Aural Pure 5ths Equal Temperament

[Jim]

Hi Bob:

You are right about the main two kinds of 5ths. In my second article
I give primary tests as the 6th 10th test to give prominence to the
lowest coincident partials of the 5ths. When I have more experience
with this system, I may come to a combination conclusion.  I just don't
know at this time.

Thanks for your input.

On the subject of TuneLab, I guess I am experiencing a comedy of errors.
I downloaded your new version, and when I tried to load it on my son's
computer, I had a disk read error.  I have re-downloaded it and hope to
get it up and running soon.

Jim Coleman, Sr.

On Wed, 21 May 1997, Robert Scott wrote:

> When we talk about pure octaves we have the distinction between
> 2:1 octaves (where the 2nd partial of the lower note zero beats
> with the fundamental of the higher note) and 4:2 octaves (where
> the 4th partial of the lower note zero beats with the 2nd partial
> of the higher note.  Due to the variability of inharmonicity these
> two tunings are not necessiarily the same.
>
> Doesn't the same consideration hold true for pure 5ths?  There
> can be a 3:2 pure fifth (where the 3rd partial of the lower note
> zero beats with the 2nd partial of the higher note) or a 6:4 pure
> fifth (where the 6th partial of the lower note zero beats with
> the 4th partial of the higher note).  I suppose you could even
> talk about 9:6 and 12:8 pure fifths too, but by the time the
> partials get that high they are probably too weak to need
> special attention.  How does this impact the discussion of
> tuning by pure 5ths?
>
> Bob Scott
> Ann Arbor, Michigan
>
>