Frequency to Note Converter
Convert frequency in Hz to the nearest musical note and cents deviation. Enter values for instant results with step-by-step formulas.
Formula
n = 12 x log2(f / refA); Note = noteNames[(69 + round(n)) mod 12]
Calculate the number of semitones (n) from the reference A4 frequency using the logarithmic relationship. Round to the nearest integer to find the closest note, then use modular arithmetic to determine the note name and octave. The cents deviation is (n - round(n)) times 100.
Worked Examples
Example 1: Identifying an Unknown Frequency
Problem: A spectrum analyzer shows a prominent peak at 329.63 Hz in a guitar recording. Identify the musical note and verify it is in tune.
Solution: Semitones from A4 = 12 x log2(329.63 / 440)\n= 12 x log2(0.74916)\n= 12 x (-0.41667) = -5.0\nMIDI note = 69 + (-5) = 64 = E4\nExact E4 frequency = 440 x 2^(-5/12) = 329.63 Hz\nCents deviation = (actual semitones - rounded) x 100 = 0.0 cents
Result: Note: E4 | Exact frequency: 329.63 Hz | Deviation: 0.0 cents | Perfectly in tune
Example 2: Concert Pitch Comparison
Problem: An orchestra tunes to A=442 Hz instead of A=440 Hz. Calculate how many cents sharp this is and find the corresponding frequency for middle C.
Solution: Cents difference = 1200 x log2(442/440)\n= 1200 x log2(1.004545)\n= 1200 x 0.006564 = 7.9 cents sharp\n\nMiddle C at A=442: C4 = 442 x 2^(-9/12)\n= 442 x 0.59461 = 262.82 Hz\nStandard C4 at A=440 = 261.63 Hz\nDifference = 1.19 Hz
Result: A=442 is 7.9 cents sharp of A=440 | C4 shifts from 261.63 Hz to 262.82 Hz
Frequently Asked Questions
How does frequency relate to musical pitch and notes?
Frequency is the physical measurement of how many times a sound wave oscillates per second, measured in Hertz (Hz). Musical pitch is our perceptual interpretation of frequency, with higher frequencies sounding higher in pitch. Western music divides each octave into 12 equal semitones using equal temperament tuning. The relationship between frequency and semitones is logarithmic, meaning each semitone represents a frequency ratio of the twelfth root of 2 (approximately 1.05946). This means that doubling a frequency always raises the pitch by exactly one octave, regardless of the starting note. For example, A4 at 440 Hz doubles to A5 at 880 Hz, and middle C at 261.63 Hz doubles to C5 at 523.25 Hz.
What is MIDI note number and how does it map to frequency?
MIDI (Musical Instrument Digital Interface) assigns an integer number from 0 to 127 to each note, with middle C defined as MIDI note 60 and A4 (440 Hz) as MIDI note 69. Each increment of one MIDI note number represents one semitone. The frequency of any MIDI note can be calculated using the formula: frequency = 440 times 2 to the power of ((midiNote - 69) / 12). This mapping covers the frequency range from C-1 (8.18 Hz, MIDI 0) to G9 (12543.85 Hz, MIDI 127), encompassing well beyond the range of most acoustic instruments. MIDI note numbers are essential in digital music production for programming synthesizers, sequencing, and controlling virtual instruments. Some systems extend beyond the 0-127 range for special applications.
How do different tuning systems affect the frequency of notes?
Equal temperament, the most common tuning system today, divides the octave into 12 exactly equal semitones with a frequency ratio of the twelfth root of 2 between adjacent notes. However, many other tuning systems exist. Just intonation uses simple whole-number frequency ratios like 3:2 for a perfect fifth and 5:4 for a major third, producing purer harmonies but making key changes difficult. Pythagorean tuning builds all intervals from stacked perfect fifths (3:2 ratios), creating pure fifths but imperfect thirds. Meantone temperament compromises between pure thirds and fifths. Each system assigns slightly different frequencies to the same named notes. For example, an E in just intonation relative to C is 5/4 times the C frequency, but in equal temperament it is 2 to the power of 4/12 times the C frequency, a subtle but audible difference.
How do harmonics and overtones relate to fundamental frequency?
When a musical instrument produces a note, the fundamental frequency (first harmonic) determines the perceived pitch, but the sound also contains overtones at integer multiples of the fundamental. For a note at 220 Hz, the harmonics occur at 440 Hz (second harmonic), 660 Hz (third), 880 Hz (fourth), 1100 Hz (fifth), and so on. The relative strength of these harmonics defines the timbre or tone color of the instrument, which is why a violin and a piano playing the same note sound different. Interestingly, the harmonic series naturally corresponds to musical intervals: the second harmonic is an octave above, the third harmonic is an octave plus a perfect fifth, the fourth harmonic is two octaves, and the fifth harmonic is two octaves plus a major third. This natural relationship is the physical basis for Western harmony and consonance.
What frequency range can humans hear and what is musically useful?
The theoretical range of human hearing spans from 20 Hz to 20,000 Hz (20 kHz), though most adults lose sensitivity to frequencies above 15-16 kHz due to age-related hearing loss called presbycusis. The musically useful range is narrower than the full hearing range. The lowest note on a standard piano is A0 at 27.5 Hz, and the highest is C8 at 4186 Hz. A standard guitar ranges from E2 (82.41 Hz) to about E6 (1318.5 Hz). The human voice ranges from roughly E2 (bass) to C6 (soprano), with most speech concentrated between 85 Hz and 8000 Hz. Frequencies below the musical range (infrasound) can still be felt as physical vibration, while frequencies above the range of fundamental notes are important as harmonics that define instrument timbre and contribute to the perceived brightness and clarity of sound.
What is the equal temperament formula for calculating note frequencies?
The equal temperament formula calculates the frequency of any note relative to a reference pitch: f = refA times 2 to the power of (n / 12), where refA is the reference frequency for A4 (typically 440 Hz) and n is the number of semitones above or below A4. For notes above A4, n is positive; for notes below, n is negative. For example, middle C (C4) is 9 semitones below A4, so f = 440 times 2 to the power of (-9/12) = 261.63 Hz. To go the other direction and find the note from a frequency, use: n = 12 times log base 2 of (frequency / 440). This formula ensures that every semitone has an identical frequency ratio, making all keys sound equally in tune (or equally out of tune from pure intervals, depending on your perspective).