The author studies the relationship between the spectral geometry of a Riemannian manifold and its holomorphic geometry. Let \(\lambda_{n}^{p,q}\) be the eigenvalues of the complex Laplacian on forms of type \((p,q)\). One says two Hermitian manifolds are strongly \(\alpha\) isospectral if for all \((p,q)\) \[ sup_{n\rightarrow\infty}\mid\lambda_{n}^{(p,q)}(M_{1})- \lambda_{n} sp{(p,q)}(M_{2})\mid n^{-\alpha} < \infty. \] Let \(M\) and \(M_{i}\) be closed Hermitian manifolds of complex dimension \(m\). The author shows Theorem A: Let \(M_{i}\) be \((-1/m)\) isospectral. Then (a) \(M_{1}\) is Kähler if and only if \(M_{2}\) is Kähler. (b) \(M_{1}\) is semi- Kähler if and only if \(M_{2}\) is semi-Kähler. (c) Let \(m\geq 3\). Then \(M_{1}\) is locally conformal Kähler if and only if \(M_{2}\) is locally conformal Kähler. Theorem B: Let \(M\) be strongly \((-2/m)\) isospectral to complex projective space with the Fubini-Study metric. Then \(M\) is holomorphically isometric to complex projective space.