Sax uses three consecutive and each time narrower conicities. But the mutual arrangement of these conicities shows variety. On the basis of our own considerations we make a choice within this framework.
For the construction of the instrument we use the adapted parts of an existing saxophone. The bell has a width which, when compared to the smaller third conicity of the right hand, promises to fit nicely to a greater instrument length (for this see the sheet with the bore profiles). Therefore we decided to extend the instrument to a (written) low A. In his third patent Sax also mentions lengthening the instrument, even up to a written low Ab, but he never realised such plans.
Short and wide bows always entail complications. Although these complications can be compensated for, we decided not to follow this path and to make the instrument straight, so that we have a perfect certainty as to the effect of the chosen profile. It's true, the choice for a straight alto in Eb to a low A is not a conventional but still a defensible one (also in view of Sax's statement that a wind instrument can be folded to our liking but that it better be straight..) and as far as dimensions go, such an instrument can still be handled.
Four different possibilities have been scanned. In order to come as close as possible to the parabolic cone, we try to give the consecutive conicities each time a greater proportion of the instrument length. The golden section proportion, which Sax more or less approximates in both the altos, is our guideline. (Most likely, it is purely accidental that Sax uses the golden section proportion in this alto, as the other instruments show quite different proportions.) In the ideal case the first, the second and the third conicity respectively would take 19%, 31% and 50% of the instrument length. Just as in the graphs of the profiles in the preparatory phase, conicities of the neck are in orange; those of the left hand are in purple and those of the right hand are in green.
Conicity is again expressed as a ratio: the number of millimeters length needed for a millimeter gain in width. From bottom up:
|1st conicity (neck)||14,7||13,8||14,3||13,9|
|relative length (%)||18||18||18||16|
|truncated length (cm)||16½||17||17¼||16|
|truncated volume (cc)||5¼||6½||6¼||5¾|
|entrance neck (diameter mm.)||11||12||11¾||11¾|
|relative length (%)||40½||29||30||25½|
|truncated length (mm)||240||240||240||240|
|truncated volume (cc)||10,6||13,2||12,3||12,3|
|relative length (%)||32||34||42-||42|
|bell, relative length (%)||10½||10||10+||16½|
|acoustistical length (mm)||1322||1322||1322||1322|
|sheet with bore profiles.|