How To Calculate Semitone Interval

Semitone Interval Formula:

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

Semitone Interval (n):

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1. What is Semitone Interval?

The semitone interval measures the musical distance between two frequencies. In Western music, an octave is divided into 12 equal semitones, which form the basis of the chromatic scale.

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:

\( n \) — Number of semitones between frequencies
\( f_2 \) — Higher frequency (Hertz)
\( f_1 \) — Lower frequency (Hertz)
\( \log_2 \) — Logarithm base 2

Explanation: The formula calculates how many 12th-octave steps exist between two frequencies, accounting for the logarithmic nature of musical pitch perception.

3. Importance of Semitone Calculation

Details: Semitone intervals are fundamental in 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 matters - f₂ should be the higher frequency for positive semitone values. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the semitone interval between A4 (440Hz) and A5?
A: 12 semitones (exactly one octave), since A5 is 880Hz and 12 × log₂(880/440) = 12.

Q2: How many semitones is a perfect fifth?
A: 7 semitones (frequency ratio ≈1.4983). For example, from C4 to G4.

Q3: Can I calculate cents with this formula?
A: Yes! 1 semitone = 100 cents. Multiply the result by 100 to get cents.

Q4: Why use logarithmic calculation?
A: Human pitch perception is logarithmic - we perceive equal ratios as equal intervals.

Q5: What if my result is negative?
A: Negative values mean f₂ is lower than f₁. The absolute value gives the interval size.