if you give me an email adress i can send what i wrote as a pdf, and it will show things as i ment them to be...
mine is dstutzel "at" yahoo.de

... as a supplement to Davids fine explaination: The illustration shows an arrangement of the overtones in a logarithmic spiral (in this case it is Archimedan, but that is also logarithmic). All even numbers are octaves of a more fundamental tone:
1-2-4-8-16-... Prime and octaves of prime
3-6-12-24-... Perfect fifth and octaves of p.f.
5-10-20-... Just major third and octaves thereof.

One spiral winding, 360 degrees, corresponds with one octave (=1200 cent). So you may logaritmically translate any cent value to an angle. Example: The axis of 5-10-20 comes from the interval 4:5.
So the cent value is log(5/4) x 1200 : log2 =386.3 cent. (whereas the value of the 12 TET major third is 400 cent ~60 degrees)
To translate 386.3 to circle degrees we only need to multiply with 0.3 (360:1200). 386.3 x 0.3 = 115.89 degrees.
This provides you a very direct way to see the deviances between for instance 12 TET tunings and harmonics.

Well, it's been 8+ years since you posted this. I thought that I'd answer it anyway.

It isn't the logarithmic scale, but the natural scale/harmonic or overtone series. If you measure it, it isn't logarithmic, it's linear. Really. It just seems logarithmic because that's how our senses work as animals. Our bodies are sensitive to things based upon our size and therefore what threatens us most. Mice hear high-pitched sounds; whales hear low-pitched sounds; we're in between. So you'll notice that the decibel scale is written along the same lines.

So your body interprets the natural scale/harmonic/overtone series as being logarithmic when in fact if you measure it, it's linear. If you measure the diatonic scale, which is octave equivalent, you'll see that it's exponential. Since our senses are logarithmic, we perceive it as being linear. However, the spacing of the notes within the octaves is not consistent. It also explains why the cycle-per-second (Hertz) between the notes increases as you get higher.

The two systems combined around c.1260+ (look at the Rutland Psalter p.98r where a king is tuning his harp to a natural trumpet playing the natural scale). From the natural scale, we get the major and minor modes, triadic harmony and V-I cadence. With the diatonic scale, we have a scale that seems linear and where you can have instruments with different ranges playing together in different octaves. The natural scale is constrained to a gamut of notes. So with the acceptance of the natural scale, you have 10-stringed frame harps quickly evolving into 30-stringed Gothic harps.