RE: [tuning-math] Digest Number 1297

Gene,

You wrote:

> > If we have a finite set of notes in an octave, AND we
> > regard octaves as equivalent, we can indeed regard the
> > gamut of notes in a scale as all those with frequencies
> > of the form 2^t s, for s a note in the octave [1, 2) and
> > octave t in N = {1, 2, ...}.
>
> Why N? I'd say t is in Z.

Remember, I was replying to your message with its explicit
assumption which you have not quoted above) -

"for s a note in the octave [1, 2). "

I took you to mean that the frequency of s, in Hz, lay in [1, 2).
In that case, non-positive octave [equitave] shifts would
result in inaudible pitch frequencies below 1 Hz.

But if your "note" s was a frequency _ratio_, then letting t
range over all Z makes perfect sense.

Regards,
Yahya

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--- In tuning-math@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

> Remember, I was replying to your message with its explicit
> assumption which you have not quoted above) -
>
> "for s a note in the octave [1, 2). "
>
> I took you to mean that the frequency of s, in Hz, lay in [1, 2).
> In that case, non-positive octave [equitave] shifts would
> result in inaudible pitch frequencies below 1 Hz.

I think most commonly when someone says something like that around
here, they mean relative to some 1/1, not necessarily 1 Hz. Anyway, I
meant that, and since audibility doesn't enter the discussion on the
upper end, it shouldn't on the lower end.