"Purple mountain majesties" refers to the shade of Pikes Peak in Colorado Springs, Colorado, which inspired Bates to write the poem.
"pˈɜːpəl mˈaʊntɪn mˈædʒᵻstiz" ɹᵻfˈɜːz tə ðə ʃˈeɪd ʌv pˈaɪks pˈiːk ɪn kˌɑːlɚɹˈɑːdoʊ spɹˈɪŋz, kˌɑːlɚɹˈɑːdoʊ, wˌɪtʃ ɪnspˈaɪɚd bˈeɪts tə ɹˈaɪt ðə pˈoʊᵻm.