Re: Oh no---JI vs. temperament rears it's ugly head for the 4356th t

i would say there are no beatless intervals ( besides the unison) , only ones are blocked out or hidden by the louder sounding tones. Pay any JI inteval high enough and you will hear the differance tone.
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

These same intervals are fund in the subharmonic series found for maybe 10,000 years on wind instruments with equally spaced holes.
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

<<< Just a quick question before we dismiss what I brought up about
beating---if 81/64 does not beat because it is a mistuned 5/4, why *does* it
beat, then? .... I still contend that 81/64 beats because the ear
'wants/tries' to hear it as a 5/4....until you come up with a better theory
about why it beats, I'm sticking with that. >>>

I think a more mathematical explanation can be given. The periodicity
frequency of the 5/4 interval is two octaves below the bottom note, i.e.
quite audible as a note, or "difference tone". But the periodicity frequency
of the 81/64 interval is 6 octaves below the bottom note, a frequency so low
it is only audible as a beat.

A just third of 550/440 (AC#), for example, has a periodicity of 110, well
within the baritone range. But make it a Pythagorean third of 556.875/440,
and it has a periodicity of 6.875 beats a second. That's a beat, not a note.

Billy

> I think a more mathematical explanation can be given. The
> periodicity frequency of the 5/4 interval

You mean "periodicity pitch"?

> is two octaves below the bottom note,
> i.e. quite audible as a note, or "difference tone".

Difference tones and periodicity (or residue) pitch
are distinct phenomena.

> But the periodicity frequency
> of the 81/64 interval is 6 octaves below the bottom note,
> a frequency so low it is only audible as a beat.

That's a nice idea, but not really how it works.

> A just third of 550/440 (AC#), for example, has a
> periodicity of 110, well within the baritone range. But
> make it a Pythagorean third of 556.875/440, and it has a
> periodicity of 6.875 beats a second. That's a beat,
> not a note.

How are you calculating periodicity pitch? It isn't the
difference of the tones, but rather the implied /1 of the
tones.

-Carl

Hello Billy. Actually the difference tone would be 116.875

Posted by: "Billy Gard" A just third of 550/440 (AC#), for example, has a periodicity of 110, well
within the baritone range. But make it a Pythagorean third of 556.875/440,
and it has a periodicity of 6.875 beats a second. That's a beat, not a note.
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles