Toaru Kagaku no Railgun SS3

One quiet afternoon at Tokiwadai, Kuroko attempts to enjoy a pleasant moment to soothe her weary body and soul when black twintailed Yuri Sakibasu causes her some trouble. When Mikoto hears about it, she suspects the girl was sent by Shokuhou's clique as part of a harassment proxy war, so they accept the challenge. The challenge is a violin competition with the other side having a Stativarius, which go for more than a hundred million yen. They need knowledge to defeat money, so with Uiharu and Saten's help, they are forced to figure out the secrets of that famous violin's sound and what the minute differences between them are. And during this thorough enemy observation, they learn how skilled Sakibasu is. What is the surprising move that overturns everything for Kuroko!? This small conflict over violins is only the prelude to an incident involving many different forms of desire.

(Source: Kadokawa, translated)

Toaru Kagaku no Railgun SS3 was included with the limited-edition Blu-Ray/DVD volumes of Toaru Majutsu no Index III.