The Equal-tempered Chromatic Scale
Since a musical interval is a ratio of frequencies, the equal-tempered chromatic scale divides the octave (which has a ratio of 2:1) into twelve equal parts.
Applying this value successively to the tones of a chromatic scale, starting from A above middle C with a frequency of 440 Hz, produces the following sequence of pitches:
| Note |
Frequency Hz |
Multiplier |
Coefficient (to six places) |
|---|---|---|---|
| A | 440.00 | 20/12 | 1.000000 |
| A♯ B♭ | 466.16 | 21/12 | 1.059463 |
| B | 493.88 | 22/12 | 1.122462 |
| C | 523.25 | 23/12 | 1.189207 |
| C♯ D♭ | 554.37 | 24/12 | 1.259921 |
| D | 587.33 | 25/12 | 1.334839 |
| D♯ E♭ | 622.25 | 26/12 | 1.414213 |
| E | 659.26 | 27/12 | 1.498307 |
| F | 698.46 | 28/12 | 1.587401 |
| F♯ G♭ | 739.99 | 29/12 | 1.681792 |
| G | 783.99 | 210/12 | 1.781797 |
| G♯ A♭ | 830.61 | 211/12 | 1.887748 |
| A | 880.00 | 212/12 | 2.000000 |
The final A (880 Hz) is twice the frequency of the lower A (440 Hz), that is, one octave higher.
Read more about this topic: Twelfth Root Of Two
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