[sdiy] db to semitones, octaves.

[Magnus Danielson]

From: Roman <modular at go2.pl>
Subject: Re: [sdiy] db to semitones, octaves.
Date: Wed, 26 May 2004 10:03:38 +0200
Message-ID: <20040526080338.AB09143E5B at rekin8.go2.pl>

> db or dB like decibels?
> 
> 1 octave means times-two, what in dB equals 6.0206dB, 1 semitone is about
> 0.5dB
> 
> 1 dB = 1.993 semitone

Actually, it may not be that simple. Bell is a power-ratio scale, such that
           P
L = log  (----)
       10 Pref

However, often is the deci-Bell scale used, so then it is

                P
L = 10 * log  (----)
            10 Pref

For voltage and current related stuff, you need to convert it into power first,
which implies squaring. The Square can then be isolated out from the log
expression and becomes a multiplication by two, so this leads to

                V
L = 20 * log  (----)
            10 Vref

The question now comes how you relate frequency to power. There are many
different power-laws which changes with frequency by different exponents.

So, is the doubling in frequency twice as powerfull or twice as high amplitude?
That gives different answers to the question. I would actually lean towards the
answer that there is no answer, you never do this for musical situations. dB
for frequency is meaningless. Octaves, semitones and cents fills this purpose
already and another logarithmic scale is as such not very meaningfull.

Cheers,
Magnus - adjusting the centibells and milibells accordingly