calculating semitones

[custos83]

Hi!

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?


I really would appreciate someone's suggestion!

Thanks
custos



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[Daniel Hirst]

Post by custos83
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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[Daniel Hirst]

oops sorry - that was posted too hastily - I did the calculations the wrong way round!!

the expected pitch range is 70 sts (about 60 Hz) to 100 sts (close to 400 Hz) and not the crazy figures I posted !!!

nonetheless I maintain the rest of my comments about the octave as a 'natural' unit for pitch



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[Paul Boersma]

Post by custos83

Post by custos83
does anyone know if is allowed to convert F0mean values to semitones by using the equation

semitone= 12*log2(f0mean)

if f0mean means "the arithmetical average of the F0 values in hertz", then this is not right. The averaging itself should be done in the logarithmic domain, as you get by setting the Units in the PitchSettings window to "loghertz" in Praat. Or you get it directly by setting the Units to "semitones re 1 Hz".
__________________________________
Paul Boersma
Phonetic Sciences, University of Amsterdam
Spuistraat 210, room 303
1012VT Amsterdam, The Netherlands
http://www.fon.hum.uva.nl/paul/



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