Frequency to Note Calculator
Closest Note
A4
Cents Offset
0 cents
Exact Note Frequency
440.00 Hz
Wavelength in Air
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How Frequency Relates to Musical Notes
Frequency-to-note conversion is the process of identifying which musical note corresponds to a given sound frequency measured in hertz (Hz). In the standard 12-tone equal temperament system used by virtually all modern Western music, each semitone is separated by a frequency ratio of 2^(1/12), approximately 1.05946. The reference pitch is A4 = 440 Hz, as standardized by ISO 16:1975.
Musicians, audio engineers, and instrument tuners use this conversion to verify tuning accuracy, analyze recordings, and calibrate equipment. Electronic tuners work by detecting the fundamental frequency of a sound and comparing it to the nearest equal-temperament note. The difference is expressed in cents, a logarithmic unit where 100 cents equals one semitone. Professional tuners typically aim for accuracy within 1-2 cents. Our BPM Calculator is another essential tool for musicians working with tempo and rhythm.
This calculator also computes the wavelength of sound in air at standard temperature (20 degrees C, where the speed of sound is approximately 343 m/s). Wavelength is important for acoustics, room treatment design, and understanding how sound interacts with physical spaces. According to the Acoustical Society of America, low-frequency sounds (below 250 Hz) have wavelengths longer than 1.4 meters, which is why bass notes are difficult to contain with thin walls.
The Frequency-to-Note Formula
The mathematical relationship between frequency and musical notes in equal temperament is defined by the formula:
f = 440 x 2^(n/12)
Where f is the frequency in Hz and n is the number of semitones above (positive) or below (negative) A4. To reverse this and find the note from a frequency:
n = 12 x log2(f / 440)
The cents offset from the nearest note is: cents = 1200 x log2(f / f_nearest)
Worked example: Given a frequency of 262 Hz, n = 12 x log2(262 / 440) = 12 x (-0.748) = -8.98. Rounding to -9 gives C4. The exact frequency of C4 is 440 x 2^(-9/12) = 261.63 Hz. The cents offset is 1200 x log2(262 / 261.63) = +2.4 cents (slightly sharp).
Key Terms You Should Know
- Hertz (Hz): The unit of frequency, representing one cycle per second. Musical frequencies range from about 20 Hz (lowest audible) to 20,000 Hz (highest audible).
- Concert Pitch: The standard reference tuning for musical ensembles. The international standard is A4 = 440 Hz (ISO 16), though some orchestras tune slightly higher (442-443 Hz).
- Cent: A logarithmic unit of pitch interval. 100 cents = 1 semitone, 1,200 cents = 1 octave. Used to express fine tuning differences that are smaller than a semitone.
- Equal Temperament: A tuning system dividing the octave into 12 equal semitones (frequency ratio of 2^(1/12) each). This is the standard tuning system for pianos, guitars, and most modern instruments.
- Wavelength: The physical distance between consecutive peaks of a sound wave. Calculated as speed of sound divided by frequency. At 20 degrees C in air, wavelength (m) = 343 / frequency (Hz).
- Fundamental Frequency: The lowest frequency component of a musical tone, which determines the perceived pitch. Overtones (harmonics) are integer multiples of the fundamental.
Note Frequencies Reference Table (A4 = 440 Hz)
The table below lists the frequencies of all 12 chromatic notes across octaves 2-6, covering the range of most instruments. All values follow the ISO 16 standard (A4 = 440 Hz, equal temperament).
| Note | Octave 2 | Octave 3 | Octave 4 | Octave 5 | Octave 6 |
|---|---|---|---|---|---|
| C | 65.41 | 130.81 | 261.63 | 523.25 | 1046.50 |
| D | 73.42 | 146.83 | 293.66 | 587.33 | 1174.66 |
| E | 82.41 | 164.81 | 329.63 | 659.26 | 1318.51 |
| F | 87.31 | 174.61 | 349.23 | 698.46 | 1396.91 |
| G | 98.00 | 196.00 | 392.00 | 783.99 | 1567.98 |
| A | 110.00 | 220.00 | 440.00 | 880.00 | 1760.00 |
| B | 123.47 | 246.94 | 493.88 | 987.77 | 1975.53 |
Practical Examples
Example 1 -- Tuning a guitar: The standard tuning for a guitar is E2 (82.41 Hz), A2 (110 Hz), D3 (146.83 Hz), G3 (196 Hz), B3 (246.94 Hz), and E4 (329.63 Hz). If a tuner shows your low E string at 83 Hz, it is 83 / 82.41 = slightly sharp. The cents offset is 1200 x log2(83 / 82.41) = +12.4 cents, meaning you need to loosen the string slightly to bring it into tune.
Example 2 -- Identifying a sound in a recording: Audio analysis software shows a dominant frequency at 587 Hz. Using the formula n = 12 x log2(587 / 440) = 4.98, rounding to 5 gives D5 (587.33 Hz). The offset is only -1.0 cents, so the sound is essentially a perfectly tuned D5. This technique is used in music production for key transposition and sample identification.
Example 3 -- Room acoustics: A home studio has a standing wave problem at 85 Hz. The wavelength is 343 / 85 = 4.04 meters. This means the room likely has a dimension close to 4 meters (about 13 feet). Bass traps effective at this frequency need to be at least 1/4 wavelength thick, or about 1 meter. Use our Wave Calculator to explore wavelength and frequency relationships further.
Tips for Accurate Tuning and Frequency Analysis
- Use a quiet environment: Background noise can confuse tuners by introducing competing frequencies. Even subtle HVAC noise at 60 Hz (from electrical systems) can interfere with low-frequency readings.
- Check your reference pitch: Not all ensembles use A4 = 440 Hz. Baroque groups often tune to A = 415 Hz, and some modern European orchestras prefer 442-443 Hz. Always confirm the reference before tuning.
- Account for temperature: The speed of sound increases with temperature. At 30 degrees C, the speed of sound is approximately 349 m/s instead of 343 m/s, which affects wavelength calculations and can shift wind instrument tuning by several cents.
- Understand inharmonicity: Real instruments produce overtones that are not perfect integer multiples of the fundamental. Piano strings, especially in the bass register, have significant inharmonicity, which is why piano tuners stretch the tuning slightly at the extremes.
- Aim for 3 cents or less: Most listeners cannot distinguish pitch differences smaller than 5-6 cents. Professional recordings typically maintain tuning within 2-3 cents for a polished sound.
Concert Pitch Standards Around the World
While A4 = 440 Hz is the international standard per ISO 16, actual concert pitch varies. The Boston Symphony Orchestra and most American ensembles tune to 440 Hz. The Berlin Philharmonic and Vienna Philharmonic tune to 443 Hz. The New York Philharmonic typically uses 442 Hz. Baroque ensembles performing on period instruments commonly tune to 415 Hz (approximately one semitone lower), while some Renaissance music groups tune as low as 392 Hz (A = G in modern pitch). These differences are significant enough that players who switch between modern and period ensembles must adjust or use different instruments.
Frequently Asked Questions
Why is A4 tuned to 440 Hz?
A4 = 440 Hz was adopted as the international concert pitch standard by the International Organization for Standardization (ISO 16) in 1955. Before standardization, concert pitch varied widely from 415 Hz in Baroque ensembles to 466 Hz in some 19th-century orchestras. Today, most orchestras tune to 440 Hz, though some European ensembles prefer 442-443 Hz for a brighter sound. The Berlin Philharmonic, for example, tunes to 443 Hz. This variation means musicians should always confirm the reference pitch before tuning.
What is equal temperament and how does it work?
Equal temperament is a tuning system that divides the octave into 12 equal semitones, with each semitone having a frequency ratio of 2^(1/12), approximately 1.05946. This system allows instruments to play in any key with consistent-sounding intervals. Before equal temperament became standard in the 18th century, other systems like meantone and Pythagorean tuning were used, each favoring certain keys over others. Equal temperament sacrifices perfect intervals (pure fifths, pure thirds) for universal key compatibility, which is why some musicians prefer just intonation for specific genres.
What are cents in music and how are they measured?
A cent is a logarithmic unit used to measure musical intervals. There are exactly 100 cents in one semitone and 1,200 cents in one octave. The formula is cents = 1200 x log2(f1/f2), where f1 and f2 are two frequencies. Most trained musicians can detect pitch differences of about 5-10 cents, while professional tuners aim for accuracy within 1-2 cents. A +10 cent offset means a note is slightly sharp, while -10 cents means slightly flat. Use our Metronome Calculator alongside pitch tuning for complete practice preparation.
What is the range of human hearing in Hz?
The human ear can typically detect frequencies between 20 Hz and 20,000 Hz (20 kHz), though this range narrows significantly with age. According to the World Health Organization, by age 50 most adults lose sensitivity above 12,000-14,000 Hz. A standard 88-key piano spans from A0 (27.5 Hz) to C8 (4,186 Hz), covering about 7 octaves. The lowest note on a large pipe organ can reach 16 Hz (C0), which is felt as vibration rather than heard as a distinct pitch.
How do I calculate the frequency of any musical note?
In equal temperament, the frequency of any note is calculated using f = 440 x 2^(n/12), where n is the number of semitones above or below A4. For middle C (C4), n = -9 (nine semitones below A4), giving f = 440 x 2^(-9/12) = 261.63 Hz. For A5 (one octave above A4), n = 12, giving f = 440 x 2^(12/12) = 880 Hz. Each octave exactly doubles the frequency. This formula works for any reference pitch -- simply replace 440 with your reference A4 value.
What is the difference between concert pitch and scientific pitch?
Concert pitch (A4 = 440 Hz) is the international standard used by virtually all modern orchestras, bands, and recording studios. Scientific pitch (also called philosophical pitch) sets C4 at exactly 256 Hz, making A4 approximately 430.54 Hz. Scientific pitch was proposed because 256 is a power of 2 (2^8), making octave calculations simpler in academic contexts. It was never widely adopted in musical performance but appears occasionally in acoustics research and sound therapy.