Semitone Calculator

Semitone Formula:

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

Number of Semitones (n):

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1. What is the Semitone Calculation?

The semitone calculation measures the musical interval between two frequencies. In Western music, an octave is divided into 12 semitones, and this calculator determines how many semitones separate any two given frequencies.

2. How Does the Calculator Work?

The calculator uses the semitone formula:

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

Where:

\( n \) — Number of semitones between frequencies
\( f_2 \) — Higher frequency (Hz)
\( f_1 \) — Lower frequency (Hz)

Explanation: The formula calculates the logarithmic distance between two frequencies, scaled to the 12-tone equal temperament system used in Western music.

3. Importance of Semitone Calculation

Details: Semitone calculations are essential for musicians, audio engineers, and instrument tuners to understand pitch relationships, tune instruments, and analyze musical intervals.

4. Using the Calculator

Tips: Enter both frequencies in Hertz (Hz). The order doesn't matter as the calculator uses the ratio between them. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What does a semitone value of 12 mean?
A: A value of 12 semitones indicates an octave difference - the higher frequency is exactly double the lower frequency.

Q2: How many semitones are in a perfect fifth?
A: A perfect fifth is 7 semitones, representing a frequency ratio of approximately 1.4983.

Q3: Can I calculate cents with this?
A: Cents are hundredths of a semitone. Multiply the semitone result by 100 to get cents.

Q4: Does this work for microtonal music?
A: Yes, the calculation works for any frequency ratio, not just standard Western intervals.

Q5: Why use logarithmic calculation?
A: Human pitch perception is logarithmic, so this matches how we naturally hear pitch differences.