Note Frequency Calculator

Convert musical notes to frequencies. Calculate the exact frequency of any note on the musical scale based on standard pitch.

Calculate Your Note Frequency Calculator

About Musical Note Frequencies

In music theory, A4 (the A above middle C) is typically tuned to 440 Hz, serving as the standard reference pitch.

The frequency of each note doubles with each octave increase. For example, A5 is 880 Hz (2 × 440 Hz) and A3 is 220 Hz (440 Hz ÷ 2).

In equal temperament tuning (the most common system today), each octave is divided into 12 equal semitones. The ratio between the frequencies of adjacent semitones is the 12th root of 2 (approximately 1.0595).

Understanding Musical Note Frequencies

Musical note frequencies are the number of vibrations per second (measured in Hertz, or Hz) that produce the pitch of a specific musical note. These frequencies follow mathematical patterns that are fundamental to the structure of music.

The Physics of Musical Notes

When a musical instrument produces a sound, it creates vibrations in the air. These vibrations travel as waves to our ears, and the rate at which they vibrate determines the pitch we hear. The faster the vibration (higher frequency), the higher the pitch.

Standard Tuning Reference

In modern Western music, the note A above middle C (A4) is traditionally tuned to 440 Hz. This standard was established by the International Organization for Standardization (ISO) in 1975, though some orchestras and musicians may choose slightly different reference tunings.

How Notes Relate to Each Other

Musical intervals are based on frequency ratios:

Octave: A frequency ratio of 2:1 (doubling the frequency)
Perfect fifth: A frequency ratio of 3:2
Perfect fourth: A frequency ratio of 4:3
Major third: A frequency ratio of 5:4
Minor third: A frequency ratio of 6:5

Equal Temperament Tuning

In equal temperament tuning, which is the most commonly used tuning system today, the octave is divided into 12 equal semitones. Each semitone has a frequency ratio of the 12th root of 2 (approximately 1.0595) to the previous semitone.

The formula to calculate the frequency of any note in equal temperament is:

f = 440 × 2^(n/12)

Where:

f is the frequency of the note in Hz
n is the number of semitones away from A4 (positive for higher notes, negative for lower notes)

Applications of Musical Frequencies

Understanding musical note frequencies is essential for:

Instrument tuning: Ensuring instruments play in tune with each other
Sound engineering: Mixing, equalizing, and processing audio
Music composition: Creating harmonies and understanding consonance and dissonance
Acoustic design: Optimizing rooms for musical performance
Digital synthesis: Creating and manipulating electronic sounds

Interesting Facts About Music Frequencies

The lowest note on a standard piano (A0) has a frequency of about 27.5 Hz
The highest note on a standard piano (C8) has a frequency of about the 4,186 Hz
The typical range of human hearing is 20 Hz to 20,000 Hz, though this decreases with age
Some orchestras use A4 = 442 Hz or A4 = 443 Hz for a brighter sound
Historical tunings before the 20th century often used A4 at lower frequencies like 435 Hz or 430 Hz

Related Calculators

Harmonic Series Calculator

Calculate harmonic frequencies based on a fundamental frequency.

Music Interval Calculator

Calculate the interval between two musical notes.

Music Transposition Calculator

Transpose musical notes and scales to different keys.

Semitone Calculator

Calculate the frequency ratio between semitones in musical scales.

Frequently Asked Questions

The internationally recognized standard frequency for A4 (the A above middle C) is 440 Hz. This standard was established by the International Organization for Standardization (ISO) in 1975. However, some orchestras and ensembles may tune to slightly different reference pitches, such as A4 = 442 Hz or A4 = 443 Hz for a brighter sound, or historically lower pitches like A4 = 432 Hz.

Frequency and pitch are directly related: the higher the frequency (measured in Hertz, or Hz), the higher the perceived pitch. When the frequency doubles, we hear a note that's one octave higher. For example, if A4 is 440 Hz, then A5 is 880 Hz, and A3 is 220 Hz. Our ears perceive these relationships logarithmically, which is why musical scales are structured the way they are.

Each octave doubles the frequency because our perception of pitch is logarithmic rather than linear. This means that we perceive equal ratios of frequencies as equal musical intervals. The frequency ratio of 2:1 is perceived as an octave, which is the most fundamental interval in music. This doubling pattern is consistent across all musical traditions and appears to be based on how our auditory system processes sound.

Equal temperament is the tuning system used in most Western music today, where each octave is divided into 12 equal semitones. In this system, the frequency ratio between adjacent semitones is the 12th root of 2 (approximately 1.0595). This standardization allows instruments to play in any key without retuning, but it slightly compromises the pure mathematical ratios found in just intonation. For example, a perfect fifth in equal temperament is slightly narrower than the pure 3:2 ratio.

To calculate the frequency of any note in equal temperament: (1) Determine how many semitones the note is away from A4 (440 Hz). Count up for higher notes and down for lower notes. (2) Use the formula: frequency = 440 × 2^(n/12), where n is the number of semitones from A4. For example, to find the frequency of C5 (9 semitones above A4), calculate 440 × 2^(9/12) = 523.25 Hz.

The typical range of human hearing spans from about 20 Hz to 20,000 Hz (20 kHz), though this range varies among individuals and diminishes with age. Most musical instruments produce fundamental frequencies within a narrower range, typically from about 27.5 Hz (A0, the lowest note on a standard piano) to around 4,186 Hz (C8, the highest note on a standard piano). However, the harmonics (overtones) of musical instruments can extend well beyond this range.

Frequency and wavelength are inversely related: wavelength = speed of sound ÷ frequency. The speed of sound in air at room temperature is approximately 343 meters per second (m/s). So, for example, a 440 Hz tone (A4) has a wavelength of 343 ÷ 440 = 0.78 meters, or about 78 centimeters. Lower frequencies have longer wavelengths, which is why bass sounds need larger speakers and can travel through walls more easily than high frequencies.

Share This Calculator

Found this calculator helpful? Share it with your friends and colleagues!