfloor ceilingceiling

LoudspeakersLoudspeakers

http://electronics.howstuffworks.com/speaker5.htm

sampling time

sampling sampling precisionprecision

Digital recordingDigital recording

Larger sampling rate and sampling precision Larger sampling rate and sampling precision improves fidelityimproves fidelity

What are the sampling rates we need for high fidelity ?What are the sampling rates we need for high fidelity ?

A sampling rate equal to the twice the maximum frequency

20.000 Hz 40.000 samples per second

Discretization (digitalization)Discretization (digitalization)

Pressure level at one instant represented by 1’s and 0’s

Two levels: 0 or 1 1 bit

Four levels: 00, 01, 10 or 11 2 bits

Eight levels: 000, 001, 010, 100, 011, 101, 110 or 111 3 bits

…

65536 levels: 0000000000000000, 000000000000001, …

16 bits = 8 bytes

Strategies for compression used in MP3Strategies for compression used in MP3

• maskingmasking

• more precision in sounds we hear bettermore precision in sounds we hear better

How to read a cd/dvd?How to read a cd/dvd?

This is a cartoon, real systems involve This is a cartoon, real systems involve several mirrors, etc, …several mirrors, etc, …

constructive constructive interferenceinterference

destructive destructive interferenceinterference

depth = ¼ wavelengthdepth = ¼ wavelength

The main problem with all string instruments is:The main problem with all string instruments is:

How to make a skinny string move a large amount How to make a skinny string move a large amount of air (impedance matching) ?of air (impedance matching) ?

Solution:Solution:

The string moves a board, the board moves the airThe string moves a board, the board moves the air

Acoustic guitar, violins, cellos, …Acoustic guitar, violins, cellos, …

String vibration body vibrationString vibration body vibration

Resonances of the body (and air inside) Resonances of the body (and air inside) help transfer the energy from the strings help transfer the energy from the strings

to sound at some frequencies,to sound at some frequencies,like the formants in the voicelike the formants in the voice

The sound of the piano is loud AND sustainedThe sound of the piano is loud AND sustained

one single string, overtones filtered outone single string, overtones filtered out

change in change in decay ratedecay rate

vertical modevertical mode

excited initially by the excited initially by the hammerhammer

sounding board “gives”sounding board “gives”

faster dumpingfaster dumping

horizontal modehorizontal mode

not initially presentnot initially present

sounding board is rigidsounding board is rigid

slower dumpingslower dumping

One reason for the two decay ratesOne reason for the two decay rates

How to generate oscillation (sound) How to generate oscillation (sound) from continuous blowing ?from continuous blowing ?

• fipplefipple

• reedreed

• lipslips

recorder: fipplerecorder: fipple

ReedsReeds

BrassBrass

Pressure antinodes (displacement nodes) appear at the Pressure antinodes (displacement nodes) appear at the position of the holesposition of the holes

what changes the wavelength (frequency) of the what changes the wavelength (frequency) of the note playednote played