本文にスキップする

Select your region & language

Global

Region

Technical Report: What is Sound Quality Evaluation? 3

6. The Concept of Sharpness Calculation

Sharpness is determined by the balance between high and low sounds. The calculation of sharpness is based on loudness data.

  1. Draw the spectrum of loudness.

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

  3. The sharpness increases as you move to the right on the frequency axis (towards the high-frequency side).

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

Sound A is a low sound, while sound B is a high-pitched sound. If they were pure tones, we could compare their frequencies numerically to see which is higher to what extent, but due to the presence of a wide range of frequency components, such comparisons are not straightforward. Therefore, we calculate sharpness to express which one is higher in pitch.

First, we will find the centroid of the area of the loudness spectrum (the area under the red curve in the figure). Next, we will drop a perpendicular line downwards from the centroid and measure the distance from the origin of frequency (0 Hz, 0 Bark) to the point where the perpendicular line intersects. The longer this distance, the greater the sharpness.

In sharpness calculation, we essentially seek the lengths of the red arrows (⇔) at the bottom of each data point. However, this alone does not align well with auditory perception. To correct this, we use weighting coefficients. We apply weighting proportional to the critical band number (critical band rate) for the loudness (loudness density) of each critical band, and then apply the weighting coefficients as shown in the figure below, after which we calculate the centroid of the loudness spectrum.

6-1 Standard of Sharpness

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

7. Concept of Variable Intensity Calculation

Humans feel variations in sound when the amplitude fluctuates (alternating between loud and soft) and when the frequency fluctuates (alternating between high and low). When the period of these fluctuations is very slow, the sensation of fluctuation (or wobbliness) is not strongly felt, but as the period becomes somewhat faster, the sensation of fluctuation is felt more strongly. It is said that the strongest sensation of fluctuation occurs at a modulation frequency of 4 Hz (four times per second). Furthermore, as the period of fluctuation increases further, the sensation gradually diminishes.

The calculation of fluctuation strength examines how much fluctuation component is included in the time history of loudness. The fluctuation strength increases when the loudness is close to a modulation frequency of 4 Hz.

7-1 Criteria for Variability Intensity

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

8. Concept of Roughness Calculation

In the case of roughness, it is felt when the loudness and frequency of sound are modulated. However, the modulation frequency is much higher, and it is felt to be the 'roughest' when modulated at a rate of about 70 times per second (a modulation frequency of 70 Hz). When we perceive sound as 'rough', human hearing is picking up on that modulation. However, since we cannot separate and hear each fluctuating sound individually, it is felt as roughness rather than a sense of fluctuation.

In the calculation of roughness, we examine how much variation is included in the time history of loudness. Roughness is greatest when the loudness is close to a modulation frequency of 70 Hz.

8-1 Roughness Standards

The standard sound for roughness is a pure tone at 1 kHz modulated at a frequency of 70 Hz with 100% AM modulation, with a sound pressure level of 60 dB. Under these conditions, the roughness is 1 asper.

9. Variability and Roughness

Even with the same modulated tone, if the modulation frequency is different, the impression heard also differs, and one may feel a sense of fluctuation or hear a rough texture.

  • modulation frequency 1 Hz
  • Can distinguish between mountains and valleys ⇒ Feel a sense of fluctuation.
  • Modulation frequency 4 Hz
  • Although I can distinguish the sounds of the valley, it has been significantly filled in, leading to a feeling of fluctuation (maximum fluctuation intensity).
  • Modulation frequency 70 Hz
  • I understand that there are fluctuations, but I cannot distinguish between peaks and valleys ⇒ rough feeling (maximum roughness)
  • Modulation frequency 200 Hz
  • Not knowing that there is variability = becomes flat ⇒ sounds smooth.

The above figure shows the sound pressure waveform and the loudness time axis waveform of a pure tone at 1 kHz modulated at 100% amplitude. When the modulation period is slow (modulation frequency of 1 Hz), it is possible to distinguish the peaks and troughs of the sound. At a modulation frequency of 4 Hz, the peaks and troughs can still be distinguished, but due to the effects of temporal masking, the troughs begin to get filled in. When the modulation frequency reaches 70 Hz, the troughs are significantly filled in, and the peaks and troughs can no longer be distinguished, although it is evident that there are fluctuations within the sound. This state is perceived as 'rough.' As the modulation frequency increases to 200 Hz, the troughs are completely filled in, and the loudness time waveform becomes flat. It also sounds smooth to the ear, and the roughness disappears.