Note Frequency Calculator

Pitch and the Musical Scale

Western music divides the octave into twelve equally spaced notes called semitones. Each step upward multiplies the frequency by the twelfth root of two, creating a system known as equal temperament. This approach allows instruments to play in any key without sounding noticeably out of tune. By starting from a reference pitch—commonly A4 at 440 Hz—we can calculate every other note's frequency with a simple mathematical formula.

How the Formula Works

The distance between two notes is measured in semitones. Each semitone corresponds to one step in the chromatic scale. When you move n semitones away from A4, the frequency changes by a factor of 2^(n/12). In MathML, the formula looks like this:

$f=440\times 2^{\frac{n}{12}}$

Here, $n$ represents the number of semitones between your chosen note and A4. A positive n raises the pitch, while a negative n lowers it. The resulting frequency is measured in Hertz.

Determining the Semitone Distance

To calculate $n$, assign each note an index within the octave. Using C as 0, C♯ as 1, up to B as 11, the value of $n$ equals the note index minus 9 (for A) plus 12 multiplied by the difference in octaves from 4. For example, C5 has an index of 0 and sits one octave above A4, giving $n=0-9+12$ or 3. This systematic approach allows software to convert any note name and octave into a precise semitone distance without large lookup tables.

The table below shows indices for each note within an octave:

Note	Index	Note	Index
C	0	G	7
C#	1	G#	8
D	2	A	9
D#	3	A#	10
E	4	B	11
F	5
F#	6

Using This Calculator

1. Select the note from the drop-down menu.
2. Choose the octave number. Middle C sits in octave 4.
3. Click Calculate Frequency to display the pitch in Hertz.
4. Use the Copy button to save the result for tuning your instruments or for reference in music theory studies.

Example Calculation

Suppose you select C in octave 5. C5 lies three semitones above A4, so n equals 3. Plugging into the formula gives 440 × 2^(3/12), which is approximately 523.25 Hz. The calculator computes this automatically, so you can explore different notes with ease.

Frequency Reference Table

The following table lists frequencies for several notes across two octaves using the 440 Hz reference. Values are rounded to two decimals.

Note	Octave 3	Octave 4	Octave 5
C	130.81 Hz	261.63 Hz	523.25 Hz
E	164.81 Hz	329.63 Hz	659.26 Hz
G	196.00 Hz	392.00 Hz	783.99 Hz
A	220.00 Hz	440.00 Hz	880.00 Hz

Such tables are helpful when tuning by ear or designing instruments, providing quick reference points across registers.

Why Frequency Matters

Understanding note frequency helps musicians tune their instruments, design synthesizer patches, and explore harmonic relationships. Frequency analysis plays a key role in audio engineering, allowing producers to sculpt sounds with equalizers and filters. By grasping the numbers behind the music, you gain deeper insight into how melodies and chords interact.

Tuning Standards

While A4 at 440 Hz is the most widely used reference, some orchestras tune slightly higher or lower for historical authenticity or desired tone. Baroque ensembles may favor 415 Hz, while certain modern groups prefer 442 Hz. This calculator assumes 440 Hz as the default but you can easily adjust the formula in the script if you work with a different reference pitch.

Alternate Tunings

Beyond equal temperament, other tuning systems adjust intervals to achieve different musical effects. Just intonation uses ratios of small integers to produce pure-sounding harmonies but limits modulation. Meantone temperaments compromise between pure intervals and the ability to change keys. If you work in these systems, the frequencies for certain notes may differ slightly from the calculator’s output. Nonetheless, understanding equal temperament lays a foundation for exploring these advanced concepts.

A Brief History of Equal Temperament

Equal temperament became the dominant tuning system in the 18th century, allowing keyboard instruments to play in any key without retuning. Before that, just intonation or mean-tone temperament produced purer intervals in specific keys, but sounded dissonant in others. The adoption of equal temperament paved the way for more complex harmonic progressions and modulations, influencing composers from Bach to Beethoven and beyond.

Practical Applications

Electronic musicians use note frequency calculations when programming synthesizers or creating digital audio workstations (DAW) automation. Acoustic players rely on tuners that reference these same formulas under the hood. Even casual musicians benefit from understanding how frequency relates to pitch when experimenting with alternate tunings or transposing music.

Exploring Harmonics

Every musical note contains a fundamental frequency and a series of overtones. These overtones are integer multiples of the base frequency. The unique balance of these harmonics gives each instrument its distinct timbre. By analyzing frequency relationships, you can craft richer sounds or troubleshoot resonance issues in a recording space.

MIDI Note Numbers

Digital audio workstations often use MIDI note numbers to represent pitch. In this system, A4 corresponds to number 69. A general formula links MIDI numbers to frequency:

$f=440\times 2^{\frac{m-69}{12}}$

where $m$ is the MIDI note. Understanding this conversion allows musicians to script pitch changes or map synthesizer controls precisely.

Final Thoughts

Music theory blends art with mathematics. This note frequency calculator bridges the gap, letting you see the numbers behind the melodies you love. Whether you're tuning a guitar, designing a synth patch, or exploring the physics of sound, knowing the exact frequency of each note empowers your creativity.

Limitations and Assumptions

• The calculator assumes equal temperament with A4 = 440 Hz; other standards will produce different values.
• Frequencies are rounded to two decimals; high-precision work may require more significant figures.
• Real instruments may deviate slightly due to temperature, material, or tuning method.

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