How Do We Perceive Pitch and Its Connection to Sound Waves?

Sound waves are special waves that travel through the air. They have different features like frequency, wavelength, and amplitude. Among these, frequency is very important for how we hear and understand pitch.

What Is Frequency?

1. Understanding Frequency: Frequency is all about how many times a sound wave completes a cycle in one second. We measure this in hertz (Hz). For example, a sound wave that is 440 Hz means it completes 440 cycles every second.

2. What We Can Hear: The average human ear can hear sounds ranging from 20 Hz to 20,000 Hz (which is also called 20 kHz). Within this range, various frequencies connect to different pitches:

   • Low frequencies (20 Hz to 250 Hz) sound like bass.
   • Middle-range frequencies (250 Hz to 2,000 Hz) relate to harmonics and main tones.
   • High frequencies (2,000 Hz to 20,000 Hz) sound like treble.

3. Detecting Small Changes: People can notice small differences in pitch, called the Just Noticeable Difference (JND). Usually, the JND for music pitch is about 1% of the frequency. So, if you have a note at 440 Hz, you can notice a change of about 4.4 Hz.

Understanding the Math Behind It

The connection between frequency and pitch can be shown with this simple formula:

$$f = \frac{1}{T}$$

Here, $f$ is the frequency, and $T$ is the time it takes for one complete cycle of the wave.

Pitch in Music

Musical notes match up with certain frequencies. For example:

• The note A4 is at 440 Hz.
• The note C5 is around 523 Hz.
• The equal temperament tuning system splits an octave into 12 parts called semitones. Each semitone has a frequency ratio of about 1.059 (which is the twelfth root of 2).

Sound Loudness and Pitch

The loudness of a sound, measured in decibels (dB), doesn't directly change how we hear pitch. But louder sounds can make the pitch feel richer or more intense, even if the frequency stays the same.

In conclusion, how we perceive pitch is closely tied to sound wave frequencies. This shows how important both the science of sound and our hearing abilities are in understanding music.