Shaku
Design
Equivalent Timbre

Updated 4/24/08

In a previous page we discussed the fact that bore and length don't scale at the same rate. What this means is that Aspect Ratio doesn't have a whole lot of meaning other than being the ratio of length/bore. By itself, Aspect Ratio won't tell you how your flute will sound. But we can define something called Equivalent Timbre which will. The idea is this: let's adopt the D shakuhachi as our standard and figure out what the AR is for flutes of other lengths--such that they will have the same timbre as our D standard. A little math is involved, but the result is pretty straight forward, EAR is Equivalent Aspect Ratio.

Figure 1 (below) contains most of the information--spend some time and study it to get a grasp of the notion of Equivalent Timbre.

In Figure 1 the yellow and green lines intersect at our D standard--an AR of 29. But one octave lower, the AR needs to be below 26 to have a timbre equivalent to the D Standard. An octave above D the AR rises over 32. The further from D (either way), the more the AR needs to be adjusted in order to have a timbre and playability similar to our D Standard. Flutes should get skinnier as they grow longer and fatter as they shorten. Nothing is straightforward with the shakuhachi--that's part of the enjoyment.

Everything on this page is computed assuming a straight, cylindrical bore. Should you want to estimate your flute's Aspect Ratio (thus it's Equivalent Timbre) see other pages for the volume method and the length method. Once your flute's AR is known, it's equivalent timbre can be estimated from the graph above.

The following two figures (below) graph bore and length relationships required to achieve suitable Equivalent Timbres.

The EAR of end-blown flutes is the biggest determinant of the flute's ability to play second (and higher) octaves. So the timbre of a shakuhachi is largely determined by a playing balance between first and higher octaves. For the most part, this is restricted to first and second octave. These two octaves are fairly balanced with an EAR of 29-30 and hence the sound (timbre) of a balanced shakuhachi is about like that of any other balanced shak. An EAR of much over 30 makes the first octave fugitive. Much under 29 and the second octave becomes fugitive. For a page on big bore, low EAR flutes.

But suppose you wanted a shak which optimized the timbre of the first octave? Suppose you wanted the ultimate shak timbre? Medieval pipe organ makers settled on an EAR for standard midrange pipes of about 26.6. Since organ pipes only play one octave, the makers could concentrate on what they considered the ultimate pipe organ sound. In any event, the ultimate shak timbre will require a lower EAR than the balanced one of 29-30. Somewhere around 26 might be a good place to start your search. Essentially, you'd have a one octave flute, but what a great octave it will be. With this flute, second octave will be a constant effort and the second octave timbre will be thin whenever you achieve it.

Bore and Length Formulas

Hole Sizes

Top of Page