The dome is the leading idea or motif in Byzantine ecclesiastical architecture; the domes are placed over square, not circular apartments, and their bases are brought to a circle by means of pendentives.
Why should a Ring-motif be transformed into the theme representing Walhalla?
As regards the sources of the narrative part of the Periodoi, it is possible that the "recognition" motif was a literary commonplace.
In A; Todtentanz; Fantasie ueber Motif aus Beethoven's ' ` Ruinen von Athen "; Fantasie ueber Ungarische National Melodien; Schubert's Fantasia in C; Weber's Polacca in E.
The motif of the former is the poet's futile endeavour, in a dream, to ward off the arrows of Dame Beautee by Reason's "scheld of gold."
This view is maintained by Richard von Muth in his Einleitung in das Nibelungenlied (Paderborn, 1877), who thus sums up the result of his critical researches: "The basis of all is an old myth of a beneficent divine being (Siegfried), who conquers daemonic powers (the Nibelungen), but is slain by them (the Burgundians turned Nibelungen); with this myth was connected the destruction of the Burgundian kingdom, ascribed to Attila, between 437 and 453, and later the legend of Attila's murder by his wife; in this form, after Attila and Theodoric had been associated in it, the legend penetrated, between 555 and 583, to the North, where its second part was developed in detail on the analogy of older sagas, while in Germany a complete change of the old motif took place."
The fact that this theme is commonly called the " Ring-motif " is a glaring instance of what Wagner has had to endure from his friends.