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Thanks to this website, I was able to create a pan flute from some straws and it really worked (I could play all the music I know on C major scale). However, the dimensions of the straws only correspond to the C major scale and I need flat & sharp notes + notes that are lower & higher.

The following dimensions are the ones I currently found:

19.5 cm : C

17 cm : D

15.5 cm : E

14.5 cm : F

13 cm : G

11.5 cm : A

10 cm : B

9.5 cm : C

But I can't find the relation between these dimensions (I know for some I have to divide by 2 due to semi tones and tones). I think it's some kind of an exponential function since the distance of a half-step lessens as a note is sharper.

Can you help me find the relation between these notes so that I can retrieve the other ones?

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  • Look up the wavelength (or frequency ) ratios of the well-tempered scale, or of whatever temperament you wish, and cut your straws to those lengths.
    – Carl Witthoft
    Commented Apr 26, 2021 at 17:39

2 Answers 2

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These measurements aren't totally accurate, as they've rounded to the nearest half inch to make it look nice. It also looks like you've built a "transposing" pan flute- your "C" is actually an A, and it should play in A major, not C major.

Anyway, to find the theoretical correct length for each straw, you want to divide the wavelength of the note by 4. You can find a table with the wavelength for each note here. The best practice if you want to be really precise would be to cut the straws a bit longer than needed and then listen to it- cut a little more off the straw until it sounds right.

In absence of a chart, each note is longer than its higher neighbor by a factor of ¹²√2, or about 1.0595.

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  • Oh no, since the values are rounded, do you think it may affect the pitch ?
    – Amin Guermazi
    Commented Apr 24, 2021 at 0:51
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    Yes, rounding the lengths will affect the pitch.
    – Edward
    Commented Apr 24, 2021 at 0:52
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    @AminGuermazi yes, obviously: depending on the rounding, the pitch might be more or less accurate, but since we're talking about a relatively small instrument, even a couple of millimeters are important.
    – musicamante
    Commented Apr 24, 2021 at 0:52
  • Also shouldn't the pitch be also related to the straw diameter ?
    – Amin Guermazi
    Commented Apr 24, 2021 at 0:59
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    The diameter only affects the pitch in the sense that there is some error between the calculated length vs actual length needed, because the airflow does weird things that I don't totally understand at the ends of the tubes. Different diameter tubes have different amounts of error because of this. The pitch doesn't really depend on diameter otherwise. I believe narrower tubes have less error here.
    – Edward
    Commented Apr 24, 2021 at 1:06
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Theory says that for the notes in between (sharps and flats), the length should be about halfway between each two. That should give you 12tet. However, the lengths quoted may well not be meant for that, and will produce a good sound just in one key. Like Just Intonation. So finding the average of two lengths and dividing by two could easily make the new note a little sharp/flat.

Using the formula from Edward's answer will give a good ballpark figure and tuning, but it's certainly worth at least cutting the sharp/flat notes a little too long, and go by ear - or use a tuner.

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    We hear pitch logarithmically — by ratio, not by difference.  So the ‘halfway point’ should be the geometric mean (√ab), not the arithmetic mean ((a + b) / 2).
    – gidds
    Commented Apr 24, 2021 at 9:40
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    @gidds the difference between the geometric mean and the arithmetic mean of 19.5 cm and 17 cm is half a millimeter, which is certainly at the threshold of the precision with which I can cut a drinking straw. On top of that, equal temperament may not be the best tuning system for a plastic pan pipe. It's quite accurate (if slightly imprecise) to say that the sharps should be "about" halfway between.
    – phoog
    Commented Apr 24, 2021 at 14:58

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