[Jared Smith]

I have encountered assertions that historic sword designers engineered visual and physical harmonic proportion and even relationships that form the “Golden Section” or Phi. A current article at a premier reproduction sword manufacturer’s web site claims this to be the case, however the article contains a typo where it specifies the rounded off value of the ratio of Phi (stating “1 to 0.618”, it should be 1 to 1.618.) I am eager to have moderate fun with this, imparting a little mysticism into the subject, as long as there is enough substance to tantalize the reader that it might actually be true while telling an entertaining story.

I am wondering how many specific relationships in historic sword designs are accepted as being deliberately designed according to “harmonic proportions” and separately “Golden Section?” Are these aesthetic proportions of furniture? Looking at blade widths, thicknesses, natural CoP location, vibration nodes, etc. it is not obvious to me where true “Golden Section” relationships exist.

As background, Golden Section refers to a relationship between two parts of an overall dimension that form a ratio of 1.618 to 1.0. http://www.goldennumber.net/goldsect.htm Ratio’s of circular section may also be of interest to some. http://www.egypt-tehuti.org/articles/sacred-geometry.html These relationships occur naturally, and human design re-invention could largely have been a matter of recognition. One documentary film (forgot which one) theorized that in ancient architecture this may have resulted from using measuring wheels to layout large scale projects.

[Chad Arnow]

I believe Peter Johnsson and Eric McHigh have discussed this before here. A search might help.

[Vincent Le Chevalier]

Indeed it has been discussed in the spotlight thread 'Swords and the golden section?'.

Note that the article is not far from the truth since, if phi is the golden ratio, 1/phi = phi - 1 wich is roughly 0.618

Personally I believe that, given the number of funny relations that can be derived from phi, such as the link to the Fibonacci sequence, you could find the golden section roughly anywhere you want to... Including in things that have not been designed with it in mind. However, I agree that it's likely that it has been used as a design guideline on at least some swords, and perhaps mostly in those made by top-notch makers that were fully aware of how to use it.

If the dimensions of the sword are chosen according to the golden section, it should be reflected in the position of pivot points and/or center of gravity, since these are linked by simple ratios that tend to make phi reappear. And since harmonic nodes are rather closely related to pivot points as well... Phi is everywhere

I wonder if it was used in other cultures as well? Has anyone been looking for it in Japanese or Chinese weapons?

[Jared Smith]

Thanks for pointing out the old thread. That former thread is a good one. I actually did a search before this posting, but think I used "harmonic proportions" rather than golden section as key words.

I personally differentiate the golden section from the Fibonacci sequence. The section is based on the circle with an infinite decimal place number. Fibanocci can approximate it acceptably well but is achievable with simple discrete integers. The 8 by 5 book page size is a good example. One of my friends has a book (an early encyclopedia printed for education of new courtisans at Versailles) from 1725 which actually does follow these proportions (about 6 inches tall by 3.75 inches wide.)

I would love to hear example details of how the Svante conforms (especially in regards to visual aesthetics) in nearly every detail to the golden section!

I can understand CoP length to overall blade length just naturally falling out as being about 1 to 1.6. This is really just a natural phenomena of how kinematics works for a long bar of fairly consistent cross section. Moderate distal taper and a hand grip on something of roughly sword length just naturally brings it closer (see Vincent Le Chevalier's post on blade simulations and study the ratio of distance to CoP over total blade length.) Once people realized where this optimum contact point was (many present day athletes exhibit instinctive, rapid, and very accurate recognition of exact true CoP on unmarked test bats) it would only make sense to tune vibrational modes in a way that they dampened at that point. I can believe this might happen naturally with the swordsmith never having heard of "golden section."