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It's Sharp and Flat in Equal Temperament Tuning
In equal-temperament tuning, all of the notes except the octave notes are either slightly flat or slightly sharp, compared with their simple-frequency-ratio counterparts. So, when you’re playing in any given key, only the two octave notes are in an exact 2:1 simple frequency relationship. Every other note is slightly out of tune, compared with the simple frequency ratio expected from the harmonic series.
For example, in Table 29 above:
- The frequency for the note G would be 392.4 Hz if it were tuned in an exact 3:2 ratio with Middle C. But the equal temperament frequency of G is 392.0 Hz (slightly flatter).
- The frequency for the note E would be 327.0 Hz if it were tuned in an exact 5:4 ratio with Middle C. But the equal temperament frequency of E is 329.6 Hz (slightly sharper).
- The frequency for the note C♯ would be 279.0 Hz if it were tuned in an exact 16:15 ratio with Middle C. But the equal temperament frequency of C♯ is 277.2 Hz (slightly flatter).