This is a question that has actually captivated me for some time.
There is a "fifth column" DTMF. Whether the actual frequencies are specified in any Bell System Practice or Bell Labs Record article is uncertain (and probably unlikely), but the tones can be easily deduced mathematically.
There are three mathematical models which describe the determination of the tones used for DTMF tones. Here's how one could predict the 5th-column DTMF tone from that:
- This method is the one officially used by Bell Telephone Labs. The ratio used is approximately 21/19. This is about the ratio of adjacent consecutive tones in any row or column:
1336/1209 = 1.1050
1477/1336 = 1.1055
1633/1477 = 1.1056
Taking the average of those (3) slightly different multipliers comes to 1.1054
1209 x 1.1054^1 = 1336.43
1209 x 1.1054^2 = 1477.2
1209 x 1.1054^3 = 1632.8
1209 x 1.1054^4 = 1804.89
- This method involves using the differences of differences between adjacent consecutive tones.
Jump 1: 1209 → 1336 = 127
Jump 2: 1336 → 1477 = 141
Jump 3: 1477 → 1633 = 156
Jump 1 → Jump 2 = 14
Jump 2 → Jump 3 = 15
Well, it seems intuitive then that Jump 3 → Jump 4 ought to be 16, following this linear pattern.
In which case, the fifth column frequency ought to be 1633 + (156 + 16) = 1633 + 172 = 1805.
- This method involves differences of differences again, but this time with square roots.
Taking square roots:
1209 - 34.770
1336 - 36.551
1477 - 38.431
1633 - 40.410
Differences are: 1.781,1.88,1.979
Differences of differences are: 0.099, 0.099
So, putting it back together:
1.979 + 0.099 = 2.078
40.410 + 2.078 = 42.488
42.488 squared = 1805.23 ~= 1805 Hz
A few phone collectors have actually tried extending WECo 2500 sets to do this. Experimental results come out to an average around ~1880 Hz or so. But the phones weren't designed for fifth-column DTMF, so it's possible that's why there's a mismatch between the theory and reality.
Here's a project you could try for yourself if you have a standard (model 2500) Touch-Tone phone:
Just locate the right-most column switch, clip it free with a small wire cutters. Then solder on some fine wires (I like to use #30 gauge wirewrap wire). Bring those wires out to (2) SPDT push buttons in series so that the 3rd column on the pad gets re-assigned by the buttons to either the 4th or 5th column.
So, to answer your question, what would the extension to 8 x 8 look like? This is my best guess:
After exhausting the alphabet, it's anyone's guess what the remaining keys ought to be used for! There's exactly enough leftover to repeat the alphabet all over. I'll be the first to say it would be nice to be able spell things out using DTMF over the phone (e.g. "Please enter your name:" beep...)
Source - PhreakNet: Touch-Tone Odds and Ends