2 Mar 2011 06:54

## Re: calculating semitones

```Custos asked:
> does anyone know if is allowed to convert F0mean values to semitones by using the equation
>
> semitone= 12*log2(f0mean)
>
> or do I must use the pitch range (f0max/f0min) instead of f0mean?

Semitones (more strictly equal-tempered semitones) represent a pitch interval which is one twelfth of an
octave. So strictly their appropriate use is to represent a pitch range which you can calculate with

range = 12*log2(f0max/f0min)

There is, however, no reason that you should not represent an 'absolute' pitch value with the formula you
mention, which is in effect calculating the interval between f0mean and one Hertz. In other words you are
calculating the interval

semitones = 12*log2(f0mean/1)

This is one of the options for units (semitones re 1 Hz) provided by Praat in the query Get mean... for a Pitch
object. The other options are semitones re 100 Hz, re 200 Hz and re 440 Hz.

You should, though, when quoting such values mention somewhere that the values are calculated in
semitones re 1 Hz so that your values can be compared to others calculated using a different formula.

The result of this will be that for human voices your values will be likely to be situated in a range from about
70 (around 60 Hz) up to about 20000000000 (410 Hz) which as rather a large range and not particularly easy to interpret.

I have always thought that a more natural unit to use for pitch is the octave (ie simply log2(Hz)) since with
this the range of human voices is generally situated between 6 and 9 octaves (re 1 Hz) which is to my mind much
easier to interpret. Added to this is the advantage that the octave is in many senses a natural unit for
studying pitch while the only reason to use semitones is that it is the basis of Western classical music.

see for example Martin Braun's page on the octave

http://www.neuroscience-of-music.se/Octave-History.htm

best regards

daniel

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```

Gmane