circumference / diameter = 3

Yes, this posting is a hoax. Also a hoax is the rumour that Indiana at
one time attempted to legislate the same thing.

And yes, the Chronicles (and book of Kings) do refer to the 30 cubits
around and 10 cubits across. Please note, though, if the item were
hexagonal, the diameter would be exactly 3.0000...this is perhaps the
rendering anticipated. Also, the lip had a finite width -- perhaps the
30 cubits was the interior circumference and 10 cubits was the exterior
diameter, making the lip 0.7 cubits thick. More likely, I think the
scribes could neither measure nor write a phrase requiring fractional
cubits.

If only the musical instruments of the time were described in detail by
the authors! I would love to know the structure and tunings.
>

>It looks an awful lot like the true fundamental is an octave below the
>period you have identified.

That's not terribly likely for three reasons:
1. This note is in the lower register of the bass clarinet. It is not an
overtone. The register key is not down.
2. If you look at the wave earlier in time, you see that the alternating
low-high of that rough slowly starts alternating the other direction, and
in about the same amount of time starts alternating the other way. There's
something going on that isn't at a subharmonic frequency.
3. Once again, if it were a component at half the fundamental frequency, we
would have seen the entire wave ooze up and down with that trough.




>Try playing
>a wind instrument without the reed and you will still get a rough idea
>of the pitches you're fingering from the way your breath-noise is
>amplified.

Analogously, one thing I've done on my orchestral string samples is to
sample and loop the sound of bowing the bridge, and then high-pass filter
it out in the original sample. That way the pitch of that noise component
doesn't change in pitch with the change in pitch of the tone, just as it
does not on a the real instruments.

>>It looks an awful lot like the true fundamental is an octave below the
>>period you have identified.

Gary wrote,

> That's not terribly likely for three reasons:
>1. This note is in the lower register of the bass clarinet. It is not an
> overtone. The register key is not down.

See my previous post about Benade or Backus and Tuvan throat singing.

>2. If you look at the wave earlier in time, you see that the alternating
> low-high of that rough slowly starts alternating the other direction, and
> in about the same amount of time starts alternating the other way.
>There's
> something going on that isn't at a subharmonic frequency.

Hmm, I wish I had a clearer picture of what you're talking about. I
wonder if a double-reed instrument might have some slow phase drift due
to slight inequalities between the two reeds, much like a guitar string
will vibrate at two slighlty different frequencies if the bridge allows
horizontal vibrations to begin at a different point or with different
resistance than vertical vibrations.

>3. Once again, if it were a component at half the fundamental frequency, we
> would have seen the entire wave ooze up and down with that trough.

Not necessarily. A physical "subharmonic" is not just a sine wave but is
a (weak) true fundamental with any or all (weak) harmonic overtones. In
this case, those overtones would be at 3/2, 5/3, 7/2, . . . the primary
pitch and could conspire to keep the bulk of the waveform intact. (I'm
sure if we knew more about the physics of the situation, this
"conspiracy" would turn out to arise in a very natural way, not one that
requires any "consciousness" on the part of the instrument).

>Not necessarily. A physical "subharmonic" is not just a sine wave but is
>a (weak) true fundamental with any or all (weak) harmonic overtones.

If you're including lower frequencies with their own overtones, then
yes, that's definitely a possibility.