You Are Reading the First 6 FREE Chapters (470 pages)
Equal Temperament: Definition of a Semitone
In equal temperament, the semitone or half-step, is not just the smallest interval, the one between adjacent notes—it has a precise definition. To get the frequencies for each semitone:
- Start with the first note of the scale and multiply its frequency by the 12th root of two.
- Take that frequency and multiply it by the 12th root of two, which gives you the frequency for the next semitone up.
- Repeat until you get to the next octave.
The 12th root of 2 is the number 1.05946 (rounded off). So the ratio of any semitone to the semitone below is 1.05946:1.
Table 29 shows the frequencies of all the notes from Middle C to the octave above middle C, with each successive frequency multiplied by the 12th root of two:
TABLE 29 Equal Temperament Frequencies for Tones from Middle C to C Above Middle C, and Associated Simple Frequency Ratios
| Note | Equal Temperament Frequency (Hz) | Interval with Middle C | Simple Frequency Ratio (SFR) | Associated SFR Frequency (Hz) |
|---|---|---|---|---|
| Middle C | 261.6 | Unison | 1:1 | 261.6 |
| C♯ | 277.2 | Minor 2nd | 16:15 | 279.0 |
| D | 293.6 | Major 2nd | 9:8 | 294.3 |
| E♭ | 311.1 | Minor 3rd | 6:5 | 313.9 |
| E | 329.6 | Major 3rd | 5:4 | 327.0 |
| F | 349.2 | Perfect 4th | 4:3 | 348.8 |
| F♯ | 370.0 | Tritone | 45:32 | 367.9 |
| G | 392.0 | Perfect 5th | 3:2 | 392.4 |
| A♭ | 415.3 | Minor 6th | 8:5 | 418.6 |
| A | 440.0 | Major 6th | 5:3 | 436.0 |
| B♭ | 466.1 | Minor 7th | 16:9 | 465.1 |
| B | 493.8 | Major 7th | 15:8 | 465.1 |
| C | 523.2 | Octave | 2:1 | 523.2 |