Interesting article

[Jim Coleman, Sr.]

Hi Richard:

In regard to the "subjective tones" mentioned in the quote in Larry's post,
these have been used by several composers over the years. I played violin
until 7 weeks ago. It is common to hear the difference tone between two 
strings when tuning a 5th. The difference tone is an octave below the lower
string of the 5th. There are also summation tones which are a 10th above 
the lower note of a 5th. Obviously when you add the frequencies of A-440
and E-660, you get C#-1100 (we're talking pure intervals here, not 
tempered). When you subtract 440 from 660, you get 220

Paul Hindemith is one composer who cited the use of these tones.

If I remember correctly, Wm. Braid White mentions this phenomena as well as
the Ellis translation of Helmholtz.

Now to the other subject of single strings exhibiting a difference of pitch
from three strings which are tuned identically. In my studies, I found 
that this difference exhibits itself more in the 5th and early 6th 
octave on the piano and not as much elsewhere. I have not found 1 and 2 
cent variances as some have claimed. What are your findings? I find 
greater differences between the pitches of the prompt sound and the 
later decay sound (the TuneLab shows this quite clearly). It is easy to 
confuse these two sources.

Jim Coleman, Sr.

On Fri, 7 Apr 2000, Richard Brekne wrote:

> Hi Larry...
> 
> This buisness of single strings "sounding" flatter then coupled strings is a
> different subject matter. Actually, you see, they not only sound flatter, they
> are measurably flatter (with perhaps some circumstances of exception) There has
> been done some experimentation on this line, but a complete explanation of this
> phenomenon is as yet lacking. Some evidence points in the direction of the nature
> of the bridge, other points towards the strings themselves.
> 
> What this article is about is something somewhat different and the disscussion
> surrounding Virgil Smiths "natural beats" comes more to my mind then anything
> else. In the last Journal there was a bit that seemed to follow quite similiar
> lines really. Both (after my readings) postulate that the sum of all the partials
> in a given vibrating string effect in some way how we percieve the fundemental.
> At least the two are not entirely dissimiliar. Its interesting enough and worth
> further ponderance for sure...grin. Anything to keep the old mind pondering..
> 
> 
> 
> LTpianoman@AOL.COM wrote:
> 
> > Richard,
> >
> > Below is an excerpt from the site you provided. Thanks. After reading it, and
> > the rest of the info on the site, it seemed to me that this Subjective Tone
> > theory (or theorem by now), would explain why unisons sound flatter (or
> > sharper, I forget) than their respective single strings played seperately.
> > Any thoughts?
> >
> > Larry Trischetta, Pocono NE Chapter,
> > Scranton, PA
> >
> > From: http://sleepy.millikin.edu/~jaskill.nsm.faculty.mu/subpitch.html  (John
> > Askill, Millikin University):
> > A facinating series of experiments were conducted by Diana Deutsch, Professor
> > of Psychology at the University of California at San Diego and shown in the
> > film "What is Music" (Nova, Coronet Films). In it she subjected a listener to
> > one series of tones in the left ear and another series in the right ear. The
> > resulting effect was a totally different series of tones, subjective tones.
> > The same effect was produced by listening to orchestra music produced by two
> > or more sections of an orchestra playing at the same time. In fact, pieces of
> > subjective music have been written in which two instruments, such as flutes,
> > play two different sequences of tones at the same time. The resulting tones
> > being the melody, a subjective melody.
> >
> 
> --
> Richard Brekne
> Associate PTG, N.P.T.F.
> Bergen, Norway
> 
> 
> 
>