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Musical scales and intervals
Intermediate
Notes relate by simple frequency ratios.
Notes sound consonant when their frequencies are ratios of small integers: octave 2:1, fifth 3:2, fourth 4:3. Equal temperament divides the octave into 12 steps of 2^{1/12}.
A440 and E at 660 Hz are a perfect fifth.
Equal temperament slightly detunes pure intervals.
In more detail
Musical intervals are defined by frequency ratios. An octave is a ratio of 2:1, a perfect fifth is 3:2, and a perfect fourth is 4:3.
Real-world uses
- Composers and tuners use frequency ratios to define harmony.
- Electronic tuners display pitch and interval relations.
- Musicians tune instruments to just intonation, where the notes of a chord have simple frequency ratios that sound smooth.
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Frequently asked questions
Why do intervals sound pleasant?
Simple frequency ratios produce waveforms that align well, which the ear perceives as consonant.
What is equal temperament?
A system that divides the octave into twelve equal semitones, slightly altering pure ratios.
Why do some intervals sound better than others?
Simple whole-number frequency ratios produce few clashing beats, so the pleasant intervals are those with small numbers.
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