What is an asper?

Acoustic roughness is measured in aspers (from the Latin word for rough). An asper is the roughness of a 1 kHz tone, at 60 dB, 100% modulated at 70 Hz. That is, the signal

(1 + sin(140πt)) sin(2000πt)

where t is time in seconds.

1000 Hz carrier fully modulated at 70 Hz

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


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))

See also: What is a vacil?

3 thoughts on “What is an asper?

  1. So now I know what an asper is, but what is acoustic roughness? To put it another way, how do I calculate how many aspers some other signal has?

  2. Calculating roughness is complicated, and the literature is very hard to read. I’ve done it, but couldn’t begin to explain it in a blog post.

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