Frequency and Pitch
A guitar string vibrates back and forth to create the distinct musical notes you hear. This physical motion sets the air particles into a rhythmic dance that your ears interpret as sound.
The Relationship Between Motion and Pitch
When an object vibrates at a specific speed, it creates a repeating pattern known as a wave. The number of these wave cycles occurring every single second is called frequency. We measure this value using the unit called hertz, which is abbreviated as . If a string completes one full back and forth movement in a second, the frequency is $1 Hz$. Most musical instruments produce complex vibrations that result in much higher frequencies than this. High frequencies cause the air to pulse rapidly against your eardrums, which your brain perceives as a high musical pitch. Conversely, low frequencies result in a slow vibration that your brain identifies as a deep, low pitch. Think of frequency like the speed of a car on a highway. A car moving at a high speed covers more distance in a set time, just as a high frequency wave completes more cycles in one second. If you press a key on a piano, you are selecting a specific frequency that the instrument is designed to produce. By changing the length or tension of the string, you force the vibration to occur at a new, different rate. This change in the rate of vibration is the exact physical mechanism that shifts the pitch you hear.
Key term: Pitch — the subjective human perception of how high or low a sound is, which directly correlates to the frequency of the sound wave.
Understanding the Logarithmic Scale of Music
Music does not follow a simple linear scale where each note adds a fixed amount of frequency. Instead, our ears perceive pitch through a logarithmic scale that relies on mathematical ratios. When you move up an octave on a piano, you are doubling the frequency of the previous note. For example, if a note vibrates at $220 Hz$, the note one octave higher will vibrate at exactly $440 Hz$. This doubling pattern continues as you ascend the musical scale, meaning the gaps in frequency get wider as the notes get higher. This logarithmic structure is why our ears can handle a massive range of sounds without feeling overwhelmed. The human ear is sensitive to a wide range of frequencies, typically spanning from $20 Hz$ to $20,000 Hz$. Because of this logarithmic design, we perceive equal musical steps as feeling like equal distance, even though the physical frequency jumps are getting larger.
To help visualize how these frequencies relate to one another, consider the following table of common musical intervals:
| Interval | Frequency Ratio | Musical Effect |
|---|---|---|
| Unison | $1:1$ | Identical pitch |
| Octave | $2:1$ | Same note higher |
| Fifth | $3:2$ | Stable harmony |
| Fourth | $4:3$ | Open harmony |
This specific mathematical organization allows musicians to create harmony that sounds pleasant to our ears. When two notes share a simple ratio, their wave cycles align in a way that our brain finds mathematically satisfying. If the ratios were random or overly complex, the resulting sound would likely be perceived as dissonance or noise. By utilizing these precise frequency relationships, instruments can produce melodies that follow consistent and predictable patterns. Your brain is essentially a biological processor that translates these physical ratios into the emotional experience of music. Every note you hear is a result of these precise, calculated vibrations working in perfect harmony with your auditory system.
Musical pitch is a direct result of how fast an object vibrates, and our ears perceive these vibrations through a logarithmic scale where each octave represents a doubling of frequency.
The next Station introduces amplitude and loudness, which determines how much energy is carried by each sound wave.