Lesson 5 of 15
Interval Ratios
Intervals and Frequency Ratios
An interval is the distance between two notes measured in semitones.
In 12-TET, every interval has a precise frequency ratio:
ratio = 2^(semitones / 12)Common Intervals
| Semitones | Name | Ratio |
|---|---|---|
| 0 | Unison | 1.0000 |
| 3 | Minor 3rd | 1.1892 |
| 4 | Major 3rd | 1.2599 |
| 7 | Perfect 5th | 1.4983 |
| 12 | Octave | 2.0000 |
The perfect fifth (7 semitones) has ratio ≈ 3/2, making it one of the most consonant intervals. Two notes a perfect fifth apart sound naturally "in tune" together.
From Ratio to Frequency
If the root is at frequency f, the note n semitones above is at:
f × intervalRatio(n)Your Task
Implement intervalRatio(semitones) that returns the frequency ratio.
Run your code to hear A4 and its perfect fifth (E5) played together.
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Click "Run" to execute your code.