Interval Calculator

Interval Formula:

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

Interval (n):

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1. What is the Interval Formula?

The interval formula calculates the musical distance between two frequencies in semitones. This measurement is fundamental in music theory and sound engineering for understanding pitch relationships.

2. How Does the Calculator Work?

The calculator uses the interval formula:

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

Where:

\( n \) — Interval in semitones
\( f_2 \) — Second frequency in Hertz
\( f_1 \) — First frequency in Hertz

Explanation: The formula calculates how many semitones apart two frequencies are in the equal temperament tuning system.

3. Importance of Interval Calculation

Details: Interval calculation is essential for music composition, instrument tuning, sound design, and audio analysis. It helps quantify the perceived pitch difference between sounds.

4. Using the Calculator

Tips: Enter both frequencies in Hertz (Hz). The frequencies must be positive numbers. The result shows how many semitones apart the two frequencies are.

5. Frequently Asked Questions (FAQ)

Q1: What is a semitone in music?
A: A semitone is the smallest musical interval commonly used in Western music, equal to one twelfth of an octave.

Q2: How many semitones are in an octave?
A: There are 12 semitones in an octave, which represents a doubling of frequency.

Q3: What does a negative interval value mean?
A: A negative value means f2 is lower than f1. The absolute value represents the interval size.

Q4: Can I use this for non-musical frequencies?
A: Yes, the formula works for any frequencies, though the musical interpretation only makes sense for audible pitches.

Q5: How precise is this calculation?
A: The calculation is mathematically precise, though human pitch perception has limited resolution (about ±0.5 semitones).