Middle C has a frequency of approximately 261.63 Hz in 12-tone equal temperament when A4 is tuned to 440 Hz. Its more precise theoretical value is 261.6256 Hz. In scientific pitch notation, Middle C is C4; in MIDI, it is note number 60.
That answer depends on the tuning reference. Change A4 from 440 Hz, and Middle C changes with it. This is why you may see 256 Hz or different octave labels in books and software. To understand where C4 fits, compare it with a musical-note frequency chart.
What Is the Frequency of Middle C?
The standard Middle C frequency is 261.63 Hz under A440 equal temperament. “A440” means the A above Middle C is tuned to 440 Hz, while equal temperament divides every octave into 12 equal frequency ratios.
| Tuning system or reference | Middle C frequency | What it means |
|---|---|---|
| A4 = 440 Hz, equal temperament | 261.63 Hz | The modern standard used by many instruments, tuners, and recordings |
| A4 = 432 Hz, equal temperament | 256.87 Hz | Every note is about 1.82% lower than in A440 |
| Scientific or philosophical pitch | 256 Hz | C4 is fixed at an exact power-of-two value |
The frequency is not a property of the letter C alone. The tuning reference determines its numerical frequency, which is why concert pitch standards must be agreed upon before an ensemble plays together.
Why Middle C Is Approximately 261.63 Hz
Equal temperament is built from ratios rather than equal gaps in hertz. Each semitone multiplies frequency by (2^{1/12}), or approximately 1.05946. Middle C lies nine semitones below A4.
The result, 261.6256 Hz, is normally rounded to 261.63 Hz. A displayed value of 261.6 Hz or 262 Hz can therefore describe the same theoretical note at lower precision. For more context on the reference note, see the explanation of A4 and its frequency.
Does a Real Instrument Produce Exactly 261.63 Hz?
A real performance rarely stays fixed at exactly 261.6256 Hz. Piano tuning may involve small adjustments, a singer’s pitch fluctuates, and acoustic sounds contain harmonics above the fundamental. The calculated value is the target under a defined tuning system, while a tuner estimates the incoming sound’s fundamental.
How Is the Middle C Frequency Calculated?
Middle C can be calculated with the equal-temperament formula (f = 440 \times 2^{(n-69)/12}), where (f) is frequency in hertz and (n) is the MIDI note number. Middle C is MIDI note 60, while A4 is MIDI note 69.
Calculating C4 From A4 at 440 Hz
Substitute 60 for (n):
[
f = 440 \times 2^{(60-69)/12}
]
[
f = 440 \times 2^{-9/12} \approx 261.6256\text{ Hz}
]
Frequency differences are not evenly spaced. A semitone near C4 covers fewer hertz than the same interval several octaves higher. The broader relationship between note height and vibration is explained in pitch versus frequency.
How Changing the Reference Changes C4
If A4 is set to a reference other than 440 Hz, replace 440 in the formula. With A4 at 432 Hz:
[
f = 432 \times 2^{-9/12} \approx 256.87\text{ Hz}
]
The interval structure remains unchanged; the tuning grid shifts lower. Setting C4 to exactly 256 Hz instead produces an A4 of approximately 430.54 Hz. A detailed 432 Hz and 440 Hz comparison explains the difference.
Why Is Middle C Called C4?
Middle C is called C4 in scientific pitch notation because it begins the fourth numbered octave. In that system, each octave number changes at C rather than at A, so the notes immediately below Middle C are B3, A3, and G3.
Where Middle C Appears on a Piano
On a standard 88-key piano, Middle C is the 40th key from the left. That leaves 39 keys below it and 48 keys above it, so it is near the keyboard’s center but not the exact middle key.
You can locate it visually as the C immediately to the left of the pair of black keys nearest the keyboard’s center. The surrounding values in a piano-note frequency reference help show how quickly frequencies rise across the keyboard.
Where Middle C Appears on the Staff
In grand-staff notation, Middle C sits between the bass and treble staves. It is written on the first ledger line below the treble staff or the first ledger line above the bass staff.
This central notational position is the main reason for its familiar name. “Middle” refers more usefully to its role between the two staves than to an exact physical midpoint on every keyboard.
Why Do Some Programs Call Middle C C3 or C5?
Some programs label Middle C as C3 or C5 because octave-number conventions are not universal. The audible pitch can still be 261.63 Hz, and the MIDI identifier can still be note 60, even when the displayed octave number differs.
MIDI Note 60 Stays the Same
MIDI identifies keys with numbers, not mandatory scientific-pitch labels. Note 60 consistently represents the same key number, but software developers may choose different names for its octave.
This is a labeling disagreement, not a frequency disagreement. A displayed C3 at 261.63 Hz may sound identical to scientific-pitch C4.
How to Avoid Octave-Number Confusion
Check both the frequency and the MIDI note number when transferring music between programs. “C4, MIDI 60, approximately 261.63 Hz under A440” is much less ambiguous than “C4” alone.
Octave labels matter when programming virtual instruments or exporting MIDI. A guide to scientific pitch notation can help translate note names and octave numbers.
Why Is Middle C Sometimes Listed as 256 Hz?
Middle C is listed as 256 Hz in scientific or philosophical pitch, a historical tuning proposal that assigns C4 an exact power-of-two frequency. It is not the standard C4 value produced by A4 = 440 Hz in equal temperament.
256 Hz Is a Different Tuning Standard
Calling 256 Hz “Middle C” is valid only when the tuning system is stated. Under standard A440 equal temperament, 256 Hz falls about 37 cents below C4, where 100 cents equals one equal-tempered semitone. It is therefore noticeably lower in careful comparison.
Confusion arises when a chart gives the number without naming its reference. Always look for terms such as A440, A432, equal temperament, or scientific pitch before comparing frequency tables.
Why 256 Is Mathematically Convenient
The number 256 equals (2^8). Doubling or halving it produces whole-number C frequencies—128, 512, and 1,024 Hz—which makes octave calculations simple. Mathematical neatness, however, does not make 256 Hz the current A440 value.
Under standard tuning, octaves still follow exact doubling: C3 is about 130.81 Hz, C4 is about 261.63 Hz, and C5 is about 523.25 Hz. This doubling relationship is covered more fully in the guide to how musical octaves work.
What Are the Frequencies Around Middle C?
The C notes surrounding Middle C are related by powers of two. Moving up one octave doubles frequency, while moving down one octave halves it.
| Note | Frequency under A440 | Relationship to Middle C |
| C3 | 130.81 Hz | One octave below; half the frequency |
| C4 | 261.63 Hz | Middle C |
| C5 | 523.25 Hz | One octave above; double the frequency |
These are theoretical equal-tempered targets. A live reading may move slightly around them because of tuning, technique, vibrato, or measurement conditions.
Frequently Asked Questions
Is Middle C C3, C4, or C5?
Middle C is C4 in scientific pitch notation and corresponds to MIDI note 60. Some software calls the same pitch C3 or C5, so confirm the program’s octave-label convention rather than relying on the label alone.
Why is Middle C 261.63 Hz instead of 256 Hz?
Middle C is 261.63 Hz when A4 equals 440 Hz and the octave uses 12-tone equal temperament. The 256 Hz value comes from scientific or philosophical pitch, which uses a different reference.
What MIDI number represents Middle C?
Middle C is MIDI note 60. MIDI note numbering remains consistent even when different programs give that pitch different octave labels.
What is the frequency one octave above Middle C?
One octave above Middle C is C5 at approximately 523.25 Hz under A440 equal temperament. Its frequency is exactly twice C4’s theoretical frequency before rounding.
Does Middle C change when A4 is tuned to 432 Hz?
Yes. With A4 tuned to 432 Hz in equal temperament, Middle C becomes approximately 256.87 Hz. Lowering the reference pitch shifts every note in the tuning system by the same proportional amount.
Is Middle C exactly in the center of an 88-key piano?
No. Middle C is the 40th key from the left on an 88-key piano, with 39 keys below it and 48 above it. Its name primarily reflects its central role between the treble and bass staves.
Vincent is a pitch detection and vocal analysis writer at OnlinePitchDetector. He focuses on pitch recognition, vocal frequency analysis, singing tools, and real-time audio testing for singers, musicians, producers, and beginners.