Semitone Interval Calculator

Semitone Interval Formula:

\[ n = 12 \times \log_2\left(\frac{f_2}{f_1}\right) \]

Semitone Interval (n):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Semitone Interval?

The semitone interval measures the musical distance between two pitches. In equal temperament tuning, one semitone equals one twelfth of an octave. This calculator computes the exact semitone difference between any two frequencies.

2. How Does the Calculator Work?

The calculator uses the semitone interval formula:

\[ n = 12 \times \log_2\left(\frac{f_2}{f_1}\right) \]

Where:

\( n \) — Semitone interval
\( f_2 \) — Higher frequency (Hz)
\( f_1 \) — Lower frequency (Hz)
\( \log_2 \) — Logarithm base 2

Explanation: The formula converts the frequency ratio to a logarithmic scale (base 2) and scales it to semitone units.

3. Importance of Semitone Calculation

Details: Semitone calculations are essential for music theory, instrument tuning, audio engineering, and sound design. They help quantify pitch relationships precisely.

4. Using the Calculator

Tips: Enter both frequencies in Hertz (Hz). The order doesn't matter as the calculator will return both positive and negative values (higher/lower pitch).

5. Frequently Asked Questions (FAQ)

Q1: What does a positive/negative value mean?
A: Positive means f₂ is higher than f₁; negative means f₂ is lower than f₁.

Q2: How many semitones are in an octave?
A: There are exactly 12 semitones in one octave in equal temperament tuning.

Q3: What's the semitone value for perfect fifth?
A: A perfect fifth is 7 semitones (frequency ratio of 3:2).

Q4: Can I use this for microtonal music?
A: Yes, the calculator gives precise decimal values for microtonal intervals.

Q5: How accurate is this calculation?
A: Mathematically precise for any valid frequency input, assuming equal temperament.