Heatmap Color Ramp on 3D model

I'm trying to generate a smooth continuous heat map color ramp of a 3D model, but I get a discrete looking shader on my model. Below is the code I used to generate the heatmap color ramp shader. In particular, I iterate through the vertices of the mesh and assign them new color values correlating to the y value so the lowest y value is given blue and the highest value is given red and the in between are cyan, green, and yellow. I want to scale the values based on height so there are more colors and the model then looks better/smoother.

I'm thinking my issue in how I am taking the Y values (the order of the vertices are stored in the mesh.vertices array) or I am not allowed to create that many colors.

Below is the model with the shader and vertex coloring method applied followed by the code.

 public class TopoHeatMap : MonoBehaviour {
     public Mesh mesh;
     public Material material1;
     public Shader vertexShader; // Material with a Custom/Vertex Colored shader assigned in Inspector
     public Renderer myRenderer;
     public void renderHeatMap()
     {
         myRenderer = GetComponent<Renderer>();
         vertexShader = Shader.Find ("Custom/Vertex Colored");
 
         if (myRenderer.material.shader != vertexShader) {
             vertexShader = Shader.Find ("Custom/Vertex Colored");
             myRenderer.material.shader = vertexShader;
 
             Mesh mesh = GetComponent<MeshFilter> ().mesh;
             Vector3[] vertices = mesh.vertices;
             Color[] colors = new Color[vertices.Length]; //stores colors for all vertices in mesh
             float partition = vertices.Length / 4;
 
             for (int i = 0; i < vertices.Length; i++) { //iterated through mesh vertices
                 if (i < vertices.Length / 4) {
                     colors [i] = new Color (0f, i / (partition), 1f, 1f); //populates color array of vertices with new color
                 } else if (i < vertices.Length / 2) {
                     colors [i] = new Color (0f, 1f, (i-partition) / (partition), 1f); //populates color array of vertices with new color
                 } else if (i < 3 * vertices.Length / 4) {
                     colors [i] = new Color ((i-2*partition)/ (partition), 1f, 0f, 1f); //populates color array of vertices with new color
                 } else {
                     colors [i] = new Color (1f, (i-3*partition)/ (partition), 0f, 1f); //populates color array of vertices with new color
                 }
             }
             mesh.colors = colors;
         } 
         else {
             vertexShader = Shader.Find ("Standard");
             myRenderer.material.shader = vertexShader;
         }
 
     }
 
 }