# Length/Bore (L/B) RATIO

Posted 22-March-1999

In designing Tin Whistles, Penny Whistles there are limitations on choosing the tube diameters depending on the size of the instrument which you are building. Air friction, pipe restriction, air velocity are some of the many factors involved in this choice.

Many years ago, a man by the name of Theobald Boehm designed the modern transverse flute. In his writings, he discussed the Length to bore ratio. The L/B ratio is comparison of the length of the tube from the fipple to the end of the tube.

Although, the L/B ratio has a few problems with it, (Note - you see these problems when you make huge instruments like Contrabass Recorders (Tone column of 101 inches) and the like) Normally these problems are miniscule for making small instruments such as Tin Whistles.

NOTE: By comparison, LOW-D Tin Whistles are small compared to many of the Renaissance Bass Instruments.

Typical Length to Bore Ratios can run from 20:1 to about 34:1.

To obtain number: L/B = Bore Size / Musical Length

Note: Musical length is defined as the distance from the tubing wall in the fipple section down to the bottom of the instrument. L/B ratios can be used with the metric system as well.

Let do some examples:

Low-D Whistle with 3/4 inch (0.82" ID) PVC Schedule 40 Pipe: 25.5

Low-D Tin Whistle with 3/4 inch (0.80" ID) Copper Pipe: 26.8

High-D Whistle with 1/2 inch ((0.60" ID) PVC Schedule 40 Pipe: 17.57

As you can see, I have a small whistle listed with an L/B ratio of 17.57. This tells us that tubing is a little too wide and it could causes weakness of lack of notes in the second register. If you apply Peter Hoekje Spreadsheet to the holes on the instrument, you will get cut-off frequencies between 2000 through 2600 Hz depending on the tone hole placement. A high-D is a base frequency of 587.33 Hz, the highest note of this instrument would thus be 1761.99 Hz or the base frequency times three. If the cut-off frequency on the tone holes exceeds 1761.99 Hz, then we're in. However, the tone could be somewhat lacking in harmonics. The result, is an instrument that works but it is borderline with performance. In order for it to even sound well, the fipple would be very sensitive for being properly voiced. If a smaller diameter tubing had been used to bring up the Length/bore ratio, this would raise the general cutoff frequency and the fipple voicing would also be less picky.

In view of all this is that all of these factors, tubing diameter, fipple design, tonehole placement, cutoff freqency are all interrelated.

If the LB ratio were too high, the Lower notes would either not sound at all or be weak.

Check this page, time-to-time, it like all other Web Pages is continually being updated.

Calculate Length/Bore Ratio Online!

Daniel Bingamon

Jubilee Music Instrument Co.

RETURN