Rush's road manager Howard Ungerleider came up with the title at a party. There were two dogs at the party, one a German shepherd and the other a tiny white nervous dog. Howard used to call the shepherd By-Tor because anyone that walked into the house was bitten. The other dog was a snow-dog (white). So from that night on Howard called the pair of dogs "By-Tor and the Snow Dog." The dogs belonged to Rush's manager.
The song is divided into 4 chapters: I) At the Tobes of Hades, II) Across the Styx, III) Of the Battle, IV) Epilogue. Chapter 3 (Of the Battle) is divided into 4 chapters in and of itself: i) Challenge and Defiance, ii) 7/4 War Furor, iii) Aftermath, iv) Hymn of Triumph. Total running time, according to the label, is only 8:37.
On the back cover of the album Alex Lifeson is identified as "Snow Dog", and Geddy Lee is identified as "By-Tor".
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