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Technical Report: Sound Quality Evaluation (Part 3)

6. The concept of sharpness calculation

Sharpness is determined by the balance between high and low frequencies. Sharpness is calculated based on loudness data.

  1. Drawing the loudness spectrum

  2. Find the centroid of the area of the spectrum.

  3. Sharpness increases as you move to the right (higher frequency) on the frequency axis.

First, we calculate the loudness. Then we plot the spectrum of the calculated loudness.

Sound A is a low pitch, and sound B is a high-pitched pitch. If they were pure tones, we could numerically compare how much higher each is by comparing their frequencies. However, because the frequency components are spread across a wide range, this is not so simple. Therefore, we calculate the sharpness to represent which is higher pitched.

First, we find the centroid of the area under the loudness spectrum (the area below the red curve in the diagram). Next, we draw a perpendicular line downwards from the centroid and find the distance from the frequency origin (0 Hz, 0 Bark) to the point where the perpendicular line is drawn. The longer this distance, the greater the sharpness.

In sharpness calculations, we basically determine the length of the red arrow (⇔) below each data point. However, this alone doesn't quite match auditory perception. To correct this, we use weighting coefficients. We assign a weight to the loudness (loudness density) for each critical band, proportional to the critical band rate, and then multiply it by the weighting coefficients shown in the figure below. Finally, we find the centroid of the loudness spectrum.

6-1 Criteria for Sharpness

The reference sound for sharpness is a narrowband noise centered at 1 kHz, with a bandwidth of 1 Bark and a sound pressure level of 60 dB. At this point, the sharpness is 1 acum.

7. Approach to calculating fluctuation intensity

Humans perceive fluctuations when the loudness of a sound changes (alternating between loud and soft) or when the frequency changes (alternating between high and low). When the period of this fluctuation is very slow, the sense of fluctuation (fluctuation) is not felt much, but when the period of fluctuation becomes somewhat faster, the sense of fluctuation is felt strongly. It is said that the strongest sense of fluctuation is felt when the fluctuation occurs at a rate of 4 times per second (modulation frequency of 4 Hz). As the period of fluctuation becomes even faster, the sense of fluctuation gradually decreases.

The calculation of fluctuation intensity examines how much of the time history of the loudness contains fluctuation components. The fluctuation intensity increases when the loudness is close to the modulation frequency of 4 Hz.

7-1 Criteria for Variation Intensity

The reference sound for fluctuation intensity is a 1 kHz pure tone modulated at a modulation frequency of 4 Hz with 100% AM modulation, resulting in a sound pressure level of 60 dB. At this point, the fluctuation intensity is 1 vacil.

8. Concepts of Roughness Calculation

Roughness is also perceived when the loudness or frequency of a sound is modulated. However, the modulation frequency is much higher, and the sound is perceived as "roughest" when it modulates at a speed of about 70 times per second (modulation frequency of 70 Hz). When we perceive a sound as "rough," the human ear is picking up the modulation of that sound. However, because we cannot separate and hear each individual fluctuating sound, we perceive it as roughness rather than fluctuation.

Roughness calculations examine how much of the loudness's time history contains fluctuations. Roughness is greatest when the loudness is close to the modulation frequency of 70 Hz.

8-1 Roughness Criteria

The reference sound for roughness is a 1 kHz pure tone modulated at a modulation frequency of 70 Hz with 100% AM modulation, resulting in a sound pressure level of 60 dB. In this case, the roughness is 1 asper.

9. Fluctuation and roughness

Even with the same modulated sound, different modulation frequencies can create different listening impressions, resulting in a sense of fluctuation or a rough, grainy sound.

  • Modulation frequency 1 Hz
  • Being able to distinguish between peaks and valleys ⇒ Sensing fluctuations
  • Modulation frequency 4 Hz
  • I can distinguish between peaks and valleys, but the valleys have largely filled in ⇒ I feel a sense of fluctuation (maximum fluctuation intensity)
  • Modulation frequency 70 Hz
  • While fluctuations are discernible, the peaks and valleys cannot be distinguished ⇒ Roughness (maximum roughness)
  • Modulation frequency 200 Hz
  • Fluctuations are not noticeable = becomes flat ⇒ sounds smooth.

The image above shows the sound pressure waveform and the time-domain waveform of loudness for a 1kHz pure tone modulated at 100% amplitude. When the modulation period is slow (modulation frequency 1 Hz), the peaks and valleys of the sound can be distinguished. At a modulation frequency of 4 Hz, the peaks and valleys can still be distinguished, but the valleys are filled in due to the effect of temporal masking. At a modulation frequency of 70 Hz, the valleys are largely filled in, and the peaks and valleys can no longer be distinguished, but it is clear that there are fluctuating components in the sound. This is the state that is perceived as "rough." As the modulation frequency increases further to 200 Hz, the valleys are completely filled in, and the time-domain waveform of the loudness becomes flat. It sounds smoother to the ear, and the roughness disappears.