Vocal Capability Battery: Pitch

Hertz vs Semitones

If you read medical papers on voice, chances are you have encountered a statement like “The pitch increased an average of 20 Hz (Hertz) with the procedure.” This is a relatively meaningless statement unfortunately. Hertz is a logrithmic/exponential scale. Averaging numbers (adding up a group of numbers and dividing by the total) in an exponential scale is a non-simple task. It mixes up addition with multiplication and the order in which one adds and multiplies has an effect on the answer. It can be done with logrithms, but not directly. The effect is perhaps most noticeable when you compare pitch notation in Hertz with pitch notation in semitones.

Perhaps thinking about a piano might be helpful. If you played a major scale, Do, Re, Mi, Fa, So, La, Ti, Do. There is a full tone between the Do and the Re, between the Re and the Mi, while there is a half-tone or a semi-tone between the Mi and the Fa. On the other hand if you play every key in a row, including the black keys, the distance between each note is a semi-tone. Whether you are at the bottom of the piano or at the top, the sound interval between a C note and a D note sounds like the same interval or distance.

Each note in the 12 note scale goes up an equal amount, that is, an equal amount exponentially speaking. The jump between C3 and C3# is 15.56 Hertz and the very next jump between C3# and D3 is 16.48 Hertz. Although the Hertz jump is not equal between the notes, it is an equal jump in the exponent number and it sounds like an equal jump to our ears going up the scale.

For a more extreme example at the top of the piano, if you jump from C to D you may have jumped 256 Hz, while at the bottom of the piano, the interval between C and D measures only 8 Hz.

I utilize musical notation to describe pitch range. Middle C on the piano is called C4 (the beginning of the fourth octave on the piano). Men typically speak comfortably in a range from B2 to E3. That is to say, on the piano B2 is the B in the second octave (13 notes or 13 semi-tones below middle C) and E3 (the E below middle C or 8 semi-tones below middle C) is the typical range that most males speak in comfortably.

Most females speak in a range between F3 and A3. These notes are found in the octave below middle C. There are some women who speak outside this range. One example could be a woman who smokes cigarettes and has smoker's polyps might have a speaking pitch of E3 or D3 in the upper end of a typical male's range. Pitch is not the only component of the perception of male and female. Resonance plays into that perception as well. Thus the a woman with a speaking pitch of E3 may still sound like a woman rathar than a man despite being in the typical male speaking pitch range.

Because the perception of the distance between notes on the piano, where ever they lie is equal, it seems fair to say that a surgical change that raises the voice from a C to a C# and a surgery that raises a voice from a F to a F# has had an equal effect by raising the voice one semi-tone.