Aerodynamics is also important to the flute, but in questions relating to efficiency, attendant noise, etc rather than tuning.Įven without turning to other sciences, the mathematics of flute acoustics are incredibly complex. I feel confident we can rely on the field of Acoustics to provide us reliable answers to acoustics questions, such as this one. I find that Mathematics is the "Traders Language" that ties all these physical sciences together and provides me with epiphany. Using the combined knowledge of Acoustics/Hydraulics/Aerodynamics/Pneumatics and Applied Physics will help the field of "Woodwind Acoustics" tremendously. but the field of Acoustics does not always provide answers. I'm sure Terry is an itelligent man, but the field of Acoustics does not always provide answers. The "nodes and anti-nodes" also shift farther down the bore with the increased velocity in the upper registers and this aggravates the problem of "blow-by" that reduces acoustic energy at the tonehole. The "Ideal" situation is a hole that has the shape of the inside of a Doughnut so the air will flow in/out without "tripping" on any sharp edges.īy means of "surface tension", the air follows the curve of the undercut and most of the pressure/energy finds it's way out the hole. The aircolumn cycles into/out of the tonehole every frequency cycle, so tapering the top helps the tonehole as well. If the bottom of the tonehole has a sharp edge, the aircolum will pass most of the open hole before the pressure pushes it up and out. The reason undercut toneholes are more accurate in the upper registers, has to do with aerodynamics/pneumatics. #Bart Hopkin AIR COLUMNS and TONE HOLES manualsThe Manuals of Lew Paxton Price and Bart Hopkin are best for simplified mathematics concerning tapered playing holes and simplified flute acoustics. I suggest the Craft manuals located here. Once averaged, you can use the resulting value in the Flutomat Calculator. This value is used in the playing hole formula when solving for tonehole placement. The secret to calculation is to average the tonehole diameter(this is, in fact, a trucated cone). Undercutting also helps with this shifting by providing a larger inner hole to align this nodal phase shift by slight changes in the "tonehole lattice structure"under increased velocity. Recorders deal with this by using a tapered bore that corrects for nodal shifting. This shifting changes the ideal placement of toneholes in the upper registers. There is some phase shifting of the nodes in a bore due to increased air column velocity. This is verydifficult to explain without mathematics. So Undercutting at the anti-node flattens the pitch, but the increased size of the hole sharpens it. Because of this fattening, the tonehole can then be slightly moved up the bore to correct for increased air column velocity in the upper registers.The amount of undercutting is directly proportional to the rise in pitch. Because a tonehole is located at an "anti-node" or place of greatest vibration, the undercut hole will flatten the pitch. Undercutting is a form of Bore Perturbation.
0 Comments
|
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |