Whistle and Flute Hole Calculator

for calculating positions for finger holes, with input for key, intonation, tube size and fine calibrations; plus additional graphical output. Based on Pete Kosel's Flutomat
Instructions: pink fields are for input — for no hole enter 0 as hole diameter — all measurements in mm — see legend below.

design for in the key of intonation: tube OD: wall: bore: optimum: % diff:
Hole locations
window/embouchure hole L x W x H -> window to end ca. + tip = total length ca.
hole freq. note cΔET hole diameter from end finger spacing cutoff*f
T1  L1-2 
Th  L1-T 
T2  L2-3 
T3  L1-3 
B1  R1-2 
B2  R2-3 
B3  R1-3 
End  bore:
calibration: A=Hz end effect: slide: ± cents = ± mm temperature: C = F


tube OD
outer diameter of tube
thickness of tube wall
inner diameter of tube, outer diameter less 2x wall thickness
calculated optimum bore according to lowest frequency, see also Searching For The Optimal Whistle Bore
% diff
difference in percent of bore to optimum bore. Negative values mean narrower bore, positive values wider bore
ET = equal tempered; just = just intonation (sweet intervals); HB-trad = my preferred intonation for traditional tuning, a variation of just intoned, arrived at purely empirically.
embouchure hole
window/embouchure L x W x H
length (along the tube), width (across the tube), height (wall or box thickness at window)
T1, T2, T3 = top 3 finger holes, Th = top thumb hole, B1, B2, B3 = bottom 3 finger holes. Enter 0 for thumb hole diameter to see no thumb hole, or just ignore that value (the thumb hole value does not affect the others)
note frequency in Hz
common note name
c Δ ET
difference in cents from equal tempered note
hole diameter
choosen hole diameter (drill hole first a little smaller, and check tuning)
from end
calculated distance of hole centre from end of tube
factor for cutoff frequency (should be 2 or more to get second octave note)
calibration of middle A (standard is 440 Hz)
end effect
end effect factor, a factor used in the calculation to determine how far the vibrating air column protrudes beyond the end of the tube. It can vary a little, depending on the roundness of the edges at the tube end. Tweak this if all your calculated distances are off by about the same amount to your experimental results.
can be used to calculate slide length for a given variation in tuning (50 cents is half a semi tone up or down)
temperature of air inside the tube the whistle or flute is designed for (usually a bit higher than room temperature).