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Here is a related information from wikipedia:

For touchtone service, the signal is a dual-tone multi-frequency signaling tone consisting of two simultaneous pure tone sinusoidal frequencies.

enter image description here

Above shows that if one pushes number 1 he sends the mix of 697Hz and 1209Hz to the telephone station/center through a wire.

My questions are:

  1. What is the practical reason or advantage to mix two signals instead of a single pure tone?

  2. Is there a reason to use such frequencies like 1209Hz which do not belong to any music tones(modern western twelve-tone equal temperament)?

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  • \$\begingroup\$ Comments are not for extended discussion; this conversation has been moved to chat. \$\endgroup\$ – Dave Tweed Jan 8 '18 at 16:57
  • \$\begingroup\$ You left out the most important signaling tone, something familiar to all hackers: 2600 Hz. \$\endgroup\$ – richard1941 Jan 11 '18 at 18:23
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The two reasons are simple:

  • Eight frequencies are easier to discriminate with simple analog electronics - banks of bandpass filters or even vibrating reeds - than sixteen frequencies.

  • The equally tempered scale is too close to the natural scale, which has simple fractional relationships between the frequencies.

Consider that a phone line may be highly distorted : the second harmonic is one octave above the fundamental, and the third harmonic of a note is an octave plus a fifth. If you used more musical intervals between dialing tones, harmonic distortion could result in dialing the wrong number.

The frequencies were chosen (citation needed, no doubt - here for example ) to reduce or eliminate the possibility of harmonic or intermodulation distortion between tones being mis-detected as the wrong number.

The tone frequencies, as defined by the Precise Tone Plan, are selected such that harmonics and intermodulation products will not cause an unreliable signal. No frequency is a multiple of another, the difference between any two frequencies does not equal any of the frequencies, and the sum of any two frequencies does not equal any of the frequencies. The frequencies were initially designed with a ratio of 21/19, which is slightly less than a whole tone. The frequencies may not vary more than ±1.5% from their nominal frequency, or the switching center will ignore the signal.

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    \$\begingroup\$ I really didn't get the answer of yours to the first question. 8 frequencies? Discriminate? \$\endgroup\$ – user16307 Jan 6 '18 at 20:58
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    \$\begingroup\$ The system has one tone per row and one tone per column. 4 rows + 4 columns = 8 tones. As Brian says, this is more efficient than having one tone per button (16 tones) and the receiver will only give an output when a row and a column tone are received simultaneously reducing the chance of speech, noise or music being interpreted as signal tones. The tones have to be within telephone bandwidth (300 Hz - 3 kHz). It's easier to get eight filters into that band than 16. \$\endgroup\$ – Transistor Jan 6 '18 at 21:02
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    \$\begingroup\$ @user16307, discrimate = tell the difference between \$\endgroup\$ – TonyM Jan 6 '18 at 21:12
  • \$\begingroup\$ DTMF is similar to the ITU R2 signalling (often called MFC) adopted in ~1950. R2 is slightly more complex, with a different set of frequencies used for backward signalling. North America had a related R1 standard. These were adopted for in-band signalling to support international automatic telephony as replacement for the slow out of band (pulse and line) signalling. Now replaced by digital Common Channel Signalling. \$\endgroup\$ – Milliways Jan 8 '18 at 4:34
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If you used single tones instead of dual tones, you'd need 16 of them instead of only 8 as in the DTMF system.

Given that they have to be spaced far enough apart for reliable detection, and that you only have the range from 300 to 2700 Hz to work with, you'd probably find it difficult to decode that many different tones reliably using the technology available between 1950 and 1963 (when touch tone dialing became available.)

Two tones also helps to reduce false detections. If you only pick up one tone, you ignore it. If you pick up two valid tones at once then it is much more likely to be an intentional dial command.

As to why they didn't use musical notes, I'd guess because they were more concerned with getting tones in a range and spacing that was good for detection and easy to generate. Also, you don't want a harmonic of one tone to be the same as one of your higher tones. If you used musical notes, that would be the case. Look at the frequencies used. None of the higher tones are a multiple of the lower ones.

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    \$\begingroup\$ They also didn't want people dialing their phone with a piano. \$\endgroup\$ – Harper Jan 7 '18 at 17:04
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    \$\begingroup\$ @Harper, they didn't want people dialing their phone with a whistle, either...oops. \$\endgroup\$ – Mark Jan 8 '18 at 2:10
  • \$\begingroup\$ Further on why avoid musical notes: Any tone that isn't a perfect sine wave has harmonics, and you must avoid any harmonics matching any of the other tones you are detecting. Even when using perfect sine waves, any distortion in the phone line will introduce harmonics. By contrast, our musical scale of 12 semitones was designed specifically so that as many of the notes as possible closely matched harmonics of other notes, in order to sound musical. So DTMF tones had to be designed with a very different goal. \$\endgroup\$ – thomasrutter Jan 9 '18 at 0:52
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It is because phone systems were designed with in-band signalling due to technical limitations at the time.

The signaling worked over the existing telephone infrastructure that previously was operated by hand, aka hello operator, connect me to 4562.

The dual tones required allow to distinguish the tones from normal speech that could have the same frequency, but would not have both at the same time.

The frequencies used were spread out to make it easy for the signaling system to distinguish them even when noise was present over the line. I doubt it had anything to do with musical tones.

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    \$\begingroup\$ It had to do with not being musical tones. \$\endgroup\$ – Transistor Jan 6 '18 at 21:05
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    \$\begingroup\$ DTMF was developed as a replacement for pulse dialing, not for operator-assisted dialing. \$\endgroup\$ – duskwuff Jan 7 '18 at 1:24
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Less frequencies needed => simpler to produce digitally, analog base timing oscillator can be accurate enough because the allowed error is bigger, less tuned detectors needed: 8 vs 16.

2 frequencies at the same time (carefully selected for preventing distortion to make false mixing products) => not highly probable to be produced accidentally in ordinary sounds.

A legend I have heard: Single tone coding has been in use as internal telephone system signaling method until a boy with capable brain, criminal mind and perfect pitch ear learned how to whistle transcontinental free calls and how to put the central down.

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    \$\begingroup\$ That was the famous "Captain Crunch" hack, and it is not a myth. It is called "Captain Crunch" because there is a brand of breakfast cereal by that name. In the 1970s, they distributed a whistle in the box that hit exactly one of the internal single tones that could get you free service like the guy with perfect pitch coukd generate. \$\endgroup\$ – JRE Jan 6 '18 at 21:11
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    \$\begingroup\$ @JRE and lest we forget, that magical tone is 2600 Hz. \$\endgroup\$ – casey Jan 7 '18 at 14:45
  • \$\begingroup\$ My older brother told me about the "blue box" that would get you free long distance calls, back in the 70s. \$\endgroup\$ – user56384 Jan 7 '18 at 16:20
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    \$\begingroup\$ Captain Crunch is a real person \$\endgroup\$ – Bob Jarvis Jan 7 '18 at 18:52
  • \$\begingroup\$ @BobJarvis: Yes, and he got his nickname from the Captain Crunch hack. \$\endgroup\$ – JRE Jan 9 '18 at 6:51

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