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English-style full-circle bell-ringing.

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Sound of Bells – Definition of Cents

There was a convention in some areas to use the "#" and "b" suffices to indicate closeness of pitch: e.g. C# might indicate a note closer to C, and Db might indicate a note closer to D. Nowadays musicians are more precise with how flat or sharp a note is compared with a standard pitch. To do this a semitone is divided into 100 cents, and with 12 semitones in an octave, there are 1200 cents in an octave. As the interval between consecutive notes is a logarithmic series, the interval between consecutive cents is also logarithmic. The following formula may be used to convert a frequency into a Note:

 Result (in Cents) = 1200    log   fnote                           

                                 log(2)          finternational      


 fnote is the frequency to be transposed into a Note.

 finternational is the frequency of the closest International Scale Note (See previous page)

 The result is the offset in Cents from the International Scale Note.

For example a frequency 798Hz is near to the International Scale note "G". The note would be :

          1200    log   798      which evaluates to +31 cents

          log(2)          784

The frequency of 798Hz is equivalent to the International scale note of G+31 cents, meaning the frequency is almost a third of a semitone sharp of G. Likewise a frequency of 762Hz would evaluate to G-49 cents, indicating the frequency is almost half a semitone flat of G International scale.

The result is always relative to the reference used in the calculation. For example if the frequency for "C" is used instead of for "G", the result would be :

           1200    log    798        which evaluates to +731 cents

          log(2)          523.25

The result of 731 cents indicates the frequency is 7 semitones and 31 cents sharp of "C" International scale.