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From: wales@cs.ucla.edu (Rich Wales)
Newsgroups: comp.dcom.telecom
Subject: DTMF Frequencies From a Musician's Point of View
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Date: 9 Aug 89 19:54:04 GMT
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X-TELECOM-Digest: volume 9, issue 284, message 1 of 9

In article 
Mike Morris  gives the DTMF tones as follows:

	           1209     1336     1477    1633

	    697     1        2        3       A   FO

	    770     4        5        6       B   F

	    852     7        8        9       C   I

	    941     *        0        # A     D   P

Note that these frequencies occur in a well-tempered scale with a mul-
tiplier between steps of 1.05135 (i.e., 13.84 steps per octave).  If
"tone N" has a frequency of 697*(1.05135^N), we get the following:

	    697.0 Hz = tone 0		1209.1 Hz = tone 11
	    770.4 Hz = tone 2		1336.4 Hz = tone 13
	    851.6 Hz = tone 4		1477.2 Hz = tone 15
	    941.3 Hz = tone 6		1632.8 Hz = tone 17

This particular well-tempered scale fits each of the stated frequencies
to within 0.5 Hz, if you assume that 697 Hz is exact by definition.  I
suppose it might be possible to come up with an even better fit via a
least-squares linear approximation to the logarithms of the frequencies.

The upper set of tones is selected in such a way as to be roughly half-
way between the octaves of the lower set of tones.  That way, there is
no chance for the upper tone of any pair to be "lost" in the harmonics
from the lower tone.

I'm not sure why they didn't use a scale with exactly 14 steps per
octave (multiplier = 1.05076).  That would seemingly have been simpler.

The reason why you can do crude approximations to a few common tunes
(e.g., "Mary Had a Little Lamb") with DTMF tones is that the Western
musical scale is built on 12 steps per octave (multiplier = 1.05946) --
fairly close to the DTMF scheme if you don't stretch it too far.

	I have an old 5-line 4-wire Autovon phone here that I modified
	(added a network) for 25-pair 2-wire use.  It has a "A" on the
	key that would normally be a "#". The 4th column keys are
	labeled with FO-F-I-P.

I recall someone mentioning on TELECOM, some time ago, that Autovon used
the keys in the 4th column to indicate the precedence of the call.  The
abbreviations mean something like "Priority", "Immediate", "Flash", and
"Flash Override" (the latter heralding World War III for all practical
purposes).  By pressing one of these keys before dialing a number -- and
assuming that your phone line had authorization to invoke that particu-
lar precedence -- the Autovon system would automatically disconnect any
call in progress of *lower* precedence in favor of your call.  (I'm not
sure whether the disconnected party got any kind of notification of why
he had suddenly gotten cut off.)  Maybe someone who has used Autovon can
confirm this info and/or correct my details.

-- Rich Wales // UCLA Computer Science Department // +1 (213) 825-5683
   3531 Boelter Hall // Los Angeles, California 90024-1596 // USA
   wales@CS.UCLA.EDU      ...!(uunet,ucbvax,rutgers)!cs.ucla.edu!wales
"K-9, I think we're going to find out what it's like to be a cricket ball."