Note(!) that the ratios of DTMF tones form a "persymmetric" matrix (symmetric about the minor/anti diagonal). The matrix below shows the number of semitones (times 10) between the row tone and the column DTMF tone: [ 95 78 61 43 ] [ ] [ 113 95 78 61 ] [ ] [ 130 113 95 78 ] [ ] [ 147 130 113 95 ] The only real musical chords are the entries "130" (touch tones "3" and "B") in this table above. This chord is an octave + minor second. Curiously, the entries "61" (touch tones "7" and "0") are quite close to the "tritone" dreaded by classical composers. Leonard Bernstein famously (in musical circles, at least) included a musical joke in "West Side Story" with the first two notes of the song "Maria", which form a *tritone* (the two "Ma ri" notes of the "Ma ri a"). Re the "musicality" of DTMF: Back in the "Captain Crunch" days of hacking ATT lond distance, there was a (probably apocryphal) story meant to illustrate the difference between MIT and Harvard students. MIT students hacking LD built "blue boxes" which generated all 16 DTMF tones (in addition to other tones). Blue boxes could be used to dial free long distance calls. Harvard students supposed gathered together a group of their musical friends, who then *played the DTMF tones on their instruments*. As you can see from the matrix above, this requires some skill from the musicians, as these notes are all seriously out of tune. BTW, the Bell 202 frequencies are almost exactly halfway between a "minor seventh" and a "major seventh". So Keith is absolutely right about DTMF chords being unmusical. At 04:26 PM 1/16/2018, Keith F. Lynch wrote:
Inspired by Henry Baker's musing about modem tones:
Each Touch Tone button on a telephone sends two simultaneous audio frequencies through the phone line, one associated with the row it's on, and one associated with the column it's on. There are four rows and four columns (though only the first three columns exist on most telephones) for a total of eight frequencies.
The frequencies were chosen such that the sums or differences of any two of the eight frequencies are as far as possible from any of the eight frequencies. Similarly with whole-number multiples ("harmonics") of the eight frequencies or of their sums or differences. This is to prevent the phone company equipment from getting confused, since non-linearities in the circuits could result in such sum and difference frequencies appearing.
This is probably why Touch Tones are so unmusical. Music relies on frequencies with small whole-number ratios, almost the exact opposite of the Touch Tone criteria.