The unit of measurement for loudness levels is the phon, and is arrived at by reference to equal-loudness contours. By definition two sine waves, of differing frequencies, are said to have equal-loudness level measured in phons if they appear equally loud to the average young person without significant hearing impairment.

Loudness level (phon)An equal-loudness contour is a measure of sound pressure (dB SPL), over the frequency spectrum, for which a listener perceives a constant loudness when presented with pure steady tones.

Phon is equal to the sound pressure level in decibels

at f = 1 kHz

Hearing sensitivity is maximum near the first resonant frequency 3.5 - 4.0 kHz of the outer ear canal, and has another peak at the second resonance ~13kHz

Equal Loudness Curves

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2

sone   1    2    4    8   16   32   64  128 256 512 1024

phon 40 50 60 70 80 90 100 110 120 130 140

Loudness of pure tones (sone)

10/402 LLSLoudness S in sones:

LLLoudness level in phons:

Loudness level (see previous slid) has been constructed using sound pressure level, which is logarithmic function of intensity. Because of that loudness level is slow function of intensity. Sone has been introduced to “return beck “ .

• Loudness level and sone are based on the average listener sensation of loudness.

• Sound pressure level and intensity are independent on the listener sensation.

One sone is the loudness of a 1 kHz tone at a sound level of 40 dB (loudness level 40 phons)

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Musical dynamics and loudness

Dynamic range: the range of sound level in musical performance

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Loudness and Masking

When the ear is exposed to two or more different tones, one can mask the other.Example: Hearing threshold of the weaker tone is shifted up by the louder tone

1. Pure tones close together in frequency mask each other more then tones widely separated

2. Pure tone masks tones of higher frequency more effectively then tones of lower frequency

3. The grater intensity of the masking tone, the broader the range of frequencies it can mask

4. Forward masking – masking of a tone by a sound that ends a short time (~ 20 – 30 ms) before tone begins (recently stimulated cells are not as sensitive as fully rested cells)

5. Backward masking – a tone can be masked by a noise that begins up to 10 ms later

6. Narrow band masking is similar to pure tone masking7. Broad band (white) noise masking approximately linearly increase with

the noise level8. Noise in one ear can mask tone in the other ear 5

Loudness and duration: impulsive sounds adaptation

•Ear averages sound energy over about 0.2s(so loudness grows with duration up to this value)

•Acoustic reflex–Ear has protection against very loud sound (above 85 dB) and sudden pressure changes. –It is protected by muscles attached to eardrum and the ossicles of the middle ear. They tightens the eardrum and move stirrup-shaped bone away from the oval window. –The reflex does not begin until 30-40 ms after sound overload occurs.

•Adaptation – sensation decrees with prolonged stimulation (small effect)

•Auditory Fatigue (a temporary threshold shift) – laud sound effects ability to hear another sound at a later time. In extreme situation: a temporary loss of hearing after exposure to sound.

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Fourier analysis

Any periodic vibration, however, complicated, can be built up from a series of simple vibrations, whose frequencies are harmonics of a fundamental frequency, by choosing the proper amplitudes and phases of these harmonics.

Compare this mathematical statement with the fact that practically any music can be played on piano.

Periodic function: tFTtF T is period f1 = 1/T is fundamental frequency

nnn

n tAtF

sin...2,1

Tnnff nn /222 1

•Fourier analysis – the determination of harmonic component of a periodic function•Fourier Synthesis - the construction of a complex function from its harmonics (the opposite of Fourier analysis)

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0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

tsin

t2sin

t3sin

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Spectrum - specification of the strengths of the various harmonics

Examples:•A square wave has a spectrum with a fundamental followed by odd harmonics with the ratio of the amplitudes being 1/n•A triangle wave has a spectrum with a fundamental followed by odd harmonics, but the ratio of the amplitudes is 1/n2

•A saw tooth wave has a spectrum with both odd and even harmonics and amplitude ratio of 1/n2

f

An

1 3 5 7

0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

f

tnnn

2

sin1

7,5,3,1

Square wave

9

0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

tnnn

sin1

5,3,1

tnnn

sin1

7,5,3,1

0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

tnnn

sin1

9,7,5,3,1

0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

tnnn

sin1

,3,1

10

0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

tnnn

sin1

9,7,5,3,12

0 0.5 1 1.5 2 2.5 3 3.5 4-8

-6

-4

-2

0

2

4

6

8

9...2,1

sinn

tn

0 0.5 1 1.5 2 2.5 3 3.5 4-4

-3

-2

-1

0

1

2

3

4

9,.7,5,3,1

sinn

tn

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The spectra for musical instruments vary depending on: •the way in which the instrument is played (soft, loud, high, low or midrange) •how the sound is recorded (near field, far field, reverberant field, direction of microphone from the instrument)

•Typical spectra of voiced instruments (such as a violin, trumpet, guitar) have sharply defined peaks

•The spectra of unvoiced instruments (such a drums) have a broadband of frequency responses with no clearly defined peaks

Comments about spectra of musical instruments

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