Frequency Theory for the Phone Hacker/Musician

by The Piano Guy

Like many computer folks, I'm also a musician.  I'm much more competent at that, but I have this habit of liking to pay my bills, which is why I also work in computers.  Unlike more people, I happen to have absolute pitch memory (which is more commonly but incorrectly referred to as perfect pitch).  As a result, I have a polite correction and amplification to autocode's interesting article in 20:1.

For all intents and purposes, the dial tone frequencies in my neighborhood are a 440 A and the F below it.  Autocode makes a big deal that an F is 349.23 Hz and that the actual lower tones is 350 Hz.  The doesn't make enough of a difference to matter.  The note is an F.  Partial tones in musical notes are expressed in cents.  There are 100 cents between half tones.  The distance between an E and an F at that frequency is 19.6 Hz.  To be off 0.8 Hz at that point (the difference between 350 Hz and 349.2 Hz) is about four cents.  This isn't enough to make a difference to anyone whatsoever.  The vast majority of people on the planet can't even recognize the difference (including many with absolute pitch memory).  Most piano tunes won't even fix that if the strings match each other.

All this is moot when it comes to tuning your guitar to the phone because the top note (which is right on) is exactly one octave above the A-string on a guitar, which makes it ideal for tuning (for those that lack absolute pitch memory).  For those with relative pitch (much more common - being able to hear intervals), the F below the A is a perfect fourth below the note to tune a trumpet.

Of more relevance to the target audience (this is 2600, after all), is that there is a reason for this very minor frequency shift.  Frequencies tend to beat at twice and half their original frequencies.  That 440 A tone has harmonic tones at 220 and 880 Hz.  Harmonics colliding could confuse phone switch circuitry.  The phone company in their wisdom (not sarcastic, for a change) picked frequencies that were not harmonics of each other.  This is why hackers have to have precise tone generators.  Close isn't usually close enough.  The difference between the E-flat and the E (in the neighborhood of 2600 Hz) is enough that someone playing the organ in the background wasn't likely to get anyone a free phone call back when a Cap'n Crunch whistle did the trick.  I'm sure this was a conscious choice also.

I'm not aware of a software frequency counter, but I have to think that one exists.  If someone has a good keyboard with tuning capability (to work with detuned instruments), then it is probable that the keyboard can be made to generate whatever single frequency is required for whatever purpose.

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