Touch-tones and Musical Tones

[Rob Warnock]

In article <73...@accuvax.nwu.edu> cmo...@brl.mil writes:

| I have seen these displayed for the touch-tone frequencies.
| 697Hz 770Hz 852Hz 941Hz 1209Hz 1336Hz 1477Hz 1633Hz
| I cannot fit the above to the musical scale which I derive as follows...

The reason is that the Touch-Tone freqs are *not* a musical scale!

Those frequencies were picked to minimize the possibilities of false
selection due to harmonics of each other and of other tones such as
dial tone, busy, and 60 Hz hum, and other single-frequency signals,
such as might be generated by harmonic distortion in the transmission
path.

Recalling an illustration I once saw in an old Bell System Technical
Journal, if you plot an X-Y chart of the DTMF frequencies, you will
have a small square around each correct "pair", representing the range
of frequencies which will cause that pair (key) to be accepted by the
decoder. The plot is *not* dense: There is a goodly amount of empty
space around each pair's "square". Now if you plot where various
harmonics of single frequencies go, you'll get a series of slanted
lines. For example, consider the third and fifth harmonics of various
pure tones. That will be a slanted line at 59 degrees
[==arctan(5/3)]. If you plot a whole bunch of "probable" or "common"
distortion products, you'll get lines at various angles and slants.

The Touch-Tone frequencies were chose such that *none* of these
unwanted pairs (slanted lines) goes through a "correct" pair's square,
with the exception (as I recall) of the 5:7 line which nicks the
lower-right corner of the pair for the "1" key (or something similar,
you get the idea).

And that was viewed as o.k., because there's *another* criterion which
is used to exclude bad signals from decoding as DTMF tones, and that's
that the tones being decoded must be a large part of the total energy
of the incoming signal, *except* for the other band.

That is, the DTMF pairs are not separated with band-PASS filters, but
with band-REJECT filters. What you do is take the whole signal, put it
through a (say) upper-DTMF band-reject filter, *then* limit (clip) it,
then pass it through the four low-DTMF specific detectors (and
vice-versa for low-reject/ upper-pass). This will ensure that if there
are significant signals *except* in the "other" DTMF band, the signals
in the band you're decoding won't be a large enough fraction of the
(clipped) signal to trigger the decoder. Or saying it another way,
not only must there be sufficient energy *in* the target pair of
frequencies, there must *not* be very much energy *outside* the pair
-- the tones must be fairly "pure".

So it is not surprising that the DTMF frequencies aren't "musical"...
they were chosen for an entirely different set of criteria.

p.s. I believe that BSTJ issue may have been the "Special Issue on ESS-1",
but I'm not sure. Anyway, the article itself was all about the design of
the "Touch-Tone" (DTMF) system.

p.p.s. The article included all sixteen frequencies, and gave some
mention to the use of the A, B, C, and D keys. So again, that info has
been publicly available for at least two *decades*!

Rob Warnock, MS-9U/510 rp...@sgi.com rp...@pei.com
Silicon Graphics, Inc. (415)335-1673 Protocol Engines, Inc.
2011 N. Shoreline Blvd.
Mountain View, CA 94039-7311