Psychoacoustic Roughness

acoustic roughness is measured in aspers. an asper is the roughness of a 1 khz tone, at 60 db, 100% modulated at 70 hz. that is, the signal

(1 + sin(140π t )) sin(2000π t )

where t is time in seconds.

here’s what that sounds like (if you play this at 60 db, about the loudness of a typical conversation at one meter):

http://www.johndcook.com/one_asper.wav

and here’s the python code that made the file:

from scipy.io.wavfile import write
from numpy import arange, pi, sin, int16

def f(t, f_c, f_m):
    # t    = time
    # f_c  = carrier frequency
    # f_m  = modulation frequency
    return (1 + sin(2*pi*f_m*t))*sin(2*f_c*pi*t)

def to_integer(signal):
    # take samples in [-1, 1] and scale to 16-bit integers,
    # values between -2^15 and 2^15 - 1.
    return int16(signal*(2**15 - 1))

n = 48000 # samples per second
x = arange(3*n) # three seconds of audio

# 1 asper corresponds to a 1 khz tone, 100% modulated at 70 hz, at 60 db
data = f(x/n, 1000, 70)
write("one_asper.wav", n, to_integer(data))