Pure and Complex tones

Pure tone

A pure tone is created by a single sine wave with one frequency, such as a sound at 400 Hz. It has no harmonics and is represented as a smooth, regular sine wave.

How does tone help distinguish different sounds?

Tone helps us distinguish between different sounds, such as a piano and a violin, even if they are playing the same note.

frequency spectra

Frequency spectra refer to the range of frequencies present in a sound. This helps define timbre, or the quality of the sound, allowing us to distinguish different instruments or voices, even if they produce the same pitch.

harmonics

additional frequencies that accompany the fundamental frequency. Contribute to the uniqueness of the sound.

Why is amplitude represented in decibels instead of a linear scale like 1-100000?

Amplitude is represented in decibels because sound volumes vary across a vast range. A logarithmic scale like decibels (dB) compresses this range, making it easier to work with.

decibels and loudness

higher decibel level indicates a louder sound

Formula for calculating decibles

Sound pressure level (SPL)

• the term used when the reference pressure is set to P₀= 20 , the standard for calculating decibels.

• 20 is the pressure near hearing threshold.

Practise question)

Calculate the dB SPL for a sound that produces 2000 micropascales

dB=20xlog(2000/20)= 40

log (p)

gives us an absolute measure of pressure change

what does dB tell us?

it gives a ratio of volume relative to something just audible to the human ear.

• how much louder is the noise?

• in the case above the sound is 40 dB louder than the threshold of hearing.

What is Stevens' magnitude estimation procedure for measuring loudness?

Involves subjects judging the loudness of pure tones relative to a reference tone (a 1,000 Hz tone at 40 dB). The perceived loudness of the baseline tone is set to 1, and sounds judged as "2" are perceived as twice as loud.

How does physical loudness (dB) relate to perceived loudness?

The relationship between physical loudness (dB) and perceived loudness is not linear. Using Stevens' magnitude estimation, an increase of 10 dB is perceived as doubling the loudness, though the actual relationship is more complex.

What happens when multiple pure tones are combined into a complex tone?

When multiple pure tones are combined into a complex tone, the pitch of the sound is determined by the fundamental frequency, which is the greatest common divisor (GCD) of all the frequencies.

What determines the pitch of a complex tone?

Determined by the fundamental frequency, which is the greatest common divisor (GCD) of all the frequencies in the complex sound. This is typically the lowest frequency in the sound and is also known as the first harmonic.

Harmonics in a complex tone

Harmonics in a complex tone are integer multiples of the fundamental frequency. For example, if the fundamental frequency is 200 Hz, the higher harmonics would be 400 Hz, 600 Hz, 800 Hz, and so on.

What is the fundamental frequency for a complex tone with frequencies 200 Hz, 400 Hz, 600 Hz, and 800 Hz?

200 Hz, as it is the greatest common divisor (GCD) of all the frequencies in the sound.

What are the harmonics in a complex tone made of 200Hz, 400Hz, 600Hz, and 800Hz?

• First harmonic: 200Hz (fundamental frequency)

• Second harmonic: 400Hz (2x the fundamental)

• Third harmonic: 600Hz (3x the fundamental)

• Fourth harmonic: 800Hz (4x the fundamental)

Periodicity of Complex Tones

A complex tone is periodic because it has a repeating pattern every 5ms, which corresponds to the period of the fundamental frequency.

Example to take note of

Even when the 200 Hz pure tone is not explicitly mixed in, we still perceive the fundamental frequency as 200 Hz bc its the GCD.

What happens when the fundamental frequency (first harmonic) is removed from a complex tone?

Removing the fundamental frequency doesn't change the perceived pitch but alters the timbre of the sound. This phenomenon is called periodicity pitch.

• The pitch will only change if the GCD changes.

Periodicity Pitch

Periodicity pitch is when the perceived pitch stays the same even after the fundamental frequency (first harmonic) is removed. The sound's timbre changes, but the brain still "fills in" the missing pitch based on the pattern of remaining harmonics.

Pitch Perception Over the Phone

Most phones can’t reproduce sounds below 300 Hz, yet we still perceive accurate pitch (e.g., male voices at ~150 Hz) due to periodicity pitch—the brain infers the missing fundamental from the pattern of higher harmonics.

Timbre

all other perceptual aspects of a sound besides loudness, pitch, and duration. Timbre is what makes sounds distinct from each other, even if they share characteristics like pitch, loudness, and duration.

• includes:

  1. attack of tones → buildup of sound at the beginning of a tone

  2. decay of tones → decrease at end of tone

  3. Frequency spectrum

What if we play 3 different instruments at the fundamental frequencies 200Hz, but different harmonics

• Timbre varies due to the different harmonic structures produced by each instrument and the spectrum (harmonics and their relative strengths) significantly influences the perceived quality of the sound.

we will have a similar pitch fir each and different timbres.

Role of Attack and Decay in Timbre

Attack and decay are key to distinguishing between instruments. Without them, it's much harder to tell instruments apart, even when playing the same pitch.

Sound wave

pattern of aur pressure changes

pitch

perceptual quality of sound, ranging from high to low

• e.g) tuba: low pitch (low fundamental frequency)

• cant be measured in a physical way, only based on perception. we cant say there is a pitch of 200Hz but we can say theres a low pitch.

• remember the higher the pitch, the higher the freqeuncy and vice versa.

Fundamental Frequency

determined by the repetition rate of its overall waveform pattern. It defines the perceived pitch of the sound.

Pitch on the piano

As we move from left to right the pitch increases

Are tone and pitch the same

No. Pitch refers to the perceptual quality of how "high" or "low" a sound is, based on its frequency.
Tone is a broader term that refers to a sound with specific features, including pitch, duration, loudness, and timbre. So, pitch is one feature of a tone.

Tone Height

The perceptual experience of pitch increasing as fundamental frequency increases. Higher keys on a piano = higher tone height.

Tone Chroma

The quality of a tone that remains consistent across octaves (e.g., notes A1, A2, A3 share the same chroma). It reflects the "color" or cyclical nature of pitch.

• notes seperated by octaves have the same tone chroma

we notice that a1, a2, a3 all sound similar but have different pitch.

• If you play two A at the same time, they have the same chroma so it feels different then when u play a and c a and a are more similar.

octave

doubling the fundamental frequency

Does freqeuncy also affect how loud a sound is percieved to be?

yes, we have different sensitivities to different frequencies.

Audibility curve

on y axis we see dB and x axis is frequency in Hertz

• we can only hear sounds above the audibility curve

• Audibility Threshold (Green Line):

  • The audibility curve represents the threshold below which we cannot hear sounds.

  • Only sounds above this curve (the green line) are audible to us.

• Low Frequencies (Less Sensitive):

  • For low frequencies (e.g., 20 Hz), we need much louder sounds to cross the audibility threshold.

  • For example, a 20 Hz sound may need 80 dB to be heard, whereas a higher frequency sound may be audible at a much lower volume.

• Auditory Response Area (Between Green and Blue Lines):

  • The area between the green and blue lines is the auditory response area.

  • Sounds within this range are audible, and we can perceive them.

• Perception of Volume for Same Decibels:

  • If two sounds (A and B) have the same decibel level (e.g., 70 dB), they might still be perceived differently.

  • Sound A (lower frequency) might need more physical loudness to be heard, while Sound B (higher frequency) is heard more easily at a lower decibel level.

• Threshold of feeling (blue line)

  • above this line is when sound becomes to dangerous for us (120db) if we hear it for too long.

• Example of Perception:

  • Sound A (Low Frequency): 70 dB, but you can't hear it because it's below your threshold for that frequency.

  • Sound B (Higher Frequency): 70 dB, and it’s perceived louder because it’s within a range you're more sensitive to, making it easier to hear at a lower physical loudness.

Equal loudness curves

For humans, what is the most sensitive frequecnies?

2000-4000hz which is the freqeuncy of conversational speech.

• where audibility curve is lowest (so sensitive)

What the frequency range that humans can hear from?

20-20000Hz

Hearing range varies for different species

Elephants hear lower thresholds then humans meaning they can hear lower frequencies (below 20Hz), dogs and humans can hear higher.