Why is it called *spectral* triple?

I know the definition a spectral triple and that it is some kind of non-commutative generalisation of (the ring of functions on) a compact spin manifold.

But, why is it called spectral triple?

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Well, it uses the spectral properties of the Dirac operator $D$ in the spectral triple quite extensively. Also, in the article where he (essentially) introduces the notion of spectral triples ( http://www.alainconnes.org/docs/reality.pdf ) Alain Connes writes about the naming: