Re: higher-prime translated out of academese]]

"Paul H. Erlich" <PErlich@Acadian-Asset.com> wrote:
> Fred Reinagel wrote,
>
> >Perhaps more importantly, the subjective difference tone is not a
> subharmonic
> >or near-subharmonic of either incident tone.
>
> This is a poor criterion for consonance. For example, most of us would
agree
> that 5:2 (just major tenth) is a consonant interval, yet the difference
> tone, 3, is not a subharmonic of either 5 or of 2.

I agree. What I meant to say was that the difference tone does not fit into a
low-order harmonic series which includes the incident tones.

Fred Reinagel

____________________________________________________________________
Get your own FREE, personal Netscape WebMail account today at http://webmail.netscape.com.

robert grimble <cthulhu@pipeline.com> wrote:
> There may be more to it than the consonance between harmonics. Your ear is
> a non-linear device and it has both harmonic and intermodulation
distortion.
>
> Have you ever heard the demonstration of what happens when you play two
> pure sing waves that are sepaarated by a perfect, 2:3 ratio fifth? You
> "hear" the fundamental. There is a demo of this on a Wenday Carlos disk
> (secrets of syntheis??) and it was mind blowing to me. I don't know if
> this is psychological or physiological or both.
>
> Bob G.

This is the phenomenon which I called difference tones, and their perception
is due to real physical energy being produced by the non-linear interaction of
the incident tones in the ear. The same type of thing happens in the
electrical domain (as opposed to the acounstical) in a radio receiver design
called a superhetrodyne. The received signal is mixed with a constant
frequency local oscillator in a non-linear circuit, and the resulting
difference frequency (called the intermediate frequency) is then amplified.

Fred Reinagel

____________________________________________________________________
Get your own FREE, personal Netscape WebMail account today at http://webmail.netscape.com.

Fred ---

I understand the concenpt of the difference tones.

However, the effect I am speaking about is a little more complex.

If your ear would "hear" the difference tone of two notes, then a slight
mistuning would not suppress the effect; i.e., if you played something
that was almost a 2:3 fifth (for argument's sake, lets say it is a
2:3.001), you would hear a tone that is very close the the "1" -- 1.001 in
that example.

In practice, when the 2:3 interval is hit, you suddenly get another effect
where what you perceive is a a very pure note below the two notes actually
played.

As I say, it is a really startling effect, at least to me. I hade been
listening to music and playing music for 30 years before I heard it
demonstrated, although I had read about it, and my jaw just dropped. I
think you need to have a really stable signal for it to work, a synthesizer
or a well maintained pipe organ

Bob G.

At 11:31 AM 11/5/99 EST, you wrote:
>From: Fred Reinagel <freinagel@netscape.net>
>
>robert grimble <cthulhu@pipeline.com> wrote:
>> There may be more to it than the consonance between harmonics. Your ear is
>> a non-linear device and it has both harmonic and intermodulation
>

--- clip----

>
>This is the phenomenon which I called difference tones,

---clip---

>Fred Reinagel
>
>____________________________________________________________________

Roberet Grimble wrote,

>I understand the concenpt of the difference tones.

>However, the effect I am speaking about is a little more complex.

>If your ear would "hear" the difference tone of two notes, then a slight
>mistuning would not suppress the effect; i.e., if you played something
>that was almost a 2:3 fifth (for argument's sake, lets say it is a
>2:3.001), you would hear a tone that is very close the the "1" -- 1.001 in
>that example.

>In practice, when the 2:3 interval is hit, you suddenly get another effect
>where what you perceive is a a very pure note below the two notes actually
>played.

I think what you are perceiving is partially due to the fact that for
2:3.001, the difference tone and the virtual fundamental are slightly
different in pitch and beat against one another, while at 2:3 the two are
the same and the beating ceases.