Spectral enrichment parameter E from a bore profile

Load a brass instrument bore profile (.csv) to calculate the spectral enrichment parameter E using the discrete approximation given in the paper (referenced below).

E \approx \frac{C}{2 L_{eff}} \sum_{m = 1}^{M} (\frac{1}{D_{m}} + \frac{1}{D_{m + 1}}) l_{m}

Segment m has length l_m, entry diameter D_m and exit diameter D_m+1; D₁ is the diameter at the input plane x_in, and L_eff = L − x_in.

Scaling constant C mm (paper: 88)

Input plane x_in mm (paper: 20)

No file loaded

E = –

Input plane diameter D₁– Instrument length L– Effective length L_eff– Measurement points used–

File format: two columns and no heading row, position (mm), diameter (mm), separated by commas, semicolons, tabs or spaces. Positions are measured from the mouthpiece end of the bore, so the last position is the instrument length L. Repeated positions (steps in the bore) are allowed. Drag a file onto the plot, or use Choose file. All calculation happens in your browser; no data is uploaded.

Reference. M. J. Newton, D. M. Campbell and A. Myers (2026), “A parameter for predicting spectral enrichment in brasswind instruments,” in submission.