Quoted:
For some odd reason, I always thought that a DSL modem made the dial tone for the phones connected to it.
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Nope.
The dial tone is generated by the phone company.
The DSL modem is only "interested" in frequencies well above the audio range. It really couldn't care less what the phone company is doing down in the audible frequency range (including the presence or absence of a dial tone).
If you're not getting a dial tone, don't blame the DSL modem - Look for a poor connection on the phone line, an off-the-hook phone somewhere, or missing/improperly installed DSL signal blockers.
Also, some DSL service providers can provide internet service through a "dead" phone line - i.e., a line that doesn't have phone service. So, if you haven't paid your phone bill in a while...