Overtone Flute Calculator
Calculate pitch or pipe length for overtone flutes. The calculator is made for instrument makers, musicians and anyone who wants to build, tune or adjust their own flute.
An overtone flute is a wind instrument without finger holes, where you change notes by blowing further up the overtone series — the row of partials (natural overtones) the pipe can produce. The Norwegian willow flute (seljefløyte) is the local representative of this family, but the same acoustic principle applies to kalyuka, koncovka, pitkähuilu and other open cylindrical pipes without finger holes.
With this calculator you can:
- calculate the fundamental of a pipe from its length and diameter
- find the right pipe length for a desired note
- see which partials (overtones) are available on the same pipe
20 °C is standard for indoor use. Only change this if you work outdoors or in a cold room.
The 1st partial requires gentle blowing — in practice the 2nd partial is the home tone on the willow flute.
20 °C is standard for indoor use. Only change this if you work outdoors or in a cold room.
Advanced
The A4 reference pitch. Modern (440 Hz) is standard. Historical tunings give lower or higher pitch for the same pipe length.
Ando correction (1969): thick walls make the air column slightly longer because the opening behaves as if partially flanged. Thin walls (PVC, thin-walled PLA) need no correction. Medium suits standard 3D prints; thick suits wooden flutes and thick-walled prints. The effect is roughly 0.5–1 % in pitch.
A printable A4 sheet with a dimensioned drawing of the pipe and all partials. Print to PDF or paper from your browser.
Go to the arranger with this fundamental pre-selected. There you can paste ABC notation for a melody and see how well it fits the instrument.
Reset all values to default and clear the detected cent offset.
Willow flute player
Light buttons = open end (all partials). Dark = closed end (odd partials only). The tones update when you change the calculator.
How to use the calculator
Length → Note:
- Enter or adjust the slider for pipe length
- Enter or adjust the slider for inner diameter
- Read off the fundamental and partials immediately
Note → Length:
- Choose the desired fundamental and octave
- Enter or adjust the slider for inner diameter
- See how long the pipe needs to be
Where should I measure on the flute?
For the calculator to give the most accurate result, you need to measure the acoustically active length of the flute, not just the total length of the blank:
Measure from the lower edge of the mouth opening — the labium edge where the airstream is split — down to the open end of the flute. This is the part that actually vibrates with the air column and determines the pitch.
Do not measure from the top of the plug. That part is acoustically inactive and gives the wrong result. The top section by the windway is in practice acoustically inactive, and will give too long a measured length and hence an incorrect calculation.
About the formula
The calculator is based on the acoustic formula for open cylindrical pipes, with end correction and an additional correction for the block end (fipple):
0.6133 · d — End correction for both ends of the pipe. Even though the block end looks closed, the windway and labium behave acoustically like an open end. The air column "extends" slightly beyond the pipe at both sides.
0.9 cm — A fixed embouchure correction for the block end. The geometry of the windway and labium gives a greater effective length than a simple open pipe. The value is typically 0.7–1.5 cm depending on construction.
v — Speed of sound in air, temperature dependent. The formula applies to ideal cylindrical pipes; conicity, finger holes and mouthpieces will cause deviations.
k · d (Ando 1969) — Optional wall-thickness correction under «Advanced». Thick walls partially flange the opening, so the air column extends slightly further beyond each end. Default is k = 0 (thin wall) — enable only when building in wood or thick-walled 3D print.
Frequently asked questions
How accurate is the calculator?
The calculator is well suited as a starting point for building and tuning, but real instruments will often deviate somewhat. Small differences in material, diameter, labium and temperature can affect the actual tone.
Does the calculator only apply to the willow flute?
No. It can also be used for kalyuka, koncovka, pitkähuilu and other overtone flutes as long as the instrument essentially behaves as an open, cylindrical pipe without finger holes.
Why doesn't my flute match the calculation exactly?
It's usually because real instruments aren't entirely ideal. Windway, labium, wall thickness, natural material and small measurement deviations all affect the result. That's why you often need to fine-tune by ear in addition.
How accurately do I need to measure?
As accurately as possible. A few millimetres can be enough to shift the tone noticeably, especially on short flutes.
Should I cut the pipe exactly to the calculated length?
It's wise to cut a little too long and then check the pitch. A flute that's too long can always be gently trimmed down to the right tone — but one that's too short can't be made longer again. So cut a couple of millimetres extra and work your way towards the desired tone with small cuts.
Should I measure the whole flute?
No. You measure from the labium edge at the mouth opening down to the open end of the pipe. Don't include the block or plug section as part of the sounding length.
What is a partial, and why does the calculator use that term?
A partial is one of the individual tones in the overtone series of a pipe. The "1st partial" is the fundamental, the "2nd partial" is what is often called the 1st overtone, and so on. The calculator uses "partial" because it's more precise: "2nd overtone" is ambiguous and can be interpreted differently by different musicians. Want to test how a melody fits the partial series of a specific flute? See the Overtone Flute Arranger.
What does end correction mean?
When air columns vibrate in a pipe, they behave as if the pipe were slightly longer than its purely physical length. End correction is the way the calculation accounts for this.
What is the fundamental?
The fundamental (1st partial) is the lowest tone the pipe can produce. It requires soft, precise blowing. On the willow flute it's common to use the 2nd partial as the home tone in practice, since the 1st partial is technically demanding to produce cleanly.
Can I use the calculator to tune a finished instrument?
Yes. If you know the length and inner diameter, the calculator can indicate where the fundamental and partials should lie. Click "Match my fundamental" at the top of the page to let the microphone detect the tone directly from your instrument. Want to play specific melodies on the instrument? See the Note Archive. Want to try instruments you haven't built yourself? See Blåsebanken — where you can borrow instruments to try out.