# Note Frequency Calculator

> Convert between musical notes and Hz frequencies with octave selection

**Category:** Media
**Keywords:** note, frequency, hz, hertz, music, octave, pitch, midi, wavelength, audio, musical note, A4, concert pitch
**URL:** https://complete.tools/note-frequency-calculator

## How it calculates

All calculations use the equal temperament tuning system with A4 = 440 Hz as the reference pitch. This is the international standard for concert pitch adopted in 1939.

**Note to Frequency Formula:**
```
f = 440 × 2^((n - 69) / 12)
```
Where `n` is the MIDI note number. MIDI note 69 corresponds to A4 (concert A). Each semitone up or down multiplies or divides the frequency by the twelfth root of 2 (approximately 1.05946).

**Frequency to Note (Reverse):**
```
MIDI = 69 + 12 × log₂(f / 440)
```
The result is rounded to the nearest integer to find the closest note. The fractional difference is converted to cents (hundredths of a semitone) to show how far off the input frequency is from perfect pitch.

**Wavelength:**
```
wavelength = speed of sound / frequency = 343 / f
```
The speed of sound at 20°C (68°F) at sea level is 343 m/s. Wavelength gets shorter as frequency increases.

**MIDI Note Numbering:**
Middle C is C4, which is MIDI note 60. A4 (concert A) is MIDI note 69. Notes go from MIDI 0 (C-1, approximately 8.18 Hz) to MIDI 127 (G9, approximately 12,544 Hz).

## Understanding cents and tuning

A cent is one hundredth of a semitone. Since there are 12 semitones in an octave, there are 1,200 cents per octave. Cents are a logarithmic unit, which means the ratio between two frequencies is constant regardless of where in the pitch range you are.

**Tuning reference:**
- 0 cents: perfectly in tune
- ±5 cents: very close, most listeners cannot detect the difference
- ±10 cents: slightly out of tune, trained ears may notice
- ±25 cents: noticeably out of tune in a musical context
- ±50 cents: exactly halfway between two notes (a quarter tone)

When a synthesizer or instrument is described as "in tune," it means its pitch deviates less than ±5 cents from equal temperament. Older instruments, stretched strings, and wind instruments at unusual temperatures often deviate more.

## FAQs

**Q:** What is the frequency of middle C?


**A:** Middle C is C4, which has a frequency of 261.63 Hz. It sits at MIDI note 60. The name "middle C" comes from its position near the center of the piano keyboard and roughly in the middle of the range of human hearing used in music.


**Q:** Why is A4 = 440 Hz the standard?


**A:** The 440 Hz standard for A4 was adopted by the International Organization for Standardization (ISO) in 1975, though it had been in widespread use since the 1939 London conference. Before standardization, concert A varied from about 415 Hz to 466 Hz depending on region and era. Some orchestras still use 442 or 443 Hz for a slightly brighter sound.


**Q:** What is equal temperament?


**A:** Equal temperament divides the octave into 12 equal semitones, each with a frequency ratio of the twelfth root of 2 (about 1.05946). This allows instruments to play in any key without retuning. Other tuning systems like just intonation or meantone temperament use slightly different ratios that sound purer in some keys but worse in others.


**Q:** What is a MIDI note number?


**A:** MIDI (Musical Instrument Digital Interface) uses integers from 0 to 127 to represent pitches. Middle C (C4) is MIDI 60. A4 is MIDI 69. Each step up or down is one semitone. MIDI note numbers are used universally in digital audio workstations, synthesizers, and music software.


**Q:** Why does wavelength matter in music?


**A:** Wavelength determines how sound interacts with physical space. A bass note at 80 Hz has a wavelength of about 4.3 meters, which is why bass frequencies can wrap around walls and are harder to localize. A high note at 8,000 Hz has a wavelength of about 4 cm, making it very directional. This affects speaker design, room acoustics, and instrument construction.


**Q:** What frequencies can humans hear?


**A:** The human audible range is generally described as 20 Hz to 20,000 Hz (20 kHz), though this varies significantly with age. Most adults over 30 cannot hear above 15-16 kHz. Infants can sometimes hear up to 20 kHz. Musical instruments rarely exceed 15 kHz in their fundamental tones, though overtones extend higher.

## How to use

1. Choose your direction: select "Note → Hz" to convert a note to a frequency, or "Hz → Note" to find the note nearest to a given frequency.
2. In Note to Hz mode: pick a note (C through B, including sharps and flats) from the dropdown, then select the octave (0 through 8). Octave 4 contains middle C.
3. Click "Calculate Frequency" to see the result, including the frequency in Hz, the MIDI note number, and the wavelength in meters.
4. In Hz to Note mode: type a frequency in the input field (any value from 1 to 20,000 Hz is accepted). Click "Find Nearest Note."
5. The reverse result shows the nearest note name and octave, the MIDI note number, the exact frequency of that note, the wavelength, and the cents deviation — how many hundredths of a semitone your entered frequency differs from perfect pitch.
6. Use the cents deviation to determine how in-tune a frequency is. Values within ±5 cents are considered very accurate; values beyond ±25 cents are noticeably out of tune.

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