Just to keep things straight I moved this thread from Spy Numbers to Utility. These HF-GCS transmissions are not generally considered numbers transmissions, although they definitely do send coded messages in letters and numbers. Unlike spy numbers transmissions these messages are generally just grouped with other military coded transmissions.
To the OP, these are not computer generated voices, this is a human, often a young airmen, setting at a mic reciting these messages. The type of message you heard is referred to as an "EAM", or "Emergency Action Message". This is one of several formats of message you will hear on this network. The most commonly used frequencies are 4724, 6712, 6739, 8992, 11175, 13200, and 15016 kHz, all in USB mode.
Most messages are simulcast on all of those frequencies at the same time, and by up to 13 different ground stations at the same time. These multiple ground stations all sending the same message at the same time are what causes the "echo" sound you heard. On top of normal propagation delay, this would cause a relatively small echo to be heard, they use a VOIP like backbone to transport the audio to each node, and there is some variable network latency, this network latency causes the sometimes quite deep echo that is frequently heard.
If you want to research this network do a search on HF-GCS, High Frequency Global Communications System. Just be aware that many details on the network are classified, and so in addition to the good information to be found there is also some pretty bad stuff out there, incorrect and misleading information, floating around out there. For example, if you read anything about the number of "Skykings" said in a row (a "Skyking" is another type of message heard on this network) relating to message importance, ignore it. That started as a joke in chat, and became internet "fact", now with charts and web sites supporting and repeating it.
T!