Cents & Interval Calculator

Frequently Asked Questions

How many cents can people hear?

Trained ears notice mistuning of about 5-10 cents on sustained tones. Beating between close pitches is audible at even finer differences, especially on pure sine tones.

Why are cents better than Hz for describing tuning?

A 1 Hz error at 100 Hz is a large interval but trivial at 1000 Hz. Cents normalise this so a fixed value means the same musical amount anywhere on the pitch spectrum.

What is the syntonic comma?

The gap between four pure fifths and two octaves plus a pure major third, about 21.5 cents. It is the historical inconsistency that led to the development of various temperaments.

Can I build microtonal scales with this calculator?

Yes - pick a step size in cents (e.g. 1200/19 for 19-EDO) and use reverse mode to generate every pitch from a reference frequency.

What is the difference between equal temperament and just intonation?

In 12-TET every semitone is exactly 100 cents. In just intonation, intervals use simple whole-number frequency ratios that differ from 12-TET by a few cents.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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How It Works

A cent is the standard fine unit of musical pitch: there are exactly 100 cents in an equal-tempered semitone and 1200 cents in an octave. This calculator measures the interval in cents between any two frequencies, reports the underlying frequency ratio, and in reverse computes the frequency you get by detuning a base frequency by a given number of cents.

Tuners, intonation analysis, microtonal scales, and comparisons between tuning systems (equal temperament versus just intonation) all live in cents because the unit is logarithmic and therefore matches how we perceive pitch - a fixed cent difference sounds like the same amount of detuning whether the notes are low or high.

The formula for cents between two frequencies is c = 1200 x log2(f2 / f1). To apply N cents to a base frequency: f = f_base x 2^(N / 1200). Because the relationship is logarithmic, intervals add: stacking a 700-cent fifth on a 400-cent third gives an 1100-cent interval.

Use Cases

Cents and interval calculations are used across a wide range of musical and technical contexts:

Measuring how far a string, wind, or brass instrument is from equal temperament during intonation work

Comparing just-intonation intervals to their equal-temperament equivalents in music theory

Designing microtonal scales by generating pitches at a fixed cent interval from a root

Setting up a synth oscillator's fine-tune or detune control to a specific amount of detuning

Analysing historical temperaments (meantone, Pythagorean) by measuring their deviation from 12-TET

Tips

Trained ears notice mistuning of about 5-10 cents on sustained tones; beating between close pitches is audible even finer.

Cents are signed: f2 below f1 gives a negative value (a descending interval).

A pure perfect fifth has ratio 3:2, which is about 701.96 cents - just 2 cents wider than the equal-tempered 700-cent fifth.

To build a microtonal scale, pick a step size in cents (e.g. 1200 / 19 for 19-EDO) and use reverse mode to generate every pitch from a reference.

Always use log base 2 for cents calculations, not log base 10. The 1200 factor pairs specifically with log2.

FAQ

How many cents can people hear?

Trained ears notice mistuning of about 5-10 cents on sustained tones. Beating between close pitches is audible even at finer differences, especially on pure sine tones.

Why are cents better than Hz for describing tuning?

A 1 Hz error at 100 Hz is a big interval but trivial at 1000 Hz. Cents normalise this so a fixed value means the same musical amount everywhere on the pitch spectrum.

What is the syntonic comma?

The gap between four pure fifths and two octaves plus a pure major third, about 21.5 cents. It is the historical headache that led to the development of various temperaments.

Can I build microtonal scales with this?

Yes - pick a step size in cents (e.g. 1200/19 for 19-EDO) and use reverse mode to generate every pitch from a reference frequency.

What is the difference between equal temperament and just intonation?

In 12-TET every semitone is exactly 100 cents. In just intonation, intervals use simple whole-number frequency ratios. Most just intervals differ from their 12-TET counterparts by a few cents.

Cents & Interval Calculator

Frequently Asked Questions

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