Pitch, Loudness, and Localization
Will Styler - LIGN 113
Today's Plan
Perception of Frequency
- Mel and Bark Scaling
Perception of Loudness
- Equal Loudness Contours
Perception of Location
- Vertical and Horizontal Localization
Perception of Frequency
Our perception of frequency is non-linear
- We now know a bunch of reasons!
Differences in critical frequency bands
Evolutionary Differences!
- We care primarily about ~80-4000Hz!
... but Hertz doesn't capture this at all
Hertz captures cycles per second
... but not our perception of frequency!
Our perception of frequency is weird!
We've already talked about auditory masking
Two sounds within the same 'critical band' seem like one sound
We also percieve jumps in frequency non-linearly
Do we hear frequency in a linear and reliable way?
Is the jump in file A the same as in file B?
A.
B.
- Both of these are a 200Hz Jump!
Is the jump in file A the same as in file B?
A.
B.
- Both of these are a 100Hz Jump
So, our perception of frequency isn't Hertz-like
- We want a perceptual scale for hearing!
Perceptual scales
Mel scaling
Bark scaling
Mel Scale
Maps numerical pitch measures to human perceptions of changes in pitch
People will tell you that a sound's pitch is 'half as high' at x/2 mels relative to x mels
Mel is the dominant perceptual frequency scale in use
It underlies Mel-Frequency Cepstral Coefficients which are the dominant processing method in computational linguistics
Mel Scale
Mel Formula
Mel(f) = 1125 * ln(1+f/700)
f = Frequency in Hertz
This is a natural log
There are multiple formulae!
Bark Scale
The same basic idea, but using the critical bands themselves!
Each 'band' in bark is centered around the psychoacoustic critical bands
Bark Scale
Bark Formula
Bark(f)=13*arctan(0.00076*f)+3.5*arctan((f/(7500))*(f/(7500)))
f = Frequency in Hertz
Again, there are other formulae!
Bark vs. Mel vs. Equivalent Rectangular Bandwidth
Which should you use?
Doesn't really matter!
Linguists tend to use Bark
But you'll see Mel too!
The important part is knowing that we don't hear Hertz linearly!
You know what else is non-linear?
Amplitude Perception
The auditory system is tuned to amplify some frequencies!
We've already talked about wanting different units for amplitude
Perceived amplitude is not linear with pressure
Hence using dB, rather than Pascal!
... and let's not forget the relationship between frequency and amplitude
- We don't hear equivalent loudness for equivalent amplitudes at different frequencies
This is the basis of dB HL
dB HL sets the minimum perceptible amplitude as zero!
- Regardless of frequency!
So, our perception of the basics of sound is far from physics
Duration perception is odd, if undiscussed here
Amplitude is heavily convolved with frequency, and logarithmic!
Frequency (Period, Wavelength) is not at all linear
Phase is completely imperceptible
... but that's OK!
Our perception is shaped by our evolution!
The most important ranges for speech and survival are amplified
None of our perceptions of anything are accurate
We have nothing but our flawed perceptions to build a model of the world from
Everything you've ever known is just a matrix of perceptual data
You can't prove anything you've ever experienced happened, just that you perceived that it did.
We're just isolated mindstates groping through an invisible world using our strange detectors
Wait, where did that come from?
- Which brings us to...
Sound localization?
We want to know where sound came from
"Did that lion just roar from behind me or in front of me?"
"Where is that bird tweeting from?"
"Where did that spring just go?"
We need two kinds of localization
All positions can be calculated based on vertical and horizontal knowledge
So, we just need to figure out two dimensions!
Many animals can change the position of their ears
Turns out that we still try, even though it doesn't work anymore
... but we can't, so we need to figure out how to do...
Horizontal Localization
We use two sources of data for horizontal localization
Both rely on binaural information
Differences in timing between ears
Differences in loudness between ears
Time-of-arrival differences
Interaural Time Differences
Shotspotter
Interaural Amplitude differences
Think about a post in the water...
Interaural Level Differences
Both play a role
Interaural time differences are used mostly in low frequencies
Interaural amplitude differences are usable only in high frequencies
The trade-off happens around 1 kHz
This is acquired
Each time my hearing changed, I re-learned where sounds are!
Primarily at higher frequencies
Take a second to ponder why...
Binaural effects can only give you horizontal cues
Provided that your head is vertical
How do we get vertical information?
Vertical Localization
For vertical information, we use the pinna
Different resonances imply different angles of incidence
These are pinna-specific
You cannot localize sounds recorded with a fake pinna
They also involve the resonances of the neck and shoulders
Pinna cues are most important over 6,000 Hz
Localization is hard!
We're best at it directly in front of us
We're pretty bad at it behind us, and directly to our sides
This leads to the Cone of Confusion
The cone of confusion
- These have exactly the same ITD
There's other information too!
We can move our heads
We can use information from the room
We can use frequency decay over time to judge distance
We can use the doppler effect to identify fast movement
We can identify the source visually
Aside: Localization is hard to preserve
We're worse at localizing sound when wearing hearing protection
... especially when the pinnae are covered
Modeling this is very, very complex
Surround Sound systems cheat by actually playing sounds from different places
There's a lot of research in Localization
Wrapping Up
Our perceptions of frequency are deeply non-linear
Our perceptions of amplitude are deeply non-linear
Localization is a hard task
Horizontal Localization uses differences in timing and loudness between ears
Vertical localization relies on pinna cues
This is super complicated
- ... and an area of major research!
