Hi Rick,

> The experience of singing through a telephone would be dramatically
> impacted by the choice of scale.  If frequencies are rounded off to
> the nearest match on a linear scale, then they are bound to be off-pitch.
> On the other hand, if musical halftones (or perhaps halfway these) were
> used as a rounded value, then Codec2 would pass musical tones at the
> perfect pitch -- the roundoff could actually improve the song ;-)

I feel you are into something here. From what I believe, it is not
the absolute pitch though (unless you have absolute hearing ?? )
but the relation between various frequencies that is percieved
as on key or false. This is often referred to as the reason certain
(3-order) distortion in amplifiers is objectionable. (2nd harmonic
is in key, 3-d is NOT, 4th is, 5th is not...)

>      Two subsequent musical halfnotes are a factor of 12'th root of 2 apart,
>      so 12 such halfnotes make up a factor 2 or an octave.  The frequency
>      440 Hz is defined as an A.  Using step sizes of the 24'th root of 2
>      or 1.0293022366434921 should give a comparable experience, but be
>      friendly to music.  It is also slightly more compact.

How would this impact the necessary math? Working from sampling, discrete
time, what is the "natural" result in frequency? 

> Am I the only one who would find it a pitty if we missed out on this,
> if the only reason would be the existing implementations in the field?

I have a sensitive ear to some kinds of distortion, I had severe
problems with first generation GSM phones ( good for the economy though,
short calls)

73 de Gullik /SM6FBD


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