# Why are PL tones strange numbers?

PL tones have very specific odd numbers with a decimal place like 103.5 or 107.2 or 88.5. The only PL tone that does not have this decimal is the 100.0 hertz tone.

Why don't they just use integers with a standard increment of lets say 10 hertz so it would just be 100, 110, 120 etc. instead of the random numbers?

Greg Hewgill's answer is correct, but merits a slight explanation.

1. Constant (percentual) relations mean that the Q-factor of the detector for the tones remains constant. Most detector chips (like the old NE567) and algorithms are designed for a single Q, and the frequency changes don't change the Q.

2. Distortion is quite normal in electronics — low tones like these are no exception. In fact, they are more sensitive than others as the audio channel was designed for higher (voice) frequencies. A side effect of distortion is what is called intermodulation: new frequencies being generated by the presence of two (or more) other signals.

For example, if the subtones were 100, 105 and 110 Hz, then the second harmonic of 105 (210) minus the first (100Hz) could conceivably generate a difference of 210 − 100 = 110 Hz, which would be the next subtone, and could possibly trigger some detector. This cannot happen with the actual tone.

3. You may have noticed that the DTMF basic tones are also organized in a similar way — for the same reasons. In fact, the musical notes on any instrument are like this, because our ears discern differences in a similar way to detectors — constant Q.

I am not sure why the separation was chosen to be 1.035, but the exceptions are very probably because the tones which are near multiples of 60 and 50 Hz are shunned because of mains frequency interference, which can filter into the signal via power supply issues/microphone cables, etc.

The ratio between PL tones is roughly constant. From a list of PL tones, you can calculate the ratio between each frequency, which turns out to be about 1.035 (with some exceptions, not sure why).

Using a constant ratio rather than a constant difference avoids two different tones being exact multiples of each other. If you used a constant difference of 10 Hz, then you would have both 100 Hz and 200 Hz which would tend to interfere with each other, as a detector will be more reliable when the target tones are not integer multiples of each other. With the constant ratio scheme, that won't happen.