resultant tones

[Michael Jorgensen]

Hi Don, Richard, Terry, Howard,
     Don, You explained it!  --Thank you.  Since the F A third in the dial tone
is pure, it would sharpen the resultant tone of F2 even a little more than the ET
explanation you gave.  The piano I tested it against was flat, with stretched
octaves which would explain why I chose the F# 2.   I do hear the dial tone as a
pitch between F and F# 2.
     I have always heard the dial tone as a low drone,  even as a kid, so I
expect to hear it that way.  Hearing it as A 440 or as an F to A pure third, I
never noticed, until I listened for it, and suddenly it was there also.
     I believe perception of the dial tones' pitch is a matter of mental
interpretation of tone rather than hearing.  The typical hierarchy of relative
strengths of harmonics, resultant tones and fundamentals isn't there.  A visual
comparison is like viewing a ship or airplane from far away, where it is possible
to mentally switch directions of the craft, and similar also to Eschers'
confounding drawings of perspective    Laymen, kids, dogs, and musicians all hear
harmonics and beats and likely have better hearing than many tuners.  Yet they
don't perceive them mentally, and can even refuse to believe beats and harmonics
exist..
     I could not get any conclusive pitch readings using the RCT off the dial
tone, not even right against the computer mic from any notes.   I'd be curious
what other frequencies the SAT picks up from the dial tone.

     Richard,
            No, I'm not deaf yet,  and no, and I'm fairly certain I don't tune my
A440s equal to F or F# 2, at least I'd be in some real serious trouble by
tonight.

-Mike Jorgensen



Don wrote:

> Hi Mike,
>
> Assuming ET and zero inharmonicity the theoretical values are:
>
> A4 =~ 440    hertz
> F4 =~ 349.43 hertz
>
> difference is 90.57 hertz which is a bit closer to F2 (87.31) than F#2.
>
> A "just" (non tempered) third would produce a resultant tone exactly two
> octaves below the lower note.
>
> Of course the values will vary from location to location slightly as there
> is no guaranttee of accuracy from the telecos!
>
> http://www.allchurchsound.com/ACS/pdf/PIANO.pdf
>
> At 09:32 AM 2/22/01 +0000, you wrote:
> >I once heard from a theory teacher that a dial tone in the United States is a
> >difference tone and some people hear it as two distinct high treble
> pitches.  I
> >hear one tone equal to F# 2.  Is there anybody on this list who hears it
> >differently?
> >
> >-Mike Jorgensen
> >
> >Richard Moody wrote:
> >
> >> ----- Original Message -----
> >> From: Richard Brekne <Richard.Brekne@grieg.uib.no>
> >> To: <pianotech@ptg.org>
> >> Sent: Tuesday, February 20, 2001 10:42 AM
> >> Subject: Re: resultant tones
> >>
> >> >
> >> >
> >> > Richard Moody wrote:
> >> >
> >> > >  I don't know what the difference would be of a tone between say 100
> cps and
> >> 130
> >> > > cps as compared to 400 cps and 430 cps.
> >> >
> >> > Now thats an interesting question... I wonder if there is a difference in
> >> resultant
> >> > tones of same frequencies created by differing fundementals, and if
> so... why
> >> and
> >> > what kind of differences there are.
> >> >
> >> >
> >> > --
> >> > Richard Brekne
> >>
> >> As long as we are on it, what then would be the difference between say
> 22,000
> >> and 22,440 ?   Or are there audible resultants from two supersonic
> frequencies?
> >> Would they have to be loud or very loud and how loud would the
> resultants be?
> >> Perhaps two dog whistles would shed light.  No two dog whistles can
> possible be
> >> the same freq.
> >> The diff between the two above freqs is about 34 cents ---ric
> >
> >
> >
>
> Regards,
> Don Rose, B.Mus., A.M.U.S., A.MUS., R.M.T., R.P.T.
>
> Tuner for the Saskatchewan Centre of the Arts
>
> mailto:drose@dlcwest.com
> http://donrose.xoasis.com/
>
> 3004 Grant Rd.
> REGINA, SK
> S4S 5G7
> 306-352-3620 or 1-888-29t-uner