Shaku Nodes

In the first octave, pressure nodes (where the air pressure fluctuates ) are at the ends of the effective flute length. In between, the air flows (flow node) back and forth from one pressure node to the other (Blue arrows). All first octave notes have two pressure nodes separated by one flow node.

All second octave notes have three pressure nodes interspaced by two flow nodes. Red arrows signify the air movement. The movement of air between pressure nodes is what's perceived as sound.

Benade writes:
The interlacing of pressure nodes and flow nodes allows us to deduce the following general principle, which was first enunciated a century ago by Lord Rayleigh: A localized enlargement of the cross section of an air column (a) lowers the natural frequency of any mode having a large pressure amplitude (and therefore small flow) at the position of the enlargement, and (b) raises the natural frequency of any mode having a flow node (and therefore large flow) at the position of the enlargement.

This is the whole basis for perturbation. The effects are just reversed for an area of constriction. This explains the great mystery of the shakuhachi bore and what people are trying to accomplish while adding and subtracting from it. Benade goes on to describe how curves called Perturbation Weight Function Curves ('W' waves for short) can be deduced from the standing wave patterns and Rayleigh's principle. These are presented on the tuning page.

Following up on the principle governing shifts in frequency by way of perturbation, let's look at the facts. Perturbations have different effects depending on where in the bore they're placed. For this example, let's pick the most effective location. Perturbation length is likewise conditional--let's pick the most effective length. With these two optimal conditions the maximum percentage change in the frequency (up or down) is equal to the percentage change in the total air volume produced by the perturbation. Take the total air volume of a 1.8 flute as somewhere around 135cc. Now, let's take the volume of a 25mm square of newsprint--0.0476cc. Placing it in the most auspicious location, we'll get a frequency shift in Ro of plus or minus 0.104hz. That's a shift of 0.6 cents or about 1/3 of the threshold of just being able to hear a difference. The point is that all the talk about micro adjustments to the bore making significant differences is just that--talk. When somebody tells you that adding a thousandths of an inch somewhere suddenly turns a clunker into a wondrous flute you can be assured that they don't know what they're talking about. Another myth bites the dust. Micro bore adjustments make micro difference.

Have you ever wanted to see the air pressure nodes within a flute bore? Well you can. It's a simple proposition. Make a flute of clear PVC, cool it and then play Ro. The humidity from your breath will condense on the inner wall of the tube at both ends of the flute--the pressure nodes. Play ro and you'll get three areas of condensation. Pressure nodes is where the air is static and at flow nodes it's moving (oscillating) and thus is dynamic.

The bamboo nodes have nothing to do with the air pressure nodes or the perturbation nodes except when they are left partially exposed in the bores of jinashi flutes. Then they create perturbation as they are bore constrictions. That bamboo grows with its nodes in the correct placement for tuning constrictions is very fanciful thinking.

See The Synthesis for a final flute design.