saurons fall

[Amarie of the Vanyar]

Gilbo, you are right that it is likely that Volcanos are a combination of Aulë's and Morgoth's songs, just as snow is the combination of Ulmo's waters and Morgoth's extreme cold. But Ulmo didn't sang in harmony with Morgoth, as Eru says in the Ainulindalë, and the same applies to Aulë. As it is said in the Valaquenta:

In the beginning he (Aulë) wrought much in fellowship with Manwë and Ulmo; and the fashioning of all lands was his labour. (...) Melkor was jelous of him, for Aulë was most like himself in thought and in powers; and there was long strife between them, in which Melkor ever marred or undid the works of Aulë, and Aulë grew weary in repairing the tumults and disorders of Melkor (...) But Aulë remained faithful to Eru and submitted all that he did to his will
Valaquenta; the Silmarillion

Therefore, it is clear for me that Aulë never harmonised with Morgoth.

Even though I consider it the 'best' option, the allignment of Sauron with Morgoth during the Music also poses some questions: why did then Sauron enter in Eä as a follower of Aulë? Why didn't he follow Morgoth from the beginning if the discords seduced him from singing Eru's theme?