A harmonic cycle λ, also called a discrete harmonic form, is a solution of the Laplace`s equation with the combinatorial Laplace operator obtained from the boundary operators of a simplicial chain complex. By combinatorial Hodge theory, harmonic spaces are isomorphic to homology groups with real coefficients. In particular, if a cell complex has a one dimensional reduced homology, it has a unique harmonic cycle up to scalar multiplication, which we call the standard harmonic cycle. We will present a formula for the standard harmonic cycle λ of a cell complex based on a high-dimensional generalization of cycletrees. Moreover, by using duality, we will define the standard harmonic cocycle λ* and show intriguing combinatorial properties of λ and λ* in relation to (dual) spanning trees, (dual) cycletrees, winding numbers w( · ) and cutting numbers c( · ) in high dimensions. Finally, we will also suggest application methods; an analysis to detect oscillations by using winding number, and cutting number, and a network embedding method, called harmonic mirroring.