According to the study of Fletcher & Thwaites (Scientific Monthly Jan '83 ed), lip offset effect diagram p 102, "if the lip were exactly centred on the jet, the pipe would deliver only the fundamental frequency and the third harmonic. With the lip offset at the location shown (ie slightly to the outside of the centre of the wind jet), the second and fourth harmonics are introduced, greatly enriching the quality of sound."
It would appear Fletcher & Thwaites were speaking only of cylindrical pipes, though one would suspect that if theirconclusions were correct, the same would hold true for wooden "rectangular" pipes as opposed to cylindrical.
One would conclude that, in order to get the harmonics desired for principal tone, the position of the upper lip to divide the wind-jet is all-important (aside from scaling). The drawings of Audsley Vol II Art of Organ Building would tend to bear this out for in Fig CCLIX p 440, the drawing of the English "Stopped" Diapason would seem to direct the air stream for principal tone more closely than Samples B and C, delivering tones without the second and fourth harmonics. The fact that the.......................... end of fragment
1. - Lower lip set flush with top of block
Moderate flue spacing
Moderate supply of wind three pipe foot
Sharp 45 degree upper lip set scale distance above block
Result - overblown to harmonic (octave)
Modification (1) (a) reduce wind pressure:
Result - harmonic (octave), but by holding note sometimes prime enters, then over to harmonic again
(b) reduce w.p. further:
Result - same as above but weaker and unsteadier
Modification (2) double flue slit
Result - overblowing, windiness
Modification (3) move cap lower
Result - prime does not come on until cap at lowest possible extremity, windy, poor note mostly octave
(still at lower pressure)
Modification (4) raise uper lip:
Result - prime returns note insecure by tapping
windy, poor, lower pressure
Modification (5) H. press. : overblows until upper lip raised still further. Speech onset octave instant then settles to prime. Windy.
2. Same as #1 but with blunter upper lip.
Result - harmonic but with evidence of prime tone concurrent
Modification (1) lower pressure
Result - lost prime, weak octave
Modification (2) raise upper lip
Result - prime returns, octave onset, windy, insecure, impure
Modification (3a) double flue spacing
Result - prime returns with lowering of upper lip
windy with octave onset. Best to date.
Modification (4) lower w.p. of above - poor weak note.
Modification of Modification #2 (3a) sharp, thin, upper lip
Result - same as 3a above ;but perhaps less windy. upper lip raised
Mod. of above - decrease wind slit 50%
Result good prime, prompt attack but with very sharp octave click at onset of speech
Conclusions reached thus far:
1. The block (languid) is best with a moderate face as at (a). (b) is of no advantage (sharp face)
(c) is unsuitable for directing wind jet.
3. Higher pressure with narrow windway give best results
4. Directing the air jet toward the interior of pipe by
(a) offsetting the upper lip by an equal amount as the interior edge of cap (a) or
(b) chamfering the inside of the upper lip to get the same effect results in the loss of prime tone altogether
5. Best results were, so far, with thin upper lip, moderate chamfer, and moderate edge. But lip must be set
higher (cut up) than scaling indicates. The speech is quick, the attack sharp because the pipe begins with
the 2nd harmonic (octave) for an instant before prime. Lowering the pressure and lip also produces prime
but unsteady and weak tone.
* * *
The following is Stuart's partial translation from a German technical work. He made a listing of German/English expressions that were unusual, eg Rauschspectrum - rustling spectrum; Teiltone - partials (tones); schlagartig - violent, in bursts; and a number of others that I would need assistance in transcribing.
Tone Developing in the Labial Pipe
Organbuilders for the most part seek no scientific understanding for their art of voicing. They use techniques handed down from experience. We home-workers lack critical workshop rearing, and we lose ourselves in pointless experiments as we have never been allowed the opportunity to be introduced to the craft of pipe voicing. With the conciseness of the physicists' overtone-building "a periodic stream of air entering the pipe-body superimposes itself along volume and impulse waves" - leaves us bewildered. But if you are interested, consult the higher mathematics as written in the books of Adelung, Gravner & Klotz:
Let us set ourselves in front of illustration #40:
(translation)
The stream of air arriving at the narrow slit between block and cap becomes a flat sheet, thereby a somewhat divergent air-sheet to the upper lip; its compressed front in the frequency of the ground-tone swings back and forth over the edge of the lip, but not vibrating as in a reed. On the inner side of the upper lip arising from the release of the waves (think of the hindrance in flowing waters) a rustling with a broad frequency band, that together with a very audible swinging between the wind slit and upper lip excites harmonic movements in the pipe body.
By means of the exchange of energy of the air in front of the mouth of the pipe with that of the lip, is set up a swinging motion of molecules, which makes in length of time in the order of 1/100,000 mm over and out of the mouth. Other influences with inflections is the length of the swinging (vibrating) air column; around a somewhat two times depth of pipe (twice as deep as wide), the vibrations are greater than the simple Theory allows one to expect because the ground tone is deeper thereby. For the next partial tones, the Factor is smaller, the even reflects lay nearer to the mouth, the partial tones thereby higher than the ground tone. That the vibrating column can only be a division of the whole number of the ground tone makes the faster vibrations swing downward or dampened and its loudness diminished in sensitive amplitude. The deeper the pipe these upper partials are smothered, the pipe becomes poorer in overtones (Gedackts, wide Flutes), the opposite effect is attained by narrow principals and the overtones of the ground tone is favored. Mid-scaled principals make the best use of the airstream.
The lower the cut-up, the more the airstream reaches the upper lip and thereby the broader and louder becomes the "rustling spectrum" with its "drum tone." The more the stream grazes the outer or inner side of the upper lip, the more strongly the partial tones are developed.
Study the appearance of a wooden principal pipe with moveable lip and cap. Set the cap as deep as you can to get a note. The wind grazes the outer side of the upper lip, the note comes "slowly" with impure following sounds and a strong octave sound, also a sound spectrum somewhat about point 3 in the diagram. By further heightening the cap, the pipe becomes "quicker," reaches a secure onset of speech and typical principal sound at point 1.5. Raise it more, then the note becomes even quicker and the sound of the overtones is almost violent, becoming really flutey.
(end translation)
