So let's crunch some numbers given this update.
"... roughly a tenth of Confederate war dead..." 94,566 CSA killed in Nashville, times ten means the CSA has roughly 945,660 soldiers killed during this war.
"....sixth of total aggregated casualties..." 514,920 total CSA casualties, times six means 3,089,520 CSA killed, wounded, and captured soldiers during the war.
"...one in five of every casualty sustained by the United States occurred in the Nashville Campaign." 880,549 total American killed and wounded (no captured total provided) times five means 4,402, 745 American casualties overall.
Roughly 4.4 million American military casualties compared to "only" 3.1 million Confederate ones. And these numbers do not include any civilian casualties (of which there are probably at least in the tens of thousands if not hundreds of thousands by war's end), any free blacks kidnapped and sent south, or any incidental casualties, such as death by malnutrition, famine, or disease among civilians.