How your score is calculated in the Dialed GG Sound memory game.
Each game consists of 5 rounds. In each round, you hear a target tone and then try to recreate its frequency by dragging a slider. Your score for each round ranges from 0.50 to 10.00. The maximum total score is 50.00.
We don't measure accuracy in raw Hz. Instead, we use the Equivalent Rectangular Bandwidth (ERB) rate, a psychoacoustic model developed by Glasberg & Moore (1990). The ERB formula is:
ERB-rate(f) = 21.4 Γ logββ(1 + 0.00437 Γ f)
This models how the human cochlea perceives frequency. At low frequencies (e.g., 100 Hz), a 20 Hz difference sounds much larger than at high frequencies (e.g., 1000 Hz). Our scoring respects this biological reality.
The perceptual distance between the target frequency and your guess is:
distance = |ERB-rate(target) β ERB-rate(guess)| Γ· ERB-span
Where ERB-span is the full ERB range for the difficulty level. This normalizes the distance to [0, 1] so that scores are comparable across all frequencies.
Your round score is the maximum of three Gaussian curves, plus a floor:
| Layer | Max Points | Sharpness (ΟΒ²) | Description |
|---|---|---|---|
| Sharp | 10.0 | 1000 | Extremely precise β within a few Hz |
| Good | 7.5 | 45 | Solid ear β within a moderate range |
| Wide | 3.5 | 8 | In the neighborhood β rough estimate |
| Floor | 0.5 | β | You always get at least 0.50 |
The formula for each layer:
score = maxPoints Γ e^(βdistanceΒ² Γ sharpness)
Your final round score = min(10, max(floor, max(sharp, good, wide)))
| Setting | Easy | Hard |
|---|---|---|
| Frequency range | 80 β 1,200 Hz | 60 β 1,400 Hz |
| Listen time | 2.5 seconds | 1.25 seconds |
| Hz display while tuning | β Shown | β Hidden |
| Min distance from target | 15% of range | 30% of range |
| Total Score | Rating |
|---|---|
| 45 β 50 | π£ Audio Freak β Top 1% |
| 38 β 44 | π’ Excellent β Trained ear |
| 30 β 37 | π΅ Good β Above average |
| 20 β 29 | π‘ Average β Room to grow |
| 10 β 19 | π Needs Work β Keep practicing |
| 0 β 9 | π΄ Random β Were you guessing? |
Simple percentage-based scoring would unfairly penalize guesses at low frequencies. A 20 Hz miss at 100 Hz is far more noticeable to the ear than a 20 Hz miss at 1000 Hz. The ERB model ensures your score reflects what you actually hear, not just mathematical distance.
This approach is the same model used in professional audiometry and hearing aid calibration research, making our game not just fun β but scientifically meaningful.