Concentric Circles Eccentric Circles
Red : Orange = 2:1 Red = 1
Orange:Yellow = 3:2 Orange = 1/2
Yellow:Green = 4:3 Yellow = 2/3
Green:Blue = 5:4 Green = 3/4
Blue:Violet = 6:5 Blue = 4/5
Violet = 5/6
The construction will find the Harmonic Median of any two lengths, but I would like to be able to find the third given any two values i.e. solve for A or C as well as B.
Table working out Harmonic Means for simple whole number pairs, and developing these to the simplest whole number triads.
N.B This one gives A:C:B, placing C at the median, which seems to be more traditional? 300 : 350 : 420 : 525 : 700 : 1,050 : 2,100 : complete! Look at the ratio between each number pair!
Not sure why I had to multiply by 5 to get this started, but it's pretty neat! p.s. Divide by ten to make things simpler as long as you can tolerate 52.5 Going for a sequence of twelve I come up short - two proportions are missing! Here's what I have: 770 : 840 : 945 : 1,080 : 1,260 : 1,512 : 1,890 : 2,520 : 3,780 : 7,560
So what happened? Still some nice numbers to play with! I think I get this now!
When I am constructing a fretboard I am more likely to work with: A:B = (C-A):(B-A) which effectively repeats the same proportion over again on the remainder, whereas the Pythagorean Proportion gives a developing sequence.
. . . . I think . . . . 105 : 120 : 140 : 168 : 210 : 280 : 420 : 840 | 
