From SimpsonDan@aol.com Wed Jan 02 13:58:22 2002
Subject:Re: drawbar question: why is 5 1/3 not between 8' and 4'?

[But daddy, why is 5_1/3 as an exception not in ascending line? And why is it brown and not black like the other "odd" numbers?]

There seems to be lots of myth around this. The 5-1/3 drawbar is not a subharmonic. It is the second harmonic (an octave and a fifth) of the sub-harmonic (an octave below the fundamental).

This may be best explained by an example. If the fundamental (the third drawbar and the first white one) is middle C, then the subharmonic (the first drawbar - brown) is the C below middle C. It is brown because it is not a natural harmonic of the fundamental, as all the other drawbars above the fundamental are.

In the example, the second drawbar (5-1/3 - brown) sounds the G above middle C, but because it is a natural harmonic of the sub (the first drawbar) and not a harmonic of the fundamental (the third drawbar), it is positioned relative to the sub, and retains the brown color. That is why it is out of order from a frequency point of view.

The other drawbars are all harmonics of the fundamental. The white ones are octaves and the others are non-octave natural harmonics. In the example, there are two additional G tones (an octave and a fifth above the fundamental and an octave above that), and one E tone (two octaves and a third above the fundamental.

Hope that clears up the drawbar mystery.

Dan